Unusual Attitudes and the Aerodynamics of Maneuvering Flight Attitudes and... · 2017. 9. 29. ·...

Unusual Attitudes and the Aerodynamicsof Maneuvering Flight

Bill Crawford: WWW.FLIGHTLAB.NETii

Author’s Note to Flightlab Students

The collection of documents assembled here, under the general title “Unusual Attitudes and theAerodynamics of Maneuvering Flight,” covers a lot of ground. That’s because unusual-attitude training isthe perfect occasion for aerodynamics training, and in turn depends on aerodynamics training for success.

I don’t expect a pilot new to the subject to absorb everything here in one gulp. That’s not necessary; in fact,it would be beyond the call of duty for most—aspiring test pilots aside. But do give the contents a quickinitial pass, if only to get the measure of what’s available and how it’s organized. Your flights will be moreproductive if you know where to go in the texts for additional background.

Before we fly together, I suggest that you read the section called “Axes and Derivatives.” This willintroduce you to the concept of the velocity vector and to the basic aircraft response modes. If you pick upa head of steam, go on to read “Two-Dimensional Aerodynamics.” This is mostly about how pressurepatterns form over the surface of a wing during the generation of lift, and begins to suggest how changes inthose patterns, visible to us through our wing tufts, affect control.

If you catch any typos, or statements that you think are either unclear or simply preposterous, please let meknow. Thanks.

Bill Crawford

Bill Crawford: WWW.FLIGHTLAB.NET iii

Unusual Attitudes and the Aerodynamics of Maneuvering Flight

© Flight Emergency & Advanced Maneuvers Training, Inc. dba Flightlab, 2009. All rights reserved.For Training Purposes Only

Contents

Flightlab’s Upset Recovery and Basic Aerobatics Program(Introduction to unusual-attitude and aerobatic training)

Maneuvers and Flight Notes(Describes training maneuvers and associated aerodynamics)

Flightlab Ground School Texts:

(More on aerodynamics: This background material is useful for pilots who want to prepare for the coursebeforehand, and for follow-up reading.)

1. Axes and Derivatives(Descriptive concepts, vectors, moments, cause and effect)

2. Two-Dimensional Aerodynamics

(Lift and stall fundamentals: pressure, boundary layer, circulation)

3. Three-Dimensional Aerodynamics(How wing planform affects stall behavior)

4. Lateral-Directional Stability(Sideslips, yaw/roll coupling, straight and swept-wing dihedral effect, Dutch roll)

5. Longitudinal Static Stability(Aircraft in trim, pitch control forces in 1-g flight)

6. Longitudinal Maneuvering Stability(Pulling g)

7. Longitudinal Dynamic Stability(Oscillations in pitch)

8. Maneuvering Loads, High-G Maneuvers(V-n diagram, corner speed, radial g)

9. Rolling Dynamics(Roll performance, adverse yaw, coordination)

Contents

Bill Crawford: WWW.FLIGHTLAB.NETiv

10. Spins(History, spin phases, momentum effects, recovery)

11. Some Differences Between Prop Trainers and Passenger Jets(Differences in control and response)

12. Vortex Wake Turbulence(Vortex flow field/aircraft interaction)

13. A Selective Summary of Certification Requirements(What the regulations say about aircraft stability and control)

Bill Crawford: WWW.FLIGHTLAB.NET Intro.1

Flightlab’s Upset Recovery and Basic Aerobatics ProgramUnderstanding the Aerodynamics of Maneuvering Flight

Copyright Flight Emergency & Advanced Maneuvers Training, Inc. dba Flightlab, 2009. All rights reserved.For Training Purposes Only

Summary

Flightlab’s Upset Recovery and BasicAerobatics Program provides intensive groundschool and flight training in aerobatics andunusual-attitude/upset recovery for flight crews,flight instructors, and individual pilots of allexperience levels. Our ground school features acomprehensive but nonmathematical review ofaerodynamics—taught using digital wind tunnelsand flight-dynamics software designed foranalysis and comparison of aircraft response. Inthe air, we use actual engineering flight-testprocedures to demonstrate upset aerodynamics,and training disciplines from competitionaerobatics to teach attitude perception andrecovery skills. Because flying different aircraftreinforces the ability to adapt recoverytechniques learned in one cockpit to another,students compare the stability and unusual-attitude characteristics of two aerobatic aircraft:a SIAI Marchetti SF260 and a Zlin 242L.

Course duration is typically three days, but canbe extended over a longer period. Total flighttime is approximately four hours. Studentsreceive a detailed training record for insuranceand employment purposes, and extensive groundschool notes. The course can also include acomplex/high-performance checkout andBiennial Flight Review.

Pilots will gain:

• A significantly increased understanding ofmaneuvering aerodynamics.

• The ability to recognize and track aircraftmotion paths and energy transitions duringunusual attitudes.

• Inverted-flight experience under real gforces in a true dynamic environment.

• Control skills necessary to recover fromunusual attitudes and energy states.

• Strategies for dealing with flightcharacteristics following control failures.

• Enhanced confidence and safety.

Ground School Topics

Pilots can choose among a variety of groundschool sessions and subjects, including:

The Aerodynamics of Lift and Control:

Angle of attack and pressure patterns.Boundary layer and separation.Wing planform: Stall pattern and vortexeffects.

Aircraft Dynamics and Upset Recovery:

Aircraft axes and derivatives.The nature of stability and control.The aircraft’s natural modes.Lateral/directional coupling.Roll dynamics.Recovery procedures.Flying qualities: Differences between proptrainers and passenger jets.Limitations on the use of rudders for largeaircraft.FAR certification requirements.Simulator alpha/beta envelopes.

Spin Dynamics:

Departure, incipient phase, steady state,recovery.Inertial and aerodynamic moments.Aircraft mass distribution and recoverytechniques.

. Upset Causes:

NASA vortex studies and encounterdynamics.

Basic Aerobatic Maneuvers and Techniques

Flightlab’s Upset Recovery and Basic Aerobatics Program

Bill Crawford: WWW.FLIGHTLAB.NETIntro.2

Introduction

Welcome to the program. The following pagesdescribe our training goals, and provide theintroduction to the Maneuvers and Flight Notesyou and your instructor will use during yourflights and briefings.

We developed our training program over manyhours of flying with test pilots from NASA’sLangley Research Center, the Empire Test PilotSchool (U.K.), and the National Test Pilot School(U.S.A.), with fighter pilots and militaryinstructors, and with International Aerobatic Clubcompetition pilots, including members of theUnited States Aerobatic Team. Each disciplinebrought its own perspective. At NASA, we flewwith experts on aircraft wake vortices to exploretraining methods based on recent studies of vortexencounters. We talked to experts about thelimitations in using simulators for upset training.We worked on ways to help pilots safely translatethe skills learned in straight-wing aerobaticaircraft to swept-wing transports.

Our program is unique in combining theaerobatic competitor’s and military pilot’semphasis on attitude awareness andmaneuvering airmanship with the test pilot’sknowledge of aircraft dynamics. And we’veintroduced to aviation training the use of flight-test methods as cockpit teaching tools.

To gain a sense of where you’re headed, take alook at the Maneuvers and Flight Notes before wefly. Review as much of our text material as youcan, but don’t be concerned if you can’t getthrough everything, or intimidated when thingsget technical. We’ll cover the essentials in ouraerodynamics presentations. Aerobatics andunusual-attitude training both require and providethe ideal time for aerodynamics training. Ourprogram is designed to help you understand theaerodynamics of upset and wide-envelopemaneuvering, and to lay the groundwork forfuture study in general. You’ll be on the righttrack if you ask lots of questions and then followup on the reading when the course is over.

Our job is to answer those questions and to makethe flying informative, appropriately challenging,and—this is important—enjoyable. Elevatedanxiety shuts down the learning process.

Your job breaks down into three closely linkedtasks: We want you to increase your

understanding of maneuvering and departureaerodynamics, become familiar with the stimulusenvironment generated by unusual attitudes, anddevelop the control skills necessary for recovery.

During your flights, the instructor will read outthe checklist for each maneuver, then guide youthrough the steps, demonstrating first whennecessary. We follow a consistent maneuverformat, with each pilot receiving the same coretraining necessary for crew coordination and fordeveloping a CRM approach to unusual attitudes.Beyond these basics, we’ll adapt to yourbackground and skills. The flights will be anopportunity to practice assertive stick-and-rudderflying—the kind not possible in most dailyoperations but fundamental in emergencies.

You’ll begin the first flight by observing theclassical free response modes around the aircraft’saxes, and the aerodynamics of high angle of attack(high α, pronounced “alpha,”) and high sideslip(or high β, pronounced “beta”). The flight alsoincludes the first set of 360-degree rolls. Duringthis and later flights you’ll learn to recognize andrecover from an increasingly challenging range ofunusual attitudes, both with full controls andduring simulated control failures. You will alsobegin to fly basic, controlled aerobatic maneuvers.

Each maneuver set in the program builds on theprevious ones, so we want to try to fly them inorder, weather (and stomach) permitting. Butwe’ll adjust the sequence to your rate ofphysiological adaptation. If you have doubts aboutmotion sickness, a cautious start and a night’ssleep between the first and second flights can besurprisingly helpful.

If your motion tolerance is low, we’ll emphasizeaerodynamics in your flight program and go alittle lighter on unusual attitudes.



Because you might be reading this while stilldeciding whether to take an unusual-attitudeprogram, the following contains some pointsworth considering, as well as a general descriptionof what to expect in our program.

Our Training Aircraft

Your flights will be divided between a Zlin 242Land a Marchetti SF260. Both are Lycoming-powered, with FAA Airworthiness Certificates inthe Utility-Aerobatic Category, and built to satisfymilitary training requirements. Because theaircraft have tricycle gear and don’t requiretailwheel experience, students can do all theflying. The flight instrumentation allows unusual-attitude practice in simulated IMC, and the lowwings allow tufting for airflow visualization. Theaircraft are responsive and aerobatic. The Zlin iscapable of outside maneuvers (including outsideloops), plus tail slides and sustained invertedflight. The SF260 is less stabile than the Zlin, andrequires a more developed piloting technique.

We chose these aircraft partly because theydemonstrate different levels of aerodynamiccoupling in yaw and roll.1 Yaw/roll coupling is akey to understanding the dynamics of unusualattitudes. Yaw/roll couple is typical of the generaland especially the swept-wing fleet, but largelyabsent in aerobatic aircraft certified under thelateral stability exemption of FAR Part 23.177(c).Our aircraft also have flaps, which allow us toanalyze changes in span loading and downwash.While our aircraft can’t achieve the rapid roll andpitch rates possible in such aircraft as the Extra orPitts, those rates are in fact undesirable. Moderaterates, more pronounced coupling, and higherstability margins and control forces are far betterfor unusual-attitude training and aerodynamicsdemonstration. Plus our cockpit environments aremuch more comfortable!

In addition to being more fun, flying differentaircraft as part of your unusual-attitude trainingallows you to make comparisons that illustrate thevariables behind aerodynamic behavior. Itreinforces your ability to adapt to those variablesand transfer recovery techniques learned in onecockpit to another. Confidence in the ability toadapt what you’ve learned is crucial to reaction 1 In a coupled response, rotation around one axiscauses rotation around another. Aircraft can haveboth aerodynamic and inertial couples.

time, and thus essential in a future upsetemergency in your own aircraft.

What’s an Unusual Attitude?

Some pilots prefer the term “unusual attitude,”others prefer “upset.” We use theminterchangeably. Here’s the definition of aircraft“upset” from the Airplane Upset RecoveryTraining Aid (or AURTA, first released in 1998and developed jointly by government agenciesand an industry-wide group of airlines, aircraftmanufacturers, and training providers). TheAURTA (page 1.1) definition takes the aircraft asthe starting point:

“Airplane upset is defined as an airplane in flightunintentionally exceeding the parametersnormally expected in line operations or training.

While specific values may vary among airplanemodels, the following unintentional conditionsgenerally describe an airplane upset:

• Pitch attitude greater than 25 deg, nose up.• Pitch attitude greater than 10 deg, nose

down.• Bank angle greater than 45 deg.• Within the above parameters, but flying at

airspeeds inappropriate for the conditions.”

The attitudes given above do set appropriate limitsfor most aircraft and operations, but they’re verynarrow in terms of the possible attitudes a pilotcan experience. This reflects an observation madeby many professional pilots: after themaneuvering lessons of primary training andperhaps time spent as a flight instructor, as hoursand aircraft size increase, maneuveringopportunities tend to diminish and proficiencytends to atrophy. There can be an inverse or atleast no positive relationship between flight hoursand wide-envelope maneuvering ability. In theabsence of in-flight training, aggressivemaneuvering ultimately becomes a simulatorexercise, with the limitations that simulationimplies.

While we take the AURTA definition as a start,we expand it in our program to underscore theaerodynamics behind upsets. Here’s an addition:

In an unusual- attitude situation there’s alsotypically an “unusual” relationship going on (or



about to start going on) around the aircraft’saxes. It’s unusual in the sense that the opposingmoments around those axes—which in a trimmedairplane normally find balance and keep thingsroughly straight and level—start to shift in waysthat produce divergent results.

The above gets into technicalities and will takesome explaining! Don’t worry; you’ll get a handleon it during our flights and ground-schoolbriefings, as the examples unfold.

We should also expand the AURTA definition interms of situational awareness: It’s fair to call anunusual attitude anything that a pilot can’timmediately recognize: that is, whenever there’s aloss of correspondence between what the aircraftis doing and what the pilot perceives. Thedisconnection can be essentially cognitive, wherea pilot just can’t figure out what he’s seeing, ortake the form of spatial disorientation provokedby the vestibular system, where he can’t believewhat he’s seeing because of conflicting motioncues. The resulting loss of “sense security” canproduce panic in even the most experienced pilot.

Choosing an Instructor

There are no FAA regulations specificallygoverning curriculum or special instructorqualifications for unusual-attitude training. Whilethere are guidelines, like the Airplane UpsetRecovery Training Aid,2 it’s up to the trainingprovider to define the tasks and training style in amanner that leads to an effective program. Forsafety, all instructors should be current inadvanced aerobatics well beyond the maneuveringneeds of the program itself.

Instructors in aerobatic or unusual-attitudeprograms typically have backgrounds in civiliancompetition aerobatics or are former fighter pilots.While both backgrounds can produce highlyqualified instructors, remember that military andcivilian aerobatic training and flying techniquesare not always the same. The same laws of natureand aerodynamics apply, but, because ofdifferences in mission and machinery, those lawsare frequently invoked in different ways. 2 The Training Aid was itself a product of debate.See “Airbus Industrie Presentation at 10th

Performance and Operations Conference.”www.ntsb.gov/events/2001/AA587/exhibits/240005.pdf

As a result, civilian aerobatic and military pilotscan develop different skill sets and ways ofthinking about aircraft maneuvering. Notsurprisingly, each tends to teach as they’velearned, sometimes inappropriately. Early in thedevelopment of airline unusual-attitude programs,for example, former fighter pilots—whosegeneration of swept-wing fighters relied on therudder pedals for lateral control at highα—encouraged far more aggressive use of therudder than airliner manufacturers thought safe.This led to what many regarded as “negativetraining,” a situation in which the pilot was lesssafe after the training than before. Yet anaerobatic instructor with a competitionbackground would have been just as likely tomake the same training mistake regarding rudderuse, although for different reasons. Don’t letyourself be too impressed by an instructor’scredentials—even the most veteran instructor hasa point of view limited by his or her own trainingand maneuvering experience.

One way to counteract this is by introducing awider, more integrated point of view—the testpilot’s. By virtue of the job, test pilots have thetechniques necessary to evaluate aircraftcharacteristics, and the experience to know howthose characteristics can vary. Our ground schoolcontains elements of the actual training a test pilotreceives. Our flight program begins with basic“flying qualities” test procedures that reveal thefundamental mechanics of aircraft behavior—andbuilds from there.

Wide-Envelope Aerodynamics

Whether you receive instruction in flight or in asimulator, in any form of unusual-attitude trainingyou’re going to find yourself placed in upsetattitudes (often while your eyes are first closed)from which you’ll be expected to recover usingthe proper control movements. We’ll do the same,but build to it in steps. First, we’ll use our flight-test tools to illustrate the aerodynamics learned inground school. We’ll examine the nature ofstability and the conditions that lead to departureby flying the aircraft carefully through theboundaries of the normal attitude envelope (butwell within speed, recovery, and g-limits) whileanalyzing its behavior in both controlled and“free” response. This means flying atcombinations of high angle of attack and highsideslip (α and β) where coupled behaviors can



predominate, and at attitudes where the aircraft’sinherently convergent, back-to-normal stabilitycharacteristics start producing undamped,divergent responses. It also means flying atenergy states where you’ll first need to reestablishdynamic pressure and reattach airflow beforecontrol can return. We’ll emphasize that theunderlying aerodynamic conditions—and notmerely the aircraft’s attitude—determine theinputs necessary to regain control.

As a result of this demonstration approach you’llgain a better understanding of aircraft dynamics,and of the circumstances that actually produceunusual attitudes, than you would if we began ourwork by placing you in already-developedattitudes and then just coached you throughtextbook recoveries. To start, we’ll tuft the wingto see how airflow, and thus control effectiveness,changes as the aircraft enters and recovers fromstalls.

As an additional way of understanding aircraftcharacteristics, we can also review the flyingqualities mandated by FAR certificationrequirements.

Accidents

Many of the training tasks in our program aredrawn from both recent and historically typicalunusual-attitude accidents. Some examples areessentially aerodynamic in provocation, likevortex encounters, stalls, and spins. Otheraccidents stem from mechanical or control systemfailures. Although the engineering causes ofsystem failures might be specific to aircraft type,there’s usually an accompanying aerodynamicslesson that’s applicable in general. That’s why, forexample, we’ll have you examine theaerodynamics of rudder hardovers—the bane ofthe Boeing 737—even if you think it could neverhappen on your aircraft.

When we practice intentional unusual attitudes,briefed and prepared, it’s easy to forget howunintentional attitudes often happen. Suddencatastrophes aside, they evolve. They’re often theculmination of a chain of events that typicallystarts while the aircraft is still under normalcontrol. Problems appear, the workload goes up,the pilot enters an overload state and fails tomonitor attitude, and a departure from the normalenvelope begins. Pilots who’ve experienced thealarming physical sensations of spatial

disorientation can almost always look back andtrace the bad decisions that set the seeds.

The National Transportation Safety Board’swebsite www.ntsb.gov contains statistics on lossof control accidents, updates on currentinvestigations, and detailed final reports.

Simulators for Upset Training?

Kinesthesia is the term for the sensation of thebody’s position, weight, and movement, asconveyed through our muscles, tendons, andjoints. Both the vestibular (inner ear) andkinesthetic systems are components ofproprioception, the general term (although usagevaries) for all the non-visual systems involved inproviding information on the orientation andmovement of the body.

The proprioception of aerobatic flight involvessustained rotation and sustained g forces. Buteven the best six-degree-of–freedom simulatorcan only supply momentary cues. You won’t feela continuous 2 g during a simulated 60-degreebanked turn, for example.

When a simulator can’t provide a reasonablyseamless motion environment in which to learn,and toward which to adapt, simulator basedunusual-attitude training is limited to drills andprocedures. The simulator can’t provideequivalent experience, as it can in other flightregimes and emergencies involving less extrememotion. And if the simulator gives a falseimpression of how vision and proprioceptionmatch, it may actually lay the groundwork foreven greater confusion during unusual attitudes inflight, when visual cues are combined with morechallenging proprioceptive inputs than thesimulator’s motions allowed.

In addition to their limited ability to produce thephysical sensations of aerobatic flight, thecomputers that drive simulators have flight modellimitations. Both civilian and military aircraft areflight tested for their intended use, with someadditional level of control abuse. Manufacturersof non-aerobatic aircraft are not required todevelop actual extreme-attitude flight-test data. Itwould often be unsafe. As an example, theillustration shows the extent of the 737 flaps-up,flight-validated envelope. Note how combinationsof high sideslip and high angle of attack are



avoided. Behavior in these flight regimes simplyisn’t known. According to AURTA, App.3-D.1:

“From an aerodynamic standpoint, the regimes offlight that are usually not fully validated withflight data are the stall region and the region ofhigh angle of attack with high sideslip anglewhere there may be separated airflow over thewing or empennage surfaces. While numerousapproaches to stall or stalls are flown on eachmodel (available test data are normally matchedon the simulator), the flight controls are not fullyexercised during an approach to stall or during afull stall, because of safety concerns. Also, rolland yaw rates and sideslip angle are carefullycontrolled during stall maneuvers to be near zero:therefore, validation of derivatives involving theseterms in the stall region is not possible. Trainingmaneuvers [in the simulator] in this regime offlight must be carefully tailored to ensure that thecombination of angle of attack and sideslip anglereached during the maneuver does not exceed therange of validated data or analytical/extrapolateddata supported by the airplane manufacturer.”

It’s worth noting that this doesn’t precludesimulated rolling maneuvers at bank angles andattitudes outside flight-test parameters, but withinα/β limits. Again from AURTA:

“Values of pitch, roll, and heading angles,however, do not directly affect the aerodynamiccharacteristics of the airplane or the validity of thesimulator training as long as angle of attack andsideslip angles do not exceed the values supportedby the airplane manufacturer. For example, theaerodynamic characteristics of the upsetexperienced during a 360-deg. roll maneuver willbe correctly replicated if the maneuver isconducted without exceeding the valid range ofangle of attack and sideslip.”

You can see that limitations in the flight modelbeyond certain α/β values should be taken intoaccount when simulators are used to re-create andstudy upset accidents. The same caution isnecessary when simulators are used to developunusual-attitude recovery techniques—asomewhat abused practice in the past. Besuspicious of simulation at high α and β,especially beyond stall.

But also put the limitations of a non-validatedflight model into perspective. An aerobaticaircraft isn’t going to “model” precisely the kindof aircraft the AURTA is concerned with, either.In-flight unusual-attitude training is illustrative. Itcan take you into, and show you how to get out of,all sorts of territory. It produces true sensations.Yet it can only provide for the transfer of generalprinciples and fundamental skills.

Unusual-Attitude versus AerobaticTraining

In typical aerobatics courses you’ll learn to fly astandard set of maneuvers: roll, loop,hammerhead, Cuban-eight, Immelmann, spin, etc.It’s valuable training and worth encouraging, butnot always the best approach for a pilot whosefirst concern might be to learn unusual-attitudeaerodynamics and recovery skills for use in non-aerobatic aircraft.

One problem is that aerobatic training focusing onperfecting standard maneuvers tends to beinherently aircraft-biased in the way musclememories are developed. Although the basicaerobatic techniques aren’t appreciably differentbetween aircraft, if you want to keep yourinstructor happy, and get the maneuvers right,you’ll have to match your control inputs to thecharacteristics of the trainer you fly. In a veryresponsive aerobatic aircraft, such as an Extra or aPitts, a little bit of input will produce a lot of

737 Flaps Up Alpha/Beta Envelope Adapted from AURTA, App. 3-D.

Left Right

Extrapolated for simulator

- 40 - 30 - 20 - 10 0 10 20 30 40

Sideslip, β

(degrees)

30

20 10

0 -10

Ang

le o

f Atta

ck, α

Flight Validated Wind tunnel/analytical



maneuvering. You’ll learn a lighttouch—otherwise you’ll have a rough ride.

Unfortunately, those light control forces (whichinclude the initial breakout force necessary todeflect controls from neutral) can lead a pilot toan unrealistic set of motor skills and responseexpectations if applied to less nimble, non-aerobatic aircraft in unusual-attitude situations.There a light touch might take a long time gettingnoticed.

Another drawback to standard aerobatic trainingis that the maneuvers, properly taught and flown,don’t present all of the control issues that anunusual attitude program really needs to address.Although the attitudes may be new to the pilot, ifthe aerobatic maneuvers have been enteredcorrectly the aircraft will be in an energy statewell within the envelope of positive andimmediate control. The pilot will have seen onlypart of the problem.

As a matter of fact, you have to fly aerobaticmaneuvers badly in order to take them to theregions of the attitude/energy envelope wherethey start to provide the most complete trainingopportunities for unusual-attitude recovery. In astandard aerobatics course, a good instructor willset up bad maneuvers for just that reason. Evenso, the experience may still be somewhat off themark as unusual-attitude training, because theattitude emergencies a student will face in cross-country flying won’t originate from a botchedhammerhead or a sloppy Immelmann, buttypically from such things as turbulence, ice,wake encounter, or systems and control failures.

We’ve created a maneuver sequence thataddresses the aerodynamics of attitude, energy,and basic upset response more completely than atypical spin-loop-roll aerobatics course, usingaircraft chosen to relate as well as possible to thegeneral fleet. You’ll start with stability andcontrol demonstrations adapted from flight testprocedures, begin to develop unusual attituderecovery skills, and then move on to the classicaerobatic maneuvers.

Wide-Envelope Attitude Awareness

You’re going to be in for trouble in an upsetsituation unless you can visually track rapid andcomplex changes in aircraft attitude. Trackinginformation can come to you in three ways: by

looking at the scene out the window, looking atthe attitude and performance instruments in thecockpit, and by scanning inside and out. In VFR,this all happens within a wide-angle visual fieldthat can develop rapid peripheral rotations thatprofoundly affect perception of the scene. In IFR,the angle narrows and potentially helpfulperipheral cues are missing. And all of this occurswhile your body is contending with abrupt andperhaps contradictory vestibular stimulation.

This environment is confusing at first. Theperceptual skills that prevent it from remaining ablur take practice to develop. The forces aredisconcerting and the usual references candisappear. Experience shows that the best way toenter it is in increments that provide a gradualexposure to increasingly unfamiliar aircraftattitudes and motions, while maintaining acomfortable sense of aircraft control. In additionto building understanding, the aerodynamicsobservations we’ll be making in the first flight aredesigned to help you relax and developconfidence in the aircraft, while gaining thetracking ability necessary for more complexmaneuvers later on.

As our maneuvering increases, you’ll becomemore familiar with the aircraft’s attitude cues andtypical motion paths. You’ll build a mental image,or model, of the aircraft’s motions, as ifvisualizing the aircraft from outside. You’ll alsobegin to acquire what aviation physiologists callearth-stationary perception: You’ll start to gainthe perceptual ability to fix the plane of the earthand horizon in place during unusual attitudes, justas you do in normal ones, and you’ll begin toexperience and anticipate the motion of theaircraft against that stationary reference. Theability to imagine aircraft motion correctly inthree axes supports the ability to perceive attitudein earth-stationary terms, since the internal modelacts as a bridge during intervals when horizonreference is temporarily lost.

Although this learning occurs in VFR, you’ll findthat it applies to instrument interpretation in IFR,as well. Unusual-attitude instrument indicationsare easier to decipher when you can associatethem with dynamics you’ve already seen outside.Interpretation can be very difficult otherwise.We’ll start you on outside references, and thenbring your focus inside.



Control Skills

Mantras: Because we want you to develop coreresponse habits based on earth-stationaryperception, we don’t rely heavily on mantras,meaning memorized control sequences or controlinputs remembered through acronyms. Mantrasfor guiding the hands and feet are fine—as longas they’re acted out in phase with the aircraft’sattitude. The trouble comes when a pilot loses orlacks earth-stationary visual tracking, appliessequenced inputs out of phase with themaneuvering requirements, and then becomesconfused when the aircraft respondsunexpectedly. Confused pilots often freeze.Aerobatics instructors see this all the time.

Also, in some cases maneuvers are actually easierto master if the necessary control motions arelearned out of sequence. The flexibility necessaryfor this in training makes mantras inappropriate,and often irrelevant once the student catches on.This is the case in learning to roll an aircraft withintegrated rudder and elevator inputs. (See “SlowRoll Flight Dynamics” in the Maneuvers andFlight Notes.)

We think mantras can be helpful, but as ways tosummarize and seal the control skills you’velearned, not as a primary training technique.

Airline training for unusual attitudes often relieson standardized “flow response” or “rule-based”performance.3 The pilot learns to interpret flightinstruments in the sequence necessary todetermine aircraft attitude and perform the rightcontrol inputs. Pilots are trained to recognize thesituation, confirm it, and then take the prescribedsteps. This approach is based on instrument flyingand suits the airline and FAA preference foruniform procedures. If the pilot follows theprocedure correctly, he or she is consideredtrained.

Our program is different. We strive for “skill-based” performance and will encourage you to flyin direct response to the visual cues, mediated aslittle as possible by mental checklists designed totell you what to do with your hands and feet.Direct response is how experienced aerobaticpilots fly. This approach isn’t meant to replaceprocedural flying where procedures are necessary. 3 Human factors experts distinguish between skill-based, essentially automatic performance, andmore cognitive, if-then, rule-based performance.

The skills gained should make upset “procedures”easier, because you’ll be able to take in attitudeinformation more efficiently.

That said, a case where talking yourself through amemorized control sequence can work best, asboth a learning and a survival technique, is duringa spin recovery—especially once a spin developsand the wrong sequence can delay or preventrecovery.

The Debate over Spin Training

The then CAA (now FAA) removed the spinrequirement from the private pilot flight test in1949, but the arguments over spin training neverlet up. There were even Congressional hearings,in 1980, in which the Subcommittee onInvestigations and Oversight of the HouseCommittee on Science and Technology, clearlywowed by a witness list of famous test pilots,recommended that spin training be restored—arecommendation the FAA did not follow.

Under FAR Part 61, an applicant for a privatepilot certificate is required to receive only groundinstruction in “stall awareness, spin entry, spins,and spin recovery techniques.” A candidate forflight instructor must demonstrate ground“instructional proficiency” in the same areas, andreceive actual spin flight instruction. The flightinstructor requirements can be satisfied with alogbook endorsement from a current CFI after justone spin-training flight.

The result is often a new instructor who speaksfrom limited direct experience.4 Unfortunately,he’ll be speaking to his eventual students aboutflying’s most complex dynamic event—an eventthat can quickly deteriorate to the point wheretraining restricted to ground instruction, howeverinformed the instructor might be, won’t provemuch help. Pilots learn spins through their hands,feet, and eyes. Not only do they have to learn thecorrect recovery response, they have to filter outthe impulsive and incorrect. That’s not a ground-based academic task.

Over the years, some authorities have argued thatstall avoidance training is the real answer to spin 4 Patrick R. Veillette, Re-Examination ofStall/Spin Prevention Training, TransportationResearch Record, No. 1379, National ResearchCouncil, Transportation Research Board, 1993.



accidents. They cite as evidence the accidents thatoccur during spin training itself, and the statisticsthat show that most fatal stall/spins happen duringtakeoffs and landings (or during buzz jobs), ataltitudes too low for recovery in the first place.5Their argument ignores the fact that only spinaccidents get recorded, while there’s no way ofknowing how many people spin training hasactually saved at recoverable altitudes, orprevented from making mistakes at low altitude byvirtue of a better understanding of how things cango wrong. It’s also a self-fulfilling prophecy: Ifyou avoid spin training because you thinkrecoveries from developed spins are statisticallyunlikely below standard traffic pattern altitude, asthe Air Safety Foundation has asserted, youprobably won’t have the skill to recover from aninitial spin departure, either.6 Yet, with training,recovery from the initial wing drop that signalsthe beginning of autorotation is possible in manylight aircraft, at least above 500 feet. So thequestion for the individual pilot becomes: Do youresign yourself to statistical outcomes—or do youtry to beat them through training that takes youbeyond stall avoidance and into actual spindepartures and recoveries?

Some aircraft put up a good barrier between stalland spin. Stick shakers and pushers on turbopropsand jets make it difficult to get into the territorynecessary for a spin. Modern wing, empennage,and aileron designs make inadvertent spins lesslikely than in the old J-3 Cubs, Cessna 120/140s,and Aeroncas in which civilian spin instructionwas once given. It was their departurecharacteristics that the classic, stall/spin-trainingscenarios were designed to reflect. Although theirstall behaviors were often gentle, they hadsignificant adverse aileron yaw and powerfulelevators and rudders—a combination that affordsplenty of pro-spin opportunity if a pilot misappliesthe controls. The ease with which these aircraft(and many other pre- and World-War-II trainersand especially fighters) could spin if mishandledmade spin training necessary. Later generations ofaircraft were harder to provoke. Making them thatway was part of the reasoning behind the removalof the private pilot spin requirement. As long asspins were required, manufacturers had to producetrainers that were easy to spin. Without the

5 Especially Leighton Collins, Air Facts, vol. 36,June 1973, pp. 80-96.6 www.aopa.org/asf/ntsb/stall_spin.html

requirement, more spin-resistant designs becamemarketable.

In our training program we’ll concentrate first onpost-stall departures and incipient spin entries,where aerodynamic moments predominate andemergency recoveries should occur. When you’recomfortable, the training moves to spins in whichthe aerodynamic and inertial moments areapproaching balance, and incorrect controlmovements can delay recovery. You’ll find thatthe stick forces necessary for recovery tend toincrease as a spin develops, and spin rate cantemporarily increase after recovery inputs. Theseare essential points to demonstrate, because theirmisinterpretation can cause a pilot to panic andmisuse controls.

It’s important to note that practice spins at safealtitudes, while necessary for learning spindynamics and recoveries, don’t recreate themental state in which many spin accidents arelikely to occur. Spins particularly happen downlow, when an anxious pilot attempts to increase aturn rate while fighting a growing sink rate. Primeexamples are turn-backs due to engine failure ontakeoff, and skidding turns when low and tight onbase to final. Pilots who claim they’d nevermishandle an aircraft in this way simply don’trealize how powerful the impulse becomes whenthe ground starts rising and there’s unfriendlyterrain ahead. In fact, spins aren’t just fatal at lowaltitude: low altitude literally provokes departureif a pilot responds to the unexpected ground threatwith visceral but inappropriate controlmovements. For the untrained pilot, the visceralresponse—stick back, opposite aileron—is pro-spin. If spin training up high fails to accomplish asafer outcome down low, it’s a good bet that theinstructor failed to point out that spin training isalso crash training! It’s certainly better to crashunder control in a more or less level attitude thanin the sudden-stop, nose-in-the-dirt verticalattitude of a low-altitude spin departure.

Also remember that the differences betweenaerobatic and non-aerobatic aircraft can besubstantial. The FAR Part 23 one-turn spinrecovery requirement for normal categorycertification can produce a much less predictableaircraft than one certified under the six-turnrequirement for aerobatics and spin-approvedutility. Part 23 twins and large aircraft certifiedunder Part 25 have no spin recovery requirementsat all. Consequently, it’s dangerous to venture far-reaching predictions about the spin behavior of a



non-aerobatic aircraft based on one’s experiencein well-mannered aerobatic trainers alone. Ourground school takes this into account.

But the good news is that spin departures areessentially alike. Aircraft have differentsusceptibilities, but they go into spins or post-stallgyrations for the same underlying reason: failureof lateral/directional stability at stalling angle ofattack. As a result, learning to enter into andrecover from spins in any one aircraft gives youthe basic lessons needed to keep them fromhappening in most others. By opening your eyesto both spin causes and consequences, spintraining can build more ingrained and technicallyproficient stall avoidance. That’s of course thefoundation on which the argument for spintraining ultimately rests: Spin training shouldmake emergency spin recoveries unnecessary.The training doesn’t have to be hair-raising andthe airmanship benefits, once you’ve experiencedthem, are too genuine to ignore—a big chunk ofmystery and vulnerability will be gone.

Maneuvers and Flight NotesCopyright Flight Emergency & Advanced Maneuvers Training, Inc. dba Flightlab, 2009. All rights reserved.

For Training Purposes Only

General Briefing

Anxiety!!!

If you’ve never flown aerobatics (or have hadsome bad experiences in the past), anxiety isnatural. Sometimes people are anxious aboutsafety, sometimes about how well they’llrespond when the instructor places the aircraft inan upset condition. Anxiety disappears as youlearn to control the aircraft. We won’t take youby surprise (well, not immediately). We’ll teachyou how to follow events so that surprisesbecome manageable.

Even so, there may be times when you feel thattoo much is happening too fast. That’s notentirely bad: it shows that you’re pushing theboundaries of your previous training. As yougain practice you’ll find that the aircraft’smotions become easier to follow and tracking thehorizon becomes less difficult. Your comfortlevel then quickly rises.

But if you feel confused or unsafe at any time, letus know.

Airsick?

The same goes if you begin to feel airsick. Youprobably don’t learn well with your head in abag, so don’t hesitate. Let us know immediatelyso that we can modify the program and flightschedule for your comfort. If you’re new toaerobatics, you’ll discover that airsickness hasnothing to do with the previous number oftrouble-free hours in your flying career.Resistance—or “habituation,” depending on yourtheory—usually arrives, but it takes time.

Most of our maneuver sets call for repetitions,but we can easily stretch those out over severalflights, if you prefer. That’s easier on theinstructor, as well. If you’re concerned aboutairsickness, a good resistance-building techniqueis to fly somewhat aggressive lazy-eights (whichyou might remember from the CommercialFlight Test) in a light aircraft a few days beforeyou fly with us. Lazy-eights supply the pitchingand rolling motions and variations in g forceyour body must adjust to. But stop at the first

feelings of discomfort. Becoming sick does nothelp you adapt faster.

Don’t fly aerobatics on an empty stomach. Eat!You look thin! Drink plenty of water, especiallywhen the outside temperature is high.Dehydration reduces g tolerance.

Research done with persons subject to motionsickness suggests what you’ve perhaps alreadyobserved: People who report that they’verecovered from feelings of nausea can remainhighly sensitized to vestibular disturbance forhours afterwards. That’s why those airsickpassengers who announce with relief that they’renow feeling much better often spontaneously re-erupt as you start to maneuver into the trafficpattern. The temporary disappearance ofsymptoms doesn’t necessarily mean the battle isover.

What to Read: Ground School Texts

The texts you’ll receive (or download) alongwith the Maneuvers and Flight Notes cover awide range of subjects, giving backgroundmaterial you can go into, more or less deeply,according to your interests. Our program is bestfor pilots who not only want to gain aerobaticand upset recovery skills but who also have abroader curiosity about the principles of aircraftresponse. Skills can be learned quickly, butsatisfying curiosity takes time—because, ideally,curiosity grows. (And the subject of airplanes isvast.) You may find it helpful to read at least theground school selections “Axes and Derivatives”and “Two-Dimensional Aerodynamics” beforethe first flight—don’t worry if you don’t have atechnical background; they’re not as nerdy asthey sound. Treat the ground school texts as along-term resource, not a short-term burden.

What to Think About

Think about searching out the basic relationshipsthat determine aircraft behavior. At very least,you need to examine two areas. The two ground

Maneuvers and Flight Notes

Bill Crawford: WWW.FLIGHTLAB.NET2

school selections mentioned above provide anintroduction.

You need to understand how an aircraftresponds to its own velocity vector, and to its liftvector. If you know where the velocity vector ispointed (relative to the aircraft’s fixed axes), andwhere the lift vector is pointed (relative to thehorizon), you know how a stable aircraft is likelyto behave. This is the core of our presentation ofstability and control.

You also need to understand the nature of thepressure patterns over the surface of the wing:how those patterns originate and how theymigrate as angle of attack changes. This isespecially important as the aircraft approachesthe stall, because pressure patterns determine theavailability of control.

Where to Look

Unusual-attitude training should take bothoutside and inside attitude references intoaccount. Aerobatic pilots look outside first. Wefly in reference to the real horizon, not theartificial one. Of course, that’s because we flyaerobatics only in VFR conditions; but even ifwe have an aerobatic-friendly attitude indicator,the real horizon provides much betterinformation.

Unlike aerobatic pilots, many IFR pilots tend tolook inside first, even in good weather. If controlof aircraft attitude is a reflexive, heads-in activityfor you, you may need to reacquaint yourselfwith the information out the window. Partlybecause of the essential role peripheral visualcues play in spatial awareness, that’s where theinformation is best during unusual attitudes.Physiological correlation between what yourbody feels and what your eyes see also happensmuch faster when you’re looking outside. Thenbegin to connect what you’ve learned aboutaircraft behavior from looking out with thesymbolic attitude information available withinthe cockpit. You’ll find that the symbolicinformation—which unfortunately lacks theperipheral cues we primarily rely on to perceiveour motion within the world—becomes easier tointerpret when you can associate it with attitudesand flight behaviors you’ve already seen outside.

One of the drawbacks of simulator trainingprograms for unusual attitudes is that this

valuable building block, outside/inside-learningprocess may not occur with sufficient repetitionfor the benefits to sink in. Pilots mightdemonstrate maneuvering proficiency in specific,directed tasks, but still have limited attitudeawareness.

Rudder Use

We want you to experience and understand theeffects of rudder deflection on aircraft responseat high angles of attack. While the same basicaerodynamic principles apply in swept-wingaircraft as in our straight-wing propeller-driventrainers, in practice large aircraft and swept-wingdynamics are different, and more limited rudderuse is recommended. On matters concerningrudders, search the Internet for BoeingCommercial Airplane Group Flight OperationsBulletin, May 13, 2002. Also Airbus FCOMBulletin, Use of Rudders on Transport CategoryAirplanes, March 2002.

Standard Procedures

• Clear the airspace before eachmaneuver.

• Acknowledge transfer of control.

• Don’t hesitate to apply your own CRMprocedures and call-outs as you thinkappropriate to the safety of the flight.

• Don’t fret about your mistakes.Mistakes are your best source ofinformation. Bracket your responsesuntil you zero-in on the correctprocedure.


Bill Crawford: WWW.FLIGHTLAB.NET 3

Maneuver Sets and Lesson Plan

Because certain maneuvers use up motiontolerance more rapidly than others, and personaltolerance varies, your maneuver sequence mightbe different than the standard schedule. You’llalso repeat some maneuvers when you fly thesecond aircraft.

The core lesson is upset recovery, but we teachmuch more than recovery procedures, as you’llsee when you begin reading. The Flight Notesbelow each maneuver description coverfundamental aerodynamic principles. Togetherwith the ground school presentations andsupporting texts, they describe aircraftcharacteristics you’ll observe and techniquesyou’ll learn. They attempt to expand your frameof reference with examples drawn from differentaircraft types. They’re part narrative, partexplanation, and sometimes a warning.

The information in the Flight Notes is obviouslymore than an instructor could give during aflight, and much more than a student could beexpected to take in. Chances are we won’t havetime to cover every detail, nor will every detailapply to your type of flying. Don’t let thematerial overwhelm you. Familiarize yourselfwith the relevant Flight Notes before each sortie,as you think best. When you review the notesafter the flight, you’ll find them much easier toabsorb, because you can connect them with whatyou’ve just done. The ground school textsreinforce the Flight Notes and add furtherinformation.

We use boldface italics to emphasize importantconcepts. (Boldface in the procedure descriptionreminds instructors of points to emphasize insetting up and carrying out maneuvers.)

Here’s how the maneuvers break down intogeneral categories:

Natural Aircraft Stability Modes, Yaw/RollCouple:

1. Longitudinal & Directional Stability, SpiralDivergence, Phugoid

2. Steady-Heading Sideslip: Dihedral Effect &Roll Control

High Angle of Attack (Alpha):

3. Stall: Separation & Planform Flow (Wing tuftobservation)

4. Accelerated Stalls: G Loads & BuffetBoundary, Maneuvering Stability

5. Nose High Full Stalls & Rolling Recoveries6. Roll Authority: Adverse Yaw & Angle of

Attack, Lateral Divergence7. Flap-Induced Non-convergent Phugoid

Roll Dynamics:

8. Nose-Level Aileron Roll: Rolling FlightDynamics, Free Response

9. Slow Roll Flight Dynamics: ControlledResponse

10. Sustained Inverted Flight11. Inverted Recoveries12. Rudder Roll: Yaw to Roll Coupling

Refinements and Aerodynamics:

13. Rudder & Aileron Hardovers14. Lateral/Directional Effects of Flaps15. Dutch Roll Characteristics16. CRM Issues: Pilot Flying/Pilot Monitoring17. Primary Control Failures

High-Alpha/Beta Departures:

18. Spins

Additional Basic Aerobatic Maneuvers:

Loop, Cuban Eight, Immelman, Hammerhead,Slow Roll, Point Roll



First Flight

1. Longitudinal & DirectionalStability, Spiral Divergence,Phugoid

2. Steady-Heading Sideslip:Dihedral Effect & Roll Control

3. Stall: Separation & PlanformFlow (Wing tuft observation)

4. Accelerated Stalls: G Loads &Buffet Boundary, ManeuveringStability

5. Nose High Full Stalls &Rolling Recoveries

6. Roll Authority: Adverse Yaw& Angle of Attack, LateralDivergence

7. Flap-Induced Non-convergentPhugoid

8. Nose-Level Aileron Roll:Rolling Flight Dynamics, FreeResponse

Possible:

9. Slow Roll Flight Dynamics:Controlled Response

On Return:

17. Primary Control Failures

Second Flight

9. Slow Roll Flight Dynamics:Controlled Response

10. Sustained Inverted Flight

11. Inverted Recoveries

12. Rudder Roll: Yaw to RollCoupling

13. Rudder & Aileron Hardovers

14. Lateral Effects of Flaps

15. Dutch Roll Characteristics

Possible:

19. Spins

Basic Aerobatic Maneuvers

On Return:


Third Flight

Review Maneuver Sets 9-12

16. CRM Issues: PilotFlying/Pilot-Not-Flying

18. Spins

Basic Aerobatic Maneuvers

On Return:

17. Primary Control Failures (asnecessary)

Fourth Flight

Review and additional aerobaticmaneuvers to be determined.

These maneuvers are for training purposes in appropriate aircraftonly. Follow the procedures and obey the restrictions listed in

your pilot’s operating handbook or aircraft flight manual.



Trimming for Airspeed in Level Flight

We usually trim an aircraft in climb for VY, best rate of climb, or perhaps a bit faster to preserve the view overthe nose and to keep engine temperatures from rising. In descending from altitude for landing, we might trimfor a comfortable descent rate. In the pattern we trim for pattern speed based on habitual power settings, andthen for our landing reference speed.

But we usually don’t trim for a particular airspeed in cruise. Instead, we level off at a certain altitude,accelerate a little while nudging the trim forward, and then pull back the power to cruise setting. Last, wefinal-trim to zero out the control force necessary to maintain level flight. Then we take the airspeed we get.

Sometimes in flight-testing, or in our program, you’ll want to start a maneuver from a specific, trimmed,level-flight airspeed. Here’s what you do:

• Bring the aircraft to the required altitude

• Set the power to the approximate value dictated by experience. Of course, don’t chase airspeed withlarge power changes. Just get close.

• Use pitch control to bring the aircraft to the desired airspeed.

• While holding airspeed constant, use power to center the VSI at zero climb/descent rate.

• Trim out the control force.

Note that pitch controls airspeed, power controls the aircraft’s flight path angle relative to the horizon.



1. Longitudinal & Directional Stability, Spiral Divergence, Phugoid

Flight Condition: Upright, free response in roll/pitch/yaw.

Lesson: Aircraft behavior when disturbed from equilibrium flight.

Procedures:

Longitudinal Stability: Stick force, Phugoid

Static stability: On the climb to the practice area, trim for VY. Observe longitudinal (pitch axis) stickforces needed to fly at airspeeds greater than or less than trim. Assess force gradient. Look forcharacteristics due to friction.

Simulate the effect on longitudinal stability of moving center of gravity aft: Trim, pitch up to fly 10knots slower than trim, hold speed while instructor slowly trims nose up. Note how stick forcedecreases (simulating a decrease in stability), disappears (simulating neutral stability), and thenreverses (simulating static instability).

Dynamic stability: Use pitch up and stick release to demonstrate phugoid. Observe period, amplitude,damping.

Directional Stability:

Low cruise power, airspeed white arc.Enter flat turn with rudder, while keeping wings level with aileron. Observe build up of pedal forcesto full deflection.Quickly return pedals and ailerons to neutral; observe overshoots and damping.Look for characteristics due to friction.

Lateral Stability: Spiral Mode

Power and trim for low cruise.Enter a 10-degree bank angle, return controls to neutral and observe response in roll. Note appearanceof phugoid. Repeat bank with additional 10-degree increments until onset of spiral departure.Look for asymmetries by repeating to the opposite side.

Allow spiral mode to develop as consistent with comfort and safety.Roll wings level; release controls; observe recovery phugoid.

Reduce entry airspeed and observe the increase in roll amplitude versus time.

Knife-edge recovery:Low cruise power, airspeed white arc.Roll knife-edge.Immediately release controls and observe response.



Flight Notes

We’ll start by exploring how an aircraft’s inherent stability determines its free response when disturbedfrom equilibrium. Free response is what happens when the pilot stays out of the control loop. It’s easier tounderstand the sources of an aircraft’s complex, self-generated motions when you can break them downinto simpler, free response “modes” around each axis. Usually, a moment generated around one axisproduces some form of response around another. From the standpoint of unusual-attitude training, if youunderstand and can anticipate an aircraft’s “basic moves,” managing the control loop properly to maintainor to re-establish control becomes closer to second nature.

In aircraft with basic cable-and-pushrod reversible controls, like our trainers, free response can depend onwhether the stick and rudder pedals are held fixed or literally left free so that the control surfaces areallowed to streamline themselves to changes in airflow. Irreversible, hydraulically powered controls arealways effectively fixed. See FAR Parts 23 & 25.171-181 for stability requirements.

Longitudinal Static and Dynamic Stability

• We’ll use some maneuvers borrowed fromflight test procedures to look at basic aircraftcharacteristics. We’re going to adapt theprocedures to our own purposes, take a generalapproach, have fun, and not worry about alwaysdoing things with the real precision that’srequired to gain accurate data points in actualflight test. A rough narrative follows.

• Here’s the deal on longitudinal static stability,as required by Part 23.173: “… with the airplanetrimmed … the characteristics of the elevatorcontrol forces and the friction within the controlsystem must be as follows: (a) A pull must berequired to obtain and maintain speeds below thespecified trim speed and a push required toobtain and maintain speeds above the specifiedtrim speed.’’

• On the way to the practice area we’ll observethe Part 23.173 requirement. We’ll trim theaircraft and then observe the stick forcesnecessary to fly at slower and faster airspeeds(a.k.a. angles of attack) without retrimming.When we release the force, the nose initiallypitches toward the trim angle of attack. Thisinitial tendency is what we mean by positivestatic stability (static refers to the initialtendency, dynamic refers to the tendency overtime). The more force we have to apply todeviate from trim, the greater the stability. Wecan increase static stability (and thus the stick

forces needed to deviate from trim) by movingthe center of gravity forward. We decreasestability (and decrease the forces) by moving itaft. We can fake the effect using trim, asdescribed in the Procedures, above.

• You’ll observe that the push force required tohold the aircraft 10 knots, say, faster than trim isnoticeably greater than the pull force needed tohold it 10 knots slower. That’s because thedynamic pressure generated by the airflowyou’re holding against is a function of velocitysquared, V2. The illustration below suggests howstick forces vary with speed. The force is zero attrim speed.

Con

trol F

orce

, FS

0

Pull

Push

Airspeed

Stick Force Gradient

Trim Speed



• Phugoid: Next, we’ll pitch up about 45 degreesor more, slow down and nibble at the stall, thenreturn the stick to its trim position and let go.(This is a more aggressive entry than actuallyrequired to provoke a phugoid, but it’s a goodattention-getter during unusual-attitude training.)The nose will start down, again indicatingpositive static stability, but then go below thehorizon. Velocity will increase past trim speed,and the nose will begin to rise. Although theaircraft’s attitude varies, its angle of attackremains essentially constant. The aircraft willpitch up, slow, pitch down again, speed up, andthen repeat this up-and-down phugoid cycle anumber of times. It will gradually converge backto its original trimmed state. (Had we simply letgo of the stick instead of carefully returning it tothe original trimmed position, control systemfriction might have produced a different elevatorangle and a different trim. That, in turn, couldsuperimpose a climb or a dive over the phugoidmotion.) Your instructor will point out that theamplitude of each pitch excursion from leveldecreases (indicating positive damping and thuspositive dynamic stability) while the period (timeto complete one cycle) remains constant at agiven trim speed. The period is quite long, so thephugoid is also referred to as the ‘long period”mode—and the faster you fly the longer theperiod. Damping in the phugoid comes from thecombined effects of thrust change and dragchange as the aircraft alternately decelerates andaccelerates as it climbs and descends.

• You’ll need right rudder at the top of thephugoid to counter the slipstream and p-factorand keep the nose from yawing, and maybe someleft rudder at the bottom. You might need aileronto keep wings-level, as well—but don’tcontaminate the phugoid with inadvertentelevator inputs.

Positive Longitudinal Dynamic Stability

Dis

plac

emen

t

Time →

Period

Amplitude

Period/Time to subside = damping ratio, ζ

Time to subside

Equilibrium



Directional Stability

• Flat Turn: The next maneuver is the basicflight test for static directional (z-axis) stability.When you depress and hold a rudder pedal,causing the nose to yaw along the horizon, yougenerate a sideslip angle, β. Sideslip creates aside force and an opposing moment. Notice theincreased pedal force necessary as rudderdeflection increases. For certification purposes,rudder pedal force may begin to grow lessrapidly as deflection increases, but must notreverse, and increased rudder deflection mustproduce increased angles of sideslip. The ruddermust not have a tendency to float to and lock inthe fully deflected position due to a decrease inaircraft directional stability at high sideslipangles as the fin begins to stall. If it did, theaircraft would stay in the sideslip even with feetoff the pedals. (Things could be dicey if thepedal force needed to return a big rudderexceeded the pilot’s strength. Many well-knownaircraft had rudder lock problems during theirearly careers, including the DC-3 and the earlyBoeing 707, and the B-24 Liberator bomber.)

• A given rudder deflection produces a givensideslip angle, but the force required rises withthe square of airspeed. So we won’t have to workas hard if we pull the power back to keep thespeed down.

• When you release or quickly center the pedals,the now unopposed side force causes the aircraftto yaw (weathervane) into the relative wind. Inour jargon, the directionally stable aircraft yawsits plane of symmetry back into alignment withthe velocity vector. This initial tendencydemonstrates positive static directional stability.We’ve entered a dynamic state, as well.Momentum takes the nose past center, whichgenerates an opposing side force that pushes itback the other way. The nose keepsovershooting, but the amplitude of thedivergence decreases each time. This timehistory indicates positive dynamic directionalstability. You might notice an increase indamping when you return the rudders positivelyto neutral and hold them fixed, instead of lettingthem float free. However, this behavior alsodepends on the amount of friction in the ruddercontrol circuit.

• Notice that the aircraft tries to roll in thedirection of the deflected rudder, and that youhave to apply opposite aileron to keep the wingslevel. This is caused by a combination ofdihedral effect (an aircraft’s tendency to rollaway from a sideslip angle, β, a response we’llexamine presently), and roll due to yaw rate—inwhich one wing moves faster than the other andproduces more lift. An aircraft with reduceddirectional stability may yaw faster in responseto rudder deflection than will a more stable type,and go to a higher β, and consequently needmore opposite aileron. (You’ll see a differencebetween the Zlin and the SF 260 in this regard.)

• Finally, note that when you apply aileronagainst the roll, you’re also applying anadditional “pro-rudder” yaw moment, this timecaused by the adverse yaw that occurs when theinto-the-turn aileron goes down. (There’re othermoments in the mix we won’t worry about.)

Stabilizing yaw moment.

β V

v v is the Y-axis component of the aircraft’s velocity vector, V. v = V sin β

X

Directional Stability



Spiral Mode

• When you enter a shallow bank and positivelyreturn the controls back to neutral (so thatunintended deflections or control system frictiondon’t taint the result) the aircraft should slowlystart to roll level after a few moments. Theaircraft’s velocity vector (for a definition, seeground school text “Axes and Derivatives”) has acomponent of motion (sideslip) toward the lowwing, which leads to a wings-level rollingmoment due to dihedral effect—a responsereferred to as lateral stability. The aircraft’slateral stability provides positive spiral stability.Sideslip also produces a yawing tendency, butdihedral effect predominates at smaller bankangles.

• The outside wing in the turn is moving fasterthan the inside wing—that’s a yaw rate. As youadd bank increments you’ll find a point—if theatmosphere’s not too turbulent—where bankangle remains constant (neutral spiral stability).The rolling moments produced by dihedral effectand roll due to yaw rate are now equal andopposite. (Again, there’re other moments in themix, but their contribution is minor.)

• At some point the aircraft will likely begin abanked phugoid, just like the phugoids we’veobserved, but tipped on its side. The aircraft willbring its nose up and down as it turns. Hands off,the aircraft retains a constant angle of attack,according to trim, regardless of pitch attitude orbank angle.

• When we raise the bank angle further, but don’tincrease lift by adding back stick, the aircraftslips increasingly toward the low wing. The yawrate builds due to the greater side force againstthe tail. Directional (z-axis) stability causes thenose to weathervane earthward in a descendingarc. Now roll due to yaw rate predominates overthe opposite rolling moments, and sends theaircraft into the unstable spiral mode

• Test pilots typically place an aircraft in a givenbank angle, center the ailerons (or bank theaircraft with rudder while holding the aileronsfixed), and then time the interval required toreach half the bank angle for the spirally stablecondition, or double the bank angle for theunstable. It’s important that control surfaces are

positively centered during these tests, becauseany residual deflection caused by control systemfriction can create an apparent difference inspiral characteristics. (Friction confuses thepicture when you’re trying to figure out how anaircraft behaves. Friction in the elevator systemmakes you think longitudinal stability is differentthan it is; friction in the ailerons that preventsthem from returning to center automaticallywhen released gives you a roll rate that shouldn’tbe there. Normally, you’d accommodate to suchthings without really being aware of the extracontrol input—but here we’re paying attention!)

• The coefficient of roll moment due to yaw rate,Clr, goes up with coefficient of lift, CL, so it’smore pronounced at low speeds, where α andcoefficient of lift are high. And for a given bankangle, yaw rate goes up as airspeed goes down.So you’ll double your spiral bank angle morequickly at lower entry speeds.

• Finally, note that the ball stays essentiallycentered during a spiral departure. That’sdirectional stability doing its job, unto the last.

Z axis

Effective lift less than weight results in a sideslip velocity component, v, and sideslip angle, β.

v

Resulting yaw rate, r.

Roll moment due to yaw rate, Lr, greater than opposite roll moment due to sideslip, Lβ.

Lr

Lβ.

Sideslip Becomes a Spiral Dive When Dihedral Effect x Yaw Damping < Directional Stability x Roll Due to Yaw Rate



Phugoid Again

• Recover from spiral dives by first rolling thewings level with the horizon. Now we’re back inthe more familiar wings-level phugoid. Noticehow the aircraft’s positive static longitudinal (y-axis) stability initially brings the nose back tolevel flight. You’d normally push to suppress thephugoid as the nose comes level with thehorizon, but we’ll again allow the aircraft to gopast level and progress through the first cycles ofthe phugoid mode.

• Again, you’ll need right rudder at the top of thephugoid to counteract the slipstream and p-factorand keep the nose from yawing, and some leftrudder at the bottom. Jets and counter-rotatingtwins don’t have this problem.

• An aircraft’s longitudinal stability comes fromits tendency to maintain a trimmed angle ofattack. As you ride through it, the attitudes,altitudes, and airspeeds change, but in a phugoidthe angle of attack, α, remains basicallyconstant. The attitude excursions of ourconstant-α phugoid remind us again that anaircraft’s angle of attack and its attitude are twodifferent things. When displaced, aircraft returnto their trimmed attitude and airspeed by virtueof maintaining their trim angle of attackthroughout a cycle of phugoid motions. Inessence, pilots keep altitude pegged by keepingahead of the phugoid and damping its cyclethemselves. A power change provokes aphugoid, unless the pilot intervenes to smoothout the transition.

• We’ll experience an increased g load asairspeed exceeds trim speed at the bottom of thephugoid. At a constant angle of attack, lift goesup as the square of the increase in airspeed. If wetrim for 100 knots in level flight (1 g) andmanage things so as to reach 200 knots (whichwe won’t!), airspeed will be doubled and loadfactor will hit a theoretical 4 g. If we accelerateto 140 knots, that’s a 1.4 increase in speed. 1.42

= 2; thus a load factor of 2 g. (The actual factorcan be affected by the mass balance of theelevator, or the presence of springs or bobweights.) We’ll experience less than 1 g over thetop.

• The phugoid shows us how a trimmed,longitudinally stable aircraft normally maintainsits speed if left to its own devices. After adisturbance, it puts its nose up or down, tradingbetween kinetic and potential energy, until iteventually oscillates its way back to trim speed(or to its trim speed band if control friction isevident). But the trade becomes solely potentialto kinetic when a bank degenerates into a spiraland, as we’ve seen, the bank angle becomes toosteep for the phugoid to overcome. Think of aspiral departure as a “failed” phugoid, in whichthe nose can’t get back up to the horizon becausethe lift vector is tilted too far over.

• What if an aircraft trimmed for cruise rollsinverted for some reason and the befuddled pilotjust lets go? Left unattended, the inverted aircraftwill pursue its trim by dropping its nose and“reverse-phugoiding” itself around in a rapidlyaccelerating back half of a loop (a “split-s”).Speed will rise until the structure maybe quits, orthe dirt arrives. Inverted, hands-off survivalprospects improve in the unlikely situation thatthe aircraft is at altitude but trimmed for slowflight. Trimmed for 70 knots with power forlevel flight, and then rolled inverted while thenose is allowed to fall, the Zlin will pull a 4-gsplit-s, hands-off on its trim state alone, using upsome 1,300 feet of altitude. Then it will playfullyzoom right back up into a normal but initiallyhigh-amplitude phugoid.



Knife-edge Free Response

• After you’ve observed spiral characteristics,and learned to expect divergence following ahigh bank angle, knife-edge behavior mightsurprise you. Starting at knife-edge with the noseon the horizon, when the controls are released anaircraft with positive dihedral effect willgenerally roll upright and pitch nose-down (andthen eventually pitch up into a phugoid if youdon’t touch the elevator). The roll response hasbeen associated with the amount of “keel” areaabove the aircraft’s c.g. Acting at differentlocations and in opposite directions,aerodynamic side force and gravity produce aroll couple. This wings-leveling couple, added tothat generated by dihedral effect, overcomes theopposing spiral tendencies caused by directionalstability and roll due to yaw rate.

• If you enter knife-edge flight, or even just asteep bank angle, in a nose-high attitude,however, spiral tendencies will often dominate.It’s fun to examine this by flying aggressivelazy-eights (linked wingovers) and observing

which moments win out when you let go of thestick and/or rudder at various points. Note thephugoid embedded in the maneuver as theaircraft climbs and descends.

Side force producesboth wings-level rollmoment and nose-down yaw moment.

Gravity actingthroughaircraft c.g.

Resulting roll.

Keel Effect



2. Steady-Heading Sideslip: Dihedral Effect & Roll Control

Flight Condition: Upright, crossed controls, high β.

Lesson: Lateral behavior during sideslips.

Flight Notes

A directionally and laterally stable aircraft yaws toward but rolls away from its velocity vector whenthe vector is off the plane of symmetry. Those characteristics are the “ basic moves” of directional andlateral behavior. In our steady-heading sideslips, we’ll apply cross-controls—rudder in one direction andaileron in the other—causing the aircraft to fly with its velocity vector displaced from symmetry. Thecontrol forces necessary to prevent the aircraft from yawing and rolling in response to that displacement arethe reflection of its inherent stability. They tend to change with angle of attack, especially in the buffetboundary, where aileron effectiveness often deteriorates and the rudder takes on increasing importance forlateral control. In that regime, a pilot often displaces the velocity vector on purpose, to assist roll control.(He may not know that’s what he’s doing, but nevertheless...)

Pilots of flapless (usually aerobatic) aircraft are accustomed to using sideslips to control the descent tolanding. It’s how they show off in front of the aircraft waiting at the hold line. If you rely on flaps fordescent, you may be rusty on aggressive cross-control slips. A little practice with them will improve yourability to respond to control system failures. You counter the rolling moment generated by anuncommanded rudder or aileron deflection by entering an opposing sideslip, modifying the sideslip asnecessary for turns.

• Test pilots use steady-heading sideslips toevaluate an aircraft’s lateral stability. That meansits tendency to roll away from the direction of asideslip—in other words, to roll away from the

direction the velocity vector is pointed when thevelocity vector is not on the plane of symmetry.(The mechanics of lateral stability, or dihedraleffect, are explained in more detail in the ground

Procedures:

Power for speed in the white arc.Apply simultaneous aileron and opposite rudder to rudder stop.Aileron as necessary to maintain steady heading with no yaw rate.Maintain approximate trim speed. Aircraft will descend.Hold rudder/ release stick.Repeat in opposite direction.

Hold stick/ release rudder. Observe sequence of yaw and roll.

Hold sideslip. Pitch up and down to demonstrate y-wind-axis pitch/roll couple.

Possible Maneuver: Hold the sideslip and demonstrate “over the top” spin entry, with immediate, controlsneutral recovery.



school text “Lateral-Directional Stability.”)Steady-heading sideslips are also used to assessdirectional stability and rudder effectiveness bymeasuring the rudder deflection and pedal forceneeded to produce a given sideslip angle, β.They can also be used to evaluate controlharmony and to set up the conditions forobserving Dutch roll. Wing-low crosswindlandings are steady-heading sideslips, so anaircraft’s behavior in sideslips can limitcrosswind capability.

• Pressing the rudder and yawing the aircraftcreates a sideslip angle between the aircraft’svelocity vector and its x-axis plane of symmetry,as illustrated to the right, below. This in turnproduces a rolling moment due to dihedral effect.We’ll evaluate the strength of this yaw/rollcouple at various sideslip angles by observingthe aileron deflection needed to counteract theroll and fly the aircraft at a constant, steadyheading, although sideways and wing-low.

• You’ll enter a steady-heading sideslip byapplying crossed controls: deflecting the rudderwhile adding opposite aileron to keep the aircraftfrom turning. Notice how the forces anddeflections increase as you move the controlstoward the stops. Under FAR 23.177(d), “theaileron and rudder control movements and forcesmust increase steadily, but not necessarily inconstant proportion, as the angle of sideslip isincreased up to the maximum appropriate to thetype of airplane…. the aileron and rudder controlmovements and forces must not reverse as theangle of sideslip is increased.”

• Do you notice any differences sideslipping tothe left or right, possibly caused by p-factor orslipstream?

• Dihedral effect can depend on aircraftconfiguration. It can diminish with flapextension. This is important in connection withrudder hard-overs, because flaps lower“crossover” speed, as you’ll see later.

• When you release the stick while holdingrudder, the low wing rises due to dihedral effectand to roll due to yaw rate. Dihedral effect,strongest at first, decreases as the sideslip anglegoes to zero. Roll due to yaw rate, weak at first,increases as the yaw rate rises; then suddenlydisappears when the yaw damps out. Thecapacity to raise a wing with rudder alone, incase ailerons fail, is a certification requirementfor non-aerobatic aircraft, and this stick release isa standard flight-test procedure.

• Aerobatic aircraft without much dihedral effect(such as the Great Lakes, or the Yak-52) oftentend not to roll toward level but to pitch down atstick release. An aircraft’s pitching moment dueto sideslip may be nose-up or down, minimal orpronounced, different left or right—dependingon how propeller slipstream, fuselage wake, andthe downwash generated by the wing and flapsaffect the horizontal stabilizer. The combinationof longitudinal (pitch) and lateral (roll) forcesyou find yourself holding helps you anticipatehow aggressively the aircraft will respond onrelease. The Zlin is a great trainer in this respect.

X body axis

α

Angle of Attack (α) and Sideslip Angle (β)

Angle of velocity vector, V, to xbody axis gives aircraft angle ofattack. Angle of velocity vector towing cord gives wing angle ofattack.

X-Z planeLift vector

Z body axis

Velocity vector, V, andsideslip angle, β. Sideslipto the right.

V

V

X bodyaxis

β

Y bodyaxis

Left rudderproduces rightsideslip.



When the stick is released in a sideslip to the left(right rudder down, left aileron), the Zlin canaggressively pitch-up and roll right, thecombined motions leading to a sudden increasein the angle of attack of the right wingtip, and apossible tip stall. Much fun!

• Swept-wing aircraft can build up large rollingmoments during sideslips, and mishandling canput even a large aircraft on its back. Sideslipangles are generally restricted to around 15degrees during flight test for transport aircraft.FAR 23.177(d) says that a “Rapid entry into,and recovery from, a maximum sideslipconsidered appropriate for the airplane must notresult in uncontrollable flight characteristics.”“Rapid” is a key word here, since a slow entry toand recovery from a sideslip keeps the aircraft’sangular momentum under control.

• Things get a little complicated now, and weapologize. Notice that when you first release therudder, while holding aileron deflectionconstant, the aircraft doesn’t respond to theailerons and immediately start rolling. Watchhow the nose yaws and reduces the sideslipbefore the roll begins. The vertical stabilizer’scenter of lift is above the aircraft’s center ofgravity. As a result, the rudder deflection in asteady-heading sideslip actually produces anadded roll moment in the same direction as theailerons. (See Figure 17 in the ground school text“Lateral-Directional Stability.”) Releasing justthe rudder eliminates this rolling momentcontribution, but replaces it briefly by a rollingmoment due to yaw rate as the aircraftstraightens out. (Did you get that?) Theimportant point is that only after the aircraft’sdirectional stability substantially eliminates thesideslip will the ailerons start to dominate andthe aircraft roll. This really is less confusing witha hand-held model for demonstration, or in theaircraft where you can see things unfold.

• Our trick of holding the ailerons in place whilereleasing the rudder allows us to keep the rollmoment due to aileron deflection fixed. We canthen observe the yaw as the aircraft’s directionalstability realigns the nose with the velocityvector. We can observe the ramp-up in rollresponse and properly attribute it to thevanishing sideslip. This gives us a way to use a

steady-heading sideslip to demonstrate therelationship between sideslip and aileroneffectiveness. A sideslip can either work for aroll rate, or against it. For a given ailerondeflection, in an aircraft with dihedral effect,roll rate goes down when rolling into a sideslip(right stick, right velocity vector, say, as in thesideslip seen from above, illustrated on theprevious page). Such an “adverse” sideslip couldtypically happen in an aircraft with adverse yawand not enough coordinated rudder deflectionwhen beginning the roll. On the other hand,stomping on the rudder too hard while rollingwith aileron will skid the airplane anddemonstrate that a proverse sideslip, oppositethe direction of applied aileron, increases rollrate—in addition to sliding your butt across theseat. That stomp could be a useful trick foraccelerating roll response in an emergency, butin swept-wing aircraft could lead to a severeDutch roll oscillation. The fundamentalrelationship between sideslip angle (angle of thevelocity vector versus plane of symmetry) androll rate is something many pilots never reallyget—maybe because instructors think that therudder affects only yaw. But in a laterally stableaircraft, yaw just about always provokes a rollingmoment.

• Roll couple for a given sideslip angle, β, andaircraft configuration varies in directproportion to the coefficient of lift, CL. That’scertainly the case with swept-wing aircraft, andat least apparently the case with straight-wing,although not to the same degree. (See groundschool text “Lateral-Directional Stability.”)

• Roll due to yaw rate also varies directly withCL, as noted when we observed the spiral mode.When we fly steady-heading sideslips, we try toisolate dihedral effect by keeping the headingsteady and eliminating yaw rate. But there’salways a yaw rate when we enter and leave themaneuver, and of course sideslips and yaw ratesoccur together in turbulence. Their individualcontributions at a given moment can be difficultto sort out.

• You can think of the deflected rudder (or anexisting sideslip) as setting the direction andinitial rolling tendency, and of the elevator asmodulating the rate through its control of CL.



This is easy to remember, because when youraise CL by pulling back on the stick, toward therudder, roll moment produced through dihedraleffect and roll due to yaw rate increases. Whenyou lower CL by pushing, the contributiondecreases. This relationship holds for bothstraight and especially for swept wings, althoughthe mechanisms and some details are different,as the ground school illustrates. It also worksupside-down; as long as you have positive g.You will see this when we do rudder rolls.

• Or, if you prefer a more visceral terminology,put it this way: Hauling back and “loading” anaircraft increases yaw/roll couple; “unloading”decreases it. And that’s not all unloading does,as we’ll note more than once. Imagine thatyou’re operating at an angle of attack highenough to reduce aileron effectiveness throughairflow separation, and high enough to disruptflow over the tail such that yaw-axis stability isreduced and a sideslip develops. Putting the stickforward and unloading will reattach the flow,bringing the ailerons back while also reducingthe sideslip-generated roll couple by reducingcoefficient of lift, CL. (Examples might be duringan immediate recovery from an initial stall/spindeparture—developed spins are handled withrudder first—or during a recovery from a rudderhardover.)

• With a swept wing, the dihedral effect derivedspecifically from sweep actually disappears atzero CL. A sideslip then no longer produces arolling moment, unless the wing also hasgeometrical dihedral (tips higher than roots),which does work at zero CL. (Again, see groundschool text “Lateral-Directional Stability.”)

• Wind-Axis: In this maneuver set we pushedand pulled on the on the stick while sidesliping.We watched the motion of the nose relative tothe horizon, and discovered that the aircraft waspitching about its y wind axis, not its y bodyaxis. Because of the displacement of the y windaxis from the body axis, a pitching moment alsoproduces a rolling moment, as described in theillustration to the right. This geometrical effectworks in the same direction as the CL effectdescribed above. In other words, pulling willgeometrically produce a rolling moment oppositethe velocity vector; pushing will produce a

rolling moment toward the vector. This isanother effect that’s tough to visualize, but if youspend a few minutes fiddling with a smallaircraft model you just might have a revelation.

Aircraft Pitch Around Y Wind Axis

V

x bodyaxis

β

y body axis

y windaxis

The y wind axis remains perpendicular to and moves withthe velocity vector, V. The aircraft pitches around the ywind axis. Geometrically, this also produces a roll. So in asideslip to the right, as above, pulling the control backcauses a roll to the left; pushing forward causes a roll to theright.



• Steady-Heading Sideslip Spin Departure:More confusing stuff, sorry again: Here’s whathappens when we stall the aircraft during asteady-heading sideslip, by holding crossedrudder and aileron while increasing aft stick. In asteady-heading sideslip to the aircraft’s left, asillustrated here, right rudder is deflected; aileronsare left. The horizontal component of lift createdby the bank angle pulls the aircraft to its left andthus generates a nose-left aerodynamic forceagainst the tail. We counter the resulting left yawmoment with right rudder to maintain our steadyheading. At the stall, as lift goes down so does itshorizontal component and the resulting yawingmoment to the left. This allows the rightwardyaw moment generated by right rudder to

dominate. If we hold control positions theaircraft yaws and rolls to the right in an “over thetop” entry into a spin.

• Going over the top is the most congenial wayfor the aircraft to behave, because the wings firstroll toward level and there’s more time forrecovery. Bringing the stick forward andneutralizing the other controls should keep theaircraft from entering a spin. Opposite ruddermight also help. Remember that aircraft alwaysdepart toward the deflected rudder (opposite thedisplaced velocity vector). So you won’t breaktoward the low wing in a sideslip—it just feelslike you might because that’s the direction inwhich you’re sliding off your seat.

• Note that in a side-slipping spin departure to theaircraft’s right, for illustration, the left aileron weoriginally hold to maintain a steady heading, andthen for demonstration keep in at the stall,doesn’t arrest the rightward roll off. There’s toomuch airflow separation by that point for theailerons to generate much opposite roll. But thedown aileron still produces lots of adverse yaw,which pulls the right wing back and encourages aspin entry.

W

W sin φ

Y

L

φ

The horizontal component of liftincreases as the stick is pulled backand CL rises. This component rapidlydecreases at stall, as lift drops(dashed arrow).

Roll moment due tosideslip/dihedral effect

Roll moment due to ailerons,here shown in equilibrium withthe opposing moment due tosideslip, quickly drops off asthe aircraft stalls and airflowseparates over the ailerons. Butadverse yaw increases andhelps drive the aircraft into aspin to its right.

Steady-headingSideslip SpinDeparture



3. Stall: Separation & Planform Flow (Wing tuft observation)

Flight Condition: Upright, power-off 1 g stall, high α.

Lesson: Stall anatomy.

Flight Notes

We’ll cover boundary layers, adverse pressure gradients, and wing planform effects in the ground schooland supporting texts. Then, as an accomplished aerodynamicist, you’ll be able to interpret the sometimes-surprising motions of the wing tufts and the accompanying separation of the airflow from the wing as αrises or the aircraft’s configuration changes. FAR Parts 23 & 25.201-207 cover stall requirements.

• On the way to the practice area, note theturbulence in the boundary layer as shown by themovement of the wing tufts. Note the increasedmovement as the turbulent layer thickensdownstream.

• Don’t make our stalls a minimum-altitude-loss,flight-check-style exercise. Give yourself time toobserve the full aerodynamic progression. Playaround. But remember: This is not proceduretraining. Follow the recovery techniques inyour aircraft’s AFM or POH.

• For FAR Part 23 and 25 certification, stallspeeds are determined for the aircraft configuredfor the highest stall speed likely to be seen inservice. In part, this means at maximum takeoffweight and forward center of gravity limit, trimset for 1.5 anticipated stall speed, and using anairspeed deceleration rate of 1 knot-per-secondstarting at least 10 knots above stall. We’ll try tomaintain this deceleration rate for latercomparison to a 5 knot-per-second decelerationentry. Up to a point, increasing the deceleration

Procedures:

Clearing turns.Power idle.Trim for 1.5 times anticipated stall speed.1-knot-per-second deceleration below 70 knots.Note buffet onset airspeed and stall speed.Full stall before power-off recovery.Power as required for recovery and climb.

Repeat with 5-knot-per-second deceleration below 70 knots.

Stalls while watching the wing tufts.

Provoke secondary stall in recovery.

Repeat with flaps. (Is there a difference in “break?”)



rate beyond 1 knot-per-second usually drivesdown the stall speed, but then the load factorstarts to rise and stall speed increases. Thedecrease in stall speed that comes with asomewhat increased deceleration occurs becauseof the delay in pressure redistribution as α rises.This delays separation and allows the wing tofunction briefly at a higher angle of attack andcoefficient of lift than normal, a phenomenoncalled dynamic lift to differentiate it from the liftconditions at static angles of attack measured ina wind tunnel. Lift normally creates a downwashover the horizontal stabilizer, and thus a nose-uppitching moment. The nose pitches down whenthe downwash disappears at the stall. Dynamiclift delays this to a higher angle of attack.

• It’s important that a rapid deceleration producedby a high pitch rate doesn’t compromise controlauthority. That’s not an issue with our aircraft,but can be with large aircraft in which pitchingmomentum can carry and momentarily hold theaircraft past stall angle of attack, withinsufficient airflow available for positive control.On the other hand, a deceleration rate below 1knot-per-second may not produce maximum α.

• Watch the tufts. The trainer has the root-firststall progression typical of its wing shape. Incontrast, swept wings naturally stall first at thetips. They’re coerced to behave more in a root-first manner by the use of stall fences, vortilons,vortex generators, and changes in airfoil fromroot to tip.

• Notice the definite relationship between airflowseparation at the wing root, as evidenced by thetufts, and the buffet onset in our training aircraft.Do you feel the buffet in the airframe, mostly inthe stick (as in the L-39 jet trainer), or in both?In our aircraft the buffet provides plenty ofaerodynamic stall warning. Compare this to a T-tail design where the turbulent flow largelypasses beneath the stabilizer and stall warninghas to be augmented by a mechanical stickshaker, or to planform designs where the wingroot separation happens too late to provide muchaerodynamic warning. In the MiG-15, forexample, there’s no real buffet—the stick getslight and lateral control goes to mush.

• You might want to do a couple of stalls with theinstructor assisting in directional control whileyou concentrate on the wing and play the stick tomodulate the full tuft stall progression from rootto tip. If you’ve done the relevant ground school,visualize and manipulate the adverse pressuregradient in the chordwise direction, and thechange in local coefficient of lift in the spanwisedirection. Note the change in airflow over theirsurfaces (as shown by the tufts) when the flapsor ailerons go down. When the flaps go down,note the vortex that forms on the outboard tip.Acting on the tail, the increased downwash fromthis vortex causes the pitch-up that follows flapdeployment.

• The secondary stall we provoked on purpose,by pulling too hard on recovery, reminds us of

Adverse pressure begins earlier as α increases.

Favorable pressure gradient

Adverse pressure gradient resists airflow.

Location of minimum static pressure

Adverse pressure strips the airflow from the wing.

Boundary layer separation at stall

Favorable pressure



the absence of positive (nose-up) pitch authorityat maximum lift coefficient, CLmax, regardless ofaircraft attitude. We can run out of elevator(and aileron!) authority in any attitude whenthere’s no angle of attack in reserve. Theabsence of positive pitch authority, in the formof an “uncontrollable downward pitchingmoment” is one of the ways the FAA defines astall for certification purposes under FAR Part23.201(b). We’ll revisit this loss of pitchauthority when we fly loops, and during the pull-up recovering from spins.

• Part 23.201(d) states, “During the entry into andthe recovery from the [stall] maneuver, it mustbe possible to prevent more than 15 degrees ofroll or yaw by the normal use of the controls.” Incoordinated flight, our trainers tend to stallstraight ahead, without dropping a wing—at leastnot initially. If you hold the stick back during thestall oscillation, a wing may drop. Many aircraft,like the sultry Siai Marchetti SF260, willannounce a stall more by a wing drop than by anose-down pitch-break (also called a g-break).Some airfoil and planform arrangements can bedemanding, no matter how carefully the pilotkeeps the ball centered. A venerable T-6 Texanor SNJ will generally drop to the right. The rightwing stalls first, reportedly, because it’s set at ahigher incidence. Our ground school video of aT-6 wing shows how the stall pattern leads toearly flow separation in the aileron region. Ourvideo of the Giles G-200 aerobatic aircraft showsa rapid trailing-to-leading-edge stall, which gives

no buffet warning, and in this particular aircraftproduces a sudden drop to the left.

• Stall separation can also begin at the leadingedge, and aircraft with leading-edge stallstypically misbehave. The stall break, perhapscaused by the sudden bursting of the laminarseparation bubble, is abrupt and usually happensasymmetrically due to physical differencesbetween the leading-edge spans. A wing drop islikely. On various Lear models, if the leadingedge has been removed for repair, a test pilotwill come out from the factory to do a stall testbefore the aircraft goes back in service.

• Even if meant to be, aircraft often aren’taerodynamically symmetrical in behavior. Inpractice, manufacturing tolerances simply aren’tthat tight; and a life of airborne adventure takesits toll. The PA-38 Piper Tomahawk became aparticular offender when the production aircraftwere built with fewer wing ribs than theprototype used for certification tests. Thisallowed the wing skins to deform—or“oilcan”—under changing air loads.Unfortunately, the performance of its GA(W)-1wing is very sensitive to airfoil profile. Thedeformations led to rapid and unpredictable wingdrop at stall. Prompt, proper recovery inputswere necessary. The Tomahawk has about twicethe stall/spin accident rate per flight hours as theCessna 150/152.



4. Accelerated Stall: G Loads & Buffet Boundary, Maneuvering Stability

Flight Condition: Banked, high α.

Lesson: Flight behavior under turning loads.

Flight Notes

Earlier, we increased the airspeed deceleration rate to lower the “book” stall speed. Here we use load factorto raise it.

• Stall speed goes up by the square root of theload factor, n. (n = Lift/Weight).

• Induced drag goes up by the square of the loadfactor.

• Thus whenever you raise the load factor (pull“g”), stall speed and drag also rise. You can’tfeel the latter two directly; you have to learn theassociation. The increasing stick force is one cuethat the numbers are ascending. The forcedriving you into your seat is another.

• Of course, hangar wisdom holds that a wing’sstalling angle of attack remains constant for agiven configuration (high-lift devices in or out).That’s a small fiction, but also a profoundworking “truth” because it emphasizes angle of

attack as the essential stall determinant, not just anumber on the airspeed dial—a number thatitself changes with weight and load factor for agiven configuration. If you want to be picky,stalling angle of attack depends on ReynoldsNumber, which is the ratio between inertia forcesand viscous forces in the boundary layer on thesurface of the wing. For a given airfoil, stallangle of attack rises with Reynolds Number.

• Notice the increased buffet intensity in theaccelerated stalls compared to those at 1 g.There’s more energy in the turbulent airflowshed by the wing at this higher buffet speed (theinboard wing tufts tend to capitulate and blowoff after repeated accelerated stalls), and moreenergy in the surrounding free stream flow.

Procedures:

Power low cruise.Trim.Using instrument or outside reference, roll to bank angle specified by instructor.Keep the ball centered with rudder.Apply stick-back pressure to buffet, reducing power or increasing bank angle as necessary.Note buffet speed, stall speed, buffet margin as compared to 1-g stall.

Repeat at higher bank angles. Note exponential rise in buffet speeds and stick force.

Explore aileron effectiveness in buffet by rocking wings 15 degrees left and right.



• At higher g, does the buffet margin changecompared to a 1-g stall? The comparison shouldbe made at the same knots-per-second airspeeddeceleration rate to be valid. Often stall warningvaries inversely with knots-per-second, morerapid entry producing less warning. A rapid entryis probably typical of pilot technique in anaccelerated stall.

• The accelerated stall and the 1-g stall bothoccur at the same angle of attack, but theaccelerated stall requires a heftier pull. Theaircraft exhibits an increase in pitch stability asthe g load rises (meaning a stronger tendency toreturn to trim speed, which is the tendencyyou’re pulling so hard against). That’s becausethe angular velocity of the tail, caused by thepitch rate in the turn, produces a change in tailangle of attack, as illustrated to the right, andthus an opposing damping moment. Increasingthe g load means increasing the pitch rate, andups the damping. The additional elevatordeflection needed to overcome more dampingrequires more force. This effect leads to what’scalled maneuvering stability (which we cover inthe ground school text “LongitudinalManeuvering Stability”). Damping is a functionof air density, and goes down as you climb.

• The geometry is such that, for a given g, anaircraft has a higher pitch rate (thus higherdamping) in a turn than it does in a wings-levelpull up. As a result, you’ll pull harder in a 2-gturn than in a 2-g pull up, for example.

• At a given density altitude, in aircraft withreversible control systems, like ours, thenecessary stick-force-per-g is independent ofairspeed (although Mach effects may increaseforces at higher speeds). In other words, theforce required to pull a given g doesn’t increasewith airspeed, as you might naturally think. (Ofcourse, it’s a bit more complicated. See groundschool text “Longitudinal ManeuveringStability.”)

• The table farther on shows how load factorincreases exponentially with bank angle in aconstant-altitude turn. It follows that stick forces

also increase exponentially, rather thanuniformly, with bank angle. A pilot banking intoa steep turn has to increase his pull force at afaster and faster rate. Stick force rises slowly atlesser bank angles. Past 40 degrees or so, theincreasing force gradient starts becoming moreapparent. There’s a surprising difference in theforce necessary for a 55-degree versus a 60-degree bank. Steep turns might get a little easier(maybe) once you figure this out.

• Notice the instant transformation in controlauthority at recovery due to the increasedairspeed in the accelerated stall. Watch the wingtufts to see how quickly the airflow reattacheswhen you release some aft pressure. Thedamping you generate in the turn pushes the noseright down. At 2 g’s there’s a 40 percent increasein stall speed. Because dynamic pressure goes upas the square of the airspeed increase, that meansdouble the dynamic pressure (1.42 = 2) availablefor flight control compared to a recovery from astall near 1 g. More dynamic pressure meansmore control response for a given deflection.You can recover from an accelerated stall whilethe wing is still loaded (pulling more than 1 g).You only have to release enough g to get the stallspeed back down.

Tail arm, lT

cg.

Pitch Damping

qlT (pitch rate times arm)

ΔαΤ, Change in tail angle of attack

VT

Pitch rate, q

Tail’s aerodynamic center

VT



• But releasing g may not always be equivalent toreleasing your aft pressure on the stick. In someaircraft (often former military) you may have topush to expedite things. You may find that thegradient of stick force rises more slowly as gincreases, as it does in the L-39 jet trainerbecause of the bungee cord “boost” within theelevator circuit. Or the aircraft may have an aftc.g., which increases maneuverability at theexpense of stability, and thus reduces thetendency to pitch the nose down when aftpressure is released. Early swept-wing fightershad a tendency to stall at the tips first. Becauseof the sweep, a loss of lift at the tips shifted thecenter of lift forward and caused the aircraft topitch nose-up and “dig in” during acceleratedstalls.

• The higher dynamic pressure whilemaneuvering can lead to higher rolling momentsif the wings stall asymmetrically. Any wing-dropping obstreperousness an aircraft might hintat during 1-g stalls can intensify at the higherairspeeds of an accelerated stall. Our rectangular-wing trainers stall root-first, and resist roll-off ifflown in a coordinated, ball-centered manner.But accelerated stalls in other aircraft can bedefined more by a wing drop than by a pitchbreak or a stolid, straight-ahead mush.

• As the load factor increases, the stall speedstarts coming up to meet your airspeed. At thesame time, if you didn’t or can’t increase power(“thrust-limited”), your airspeed starts headingdown because of the increased induced drag.Eventually, if you pull hard enough, the twospeeds converge. If an aircraft is thrust-limited,test pilots will perform descending, wind-upturns to explore its behavior at higher g, byturning altitude into the increasing airspeednecessary to attain increasing g levels.

• Because stall speed rises in a turn, yourcalibrated airspeed above 1-g stall dictates yourbank-angle maneuvering envelope. The closeryou are to the 1-g (wings-level) stall speed in agiven configuration, the less aggressively youcan bank and turn an aircraft while keepingout of buffet and maintaining altitude. You cancertainly enter a steep bank without stallingwhile flying slowly, since stall speed is not

directly related to bank angle. Stall speeddepends on load factor—in this case on the loadfactor required to make a turn happen at a givenbank angle without altitude loss. For a constant-altitude turn, load factor goes up exponentiallywith bank angle, as the table illustrates. Youcan’t generate the necessary load factor unlessyou’re going fast enough for your bank angle. Ifyou’re too slow, but nevertheless try to arrest adescent by hauling back on the stick, you’ll stall.Level the wings first. If you have excessairspeed, you can haul back and turn and climb.The relationship between airspeed, attainableload factor, and turning performance is discussedin the ground school text “Maneuvering Loads,High-G Maneuvers.”

• Pilots have it drilled into them that an aircraftcan stall at any attitude. Stall speed is alsoindependent of attitude. At a given weight andconfiguration, an aircraft pulling two g, for

Deg.bank

Load factorrequired forconstant-altitudeturn

Stall speedfactorincreaseover 1-g Vs

60 ktstalltimesincrease

30o 1.15 1.07 64.3

35o 1.22 1.10 66.3

40o 1.30 1.14 68.4

45o 1.41 1.19 71.2

50o 1.55 1.24 74.7

55o 1.74 1.32 79.1

60o 2.00 1.41 84.8

65o 2.37 1.54 92.4

70o 2.92 1.71 102.5

75o 3.86 1.96 117.9

80o 5.76 2.40 144



example, has the same stall speed regardless ofits attitude relative to the horizon.

• An aircraft constantly rolls toward the outsideof a climbing turn. It constantly rolls toward theinside of a descending turn. (You’re right. This isdifficult to visualize.) The rolling motion createsa difference in angle of attack between thewings, with the down-going wing operating at ahigher angle of attack. As a result, climbingaircraft tend to roll away from the direction ofthe turn at stall break. This is favorable becauseit decreases the bank angle. When descending,they tend to roll into the direction of the turn atstall break. But propeller effects, rigging, andpoor coordination can gum this up. Watch wherethe skid/slip ball is and see what happens.

• Prop-induced gyroscopic precession can affectcontrol forces in turns. Precession creates amoment that’s always parallel to the axis of theturn—the axis typically being perpendicular tothe horizon. On aircraft with clockwise-rotatingpropellers, as seen from the cockpit, precessionpulls the nose to the dirt in a turn to the right,and to the sky in a turn to the left. If the forcesgenerated are large enough (heavy prop, highrpm, high turn rate, long moment arm from propto aircraft c.g.) more up-elevator will be needed

when turning to the right. And the rudderbecomes more involved as the bank angleincreases and precession moves closer intoalignment with the aircraft’s y axis. Greaterrudder deflection may then be needed forcoordination. The WW-I pursuits equipped withrotary engines (engine and prop turned together)were famous for their gyroscopicbehaviors—quick turning to the left but awkwardand vulnerable to the right. If the nose pitcheddown gyroscopically in a right turn, the pilotcould spin out trying to counter with oppositerudder and up elevator.

• Finally, notice the greater rudder forcenecessary to stop or reverse a steep turn,compared to the coordinating rudder forcenecessary when beginning the turn. One reasonis the higher angle of attack in the turn and thusthe greater adverse yaw accompanying ailerondeflection. Also, the aircraft has picked upangular momentum, which the rudder has to helpoppose. So more rudder deflection is required forcoordination coming out.



Stick-force-per-g test procedure: wind-up turn.

Fly the test at a constant, trimmed airspeed. Airspeed variations introduce additional forces, as describedin the ground school “Longitudinal Maneuvering Stability.” At a constant airspeed and power setting, youwill descend during the maneuver as bank angle increases.

Establish trim speed in level flight at test altitude. Record pressure altitude, temperature, and power setting.

Climb with increased power to 1,000 above test altitude. Reset trim power.

Bank as required to obtain desired load while descending as necessary to remain at trim speed.

If equipped, measure stick force when airspeed and g-meter readings stabilize. Establishing a stable state,even briefly, isn’t always easy— it takes practice, especially as bank angle increases! If you’re notequipped for measuring, a subjective assessment of stick force and gradient is still a useful exercise.

If the aircraft does not have a g-meter, use bank angles to establish approximate load factors. As 60o

approaches, you might find it easier to control airspeed with your feet: for example, top rudder if speedexceeds trim.

Trim speed: Pressure altitude: Temp: Power setting:

Bank angle 30o 1.15-g 45o 1.41-g 60o 2-g

Actual g-meterreadingStick force



5. Nose-High Full Stalls, Lateral Control Loss & Rolling Recoveries

Flight Condition: Wings level, high α, nose-high, limited lateral control.

Lesson: Exposure to nose-high attitudes, limited visual references, lateral control loss.

Flight Notes

Nose-high recoveries are practiced in simulators as a standard element in upset training. The AirplaneUpset Recovery Training Aid gives a procedure based on a push—followed by a roll, as required to get thenose back down. We’ll explore the dynamics of recoveries done badly. We want you to lose lateral control,see why, and see what it takes to get it back.

• The first maneuver gets you familiar with nose-high attitudes and pitch breaks. The pitch break(or g-break) in a 1-g nose-high stall is muchmore pronounced than in the 1-g stalls done fromclose to normal pitch attitudes. The aircraftrapidly sinks and the nose will swing well belowthe horizon before it’s possible to recover a

flyable angle of attack. The initial nose-upattitude will block the horizon ahead and forceyou to use the wingtips for roll, pitch, and yawreference. (The attitude indicator will be off,unless we forget.) Don’t just stare at onewingtip. We have two! Compare them.

Procedures:

Full Stall: Nose-High Pitch Break

25”/2,500 rpm.Clearing turns.Pitch up + 60 degrees (use wingtip reference).Power idle.Hold wings-level attitude as possible, keeping the ball centered with rudder.Allow full stall with stick held back.

Pitch up + 60 degrees.Hold necessary power, with stick back, aileron neutral and feet off the rudder pedals.Allow a yaw rate to develop (aircraft will yaw left due to prop effects).Observe lateral control divergence.Recover aileron effectiveness with nose down pitch input.Recover aileron effectiveness with opposite rudder.

Rolling Recovery from Nose High

Recover nose-below-the-horizon.

Recover nose-to-thehorizon.



• We want you to experience lateral controldivergence and loss of roll damping. We set thisup by holding a nose-high attitude with poweron, stick back, feet off the rudders, and aileronsinitially neutral. We let the aircraft’s naturaltendencies in this configuration take over. P-factor and slipstream will yaw the aircraft to theleft. We’ll try to recover from the resultingcoupled roll with ailerons alone (stick still heldback). Lateral control will be lost.

• Notice that, while you can retain some aileroneffectiveness into a stall buffet and break, athighα, aileron effectiveness disappears if theairplane starts to yaw opposite the direction ofintended roll, as we let it do above. Instead ofrolling the aircraft as we intend, the aileronsgenerate more adverse yaw than lift, whichsimply makes things worse. Once the stick goesforward, however, or the pilot uses rudder to stopthe yaw, the ailerons regain authority.

• The Airplane Upset Recovery Training Aidrecommends recovery from a nose-high attitudewith a push, followed by a roll if necessary(2.6.3.2-5). Pushing starts the nose in the rightdirection and unloads the wing so that theaircraft accelerates and the ailerons retaineffectiveness. Rolling tilts the lift vector andallows the aircraft’s z-axis directional stability toassist in bringing the nose down. Confining theroll to less than approximately 60 degrees keepsthe wing lift vector above the horizon and makespitch control easier in the recovery back to levelflight. During the time it takes to roll the liftvector back to vertical, the buildup in angularmomentum in a heavy aircraft can carry the noseunnecessarily below the horizon if the initialbank angle is too steep.

• In a delayed rolling recovery, if you hold thenose in the buffet and apply ailerons, you won’thave much roll authority. The reduced rollcontrol at low airspeeds and high angles of attackcan increase the difficulty of a rolling recoveryfrom a nose-high attitude. This underscores theneed to push and unload the airplane if theailerons aren’t working.

• The “nose below horizon” and “nose to thehorizon” rolling recoveries demonstrate theproblem of flight path control at high angles ofattack. Because nose-up authority disappears athigh α, stopping the nose on the horizon isdifficult without encountering a buffet.

• In a jet, power application in a nose-highrecovery will depend on the aircraft’s thrust lineand the resulting pitching moment when poweris applied. Aircraft with engines mounted onpylons below the wings can pitch up in a mannerpossibly difficult to control when thrust isincreased at low airspeed. In addition, a jet has toaccelerate and build up speed before controlsurfaces regain authority. With a prop, horizontaland vertical stabilizers start to regain authorityonce the slipstream returns. But ailerons stillrequire airspeed. In an extreme case, if you slamthe power forward on a go-around in a P-51 orsimilar warbird while flying slowly, the torqueeffect can be more than the ailerons can handle.



6. Roll Authority: Adverse Yaw & Angle of Attack, Lateral Divergence

Flight Condition: Upright, power-off 1g stall, high α, varying β, pro-spin.

Lesson: Lateral/directional control at increasing α.

Flight Notes

In the previous maneuver set we observed the loss of aileron effectiveness during delayed nose-high rollingrecoveries. In this set we’ll continue to examine changes in lateral control. We won’t intentionally spin theaircraft at this point in the program, but the aircraft will be bopping around pretty aggressively, with thevelocity vector wagging left and right, and these are potential spin entries (high angle of attack plus sideslipand yaw rate). Just centering the rudder and ailerons and releasing aft pressure is enough for recoveryfrom an incipient spin departure in our aircraft. (As the spin develops, however, recovery techniquebecomes more critical, for reasons we’ll cover in spin training.). That said—don’t be timid. Challenge theaircraft to the point where lateral control is lost, and then get it back.

Procedures:

Spin recovery briefing as required.

Power idle.1-knot-per-second deceleration below 70 knots.Instructor demonstrates initial task.

Sample aileron authority: Decelerate toward stall while rolling 15 degrees left and right at a constant roll rate.Alternate between rudder free and coordinated rudder as necessary to hold nose on point.Note: 1. Change in aileron deflection needed to maintain roll rate.

2. Change in aileron forces.3. Increase in adverse yaw.4. Contribution of coordinated rudder to roll rate.5. Lowest speed for aileron authority.

Continue rolling inputs through stall break. At wing drop, hold opposite aileron. Observe aileron reversal.Hold aileron deflection and recover using forward stick to demonstrate return of aileron authority. Instructorwill demonstrate if required.

Sample rudder authority: (Instructor demonstrates initial task.) Establish constant rate left/right yaw temposufficient to assess rudder authority during stall entry. Note: 1. Change in required rudder deflection.

2. Change in rudder forces.3. Lowest speed for rudder authority.

Observe lowest speed for lateral control using coordinated aileron and rudder.



The subject of this maneuver set is mostly the rudder. Rudder-induced sideslips can accelerate a rollingmaneuver and contribute to maximum-performance upset recoveries. Proper rudder use is essential forcoordination at high α: but misuse of the rudder at high α can also cause spin departure, or severe yaw/rolloscillation (Dutch roll), especially in swept-wing aircraft. Following the November 12, 2001 verticalstabilizer failure and crash of American Airlines Flight 587, an Airbus A300-605R, attention has focusedon the structural loads generated on a vertical stabilizer when the rudder is deflected to opposite sides inrapid succession. Rapid rudder reversals, even below maneuvering speed, VA, and even with rudderlimiters, can result in loads in excess of certification requirements. FAR Part 25.351 rudder and fin loadrequirements are based on the demonstration of a sudden full rudder deflection (either to the stop or until aspecified pedal force is reached) at speeds between VMC and VD (design dive speed) in non-acceleratedflight. This is followed by a stabilized sideslip angle, and then the sudden return of the rudder to neutral,not to a deflection in the opposite direction.

The American Flight 587 accident also raised fears that unusual-attitude training that overemphasizesrudder can in fact provoke an upset if a pilot overreacts with rudder to an otherwise non-critical event, oruses it at the wrong time. Although we’ll demonstrate the effects of rudder and sideslip on rolling momentsas α increases, for all the reasons above we won’t define the rudder as the primary high-α roll control,especially not for swept-wing transport aircraft (historical jet fighters are a separate issue). Reduce theangle of attack if necessary to regain lateral authority, and use ailerons or spoilers for unusual-attituderoll recoveries, along with the rudder required for coordination, not roll acceleration. This is consistentwith both Boeing and Airbus philosophy, but can be applied to any aircraft. Aggressive rudder use is animportant part of aerobatic training, and of course aerobatic training is the basis of unusual-attitudetraining. But aggressive rudder use doesn’t always carry over—partly because of concern the rudder will beused at the wrong moment and partly because, even with an experienced aerobatic pilot at the controls, thedynamics following a nominally correct aerobatic input may be different in a swept-wing aircraft than in astraight-wing trainer.

• In the golden days, when tail-wheel aircraftwith lots of adverse yaw were standard, andpilots could still be seen wearing jodhpurs, flightinstructors often had students perform back andforth rolls-on-point, which instructors in jeanstoday often mistakenly call “Dutch rolls.” (In areal Dutch roll the nose wanders.) The idea wasto wake up the feet for directional control duringtakeoffs and landings, and especially to teach therudder coordination necessary to counteractadverse yaw. This maneuver set is similar, butthe dynamics are more complex and revealingbecause we roll the aircraft while simultaneouslyincreasing its angle of attack (and thus itscoefficient of lift, CL).

• Pay attention to how control authoritydeteriorates: You’ll need to increase your controldeflections to maintain rolling and yawingmoments as airspeed (dynamic pressure)diminishes. The down aileron will beginproducing proportionally less roll control andmore induced drag as the angle of attack rises(induced drag increases directly as the square of

lift), and therefore more adverse yaw. You’ll seethe result in the movement of the nose. Keepingthe nose on point with rudder will demonstratehow the rudder becomes increasingly necessaryfor directional control when using ailerons forroll control at higher angles of attack, and thenincreasingly dominant for roll control as theailerons lose authority and roll damping beginsto disappear.

• Rudder-induced roll control doesn’t decline asmuch as aileron control typically does, becausethe yaw/roll couple that the rudder provokes goesup in proportion to coefficient of lift. Aileronauthority, however, goes down as airspeeddiminishes and as flow separation begins toaffect the outboard wing sections.

• Ultimately, at aircraft stalling angle of attackthe ailerons can (legally, see below) begin to“reverse” (not to be confused with wing twisting,“aeroelastic reversal”). This happens whenadverse yaw begins to dominate, and theopposing roll moment the yaw produces (through



sideslip and yaw rate) overcomes the rollmoment generated by the ailerons. The airplanethen rolls toward the down aileron. This is calledlateral control divergence. Its natural prey is anairplane with lots of adverse yaw and lots ofdihedral effect, when flown at high angle ofattack by pilots who don’t use their feet to keepyaw under control (and thus the velocity vectoron the plane of symmetry).

• Adverse yaw goes down and aileroneffectiveness returns when you apply forwardpressure to reduce α: Push to recover aileroneffectiveness. As in the nose-high stalls doneearlier, you’ll see how quickly a “reversed”aileron regains its appropriate authority once thenose comes down.

• After the flight, compare the trainer’s stallbehavior to the requirements in FAR Part23.201-203 (for aircraft under 12,500 pounds)and to the requirements for transport certificationunder FAR Part 25.201-203. (See the Summaryof Certification Requirements.) The wording isdifferent, but 23.201(a) and 25.203(a) say thesame thing. According to the latter: “It must bepossible to produce and to correct roll and yawby unreversed use of the aileron and ruddercontrols, up to the time the airplane is stalled.”[Italics ours] Did we demonstrate capabilities atstall α beyond those explicitly required?

• We’ve demonstrated the continuing authority ofrudder, compared to aileron, for roll control inthe high-α region of the envelope. Nevertheless,in general, don’t rely on the rudder for primaryroll authority at high α, if you can avoid it. Thebest course is to push the stick forward and causenormal control authority to return. Certificationrequirements assume a pilot will do just that. Wedon’t want our demonstrations to turn into whatthe airlines call negative learning, so remember:These lateral and directional control exercisesare not procedure training. Recover roll controlat high α by pushing to reattach airflow and torestore aileron effectiveness as required. Usecoordinated, ball-centered rudder to enhanceroll rate by checking adverse yaw. This iscorrect for any aircraft, but particularly so forswept-wing—in which yaw/roll couple is morepronounced than for straight-wing aircraft andthe gyrations of the real Dutch roll are moresevere, and in which the high-α/β corners of theenvelope may not have been explored duringflight test because operational encounter wasnever intended.



The illustration below puts things in velocityvector terms.

X body axis

α

Velocity Vector, V

Velocity vector, V,projected onto x-zplane gives aircraftangle of attack, α. X-Z plane of symmetry

Lift vector

Z body axis X-Y plane

Velocity vector projectedonto the x-y plane givessideslip angle, β.

V V

β

Velocityvector

α

z bodyaxis

x body axis

X-axis

β

Y-axis

A directionally stable aircraft yaws in the direction the velocity vector is pointed, returning the vector to the x-z plane of symmetry asit does. A laterally stable aircraft rolls away from the velocity vector when the vector becomes displaced from the plane of symmetry.In the illustration, the second aircraft wants to yaw right but roll left.

As an aircraft slows, and angle of attack and thus adverse yaw increase, aileron deflection will increasingly shift the velocity vectoroff the plane of symmetry, unless the pilot uses “coordinated” rudder deflection to counter the yaw. If present, P-factor andslipstream will also increase, tending to shift the velocity vector to the right unless the pilot compensates with right rudder.

So as speed goes down, the tendency of the velocity vector to wander goes up. The resulting rolling moments away from the velocityvector increase with β, and also increase with angle of attack.

Rolling an aircraft with rudder is a matter of pointing the velocity vector to generate a rolling moment in the desired direction. Thedangers of aggressive rudder use at high angle of attack are that the aircraft enters a spin, or enters a Dutch roll oscillation the pilotinadvertently reinforces while trying to correct.



7. Flap-Induced Phugoid

Flight Condition: Longitudinally unstable, varying lateral/directional control.

Lesson: Downwash/horizontal stabilizer interaction, control practice.

Flight Notes

A dynamically stable phugoid motion is convergent. We can produce a non-convergent phugoid bylowering the flaps, but we don’t retrim. The flaps increase the downwash angle over the horizontalstabilizer and, with the stick free, the nose pitches up in response. As the wing roots stall and the downwashdisappears, the nose pitches down. When lift then returns, the downwash reappears, driving the nose backup for the next stall. Your job, during this stall-and-recovery roller coaster, is to keep the aircraft underdirectional and lateral control, using aileron and rudder only.

• The center of lift moves rearward along thewing chord when you lower the flaps. Thisproduces a nose-down pitch moment. (The dragyou create below the aircraft’s center of gravityalso contributes.) But watch the tufts when theflaps go down and note the vortices that formaround the flaps’ outboard tips. These vorticesincrease the angle of the downwash affecting thehorizontal stabilizer. This down flow produces anose-up pitch moment. The pitch-up from thedownwash on the stabilizer is greater than thepitch-down from the reward shift in lift. As aresult, the aircraft pitches up at flap deployment.

• Anytime you (or a gust) raise the angle ofattack of a wing you also increase the downwashangle. Typically, the downwash angle changesmore rapidly with AOA when the flaps aredeployed. Because the change in downwash

angle reinforces rather than opposes a change inwing angle of attack, flaps generally reducelongitudinal (pitch axis) stability. One reason forT-tails is to raise the stabilizer out of the area ofdownwash (and propwash) influence.

• As the aircraft stalls and recovers, you’llexperience changes in lateral and directionalcontrol, already familiar from earlier nose-highmaneuvers. Propeller and slipstream effects willbe more pronounced, however, because of theneed to maintain power to keep the maneuvergoing.

Procedures:

Speed for white arc in level flight.Student’s hands in “prayer” position (palms facing inward but not touching stick, rudder/aileron control only).Instructor lowers flaps approximately 15 degrees.Student maintains directional and lateral control. No pitch input.Instructor manipulates flaps as required, monitors flaps-extended speed.

Observe the effect of lowering the landing gear.



8. Nose-Level Aileron Roll: Rolling Flight Dynamics, Free Response

Flight Condition: Knife-edge & inverted, free yaw/pitch response.

Lesson: Free response behavior in rolling flight, attitude familiarization.

Flight Notes

We teach you to roll an aircraft through 360 degrees before we tackle emergency upset roll scenarios. Thisis less demanding on your motion tolerance at the start of training because the flying is smoother and youremain in control. You’ll begin by observing how the aircraft responds in pitch and yaw to changes in bankangle during a 360-degree rolling maneuver. Then you’ll learn to control that response.

• You’ll end up losing altitude, with the nose wellbelow the horizon at the completion of theseintroductory rolls. They’re not the way anexperienced aerobatic pilot rolls an aircraft—butwe start with this ailerons-only, nose-in-level-flight technique to demonstrate the airmanshipproblems that an actual unusual-attitude rollingdeparture would involve. You’ll gain moresophisticated, aerobatic control inputs as we fly.

• Because the aircraft rolls, pitches, and yaws in arelatively extreme manner with respect to thehorizon, pilots new to aerobatics usually have adifficult time tracking attitude. In the second roll,with reduced aileron, the horizon will certainlydisappear behind the nose as the aircraft rollsthrough inverted. At this point untrained pilotshave the famous tendency to release aileron andpull into a split-s. Don’t worry. This you willnever do!

• The aircraft’s free-response directional andlongitudinal stability characteristics are designedfor upright flight. They produce nose-downmoments (with respect to the horizon) during aroll. Directional stability drives the nose down ateach knife-edge, and longitudinal stability doesthe same at inverted. The more stable theaircraft, the more adverse the result.

• Notice the important relationship between rollrate and pitch attitude at roll completion. Theslower the roll rate the steeper the final pitch-down attitude. The aircraft’s free response hasmore time to bring the nose down. Largerpassenger aircraft roll far more slowly thanaerobatic trainers. As a result, a badly executedmaneuver for a trainer might actually simulate abest-case controlled-response outcome for a less

Procedures:

Check: Seat belt, cockpit, instruments, altitude, outside.

About 23”/2,300 rpm.From level flight with elevator and rudder neutral throughout.360-degree roll with full aileron.Recover from dive (instructor notes g’s pulled in recovery).

If motion sickness is not a concern, repeat the same as above but use partial aileron deflection todecrease roll rate and allow the nose to fall farther below the horizon.



responsive aircraft. So, keep the roll going at thehighest possible rate.

• While we want you to understand theimportance of holding full aileron deflection toachieve maximum-rate recoveries, the idea ofkeeping the roll going needs qualification whenwe think about vortex encounters, and for thesake of primacy we should state it right off. Bythe time a pilot reacts to a vortex with oppositeaileron the aircraft probably has already beentossed to a different part of the paired vortexflow field (and/or the individual vortex hassnaked around to a different part of the aircraft)and the imposed rolling moment has changed.The compilation of NASA vortex encountervideos you’ll see in ground school willdemonstrate how an aircraft is dispelled from avortex core. You’ll see why you shouldn’tassume that even a violent initial rollacceleration caused by a vortex encounter ishandled best by keeping the vortex-induced rollgoing through 360 degrees. That being said, notethat The National Test Pilot School, in Mojave,California, does recommend using the aircraft’sexisting rolling momentum, if advantageous, andcontinuing a roll once past 160 degrees.

• For a given control deflection, roll rate variesdirectly with airspeed. In aircraft with reversiblecontrols, like our trainers, for a given deflection,aileron stick force goes up as the square ofairspeed. Assuming no aeroelastic reversal,you’ll roll faster when flying faster, althoughyou’ll have to push the ailerons harder andharder, and eventually will come to a pointwhere the stick force is too much to handle androll rate starts back down. The problem for us isat the low-speed end, where low roll rates goinginto the maneuver permit the nose more leisureto fall below the horizon if the pilot allows, androlling recoveries back to upright take moretime.

• A recovery at higher g after a partial-deflectionroll allows you to experience sensations typicallypast the minimum 2.5-g positive limit loadallowable for an aircraft certified under FAR Part25.337(b). (Unfortunately a 360-degree rollfollowed by high g can trigger motion sicknessin some, so let’s be cautious.) For aerobatic

certification, which we operate under, FAR Part23.337(a)(3) requires a positive limit load of 6 g.

• Remember that for a given g load the radius ofa turn (or of a pull-up at the completion of a roll,as is the case here) at any instant varies directlywith the square of the true airspeed. Double thespeed means four times the altitude consumed. Arecovery in a piston aerobatic trainer’s low-airspeed/high-g envelope consumes much lessaltitude than recovery in a jet operating at higherspeeds and lower limit loads.

Con

trol F

orce

, Fa

Aile

ron

Def

lect

ion,

δa

Max force pilot can sustain with reversible controls.

Fa ∼ EAS2

Dashed line for powered controls.

Pilot maintains max force but deflection starts going down as airspeed increases.

Roll Rates Depend on Airspeed and Control System Design

Symbol ∼ means proportional.

Rol

l Rat

e, p

, deg

/s

p ∼ TAS

P∼ 1/TAS

Roll rate decreases for reversible controls because pilot can’t hold deflection.

Airspeed

Airspeed

Airspeed

Solid line for muscle powered reversible controls.

Airspeed for max roll rate with reversible controls.



9. Slow Roll Flight Dynamics: Controlled Response

Flight Condition: Knife-edge & inverted, controlled yaw/pitch response.

Lesson: Control in rolling flight.

Flight Notes

There’re three standard aerobatic rolls (and one weird one). The first exercise in this sequence is an aileronroll, so named because the ailerons do all the work. The next exercises introduce the slow roll—anaerobatic competition maneuver that uses help from rudder and elevator to keep the center of gravity of theaircraft moving in a straight line (as opposed to the climb and descent of the aileron roll). Slow rolls giveyou the tools to handle roll emergences with minimum altitude loss. The third standard roll is the barrelroll, which is actually a combination loop/roll that takes a path through the sky as if the aircraft werefollowing the outline of a barrel laid on its side. The idea behind the barrel roll is to keep the aircraft atpositive g for the sake of fuel flow and lubrication if it lacks inverted systems. It also keeps the occupantsmore confidently in their seats and permits the trick of pouring coffee from thermos to mug while upsidedown. We won’t do barrel rolls as part of your standard training sequence (although we can toss some in)but the rudder roll (the weird one), which we will do, is fairly similar.

Procedures:

Task: Complete the roll with the nose on or near the horizon, not in a dive.

Check: Seat belt, cockpit, instruments, altitude, outside.

Roll 1: 25”/2,500 rpm. Airspeed at instructor’s discretion.

Raise the nose 20-30 degrees. Release aft pressure/ rudder neutral.

Full aileron.

Roll 2: Raise the nose as instructor directs. Top rudder at second knife-edge.

Roll 3: Raise the nose as instructor directs. Forward pressure at inverted.

Top rudder at second knife-edge.

Roll 4: Raise the nose as instructor directs. Top rudder at first knife-edge. Forward pressure inverted. Top rudder at second knife-edge.

Roll 5: Roll in the opposite direction.



Learning to slow roll is actually easier—and the exercise is more informative—when you take it as aproblem to be solved by experimentation, and not as a textbook set of sequenced control inputs. Then, tomake it easier still, you learn the rudder and elevator skills in reverse.

• In Roll 1, raising the nose high enough at thebeginning of the maneuver and then rolling fastenough solves the procedure task by default.Start high and the nose simply falls through tomeet the horizon at the end. (Of course, thisdoesn’t represent a typical nose-down unusual-attitude scenario.)

• In Roll 2, the rudder helps hold the nose up atthe second knife-edge. The resulting sideslip canaccelerate the roll rate through dihedral effectand roll due to yaw rate. Your instructor willmake sure you experience this acceleration,because—with certain reservations—it’s animportant emergency skill. As you gainexperience, you’ll learn to amplify the effect byaft pressure on the stick. (The ultimateamplification becomes a snap roll, an aerobaticrather than emergency maneuver. Aerobaticpilots, especially competition pilots, actuallyavoid accelerating aileron rolls with rudder andelevator, since it leads to a sloppy-looking andphysically unpleasant maneuver. But fighterpilots have used snapping roll entries since theFirst World War to quickly reverse direction andshake an attacker from their tail, especially atlow speeds where aircraft usually snap roll fasterthan aileron roll.)

• Roll 3 uses forward pressure at inverted tokeep the nose up. Remember that the necessarystick pressure and movement is much less in anaerobatic trainer, and the response much greater,than in an aircraft with more longitudinalstability.

• Roll 4 begins to approximate the techniqueused in competition slow rolls: initial top rudderat the first knife-edge, transitioning to forwardelevator and back to the opposite top rudder atthe second knife-edge. This produces a constantnose up (with respect to the horizon)yawing/pitching/yawing moment throughout theroll, working in opposition to the aircraft’snatural stability tendencies.

• The roll sequence is done first in one directionto ease the development of perceptual and motorskills. Roll 5, done in the opposite direction, isoften confusing for the beginner because the nowexpected motor sequence is reversed. That’s whywe do it! Here, your confusion makes us happy.Consider it a memorable training opportunity.Don’t freeze! Keep the roll going with fullaileron deflection—rudder and elevator aresecondary to aileron when you are learning toroll.

• Don’t expect to fly rolling maneuvers step-by-step using a memorized formula. The maneuvercan break down dramatically if the aircraft’sattitude falls out of phase with your programmed

Top rudder causes a sideslip-induced roll moment, in addition to the aileron roll moment. This increases roll rate.

Sideslip, v.

Roll moment from sideslip (plus roll due to yaw rate).

Roll moment from ailerons.

Sideslip Enhances Roll Rate



inputs and expectations. Instead of trying toestablish a sequential muscle-motor program atthe start, concentrate on reacting to the aircraft’sattitude with the correct muscle-motorresponse—your muscles will then programthemselves. These rolls are building yourperceptual familiarity with unusual attitudesalong with the motor habits needed to respond asrequired. Learn to fly in response to what yousee.

• On the subject of “flying what you see,” youcan tell that we’re suspicious of applyingmemorized, step-by-step control sequences, or“mantras” at the initial stages of unusual-attituderecovery training. We’d rather try to help you todiscover the correct inputs—underguidance—yourself. They’ll stick that way, andyou’ll develop the necessary coordination andharmony. Memorized sequences are mostappropriate when a pilot can’t figure out what’shappening and sequenced inputs are the onlyway to catch up and get things under control. Inaerobatics, that kind of situation is most likely tooccur when spins accelerate or change modesand the pilot loses visual tracking. Mantras areonly safe when the initial input can be inserted atany time in the departure: otherwise out-of-phaseinputs can actually make things worse. You mayfeel differently about this. It’s worth talkingover.

• Once you’ve done a few rolls and experimentedwith control inputs and their results, the notionof tail-force vector will help you understandwhat you’ve in fact already begun to practice.You’re familiar with an aircraft’s lift vector fromthe standard illustrations of lift, weight, thrust,and drag. The tail-force vector is our term for thesum and direction of the “lift” produced by therudder and elevator together. In coordinated,upright flight the tail-force vector comes entirelyfrom the elevator/horizontal stabilizer (we’reneglecting any directional trim forces therudder/fin might be producing). It usually pointsearthward, normal to the relative wind over thetail, and balances the nose-down pitchingmoment that results when an aircraft’s center ofgravity is forward of the neutral point (seeground school text “Longitudinal StaticStability”). When flying inverted, forward stickis necessary to produce the same balancing,earthward tail-force vector. Otherwise, the noseheads downhill. In knife-edge flight, top rudderreplaces elevator in keeping the tail-force vectorpointed down, and the nose (as much aspossible) up.

• To prevent the nose from falling, to delay theonset, or to reduce the rate at which the nosefalls in a roll, we keep the tail-force vectorpointed toward the Earth—using whatever

Combined elevator and rudder deflection keep tail-force-vector pointing toward the Earth

Top rudder shifting to forward stick.

Forward stick. Forward stick shifting to top rudder.



changing combination of elevator and rudderthe current bank angle requires. Note that, inusing the elevator and rudder in this way, we’rekeeping the aircraft’s total lift vector pointedroughly heavenward. See “Axes andDerivatives” in the ground school texts.

• But here come the caveats: In non-aerobaticaircraft the effectiveness of these control inputsdepends on the effectiveness of the controlsurfaces in flight attitudes neither they nor therest of the aircraft were specifically designed toexperience! Jet transports typically have atrimmable horizontal stabilizer with an attachedelevator. The design facilitates wide c.g. andairspeed range, but pitch authority is limited bythe position of the stabilizer. Even if theelevators are effective enough to slow the ratethe nose drops while inverted, the resultingdecrease in positive g may lead to fuel flow,lubrication, or hydraulic system failure. In theunlikely event the elevators are effective enoughto actually push the nose up inverted, theresulting negative g may be insupportablestructurally.

• There’s more to worry about: In an aerobaticaircraft, rudder forces are usually wellharmonized with elevator and aileron. Dutch rollis usually well damped. But that may not be thecase in a jet, especially swept-wing. Intransports, rudder breakout forces can behigh—and in some designs at certain speeds canbe close to the force required for full deflection,a situation that can lead to over control. Becausethe sideslip angle has to build up before theresulting rolling moment appears, and because ofroll inertia, there may also be a time lag betweenthe rudder input and the roll response. Suchfactors make it difficult to achieve the rudder-

input harmony and timing possible in anaerobatic trainer. The result of overzealousrudder use can be the build up of such a largesideslip angle and consequent roll moment thatthe recovering aircraft continues rolling pastwings level. If the pilot reacts to the ensuingDutch roll by deflecting the rudder against thesideslip (left sideslip, left rudder, say), themoments generated by the sideslip angle and therudder together can “over yaw” the aircraft to theopposite side, causing it temporarily to reach anextreme, overswing sideslip angle. Suddenlyreversing the rudder against the swing can set upthe forces necessary to damage, or destroy, thevertical tail. Always use the rudder cautiously ina swept-wing aircraft.

• Concerning rudders, review the BoeingCommercial Airplane Group Flight OperationsBulletin, May 13, 2002, at:http://www.ntsb.gov/Events/2001/AA587/exhibits/240009.pdf

• As we’ve shown, in an intentional roll you canfinesse with top rudder at knife-edge and withforward stick through inverted in order to keepthe nose up. You can use top rudder and slightaft pressure to accelerate the roll rate afterpassing from knife-edge back toward upright (aslong as the wing isn’t too near stall and rudderlikely to cause a departure). You can apply thesame finesse to emergency recoveries asappropriate to your aircraft type, but don’t forgetthe most important control. In a recovery from aroll upset, use full aileron. It’s easy to relaxaileron pressure inadvertently. Every studentdoes it. Learn not to!



10. Sustained Inverted Flight

Flight Condition: Inverted, -1g.

Lesson: Situational awareness, trim forces, AI interpretation.

Flight Notes

We teach full, 360 degree rolls before we teach half rolls to inverted because the distracting physiologicaleffects of negative-g inverted flight are easier on the student when encountered later in training. Negative1-g level inverted flight is an interesting training experience, but it’s actually more an aerobatic than anemergency skill. In reality, unless you assert yourself with forward pressure, and the aircraft has sufficientelevator power, you’re not going to experience sustained negative-g during an upset emergency short of aninverted spin (nor would you want to in an aircraft without proper fuel and lubrication systems). Theaircraft will assert its longitudinal stability and start pitching toward positive g, as this maneuver illustrates.

• Reference points are hard to retain when you’rehanging upside-down. Students who can respondquickly to the instructor’s request to point out aninstrument inside or a cardinal direction outsidethe cockpit when right-side-up often have troubledoing the same thing when inverted under actualnegative g. There’s a tendency to tense the bodyand stare at a point, and just turning the head andlooking around can require real effort. Flightskills don’t come naturally under these

conditions, especially when you just discoveredthat your seat belt wasn’t as tight as you thought.

• When the instructor rolls inverted and transferscontrol and asks you to roll upright, you’ll besurprised at the amount of forward pressure he orshe was holding. Don’t let up and let the nosefall too far. When you roll the aircraft fromupright to inverted, remember how that pushforce felt and blend it in as you complete the half

Procedures:

Instructor: Check: Seat belt, cockpit, instruments, altitude, outside. Cruise power. Fly a cardinal heading. Instructor asks student to point quickly to cockpit instruments and outside cardinal headings. Instructor rolls aircraft inverted and maintains control. Instructor asks student to point quickly to cockpit instruments and outside cardinal headings while inverted. Student takes control and rolls upright.

Student: Raise nose about 20 degrees.

Roll inverted.Forward pressure as required to maintain level flight.Rock wings approximately 15-20 degrees left and right (note any sensation of adverse yaw).Roll upright.



roll. Notice inverted that the junk that was on thefloor or loose in your pockets is now on thecanopy. A little dust is inevitable, but anythingthat could jam the control system requiresimmediate recapture and a better preflight nexttime around.

• On rolling upright from inverted: If you’veflown or read about aerobatics, you might knowthat strict procedure often requires rudder inputopposite to aileron, followed by rudder inputwith aileron, when rolling upright from negative-g inverted flight. That’s because inverted adverse

aileron yaw calls for some rudder deflectionopposite to stick deflection. Such cross-controltechnique is usually confusing to the student atfirst, and tends to delay recovery actions. It’simportant in precision roll training with aerobaticaircraft equipped with inverted oil and fuelsystems. But it creates unnecessary confusion inunusual-attitude training for pilots who will flynon-aerobatic aircraft with conventional systemsand much heavier control forces in pitch. Even ifthe pilot pushes as the aircraft rolls throughinverted, the load will probably remain positiveand inverted adverse yaw won’t occur.



11. Inverted Recoveries

Flight Condition: Inverted, high & low kinetic energy states.

Lesson: Attitude recognition and recovery practice.

Flight Notes

Identify the Nearest Horizon (fewest degrees away): Push & Roll, Top Rudder, Pull

When using the AI, roll toward the sky pointer, or roll the lift vector toward the sky.

In this maneuver set we’ll apply the lessons learned in slow-roll flight dynamics to a more challengingattitude environment. Your instructor will fly the maneuvers to the descent line at the start, allowing you torecover. The initial goal is to get you going downhill, upside-down, horizon obscured, at as slow a speed aspossible, with as gentle an entry as possible. This makes the fewest demands on your motion tolerance, andkeeping the speed down allows you time to discover what the world looks like when you’re descendinginverted. We may use rudder to accelerate the roll recovery, but we’ll take note of the caution required.

Procedures:

Instructor:Check: Seat belt, cockpit, instruments, altitude, outside.23”/2,300 rpm.Pitch up to about 45 degrees.Student closes eyes.Roll inverted; decelerate on ascent.Idle power.Gently pull nose below horizon.

Student:Opens eyes on instructor’s command.Rolls upright to recover.

Repeat from different inverted bank angles.

Student pitches up, closes eyes, rolls inverted, opens eyes and recovers on instructor’s command.

Instructor transfers control to the student inverted at a nose-high, low-kinetic-energy state.

To prevent excess airspeed during inverted recoveries, the instructor will normally close the throttlebefore the student takes control. In that case the student should simulate proper throttle use.



• In the first maneuvers, you’ll already know thatyou’re pointing down and accelerating. In thatcase, it’s correct to Push to keep the nose fromfalling farther. In subsequent nose-high transfersof control you’ll be very slow. You’ll be able tosee the horizon, but will need to allow the noseto come down below it to let gravity helpaccelerate the aircraft so that control authorityreturns. Don’t reflexively push. If the aircraftsomehow picks up a yaw rate, pushing whileinverted at low speed could lead to an invertedspin.

• Roll to the nearest horizon with full aileron.The nearest horizon is the fewest degrees away.On instruments, that means rolling toward thesky pointer, or rolling the lift vector toward thesky.

• As the aircraft rolls upright from inverted toknife-edge, start applying Top Rudder andrelease the forward pressure. If you hold forwardpressure past knife-edge you’ll sacrifice some ofthe dihedral effect necessary to assist the roll,and you’ll push the nose down and yourself outof the seat. Top rudder holds the nose up throughknife-edge and starts a sideslip that acceleratesthe roll.

• Begin your Pull as the aircraft rolls throughroughly 45 degrees. Come off the rudder as younear upright. Ailerons are primary, but pastknife-edge combining top rudder and elevatorcan bring the nose up to the horizon followingthe shortest line.

• The top-rudder deflection accelerates the rolland also keeps the airplane from turning whenyou begin your pull. As you roll upright, rudderand elevator work together to keep the tail-forcevector pointing roughly earthward, so that thenose comes up to the horizon in a direct verticalpath and sideslip assists roll rate.

• You’re using rudder and elevator in an expertway in these recoveries. Just remember that therudder and the elevator can cause trouble. We’vealready worried about misapplication of orinappropriate reliance on rudder at high α,because of possible stall/spin departure. We’veworried about differences between aerobatic

trainers and swept-wing aircraft in their Dutchroll response to rudder deflection. Now worryabout this: If you pull an aircraft to limit loadwhile rolling with aileron and/or rudder (arolling pull-up) the asymmetrical load generatedacross the span can take the up-going wing paststructural limits. This could occur from therolling moment generated by modest rudderapplication alone, since even a small momentapplied at limit load would cause the wing toexceed that limit. This wrecks airplanes. See“Maneuvering Loads, High-G Maneuvers” in theground school text.

• Any general statement about handling anaircraft in an upset emergency has to balance therisks of misunderstanding against the rewards ofairmanship. A given control input orcombination could either get you into trouble orelse help you out of it…depending. So what’sbest to say? A general statement also has toavoid optimistic assumptions concerning both apilot’s ability and the unknown areas of anaircraft’s response. It has to assume that theexpertise shown in training will deteriorate andthat a pilot will become confused if too manyhalf-remembered nuances exist in his mind.Aerobatic instructors know this from theexperience of watching students fumble throughroll recoveries as they try to remember what todo with the rudder and elevator. In light of theabove, here’s a general, baseline, “I’m out ofpractice so what do I do now?” statement thatapplies to aircraft with standard flight controlsand flying qualities. Embed this in your mind asthe primary response: In a roll-upset emergency,go to the ailerons first. Unless you initially needthem to lower the nose to regain airspeed foraileron authority, rudder and elevator aresecondary. So much the better if you’re moreexpert than that!



Lift Vector

Sky Pointer

Earth

Sky

Roll toward the Sky Pointer

Roll the Lift Vector toward the sky



12. Rudder Roll: Yaw to Roll Coupling

Flight Condition: High α, high β, upright & inverted.

Lesson: Roll control by means of sideslip, yaw rate, and angle of attack.

Flight Notes

The rudder roll is similar to the old-fashioned barrel roll in terms of the flight path the aircraft followsthrough the sky, except the ailerons remain neutral and the heading changes are not as great. It’s also a kindof slow-motion snap roll, although the aircraft doesn’t go all the way into autorotation. It’s not often taughtin civilian aerobatics, but has a history in the military as a way of rapidly reversing bank angle in a high-gturn. We fly rudder rolls to underscore yaw/roll couple, and to add their more complex motions to yourunusual-attitude experience. The rudder roll also demonstrates that yaw/roll couple responds the same tolongitudinal stick position whether the aircraft is inverted or upright (or in any other attitude), as long asthe wing is at a positive angle of attack. Caution: Rudder rolls can rapidly erode motion tolerance.

• The aircraft will roll 360 degrees on dihedraleffect, roll due to yaw rate, and y-wind-axispitch/roll couple. Constant pitching, yawing, andsideslip drive the maneuver. Unlike the slowrolls we’ve been working on, where we try tokeep the tail-force vector pointing earthward, inthe rudder roll (and barrel roll) the tail-forcevector rolls with the airplane.

• Notice how reducing the angle of attack withforward stick (unloading) while inverted reducesthe roll rate. If you relax the stick (or rudder) toomuch the roll rate will really decrease and thenose will just head downhill. If necessary,recover with full aileron in the normal way.

• If you pull too hard the aircraft can snap rollsuddenly (high angle of attack + sideslip andyaw rate = departure!). Release aft pressure andrudder if you feel the roll begin to accelerate tooquickly. (A snap roll at the top of a loop is calledan “avalanche”—which is nicely expressive ofthe tumbling feeling it produces. A snapdeparture out of a rudder roll feels the same, andcauses the same spatial confusion on firstencounters.)

Procedures:

Check: Seat belt, cockpit, instruments, altitude, outside.25”/2,500 rpm.Pitch up to 45 degrees.Full rudder deflection.Ailerons remain neutral.Hold aft pressure.Full rudder throughout.

Repeat as above with temporary forward pressure at inverted to observe decrease in roll rate; restoreaft pressure to completion.



13. Rudder & Aileron Hardovers

Flight Condition: Uncommanded rolls.

Lesson: Effects of pitch inputs during uncommanded rolls.

Flight Notes

Concerns about rudder hardovers, and the development of the concept of crossover speed, stem directlyfrom accidents involving Boeing 737s, which were caused or complicated by uncommanded rudderdeflection. (See http://www.ntsb.gov/publictn/2001/aar0101.htm) Here we start by observing that in arudder-neutral spiral attitude, back stick gives you a pure pitch response. But during a rudder-deflectedspiral attitude, as produced by an uncommanded rudder hardover, back stick accelerates the roll.Although aircraft attitude relative to the horizon might appear identical to the pilot, in the rudder-deflected

Procedures:

Demonstrate effect of pitch input during normal spiral, rudder neutral.

Power for low cruise.Enter spiral mode.At 45-degree bank, observe response to stick-back pitch input.Release and recover.

Demonstrate effect of pitch input during rudder hardover spiral, rudder deflected.

Aileron neutral.Roll 30 degrees with rudder only.Hold rudder input.Hold aileron neutral.Aft pressure to accelerate roll.Release and recover.

Alternate aft pressure and forward pressure while holding rudder input and observe roll response.

Demonstrate recovery from rudder hardover below crossover speed.

Begin rolling the aircraft with rudder, then apply a partial aileron deflection using too little aileron to stop the roll. (The aircraft is below crossover speed for the partial aileron deflection.) As the aircraft rolls, hold rudder and aileron fixed, pitch down for speed to regain aileron effectiveness. Add power in the recovery as necessary to remain above crossover speed.

Demonstrate recovery from uncommanded aileron deflection, showing the effect of rudder and aft stick.

Partial aileron deflection. Apply rudder sufficient to slow but not stop the roll. Stick back (or nose-up trim) to increase α/CL.



case the aircraft is in a sideslip toward the high wing. Pitch will couple to roll in the presence of a sideslip.While the hardover issue may not affect all planes and pilots, it’s difficult to confirm one’s immunity, andthe exercise does provide more evidence for flying’s least instinctive but most encompassing maxim:Sometimes you have to aim for the ground to keep from hitting the ground! In the uncommanded rudderdeflection case, you aim for the ground to regain aileron effectiveness.

• Here’s an official definition, evidently approvedby the attorneys, from The Airplane UpsetRecovery Training Aid. At a given rudderdeflection, crossover speed is “the minimumairspeed (weight and configuration dependent) ina 1-g flight, where maximum aileron/spoilerinput (against the stops) is reached and the wingsare still level or at an angle to maintaindirectional control.” (2.5.5.4.3)

• In other (if only slightly more digestible)words, rudder deflection produces a rollingmoment, in the direction of deflection, due tosideslip and yaw rate. You can counter anuncommanded rudder deflection with oppositeaileron, just as you do in a steady-headingsideslip, but only if you’re going fast enough togenerate a sufficient opposing moment—that is,if you’re going above the speed where excessroll power crosses over from rudder to aileron.The more rudder deflection, the greater thecorresponding rolling moment and therefore thehigher the crossover speed. If you fly belowcrossover speed the aileron/spoilers can’t supplya sufficient opposing roll moment against therudder, and an uncommanded roll in the rudderdirection results. Wing-mounted multi-engineaircraft need powerful rudders to overcomeasymmetric thrust conditions during enginefailures. Uncommanded rudder deflections canproduce powerful roll moments, especially inswept-wing aircraft.

• You’re familiar with cross-controlledmaneuvers from our earlier steady-headingsideslips, and noticed (maybe) that we reachedthe rudder stops before reaching the aileronstops. To simulate a crossover problem at areasonable angle of attack, we simply limit ouraileron deflection and pretended we’re “againstthe aileron stops.”

• When an uncommanded rudder deflectioncreates a rolling moment, the aircraft’s nose will

begin to fall through the horizon. Since rollcouple for a given sideslip angle and aircraftconfiguration varies directly with coefficient oflift (with α), as does roll due to yaw rate, therudder-induced roll rate will increase if you tryto raise the nose with aft pressure. This just tiltsthe lift vector more toward the horizon andmakes the nose fall even faster (as wedemonstrate in this maneuver set).

• In an emergency, if the hardover rollcontinues despite full opposite aileron, lowerthe nose to regain aileron effectiveness. Divingeven more to regain bank control is not intuitiveif the nose is already coming down in anunwelcome manner! But reducing the angle ofattack will reduce yaw/roll couple, which in turnreduces crossover speed. Meanwhile, the airflowpicks up the dynamic pressure necessary foraileron authority. As you raise the nose, set thepower as required for flight above crossoverspeed. Then take a breath and pull out theEmergency Checklist for the recommendedrudder hardover flap setting, if there is such athing. (Maneuver set 14 demonstrated how flapdeployment reduces a sideslip-induced yaw/rollcouple, and thus would reduce crossover speed.)

• In an aileron hardover, you’d obviously tryopposite rudder. Then if necessary you’d raisethe nose to increase the CL and increase theyaw/roll couple the rudder provides. Flaps wouldprobably stay up, or go up if that were an option,again to increase yaw/roll couple as necessary tocombat the ailerons.

• Remember that the basic relationship betweenwhat you do in pitch and what happens in rollremains constant. Pushing forward reducesrudder/sideslip-coupling effects and increasesaileron authority, pulling back (literally towardthe rudder) decreases aileron authority andincreases rudder/sideslip-coupling effects.



14. Lateral Effects of Flap Deployment

Flight Condition: Changing β & spanwise lift distribution.

Lesson: Lateral lift distribution and lateral stability.

Flight Notes

Here we’ll alter the rolling moments in a sideslipping aircraft by changing flap position. This ties into theconcept of crossover speed during rudder hardovers. Crossover speed may go down in a flaps-downconfiguration because of the phenomena we’ll observe here.

• Putting the flaps down increases the liftgenerated at the wing roots and thus shifts the liftdistribution inboard. This is partly because of theincreased camber inboard, and partly because,after we’ve re-trimmed, the wingtips operate at alower angle of attack. In effect, we’ve increasedtheir washout. The inboard shift in center of liftreduces the effective moment arm and thereforethe rolling moment that results from the sideslip.Accordingly, when you lower the flaps in asteady-heading sideslip, the ailerons will haveless to fight against and the aircraft will roll inthe pro-aileron direction.

• Because of this inboard shift in lift, an aircraft’slateral stability (its tendency to roll away fromthe sideslip caused when a wing goes down) istypically reduced with flaps deployed. Its rolldue to yaw rate may also decrease because of thewashout effect. We’ve already noted the

Procedures:

Power as required for speed in white arc.Enter steady-heading sideslip.Hold rudder and aileron fixed.Lower and raise flaps and observe lateral response.Observe pitch response due to the changes in downwash angle.

With the flaps down in a sideslip and the aircraft trimmed, hold the rudder and release the stick:Compare the roll rate with the flaps-up condition explored in maneuver set No 2.

If desired, repeat at idle power, maintaining airspeed in descent, to assess the contribution of propellerslipstream effects.

In the Zlin, full flaps, wings level, apply full rudder.Observe pitch change with downwash/propwash shift.

Centers of lift move inboard with flaps during a sideslip, reducing the moment arm through which dihedral effect operates. Roll moment decreases.

v

v

Wing center of lift Lift Distribution

Total lift is the same (lift=weight), but shifts inboard.

Flap Effects

Wing is in a sideslip to the right.

Resulting roll moments



β

Sideslip Shifts Propwash

reduction in longitudinal stability with flapdeployment caused by downwash effects.

• The flap effect you’re seeing is magnified inpropeller airplanes by the shifting of theslipstream over the wings toward the sideopposite the sideslip, as the illustration shows.This means that the flaps on the high side duringour steady heading sideslip work in an area ofhigher dynamic pressure. This increases the lifton the high wing, reduces it on the low wing, andproduces a rolling moment in the same directionas the ailerons. With the power at idle, you’llneed more flap deflection to get the same rollresponse you got when lowering the flaps withpower on.

• The last maneuver in the set demonstrates howa sideslip combined with flaps can cause asudden change in the downwash/propwash overthe horizontal stabilizer. The nose may suddenlypitch in response. Unless you really know how itwill behave, don’t aggressively slip an aircraftwith full flaps on final.

• In some aircraft, flaps can decrease aileronauthority. This is one reason why using onlypartial flaps during a gusty, crosswind landing isa good idea. (The other, of course, is that ahigher landing speed increases overall controleffectiveness and leaves the aircraft vulnerablefor less time.)



15. Dutch Roll Characteristics

Flight Condition: Coupled yaw/roll.

Lesson: How directional and lateral stability interact dynamically.

Flight Notes

Your instructor will probably want to do this demonstration on the return from the practice area. Dutchrolls can erode motion tolerance rapidly, and that’s best saved for other things. FAR Parts 23.181 & 25.181cover the requirements for Dutch roll characteristics. (Note: Our sinusoidal rudder inputs are consistentwith FAR Part 25.351 yaw maneuver load requirements.) The Dutch roll is the natural outcome ofaerodynamic stability: an aircraft’s tendency to yaw toward but roll away from its velocity vector.

• As already mentioned, the term Dutch roll isoften misused. The real Dutch roll is not anexercise in rolling on point, but a coupledcombination of yaw rate, sideslip, and roll. Youcan think of it as a rough marriage between anaircraft’s roll axis (lateral) stability and its yawaxis (directional) stability. In the Dutch roll, adisturbance in either axis, whether pilot-induced,as here, or caused by turbulence, creates asideslip. A sideslip that sends the velocity vectorto the left, for example, leads to an oppositerolling moment to the right (through dihedraleffect and roll due to yaw rate). At the same timethe aircraft’s directional stability works toeliminate the sideslip by causing the nose to yawto the left. However, momentum causes the noseto yaw past center (past zero β), and this sets upa sideslip in the opposite direction, which in turnsets up an opposite roll. The resulting out-of-phase yawing and rolling motions would dampout more quickly if they occurred independently.Instead, each motion drives the other. Part 23

aircraft are required to damp to 1/10 amplitude in7 cycles. Part 25 requires only positive damping.

• Aircraft with lots of lateral stability (thetendency to roll away from a deflected velocityvector), compared to their directional stability,tend to Dutch roll. Reducing dihedral effect willease the Dutch roll problem, but at the expenseof reduced lateral stability. Without a yawdamper to do it for them, it’s difficult for pilotsto use the rudder to control a persistent Dutchrolling tendency because the period is short. It’shard to “jump in” with the correct rudder input atthe right time. (Failure of a yaw damper can alsocause fin overstress if Dutch roll develops.)Swept-wing aircraft are inherently vulnerable toDutch roll. Pilots of swept-wing transports arefrequently trained to damp the rolling motionwith quick, temporary applications of aileronagainst the prevailing roll. Temporaryapplications prevent the pilot from inadvertentlydriving the rolling motion. An aircraft with lotsof lateral stability may also require lots of aileron

Procedures:

About 23”/2,300 rpm.Trim.Instructor performs sinusoidal rudder inputs.Observe roll/yaw ratio at wingtip.Release rudder and observe rudder-free damping and overshoots.Compare with rudder fixed damping and overshoots.



deflection to hold the upwind wing down duringcrosswind landings.

• Aircraft with greater directional than lateralstability tend to be spirally unstable.Traditionally, the design compromise betweenDutch roll and spiral instability suppresses theformer and allows the latter, because spiral divesbegin slowly and are normally easier to controlthan Dutch rolls. And Dutch rolls make peopleairsick. (Which sounds like the dealmaker untilyou realize that spiral instability can kill you ifyou lose or misinterpret your instruments inclouds, or in poor visibility at night.)

• Watch the wingtip while driving the Dutch rollwith continuous, uniform, opposite sinusoidalrudder inputs. Observe if its motion pattern iscircular or elliptical. An ellipse lying on its side(1.) means more yaw than roll—in other words alow roll-to-yaw ratio. This is typical of aerobaticand tactical aircraft required to have fast roll

rates. A circular wingtip motion (2.) indicatesequal amounts of roll and yaw, as might betypical of a general aviation aircraft, in which apilot can use the rudder for bank control.

• An upright ellipse (3.) would indicate more rollthan yaw—a high roll-to-yaw ratio. That’stypical of a sailplane and indicates that rollperformance will require good ruddercoordination during roll maneuvering. Anyuncorrected adverse yaw will generate anopposing sideslip and large roll momentsopposite the intended roll direction. (The longwings of high-performance sailplanes producesubstantial adverse yaw due to roll rate, sofootwork is essential.)

• The tendency to Dutch roll increases at higherCL, because increasing the coefficient of liftincreases both dihedral effect (especially withswept-wings) and roll due to yaw rate. Dutch rolltendency also increases at higher altitudes, wheredamping effects diminish. Since aircraft fly athigh CL at high altitudes, the problemcompounds.

After initial disturbance,aircraft wants to yaw toright but roll to left.

Velocity vector

Yaw overshootdecreases as motiondamps out.

Yaws past centerand now wants toyaw left but rollright.



16. CRM Issues: Pilot Flying/Pilot Monitoring

Flight Condition: Various.

Lesson: Upset recovery and the two-person cockpit.

Flight Notes

“Pilot monitoring” has replaced the earlier term “pilot not flying.” The change keeps both pilots in the loop,at least rhetorically. As pilot monitoring, your ability to coach your instructor and respond as necessary willconfirm your understanding of recovery techniques. And you’ll be exposed to potential conflicts inCRM—in this case, recovery management.

• Your instructor may initiate recovery with theproper control inputs, but with inadequatecontrol deflection. In that case you might coach,“More aileron,” then push the aileron if hedoesn’t respond. Or your instructor may call out“Vertigo!” or initiate an incorrect recovery, ineither case requiring rapid intervention on yourpart. One example might be a pull wheninverted.

• If relevant, it’s important that all pilots in yourflight department discuss the results of this drillat the completion of the course, and the possible

changes or additions you might make to yourCRM procedures.

Procedures:

Ground Briefing: Students formulate a plan of response, listing potential unusual attitudes and potentialcontrol errors, plus appropriate pilot monitoring actions.

Instructor:Check: Seat belt, cockpit, instruments, altitude, outside.Places aircraft in an unusual attitude.Announces: “Now recovering.”Begins recovery.

Student:Monitors instructor’s recovery technique.Guards controls with hands against improper deflections.Verbally coaches best recovery.Takes control as required.




Flight Condition: Stick failure/loss of elevator, elevator trim, aileron.

Lesson: Re-establishing and evaluating control.

Flight Notes

This maneuver set assumes the loss of both primary longitudinal (elevator) and lateral (aileron) controlsystems. Below are the FAR Part 23 requirements concerning loss of primary controls. In this maneuver setyou’ll conduct, in essence, a FAR Part 23.145(e) and Part 23.147(c) flight test. The initial recovery from anose-high or nose-low bank angle would not be part of such a test. That’s ours. Attempting the procedurewithout elevator or trim is also ours.

FAR Part 23.145(e) By using normal flight and power controls, except as otherwise noted in paragraphs(e)(1) and (e)(2) of this section, it must be possible to establish a zero rate of descent at an attitude suitablefor a controlled landing without exceeding the operational and structural limitations of the airplane, asfollows:(1) For single-engine and multiengine airplanes, without the use of the primary longitudinal control system.(2) For multiengine airplanes --(i) Without the use of the primary directional control; and(ii) If a single failure of any one connecting or transmitting link would affect both the longitudinal anddirectional primary control system, without the primary longitudinal and directional control system.

FAR Part 23.147(c) For all airplanes, it must be shown that the airplane is safely controllable without theuse of the primary lateral control system in any all-engine configuration(s) and at any speed or altitudewithin the approved operating envelope. It must also be shown that the airplane's flight characteristics arenot impaired below a level needed to permit continued safe flight and the ability to maintain attitudessuitable for a controlled landing without exceeding the operational and structural limitations of the airplane.If a single failure of any one connecting or transmitting link in the lateral control system would also causethe loss of additional control system(s), compliance with the above requirement must be shown with thoseadditional systems also assumed to be inoperative.

Procedures:

Fly parallel to a ground reference line (simulated runway)..Instructor places aircraft in nose-high or nose-low bank angle.Student recovers and maintains control with rudder, elevator trim, and throttle only.Turn 180 degrees and descend over reference line.Establish landing attitude and a zero rate of descent at an altitude the instructor specifies.

Repeat without elevator trim.



Observations:

1. Using rudder, how aggressively should you bank the aircraft?

Does a phugoid appear during the turn?How much altitude is lost after turning if you can’t trim?

2. Do the flaps produce a pitching moment that can be easily trimmed?

3. Do flaps affect the ability to turn using rudder (diminished dihedral effect)?

4. With the aircraft at a given trim state, gear down, what power settings are necessary for:

Level flight?Positive rate of climb at moderate pitch attitude?Controlled descent along a standard glide path?

5. Without trim available, can you achieve a landing attitude using power and/or flap deployment?

• FAR Part 23.145(e) assumes that the power andtrim systems are available. It doesn’t require thetest pilot to complete an actual landing. Flyingwithout elevator but with trim in a more-or-lessnormal fashion presupposes that the elevatorfloats free, as it might with a broken cable. Ajammed elevator is rotten news, even if it jams ata favorable angle. With the elevator frozen andtrim tabs operating, trim input will reverse (nose-up trim will produce a nose-down pitch moment,for example). But don’t expect a trim tab to be aneffective longitudinal control under theseconditions. They’re designed to generate enoughmoment to deflect the elevator, not pitch theaircraft.

• Without the stick for primary longitudinal andlateral control, and without elevator trim, thephugoid suddenly becomes your constant pal.You’ll provoke a phugoid every time you bankusing rudder. It’s difficult to damp a phugoidwith power, but you should try during thisexercise, just to see. Without trim control, yourbest policy is to ride the phugoid out. An aircraftat an aft c.g. may have a neutral or a divergentphugoid, however.

• Without primary controls, a long, stabilizedfinal approach is absolutely essential. Withoutprimary longitudinal and trim control, you’restuck with an approach speed according to theaircraft’s trim state. Manipulate the glide pathwith power. Find a long runway, into the wind!



18. Spins

Flight Condition: High angle of attack plus roll due to sideslip and yaw rate.(α + Clβ + Clr)

Lesson: Departures and recoveries.

Entry Procedures:

1. Basic spin entry: 4,000 feet agl.

Rudder and elevator trim to neutral. Mixture rich. Power idle. Back stick for standard 1-knot-per-second deceleration. Ailerons neutral. Full rudder in desired spin direction at buffet onset. Stick full back.

2. Nose-high, yaw-rate entry:4,000 agl.Cruise power.Hold steep climb attitude, rudder free.Allow propeller effects to yaw aircraft to the left.Back stick until stall/spin break.

3. Skidding-turn-to-final entry:4,000 feet agl.

Rudder and elevator trim to neutral.Mixture rich.

12 inches manifold pressure or as required.Begin skidding turn with rudder.Hold wings level with aileron.Apply back stick until stall/spin break.

Experiment with power to determine propeller effects.

Apply sudden aileron toward the direction of the turn while holding rudder and elevator.

4. “Lazy-eight” departure/recovery drill:Linked opposite-side half-turn spin departures and recoveries.

PARE Recovery Procedure: Power as spin state requires. Ailerons neutral. Rudder full opposite rotation. Elevator forward to neutral or past neutral according to AFM or POH. Recover from dive with rudder neutral.



Flight Notes

Spins have become a culminating skill in wide-envelope stick-and-rudder airmanship. In earlier days, undera different training philosophy, they were a pre-solo foundation skill. Pilots—and also aircraft—aredifferent today as a result of this fundamental shift. The ground school text contains extensive material onspin procedures and theory. We review the PARE recovery technique here.

Power to idle. (Reduces propeller gyroscopiceffects and slipstream-induced yaw.)

Ailerons neutral. (Removes any inadvertentdeflection that may delay recovery. In afuselage-loaded aircraft the ailerons go towardthe spin direction to produce an anti-spin inertiamoment in yaw.)

Rudder opposite yaw direction. (Provides anti-spin aerodynamic yaw moment.)

Elevator forward to neutral or past neutral.(Unstalls the wings; for wing-loaded aircraftgenerates anti-spin inertia moment in yaw.)

When the spin stops, pull out with the rudderneutral. (If recovery rudder is still deflected andyou pull too hard, the aircraft can snap roll into aspin going the opposite way. Holding recoveryrudder is a common mistake.)

• Power to idle depends on spin state. It’s alreadyat idle in a practice spin. For an immediaterecovery from a stall/spin break, power canusually be left on in a single-engine trainingaircraft, and brought back as necessary for speedcontrol in the pull out from the dive. (A proptwin on one engine requires immediate power toidle on the operating engine, since the slipstreamproduces both rolling and yawing moments inthe direction of the dead engine. Most bets areoff in twins, however, because no spin testing isrequired for certification.)

• The PARE sequence comes from certificationdemonstration requirements that assume spinrecovery will only begin after a certain time ornumber of turns, depending on aircraft category,and not immediately after the stall/spin break.

Recovery inputs immediately following thebreak may be less critical (but not always).

• Note that in the PARE sequence, oppositerudder precedes forward stick. Forward stickapplied before opposite rudder can accelerate thespin through aircraft gyroscopic effects, and canalso cause the elevator to block the airflow to therudder in some aircraft, each of which delaysrecovery. The acceleration isn’t necessarily thecase in an immediate recovery right afterdeparture, however, as we’ll demonstrate anddiscuss. In our trainers the roll acceleration ondeparture is initially high; then the yaw ratepicks up. As a result, angular momentum isgreater in roll initially than in yaw. Pushing thestick forward causes gyroscopic precessionaround the roll axis that leads to an anti-spinmoment in yaw. Plus, pushing gets the angle ofattack back down. But once the aircraft’s yawrate and angular momentum about the yaw axishave begun to build, forward stick will causemomentary gyroscopic acceleration in roll, evenwhen it follows the rudder in proper sequence.Our introductory spins will go at least to thepoint where you can begin to feel the “pushback”—the increase in pressure needed to bringthe stick forward for recovery as angularmomentum picks up in yaw and the aircraftbecomes increasingly resistant to displacement,and also experience the momentary rollacceleration. It’s important to observe thesecharacteristics and to recognize them as normal.One to one-and-a-half turns before initiatingrecovery will accomplish this in our aircraft.Multiple-turn spins beyond that have dubiousvalue in introductory training. In the beginningit’s better to go for lots of entries and recoveries,do a careful analysis each time, and not wastetraining time recovering large chunks of altitude.

• As part of the analysis, after each spin try todescribe the aircraft’s motions to your instructor.



You may find post-stall spin behavior difficult tofollow at first, especially if your attention isoccupied with remembering the recovery stepsand wondering if they’ll actually work. Butreport each time. The task helps build trackingskills and confidence, and keeps the instructorupdated on your progress.

• The infamous skidding-turn-to-final spin (spinentry 3) will produce a departure in someaircraft, while others are resistant (too muchdirectional stability for the available rudderpower; too little elevator power). Some will do itengine power off; some need a boost in yaw andpitch from the slipstream hitting the stabilizerand tail. The slipstream increases the upwash onthe left wing, which then operates at a higherangle of attack and in a left turn stalls first.Spiraling slipstream also encourages a departureto the left. Frankly, a high-α skidding turn ishard to imagine from a properly trainedpilot—the necessary control forces ought to warnthe pilot off. But what about after an enginefailure in an aircraft with a departure-pronewing, or when some other distraction arises? Atlow altitude and low speed, no matter how goodthe pilot, if obstacles are approaching it will behard to resist the impulse to rudder rather thanbank the airplane. If the pilot then pulls up thenose—there’s your spin.

• In the Zlin, and quite probably in many otheraircraft, a rapid reversal of the ailerons towardthe turn direction, while in-turn rudder and backstick are still being held, can cause a departure.When the opposite aileron is removed, theaircraft rolls and yaws suddenly in the directionof the skidding turn, and enters a spin. This mayin fact be the true cause of many skidding-turn-to-final accidents. The pilot suddenly realized hiserror, but corrected with aileron alone.

• The fourth spin exercise is based on the lazy-eight. It’s done back and forth across a referenceline on the ground. Each reversal of direction isaccomplished as a spin departure, followed by arecovery to the half-turn point. Then you addpower and pull up across the line, then cut powerand spin a half turn to the opposite side. Next, gothe other way. Your feet and hands are busydeparting and recovering; you have to maintainorientation with the ground and stay well ahead

of the aircraft to do the maneuver smoothly. Ifyou can do all this, you’re definitely a hot stick!

• The pull up when the spin stops is full ofimportant lessons. Depending on when in thespin the recovery was introduced, and whetherthe pilot as forgotten to neutralize the rudder(holding recovery rudder too long is a universalbeginner’s mistake), the aircraft may end up in asideslip, and may roll rather than raise its nosewhen the pilot applies back stick. Or, even if thepilot uses the rudder correctly, but pulls too hardbefore the aircraft has gained sufficient speed,the aircraft may enter the buffet and lose nose-uppitch authority. Remember this: When you see asubstantial increase in pitch rate at low speed,the buffet won’t be far behind. If you penetratethe buffet too far, nose-up pitch authority maylargely disappear! Ease off.

Bill Crawford: WWW.FLIGHTLAB.NET

Flightlab Ground School Texts

This material supplements the practical demonstrations given during the training flights. It’s useful inpreparing for the course (especially 1-4, 8, and 10 if applicable) and for follow-up reading.

1. Axes and Derivatives(Descriptive concepts, vectors, moments, cause and effect)

2. Two-Dimensional Aerodynamics

(Lift and stall fundamentals: pressure, boundary layer, circulation)

3. Three-Dimensional Aerodynamics(How wing planform affects stall behavior)

4. Lateral-Directional Stability(Sideslips, yaw/roll coupling, straight and swept-wing dihedral effect, Dutch roll)

5. Longitudinal Static Stability(Aircraft in trim, pitch control forces in 1-g flight)

6. Longitudinal Maneuvering Stability(Pulling g)

7. Longitudinal Dynamic Stability(Oscillations in pitch)

8. Maneuvering Loads, High-G Maneuvers(V-n diagram, corner speed, radial g)

9. Rolling Dynamics(Roll performance, adverse yaw, coordination)

10. Spins(History, spin phases, momentum effects, recovery)

11. Some Differences Between Prop Trainers and Passenger Jets(Differences in control and response)

12. Vortex Wake Turbulence(Aircraft/vortex flow field interaction)

13. A Selective Summary of Certification Requirements(What the regulations say about aircraft stability and control)

Bill Crawford: WWW.FLIGHTLAB.NET

Flightlab Ground School1. Axes and Derivatives


Introduction

If you didn’t much care for symbols, formulas,and coefficients back in primary ground school,the following may raise warning signals. Ignorethem and don’t be a wimp. You’ll want tounderstand the axis system and also to take alook at the tables of aerodynamic derivatives(which we’ll review in person, as well). Thederivatives break aircraft behavior down to causeand effect, giving the engineers lots to calculateand giving us the terms needed to evaluateaircraft in an informed, qualitative way—a waythat links the demands of airmanship to thespecific personalities of our machines.

Aircraft Axes

The dashed lines in Figure 1 describe anaircraft’s x-y-z fixed body axes, emanating fromthe center of gravity. This system, with themutually perpendicular axes in fixed reference tothe aircraft, is the one most pilots recognize. Theexact alignment is a bit arbitrary. Boeing sets thex-axis parallel to the floorboards in its aircraft.

The geometrical plane that intersects both the xand z body axes is called the plane of symmetry,since a standard aircraft layout is symmetricalleft and right (Figure 1, bottom).

There are alternative axis systems (zero-lift bodyaxis, stability axis, for example). For pilots, thewind axis system is the most useful, because itbest helps in visualizing how aircraft actuallybehave.

+ up

+ right

Z wind axis

+ right

Lift Vector

α

Figure 1Aircraft Axes

X wind axis, VelocityVector

For the aircraft below, the x-zplane (plane of symmetry) is thesurface of the paper.

x

X body axis“Roll axis”

Y body axis“Pitch axis”

Z body axis“Yaw axis” z

Axes and Derivatives

Bill Crawford: WWW.FLIGHTLAB.NET1.2

The wind axis system sets the x-axis inalignment with the aircraft’s velocity vector,which points in the direction in which the aircraftis actually moving. Usually the velocityvector/wind axis lies on the aircraft’s plane ofsymmetry, but not always. If the aircraft is in asideslip, the velocity vector moves off the planeto some sideslip angle, β (“beta”), as Figure 2illustrates.

The velocity vector also changes direction whenaircraft angle of attack, α (“alpha”), changes.

The velocity vector is projected onto the x-zplane of symmetry for measuring α, and onto thex-y plane for measuring β. Thus it contains bothα and β, as the bottom of Figure 2 shows.

Both the y and z wind axes remain perpendicularto the x wind axis (and to one another). So, asthe velocity vector changes direction, these axeschange orientation, as well. Thus they’re carriedalong by the aircraft, but not “fixed.”

Here’s the essence of why the velocity vector isimportant to pilots: Much of aircraft response ispinned to it, both during normal flight and inunusual attitudes.

Laterally and directionally stable aircraftnormally tend to roll away from, but yawtoward, the velocity vector when the vector isoff the plane of symmetry. Unstable aircraft lackthese instincts, or lack them in propercombination.

In addition, a trimmed, longitudinally stableaircraft tends to hold the velocity vector at aconstant angle of attack, unless commandedotherwise. An unstable aircraft does not.

Aerodynamically stable aircraft tend to roll,pitch, and yaw around their respective windaxes—not around their fixed body axes, as mostpilots are taught. The picture becomes morecomplicated when those axes then begin tochange their direction in space,1 but a simplifiednotion of wind axis rotation is often helpful invisualizing maneuvering flight.

1 Kalviste, J., “Spherical Mapping and Analysisof Aircraft Angles for Maneuvering Flight,”AIAA-86-2283.

There’s another axis system, based on theaircraft’s distribution of mass: the inertia (orprincipal) axis system. The moments of inertiaabout the three, mutually perpendicular, principalaxes determine how quickly rates of roll, pitchand yaw can change around the aircraft’s centerof gravity. (For example, an aircraft with tiptanks has more x-axis roll inertia when the tanksare full than when empty, and for a givenairspeed, altitude, and aileron deflection will takelonger to achieve a roll rate. It will also takelonger to stop rolling.) The principal axes are thelines around which mass is symmetricallyarranged. They may not always be shown ascoincident with the aircraft fixed bodyaxes—although, because aircraft are essentiallysymmetrical, they’re often close enough to beconsidered as such. Differences in moments ofinertia around each axis can lead to variouscoupling effects. We’ll leave the details until ourdiscussion of spins.

Stabilizing yawmoment

Y bodyaxis

Velocity Vector

Plane of symmetry,x-z, viewed onedge

β

Velocityvector

α

z bodyaxis

x body axis

βV

X Figure 2Sideslip Angle, β

The x-y plane isthe surface of thepaper.

Y wind axis

x-z plane

x-y plane


Bill Crawford: WWW.FLIGHTLAB.NET 1.3

Lift Vector

A directionally stable aircraft returns the velocityvector to the plane of symmetry if the vectorbecomes displaced to some sideslip angle, β (asthe “stabilizing yaw moment” is doing in Figure2). In coordinated flight, the velocity vector lieson the plane of symmetry, as does the liftvector.

As illustrated in Figure 1, the lift vector is theupward projection of the z wind axis. Since lift isperpendicular to the air stream generated by theaircraft’s velocity, it makes sense to think of itsvector in wind axis terms. Fighter pilots talkcryptically of keeping the lift vector on thebogey, while an instructor might direct aninverted-attitude recovery by saying “roll the liftvector toward the sky.” They generally mean afixed vector perpendicular to thewingspan—bolted on, figuratively speaking.That’s sufficient and appropriate most of thetime. The direction relative to the horizon of thelift vector so defined has a profound effect on anaircraft’s maneuvering performance (see theground school text “Maneuvering Loads, High-G Maneuvers”), but it’s also possible to considerthe lift vector as free to rotate around the x-axis,as it does in uncoordinated flight. For example, ifa pilot uses top rudder (fuselage lift) to keep thenose up during a steep bank, the lift vector willtilt toward the high wing. Sometimes it’s usefulto think of the lift vector as staying oriented inspace while the aircraft rotates beneath it, as itdoes, essentially at least, during a properly flown“slow” roll. Halfway through the slow roll, when

the pilot pushes on the stick and the aircraft isproducing lift inverted, the lift vector pointsheavenward, as it does normally, but now pokingout the belly. At each knife-edge, when thewings are unloaded and the pilot presses toprudder so that the fuselage is used briefly for lift,the vector still points heavenward, but out theside. We’ll refer to a fixed or free lift vector, asthe situation requires.

Signs, Moments, Symbols

In the sign system used with the axis notation,positive values are in the direction shown by thecurved arrows in Figure 1, negative values areopposite. For example, when you pull the stickback and add left aileron, you’re generating apositive pitching moment and a negative rollingmoment (therefore a positive pitch rate andangle, and a negative roll rate and angle). Thesigns are not related to the aircraft’s attituderelative to the earth or to the pull of gravity.

A moment is a force producing rotation aroundan axis. An aerodynamic moment is the productof a force acting on a surface—say the center ofpressure of a vertical stabilizer with a deflectedrudder—times the perpendicular distance fromthat surface to the respective axis—the z-axis fora deflected rudder. When an aircraft is inequilibrium about an axis, all the positive andnegative moments around the axis sum to zero.

We’ll often break down our training aircraft’sbehavior into its x-y-z, roll-pitch-yawcomponents. Changes in aircraft attitude orangular velocity (rotation rate) are the result of

Axis MomentApplied

Angular Velocity Angular position Moment ofInertia

Control Deflection

x l Roll rate, p Roll angle φ(phi)

IxxRoll Inertia

Aileron (δa)

y m Pitch rate, q Pitch angle θ(theta)

IyyPitch Inertia

Elevator (δe)

z n Yaw rate, r Yaw angle ψ(psi)

IzzYaw Inertia

Rudder (δr)



changes in moments applied around each axis.You already know the primary moments(ailerons produce rolling moments, elevatorspitching moments, rudders yawing moments),but there’s a further collection of direct andcross-coupled moments essential to aircraftcontrol and often complicit in unusual attitudes.We’ll talk about them on the ground and observethem in flight.

For reference, the table above shows notationsused for moments, angular velocities, angularpositions, moments of inertia, and controldeflections about each aircraft axis. You don’tneed to memorize any of this for our course, butyou might find it useful for future technicalreading. Notice the preference for arrangingthings by alphabetical order. Thus the lettersdon’t always mean what your mnemonicallyinclined brain would like them to mean (“r”doesn’t stand for roll rate; “p” doesn’t stand forpitch rate, and, while “L” stands for lift, alowercase “l” stands for roll moment).

Stability and Control Derivatives

Moments about the axes drive aircraft attitude.Stability is the tendency of an aircraft to generatethe aerodynamic moments necessary to return itto its original equilibrium, when disturbed.During unusual attitudes, if an aircraft is left toits hands-off free response, those same momentscan become destabilizing. At high bank angles,for example, directional stability (a yawingmoment) causes the nose to descend below thehorizon and speed to increase. When an aircraftis inverted, longitudinal stability (a pitchingmoment) causes the nose to fall below thehorizon, as well. And at angles of attack paststall, rolling moments that would ordinarilydamp out can instead produce autorotation andspin departure.

In normal maneuvering in a stable aircraft, apilot uses the controls to overcome the aircraft’sstabilizing moments and to establish a newequilibrium, at least temporarily. This may beeasy or not so easy, depending on the degree ofinherent stability and the availability of controlpower to do the job

Stability and control are measured in terms ofderivatives—the rate of change of one variablewith change in another. During our flights,especially early on, we’re going to see how the

rates of change of moments in pitch, roll, andyaw can vary with angle of attack, sideslip angle,the presence of aerodynamic and/or inertialcouples, control deflections, and with airspeed.The derivatives in the tables that follow form thebasic vocabulary of cause and effect that we’llapply in analyzing departure modes and inlearning to recover from unusual attitudes. Somewill be new to you (as perhaps all the symbols),and some you’ll remember, at least in generalterms, from the days of primary ground school.Don’t worry about learning the symbols. We’llrefer to things by name.

Initially, you might want to review thedescriptions—which are by necessitycondensed—and then refer to the FlightlabGround School texts for more explanation. We’llalso brief the material before flying. Don’t feelresponsible for immediately understanding all ofthe bulleted items. You’ll get there in stages.Top priority goes to acquiring new flying skills.

A note on signs: The derivatives carry signs thatmight be confusing at first. A negative (–) signdoesn’t indicate the lack of stability, but ratherhelps determine the direction of response.Review the sign system used with the axisnotation in Figure 1. Then, in the derivativetable, note for example that Clβ, the lateralstability derivative, carries a negative sign. Whena laterally stable aircraft slips to the right(positive direction) it will roll to the left(negative direction). Algebraically, a negative(the derivative) times a positive (sideslipdirection) equals a negative (roll direction). If theaircraft slips to the left, it will roll to the right,since a negative derivative times a negativedirection equals a positive. For us, the signs willcome in handy when analyzing spins, where theysimplify the perplexity inherent in understandinga flight regime where an input in one axis canproduce an output in another.

The flow chart at the end of this section shows arelated way of describing the basics of aircraftresponse.



Selected Aerodynamic Derivatives for Roll

AerodynamicStabilityDerivativeSymbol

Name Description

-Clβ

C = coefficientl = roll momentβ = sideslip angle

Rolling momentdue to sideslip.

(Lateral stabilityproduced by

dihedral effect)

Aircraft rolls away from the direction of sideslip. Main causes aregeometrical dihedral and/or wing sweep, and fuselage-induced airflowchanges that place the wings at different angles of attack.

• Roll due to sideslip is proportional to sideslip angle, β, andto the coefficient of lift, CL, up to the stall, but may varyafterwards.

• Roll rate commanded by aileron/spoilers is affected bysideslip angle and direction.

• Wingtip washout, and/or flap deployment, reduce Clβ .• Depends on wing position relative to fuselage.• Decreased by wing taper and low aspect ratio

(wingspan2/wing area)-Clp

l = roll momentp = roll rate

Rolling momentdue to roll rate.(Roll damping)

As an aircraft rolls in response to a disturbance, the angle of attackincreases on the down-going wing and decreases on the up-going wing.The resulting change in lift produces an opposing rolling moment. Theaircraft stops rolling. If the pilot holds aileron deflection, roll dampingmoment builds until it’s equal to the opposing moment produced by theaileron deflection. Roll rate then becomes constant.

• Roll damping disappears on wing sections at stall;autorotation is the reversal of roll damping.

• Damping increases with the slope of the CL curve.• Reduced by low aspect ratios and/or wing taper.• Roll damping decreases with altitude.

+Clr

l = roll momentr = yaw rate

Rolling momentdue to yaw rate.

Yaw rate causes airflow velocity to increase on the advancing wing anddecrease on the retreating wing, causing a spanwise change in lift and arolling moment.

• The effect follows the lift curve, becoming greatest at CLmaxand then falling off after the stall. (Clr = approx. CL/4).

• Rolling moment due to yaw rate contributes to spiralinstability and to spin departure.

• When entering a sideslip, rolling moments due to thetemporary yaw rate and the growing sideslip angle areadditive.

• Wingtip washout, and/or flap deployment, reduces Clr .• Little affected by wing position on fuselage.• Increases with aspect ratio, decreases with wing taper.• Varies with the square of the difference in tip speed (since

lift varies with V2).



Selected Aerodynamic Derivatives for Yaw


Name Description

+Cnβ

n = yaw momentβ = sideslipangle

Yawing momentdue to sideslip.

(Directionalstability)

Also known as weathercock stability. Aircraft yaws toward the directionof sideslip to align the longitudinal, x-axis with the relative wind.

• The fuselage alone is usually destabilizing; principal stabilitycontribution comes from vertical tail, although swept wingsare stabilizing, an effect that increases with CL.

• Spiral instability occurs when directional stability is high andlateral stability is low.

• Low directional stability and high lateral stability promotesDutch roll.

-Cnp

n = yaw momentp = roll rate

Yawing momentdue to roll rate.

The induced change in angle of attack on a rolling wing causes the liftvector to tilt back on the wing going up, and forward on the wing goingdown. This adds components of thrust and drag, which produce a yawingmoment opposite the direction of roll (similar to adverse aileron yaw).

• Increases with aspect ratio, roll rate.• Increases with CL.• Wingtip washout, and/or flap deployment, reduces Cnp .

• Largely independent of taper.• (Cnp = approx. CL/8).

• Reverses effect when the wing goes into autorotation.

-Cnr

n = yaw momentr = yaw rate

Yawing momentdue to yaw rate.(Yaw damping)

When an aircraft has a yaw rate, opposing aerodynamic damping forcesbuild up ahead and behind the center of gravity.

• Main contribution comes from the vertical tail, but theforward fuselage can also contribute (unlike Cnβ , in which

the fuselage forward of the wing is destabilizing).• Wings also contribute, since the advancing wing produces

more induced and profile drag than the retreating wing.• Wing contribution to yaw damping increases with angle of

attack; the tail’s contribution may decrease due to disruptedairflow at high α.

• Yaw damping decreases with altitude.



Rudder/Aileron Cross Derivatives

Pitch Damping

ControlDerivativeSymbol

Name Description

Clδr

l = roll momentδ = deflectionr = rudder

Rolling momentdue to rudder

deflection.

A roll moment is produced if the lift generated by rudder deflection acts ata point above the roll axis. Right rudder, for example, produces a leftrolling moment. This can become apparent in aircraft without dihedraleffect.

• Diminishes as angle of attack increases.

Cnδa

n = yaw momentδ = deflectiona = aileron

Yawing momentdue to aileron

deflection.(Adverse yaw)

An aileron deflected down creates more induced drag than the oppositeaileron deflected up. The result is a yawing moment opposite the directionof bank. Profile drag increases on both wings when the ailerons aredeflected, the difference depending on aileron design.

• Adverse yaw increases with wing angle of attack, because dragrises faster than lift at high α.

• Spoilers for roll control can produce proverse yaw.• Differential ailerons or Frise ailerons counteract adverse yaw

with opposing drag—although their primary function is to loweraileron control force.


Name Description

Cmq

m = pitchingmomentq = pitch rate

Pitching momentdue to pitch rate.(Pitch damping)

When aircraft pitches up or down, the motion of the horizontal stabilizercauses a change in the stabilizer’s angle of attack, which generates anopposing, or damping, pitching moment.

• Pitch-damping moment increases with pitch rate (and thus with gload).

• Pitching moment due to pitch rate affects short-period responseand stick force per g in pull-ups and turns.

• Pitch damping decreases with altitude.• Pitch damping increases with increased distance between the

horizontal stabilizer and the aircraft c.g.



Directional stability(weathercock)

Aileron adverseyaw

Asymmetrical Thrust

CnYawing

Momentsaround z-axis

PrimaryControl:Rudder

Increaseswith β

Spiralingslipstream

Dihedral effect(lateral stability)

Roll due to yawrate

(spiral instability)

Geometricdihedral

Vertical tailsideforce

Wing sweep

ClRolling

Momentsaround x-axis

PrimaryControl:Aileron

Increaseswith α and

β

Increaseswith α ,yaw rate

Increaseswith a

Roll rate goes up directlywith airspeed (EAS). Stickforce goes up with airspeedsquared.

α = angle ofattackβ = sideslipangle

Decreaseswith α

Increaseswith a as

aircraftslows

Roll dampingIncreases

with roll rate,reverses

after CLmax

Propeller gyroscopics

Pitch rateproducesyawingmoment

Propeller gyroscopics

Trim setting

Flap setting

Power

CmPitchingMomentsaround y-axis

PrimaryControl:Elevator

Thrust linevs center of

gravity

Yaw rateproducespitchingmoment

Control Deflection,Pilot-Generated

Moments

Aerodynamic,Aircraft-Generated

Moments

Yaw dampingIncreaseswith yaw

rate

Pitch dampingIncreaseswith pitch

rate

Camberchange vsdownwash

at tail

C.G.location vs

Cm/α

Aileron, elevator, ruddercontrol force harmonyapproximatly 1:2:4


Flightlab Ground School2. Two-Dimensional Aerodynamics


Our Plan for Stall Demonstrations

We’ll do a stall series at the beginning of ourfirst flight, and tuft the trainer’s wing with yarnbefore we go. The tufts show complex airflowand are truly fun to watch. You’ll first see thetufts near the root trailing edge begin to wiggleand then actually reverse direction as the adversepressure gradient grows and the boundary layerseparates from the wing. The disturbance willwork its way up the chord. You’ll also see themovement of the tufts spread toward thewingtips. This spanwise movement can bemodified in a number of ways, but dependsprimarily on planform (wing shape as seen fromabove). Spanwise characteristics have importantimplications for lateral control at high angles ofattack, and thus for recovery from unusualattitudes entered from stalls. Our rectangular-planform trainers have excellent stallcharacteristics. Other planforms may need to becajoled into behaving as if they were rectangular,stalling first at the root while the ailerons keepflying.

We’ll first examine two-dimensional airfoilsections, then three-dimensional wing planforms.We’ll only spend a few minutes during ourflights watching the wing tufts, but those minutescan be full of information.

Remember Mass Flow?

Remember the illustration of the venturi fromyour student pilot days (like Figure 1)? Themajor idea is that the flow in the venturiincreases in velocity as it passes through thenarrows.

The Law of Conservation of Mass operates here:The mass you send into the venturi over a givenunit of time has to equal the mass that comes outover the same time (mass can’t be destroyed).This can only happen if the velocity increaseswhen the cross section decreases. The velocity isin fact inversely proportional to the cross sectionarea. So if you reduce the cross section area ofthe narrowest part of the venturi to half that ofthe opening, for example, the velocity mustdouble at that point.

For a fluid (like air), the density, ρ, times thecross section area, A, of the venturi times thevelocity, V, equals the mass airflow. Massairflow, in and out, remains constant, so:

ρAV = Constant

The above is known as the continuity equation.

Density (denoted by the Greek letter ρ,pronounced “roh”) is the mass of air (in slugs)per volume (one cubic foot). Air is consideredincompressible at the low, subsonic speeds wefly our trainers—so density doesn’t change forus, only velocity.

Figure 1 Velocity in a Venturi

Arrow length indicates velocity. Velocity actually starts rising before air enters the venturi.

(ρAV)A = (ρAV)B = (ρAV)C = constant

A B C

Two-Dimensional Aerodynamics


Remember Bernoulli?

Bernoulli’s Theorem deals with conservation ofenergy. It tells us that for an ideal fluid(incompressible and frictionless) the total energyof the flow in the venturi remains constant. If weconvert the total energy per unit volume of masstimes flow rate into pressures, the sum of thestatic pressure and the dynamic pressure willequal a constant total pressure. Static pressure isthe ambient pressure exerted by a column offluid at a given level. Dynamic pressure is thepressure exerted by a mass of fluid in motion. Inthe formula below, static pressure is PS. Dynamicpressure is 1/2 ρV2, or one-half the density, ρ, ofthe fluid times its velocity, in feet-per-second,squared. PT is the total pressure:

PS + 1/2 ρV2 = Constant PT

Or in English:

Static pressure + Dynamic pressure = Constant TotalPressure

So if velocity and thus dynamic pressureincreases, static pressure will decrease. In theventuri in Figure 2, the increase in dynamicpressure with velocity produces a decrease instatic pressure as the tube narrows. The staticpressure then rises again as the tube widensdownstream and the airflow slows down.

Of course, air isn’t an ideal fluid: It’scompressible and viscous. Compressibility

obviously becomes important approaching thespeed of sound, but for present purposes can beignored. But we won’t ignore viscosity for long,because the nature of the airflow within theboundary layer over a wing depends on friction.

After looking at the behavior of velocity andpressure in a venturi, it’s tempting to declare thatthe reason airflow accelerates over the top of awing, and static pressure consequently decreases,is that a wing is just one half of a venturi, withthe mass of the atmosphere playing a rollequivalent to the other half. That’s a valid wayof thinking about it, and easy to visualize. Butaerodynamics is a subject in which alternativevisualizations exist side-by-side. A different butnot necessarily contradictory understanding ofthe acceleration of flow has to do with the ideaof circulation. Circulation in turn gives us a wayof visualizing the generation of wingtip vortices,and understanding how the strength of thevortical flow relates to the particular conditionsunder which the wing was producing lift. We’llreturn to this farther on.

Figure 2 Pressure Decreases as Velocity Increases

Longer arrows indicate greater pressure drop relative to the freestream.

Pressure rise



Streamlines

An airfoil section is equivalent to a hypotheticalwing of infinite span (therefore no tips) or to awing model in a wind tunnel, when the modelextends right to the tunnel walls. Because of theabsence of the spanwise flow induced by thepresence of wingtips, no tip vortex and novariations in downwash behind the wing occur.A two-dimensional representation is all you needto depict what’s happening.

The streamlines generated by injecting smokeinto a wind tunnel, or calculated in a computersimulation (Figure 3), allow us to visualize notjust the direction of flow around a wing, but alsoits velocity and pressure. The flow direction atany instant or point along a streamline is alwaystangential to the line. An important feature ofstreamlines is that air particles never cross them;adjacent pairs of streamlines thus behave like thewalls of a flexible tube. When the flowaccelerates, the resulting decrease in staticpressure within them causes the streamtubes tocontract, and the streamlines move closertogether. The distance between streamlines isthus an indication of relative velocity and static

pressure. Notice in the figure how thestreamtubes passing over the leading edgecontract, indicating an accelerating flow and apressure decrease. As they move down the wingthey expand, indicating a decelerating airflowand a pressure rise. This is shown in closer detailin Figure 5.

Note the upwash in the airflow ahead of thewing, and the downwash behind. In the two-dimensional case illustrated, the upwash anddownwash angles are equal. In the three-dimensional case of a finite wing, the tip vortexcan add significantly to the downwash behindthe wing, as we’ll see later.

Upwash ahead of wing

Downwash behind wing

Streamlines move closer together as flow accelerates and static pressure decreases.

Figure 3 Streamlines Upwash/Downwash

Streamlines move apart as flow decelerates and static pressure increases.



Pressure Distribution

Figure 4 shows the surface pressure distributionalong an airfoil section at three different anglesof attack. The longer arrows representincreasingly higher or lower static pressures, asindicated, relative to the static pressure of thefreestream, undisturbed air ahead of the section.The velocity over the forward, upper part of thewing increases as the angle of attack increases,resulting in a greater decrease in local staticpressure, as well as a shifting of the pressurepattern. The illustrations show how the point oflowest static pressure (longest arrow) movesforward as angle of attack, α, increases.

Notice that at low α (as in the top illustration)the static pressure can drop below freestreamunder the wing as well as above. Lift results aslong as the overall reduction in pressure abovethe wing is greater.

NACA 2412 4 Deg. Angle ofAttack

NACA 241212 Deg. Angleof Attack

Decreasedpressure

Decreasedpressure

NACA 24120.3 Deg. Angleof Attack

Figure 4Pressure Distributionversus Angle of Attack

Increased pressure



Figure 5 illustrates streamlines and surfacepressures together. Pressure is highest at thestagnation point (where it equals static plusdynamic pressure). Here airflow comes to a stop,and the streamlines split on either side to followeither the upper or lower surface. (Stagnationpressure is what the pitot tube senses. The staticside of the pitot system eliminates the staticcomponent, and the remaining dynamic pressureappears as an airspeed indication.)

The low pressure generated by the accelerationof the flow over the leading edge creates asuction that draws the airflow forward from thestagnation point—against the general, leading-to-trailing-edge flow. Below stall, any increase in αfurther accelerates the upper-surface flow andfurther decreases the pressure around the leadingedge. Because the increasing suction pullsadditional lower-surface air forward, thestagnation point actually moves aft along thelower surface as α increases. It also moves aftwhen you extend the flaps or deflect an ailerondown.

Stagnation point

Leading edge streamlines and surface pressures of NACA 2412 at 12 Deg. Angle of Attack. Arrows pointing away from surface show relative pressure drop. (The scale is reduced compared to the earlier figures to make the arrows fit the frame. Arrows pointing toward surface show pressure increase.

Figure 5 Streamlines and Surface Pressures



Pressure Gradient

Air flowing over the top of the wing initiallymoves through an area of decreasing staticpressure (Figure 6). Since higher pressures flowtoward lower, this favorable pressure gradientencourages the airflow. But once past the pointof highest velocity and lowest static pressure onthe airfoil, local static pressures begin to rise(although still remain negative) and the pressuredistribution tends to retard the flow. This adversepressure gradient becomes steeper and occupiesmore of the airfoil as the angle of attack, α,increases and the low-pressure over the wingintensifies and shifts forward (Figure 7).

Figure 8 defines the concept of coefficient ofpressure, CP, and shows how its distributionchanges along the chord as α rises. Negativevalues mean local static pressures lower thanfreestream static pressure; positive values meanlocal static pressures higher than freestreamstatic. Note how the adverse gradient increasesover the top of the wing when α rises, asindicated by the increasing negative slope.

As α rises, the adverse gradient increasinglyretards the airflow within the boundary layer,until the boundary layer ultimately separatesfrom the surface, like a sheet blown away frombeneath (Figure 9). As adverse pressure rises theseparation point moves forward; lift drops andthe airfoil stalls.

CP = Local Static Surface Pressure – Freestream Static Pressure/Freestream Dynamic Pressure

5 Deg. AOA Top Pressure 1 Deg. AOA Top Pressure

1 Deg. AOA Bottom Pressure 5 Deg. AOA Bottom Pressure

CP –2.0

CP 0.0

CP +1.0

Leading Edge Trailing Edge

NACA 2412 Coefficient of Pressure, CP

Suction peak. Adverse gradient begins here.

Figure 8 Coefficient of Pressure, CP

Figure 6 Pressure Gradient

Favorable pressure Adverse pressure

Figure 7 Increase in Adverse Pressure with Angle of Attack


Adverse pressure gradient resists airflow.

Location of minimum static surface pressure

Figure 9 Separation

Boundary layer separation at stall

Adverse pressure strips the boundary layer from the wing.



Figure 10 Boundary Layer

NACA 2412

Transition from laminar to turbulent flow (separation bubble) is approximately here at a 2 deg. AOA for NACA 2412. Transition point will move forward as AOA increases.

Boundary layer thickness exaggerated. Thickness is about 1% of distance traveled. The point of boundary layer separation moves forward

as AOA increases.

Separation Point: Flow velocity reaches zero, then reverses direction and boundary layer separates from wing.

Turbulent boundary layer

Velocity profile

Laminar Boundary Layer: Laminar shear layers remain distinct, no intermixing.

Boundary Layer

In exaggerated scale, Figure 10 shows theregions of the boundary layer atop the wing, andthe changing velocity profile within theboundary layer, as indicated by the length of thearrows. In both the laminar and turbulentregions, the viscosity of air causes the particlesright next to the wing to come to a halt, due tofriction. Their velocity relative to the wing iszero. The particles flowing immediately aboveare slowed down almost to zero by friction, andthey in turn slow the particles above them.Initially, a profile of shear layers (lamina)develops, with the velocity of the layersincreasing with their distance from the surface asthe effect of friction diminishes. By definition,the boundary layer is the area from the surfaceout to the point where the flow reaches 99percent of the freestream velocity.

The viscous, frictional forces generated withinthe boundary layer are responsible for thecomponent of drag known as skin friction drag.Outside of the boundary layer, viscosity has noimportant effect when it comes to predictingairfoil characteristics.

The initial, laminar region of the boundary layeris very thin. The flow remains layered—there’sno interchange of fluid particles across thelamina. Moving downstream from the leading

edge, the laminar flow gains kinetic energy as itaccelerates through the favorable pressuregradient. The favorable gradient also helps dampout irregularities in the flow. But the flow beginsto slow as it enters the destabilizing resistance ofthe adverse gradient. The laminar boundary layerseparates from the wing, becomes turbulent, andthen reattaches, forming a separation bubble as itmakes the transition. Roughness on the wingsurface can cause the boundary layer to tripprematurely from laminar to turbulent flow.

Whether the laminar flow reattaches as turbulentflow depends on Reynolds number—on the ratioof the inertial forces to the viscous forces withinthe flow. Low Reynolds numbers are associatedwith laminar flow (viscous forces prevail), highReynolds numbers with turbulent flow (viscousforces unimportant, inertial forces dominant). Ifthe Reynolds number is too low, a detachedlaminar flow won’t reattach as turbulent flow.Up to a point, an airfoil produces highermaximum lift at higher Reynolds numbers,because the reattached turbulent flow can betterresist the adverse gradient and remain attached tothe wing at higher angles of attack. Wind tunneldata for airfoil sections often includes curves fordifferent Reynolds numbers and surface textures.(Reynolds number is more complicated, but theabove gives you a start if the concept is new.)



In Figure 11, you can see that the velocitygradient curve in the initial turbulent region(dashed line) starts out shallower than in thelaminar region, but as the curve rises becomessteeper and the boundary layer grows thicker.The turbulent boundary layer produces a lotmore drag than the laminar layer (laminar-flowwings achieve their low drag by moving thelowest pressure point farther back along thechord, thus extending the laminar region). On theother hand, a turbulent layer stays attached to thewing better than a laminar layer as angle ofattack rises, because the turbulence transferskinetic energy down to the surface, which helpsovercome the adverse pressure gradient. (Thisturbulent energy boost is the principle behindvortex generators. The vortices add energy to theflow, delaying separation caused by adversepressure.) Figure 10 shows how the velocityprofile of the turbulent boundary layer changesalong the wing chord as the retarding effects ofthe adverse gradient accumulate.

The tufts on the trainers can give you an idea ofhow the turbulent boundary layer increases inthickness. The tufts themselves would trip anylaminar to turbulent flow. At low angle of attackthe trailing tips of the first row of tufts should liefairly quietly against the surface of the wing, butby the second row the flow will have becomemore turbulent and the tips will shakeperceptibly. The tips will show increasingmovement, bouncing between the wing and thetop of the boundary layer, as you look fartherback along the chord. You can easily see how theboundary layer thickens as it goes downstream.

More important, the tufts show how flowreversal and turbulent boundary layer separationmove up the chord from the trailing edge. You’llbe able to see the effect of the adverse pressuregradient intensify as angle of attack rises. Theturbulent boundary layer’s separation point willmove forward along the chord and the tufts willreverse direction, the free ends actually pointingtoward the leading edge. The reversal of the tuftsin order back up the chord means that the wing isgenerating a larger and larger turbulent wake.Pressure drag is rising rapidly.

Laminar Boundary Layer Initial reattached

turbulent boundary layer, with higher velocity near the surface.

Intermixing in the turbulent boundary area brings high-kinetic-energy (high inertia) particles down toward the surface, increasing the boundary layer’s ability to overcome the adverse pressure gradient. Intermixing also sends low-energy (low inertia) particles up to the top, delaying the return to freestream velocity and causing the boundary layer to become thicker. The higher velocities closer to the surface increase friction in the turbulent boundary layer, and thus friction drag.

Turbulent mixing

Velocity

Thic

knes

s

Figure 11 Velocity Profiles

Adverse Pressure



The Lift Curve

Figures 12 and 13 show typical lift curves, whichplot angle of attack against coefficient of lift(CL). You may have grown accustomed to usingthe term coefficient of lift (or just as happy notusing it) without quite remembering how it’sderived. It’s just an indication of how efficientlyan airfoil shape turns dynamic pressure (definedearlier as one-half the density of the air timesvelocity squared: 1/2ρV2) into lift at any givenangle of attack. S stands for total wing area insquare feet. L stands for lift in pounds.

Looking at the formula, it’s clear that the morelift generated for a given combination ofdynamic pressure and wing area, the greater theCL. The formula for dynamic pressure istypically shortened to q, so that the abovebecomes:

You can determine q in the cockpit, in poundsper square foot, simply by multiplying the squareof the indicated airspeed in miles per hour by0.0025577. That’s q. Then multiply the result bythe wing area, found in the aircraft manual, anddivide the product into the aircraft weight (sincelift equals weight in equilibrium flight). Theresult is your current CL for the wing as a whole(the coefficient at a given section along the span,called Cl to make the distinction when necessary,is often different than that of the wing as awhole). At a constant IAS, your CL must slowlydecrease as you shed fuel weight and need lesslift. Any change in airspeed (thus in q) requires achange in CL for level flight.

It’s good aerodynamics, and good pilotingtechnique, never to think about lift without alsoconsidering its inevitable pal, drag. Substitutingdrag for lift, we derive the coefficient of drag,CD, just as above. D stands for drag in pounds:

In a lift curve, as in Figure 11, the coefficient oflift initially shows a linear increase with angle ofattack. A slope of about 0.1 in lift coefficientincrease for each degree increase in angle is

typical for all two-dimensional airfoil sectioncurves. Variations in slope come from planform,as we’ll see.

The curve begins to shallow and reverse asairflow separation occurs on the upper surface ofthe airfoil. The point where maximum CL versusα is reached (CLmax) marks the stalling angle ofattack.

At CLmax, depending on airfoil shape, airflowseparation may have already reached some 20 to50 percent of the chord. Notice that an airfoilwill still produce lift, and a lot more drag, evenpast the stalling angle of attack.

The airfoil in Figure 12 is symmetrical, andcharacteristically produces no net lift (and itsminimum drag) at zero angle of attack. Acambered airfoil, as in Figure 13, can producelift at small negative angles of attack. Its liftcurve shifts up and to the left (producing a higherCLmax), compared to a symmetrical airfoil’s. Thedrag curve shifts to the right.

- 0 Angle of Attack, α +

Figure 12 Symmetrical Airfoil

Coe

ffic

ient

s of L

ift a

nd D

rag

Symmetrical Airfoil

Cord line

CLmax

CD

CL

SV2/1LC

2Lρ

=

qSLCL =

qSDCD =

CL

CD


Figure 13 Cambered Airfoil

Coef

ficie

nts o

f Lift

and

Dra

g

Camber line

Lift due to AOA

Lift due to camber



Note how the rates of change in the lift and dragcurves vary with angle of attack. The lift curveshows a constant rate until near its peak, whenthe slope diminishes so that a given change inangle of attack produces a smaller change in lift.The drag curve is different. At low angles ofattack, drag doesn’t change much, but as theangle of attack approaches stall, drag increases atan accelerating rate. You learn this, at leastimplicitly, when you learn to land an airplane.The technique of balancing the rates of change oflift and drag at high angles of attack is one ofaviation’s foundation skills. The technique candepend on whether the wing is long or short,swept or straight, as we’ll note.

Airfoil thickness, the amount of camber andposition of maximum camber along the chord,the radius of the leading edge, plus Reynolds andMach numbers, are all factors that affect thevelocities and pressures and therefore theaerodynamic forces generated by an airfoil. Theyalso affect the characteristics of the boundarylayer, its profile and turbulent transition, and itsseparation from the wing at high angles of attack.

Increasing the camber of an airfoil increases itsCLmax. It also tends to increase the adversepressure gradient as angle of attack rises, whichin turn encourages earlier boundary layerseparation, making the section then stall at alower angle of attack, relative to one with lesscamber. A wing in which camber has beenincreased by lowering the flaps will stall at alower angle of attack (See Figure 17).

It’s usually best if the separation of the turbulentboundary layer from the wing surface movesslowly forward along the chord as angle of attackrises near the stall. This allows a relativelygradual, parabolic change in the slope of the liftcurve as the section approaches CLmax, andresults in less abrupt stall characteristics, betteropportunity for aerodynamic stall warning(which also depends on wing planform and taildesign), and less roll-off tendency if one wingstarts to stall before the other. (See Figures 14and 15.)

But abrupt turbulent boundary layer separation issometimes useful. Modern, high-performanceaerobatic wings often have large leading-edgeradii and then become flat from the point ofmaximum thickness back to the trailing edge.The profile of these “ice cream cone” wingsplaces the location of maximum thickness

forward on the chord, which limits the possibleregion of favorable pressure gradient and causesearly laminar-to-turbulent boundary layertransition. Compared to wings designed forbetter laminar flow, they tend toward higherdrag. Drag helps speed control in vertical downlines, but the major aerobatic benefit is thetendency for the stall separation point to remainnear the trailing edge as angle of attackincreases, and then suddenly to move forward upthe chord. This allows the wing to hold airflowattached during high-g maneuvers, but stallabruptly for quick snap roll, spin, and tumblingentries. Wing tufts show how rapidly theseparation point advances and how quickly thestall breaks, as you’ll see in our ground-schoolvideo.

- 0 Angle of Attack α +

Coe

ffic

ient

of L

ift

Stall Buffet/Warning Onset

Stall

Good stall warning margin, less potential roll-off

More gradual CL change with α

Figure 14 Gradual Stall



Leading-Edge Stall

A thin airfoil with a sharp leading edge radiuscan suffer sudden leading-edge stall (orsimultaneous leading-edge and trailing-edgestall) due to the sudden bursting of the leading-edge separation bubble. The bubble occurs wherethe laminar flow separates from the wing andreattaches as turbulent flow. As angle of attackrises, the bubble follows the suction peak (Figure8) forward. As the curvature of the wingincreases, the detached laminar flow can nolonger “make the turn” necessary to reattach asturbulent flow. The bubble bursts, causing rapid,complete boundary layer separation along theentire chord. This sharpens the peak of the liftcurve, with the result that, near stall, a smallchange in angle of attack produces a sudden dropin CL. This can lead to an abrupt stall withlimited or no aerodynamic warning, and to asudden roll-off when inevitable variations inwing surface or contour cause the separationbubble to burst on one wing ahead of the other.

Depending on how the airfoil section variesalong the span, it’s possible for one part of awing to have a trailing-edge stall, while anotherpart has a leading-edge stall, or demonstrates acombined leading-edge/trailing-edge stall.

Learjet wings built before the introduction of theCentury III wing section had roll-off problemsdue to asymmetrically bursting separationbubbles. A stick pusher was necessary to keepthe wing out of stall territory. In addition toadding inboard stall strips and stall fences,improving the pusher-off stall characteristicsinvolved breaking the bubble into stable,spanwise segments by mechanically tripping thelaminar flow with small triangular shapesattached to the outboard leading edge, ahead ofthe ailerons. Placed on the chord ahead of thenormal laminar separation point, the trianglescaused the flow to become turbulent andreattach, preventing a spanwise, continuousseparation bubble from forming and thus frombursting. This dramatically reduced roll-off atstall.

Separation bubble (greatly exaggerated) with circulating flow.

Bursting the separation bubble can cause leading edge stall and abrupt boundary layer separation.

- 0 Angle of Attack α +

Coe

ffic

ient

of L

ift

Rapid CL change with α. Poor stall warning and potential roll-off.

Figure 15 Abrupt Stall

Laminar flow separates.

Reattaches as turbulent flow.



Flaps

When you start to lower the flaps on our trainers,you’ll see the tufts begin to show airflowseparation along the trailing edge. The flapsincrease local wing camber, which adds a secondlow-pressure peak (as shown in Figure 16) and asteep adverse pressure gradient at the trailingedge. If you increase the flap deflection further,or increase angle of attack, the adverse gradientover the flap becomes more severe. Flowreversal and separation occur and the tufts startdancing.

By studying Figure 16 you’ll gain some insightinto how flaps (and ailerons and rudders) work.Fundamentally, they modify lift by changing thevelocity of the airflow. Notice how the increasein camber over the rear of the airfoil affects theoverall pressure pattern. Camber increases localflow velocity, which decreases local surfacestatic pressure. The result is a more favorablepressure gradient immediately forward of thedeflected surface, which in turn causes air toaccelerate over the wing ahead, resultingultimately in lower surface pressures at theleading edge. At the same time, airflow below

the wing slow down, resulting in higherpressures there. (Notice the rearward shift instagnation point that follows flap deployment.The flap-induced increase in leading-edgesuction pulls more air forward from beneath thewing, sending the stagnation point further aft.)

Figure 17 shows how the lift curve changes withflaps of different types. The Fowler flap is themost efficient because it produces the greatestincrement in lift with the least increment in drag.Flaps shift the lift curve up and to the left as youincrease the deflection angle. The shift is theresult of the increase in camber. With theexception of the Fowler flap’s curve, whichbecomes steeper, the slope of the lift curveremains unchanged with flap deployment.Maximum CL increases with flaps, but occurs ata lower angle of attack than when the flaps areup. The zero-lift angle of attack becomes morenegative (nose down).

Figure 16 Flap Deployment

Stagnation point

Stagnation point


Adverse gradient



Because it reaches a higher maximum coefficientof lift, CLmax, with flaps extended, the wing willstall at a slower speed for a given aircraft weight.The benefit is disproportional, however, becauselarge increases in CLmax are necessary to gain anysubstantial decrease in stall speed. For example,a 50 percent increase in CLmax produces only an18 percent decrease in stall speed. A 100 percentincrease in CLmax reduces stall speed by 30percent, but at the expense of a large increase indrag.

Any type of flap is less effective on a thin wingthan on a wing of greater thickness. Flaps arealso less effective on swept wings compared tostraight wings when their hinge line follows thesweep angle. You’ll often see that the flapsthemselves are not swept on an otherwise sweptwing.

Arrow shows direction of shift as flap deployment increases.


Figure 17 Lift Curve shift withFlaps

Coe

ffic

ient

s of L

ift

Fowler

Slotted

Plain

Basic section, flaps up

Split

Plain Flap

Split Flap

Fowler Flap

Slotted Flap



Circulation

Airflow passing over the top of a wing speedsup, while airflow passing beneath the wing slowsdown. These changes in velocity producepressure differences between top and bottom,and thus lift.

Figure 18 shows what happens when yousubtract the freestream flow from the acceleratedflow over the top of the wing and from thedecelerated flow beneath. The result reveals anembedded circulatory flow. (The circulation hasa positive value above the wing; a negative valuebeneath.)

Circulation of this type doesn’t mean thatindividual air particles actually travel completelyaround the wing, only that a circulatory tendencyabout the wing exists at any moment. Thecirculation is outside the boundary layer andextends well above and below the wing.

Although the idea of circulation pre-dates theWright brother’s first powered flight (thebrothers weren’t aware of it) and has greatmathematical use, it’s never been popular as ameans of explaining lift to pilots. Imaginingcirculation around a wing isn’t easy. It’s easier tothink of airfoils in wind-tunnel terms, the airmoving in streamlines past a fixed airfoil thataccelerates the air by means of an easilyvisualized venturi effect. In terms of the forcesand moments produced, it doesn’t matterwhether the air or the wing moves. But in actualflying it’s of course the wing that does thetraveling. At subsonic speeds, it telegraphs itsapproach by the pressure wave it sends ahead,and the flow field starts accelerating ordecelerating even before the wing arrives. Try toshift your frame of reference and to think interms of the effects that the wing carries alongwith it, as it whizzes by, and of the effects itleaves behind in originally stationary air.

Circulation depends on airfoil design (leadingedge radius, maximum thickness and its location,maximum camber and its location). Circulationincreases with angle of attack up to the stall, andalso with wing camber as modified by flaps. Anaileron deflected down increases circulation overthe affected part of the wing. One deflected upreduces circulation.

Other factors remaining equal, the greater thecirculation the greater the velocity difference

above and below the wing, and thus the greaterthe pressure difference and the resulting lift.

The circulation needed to produce lift of a givenvalue increases as airspeed or air densitydecreases. The pertinent formula, in plainEnglish, is:

Lift = Density x Freestream Velocity x Circulation x Span

Freestream component

Circulatory components: The flow around the wing minus the freestream

Figure 18 Circulation

Actual airflow velocities



Bound Vortex/Tip Vortex

The circulation around an airfoil is called thebound vortex (Figure 19). On an actual three-dimensional wing, as opposed to a two-dimensional section, the bound vortex in effectturns the corner and becomes a trailing, tipvortex. The tip vortex is no longer an embeddedflow bound to and carried along by thecoordinates of the wing, but now a “free” or“true” vortex that remains attached to the samefluid particles and continues circulating longafter the wing is gone. Because the tip vortex isgenerated by the pressure difference between thetop of the wing and the bottom, and by thetendency of the airflow to try to even out thatdifference by “leaking” around the wingtip, tipvortex strength is a function of circulation.

At low speeds and high angles of attack, whencirculation necessarily rises, tip vortices increasein intensity. The heavier the aircraft andtherefore the greater the required lift (lift equalsweight in steady flight) the stronger thecirculation has to be at a given airspeed.Consequently, heavy airplanes flying at slowapproach speeds produce the most dangerous tipvortices. One reason to describe circulation is togive pilots a better sense of how potentiallydangerous tip vortices are generated, and howtheir strength depends on the components of thelift formula:

Lift = Density x Freestream Velocity x Circulation x Span

As the formula indicates, the circulation neededto generate lift equal to aircraft weight is also afunction of wingspan. The longer the span theless circulation required. Consequently, at thesame aircraft weight, long wings produce lessintense tip vortices than short wings. This in turnlowers induced drag, as we’ll see.

In principle, a vortex can’t suddenly terminate inmid air. It has to form a continuous enclosedloop. Figure 19 shows the starting vortex thatcompletes the loop. Figure 20 shows the role thestarting vortex plays in getting circulation going.

Bound Vortex Trailing Tip Vortex

Figure 19 Vortex System

Starting Vortex



The Kutta Condition

The top of Figure 20 shows the theoreticalstreamline flow around an airfoil that wouldoccur in the absence of friction and the resultingviscosity. The streamlines coming out frombeneath the wing reverse direction. The rearstagnation point lies on the top of the wing,forward of the trailing edge.

That can’t happen in nature, however, becausethe viscosity of the air prevents it from makingthe necessary sharp turn. Instead, as a wingbegins to move forward from a standstill, astarting vortex forms. Because nature also saysthat the total circulation within any arbitrarilydefined area must remain constant, an oppositevortex begins to form, the bound vortex. Thewing begins to develop the circulation describedearlier, and the airflow leaves the trailing edgesmoothly, as shown in the bottom illustration.The starting vortex is left behind. This smoothdeparture is known as the Kutta condition. Theupshot is that as angle of attack, camber, orairspeed change, the wing develops whatevercirculation is necessary to maintain the Kuttacondition. An increase in angle of attack, forexample, causes a new starting vortex to formand be left behind. If angle of attack isdecreased, a stopping vortex of opposite sign isformed and shed. A stopping vortex forms if theaircraft accelerates (since circulation required forlift goes down as airspeed increases). Ultimately,the vortices left behind break down due tofriction and turbulence.

Bound vortex

Starting vortex

Figure 20 Kutta Condition

Inviscid Flow

Real viscid airflow requires meeting the Kutta condition. The circulation generated causes the front and rear stagnation points to shift as shown.

Stagnation point

In the absence of viscosity, the low pressure ahead draws the rear stagnation point forward.

Stagnation point

Starting vortex circulation

But in Viscid Flow

Starting vortex induces circulation of the bound vortex.

+ = Constant

Defined area


Flightlab Ground School3. Three-Dimensional Aerodynamics


Real Wings

So far, we’ve been talking about two-dimensional airfoil sections. When you movefrom a two-dimensional, or “infinite,” section toan actual three-dimensional wing of finite span,the slope of the lift curve changes. Figure 1shows how decreasing the aspect ratio orincreasing wing sweep decreases the CL/α slope.

Notice in the figure that, while the zero-lift angleof attack stays the same (the curves all start atthe same point), the maximum CL decreases andrequires a higher angle of attack to attain.

Wing sweep tends to generate weaker adversepressure gradients, which in turn causes the stallarea of the curve to become flatter. Larger angleof attack changes are necessary to producechanges in lift, compared to wings of higheraspect ratio. Because lift changes more slowly ona swept wing, stalls are less pronounced than isusually the case in straight-wing aircraft thatgenerate stronger adverse gradients—althoughdrag increases quite fast with swept wings andthe airplane can develop a high sink rate.

While watching the tufts on our trainers, you’llsee that the boundary layer separation movesoutward along the span, as well as up the chord.How that separation advances depends on howthe local, section angle of attack varies along thespan. This is key to understanding how a three-dimensional wing operates, but several conceptshave to be brought together to make thatunderstanding work.

Here’s the short explanation: A lifting wingproduces a downwash in the air behind it, andan upwash ahead. We described earlier how atwo-dimensional (no tips) wing section generatesequal upwash and downwash. In the three-dimensional case, however, the downwash isgreater because of the added wingtip vortices.Variations in downwash along the span behindthe wing, caused by vortex effects, can producespanwise variations in the oncoming flow ahead

of the wing, and thus local differences in sectionangle of attack.

As we’ll see, that’s also the reason why the slopeof the lift curve changes with aspect ratio.

- 0 Angle of Attack , α +

Figure 1 Lift Curve Slope

Coe

ffic

ient

of L

ift

High aspect ratio

Wing sweep

2-D wing/infinite aspect ratio

SbAR

2=

Aspect ratio = wingspan (b) squared, divided by the wing area (S). Wingspan is measured directly from tip to tip.

Lower aspect ratio

Three-Dimensional Aerodynamics


The pressure differences between the top andbottom of a wing, which generate the tipvortices, also produce an overall spanwise flow,as shown in Figure 2. Air over the top of thewing flows somewhat inward, while air on thebottom flows outward. The result is that smallvortices form along the trailing edge where theinward and outward flows meet. Since therelative deflection of the two flows is smallest atthe wing roots, the vortices there are less intensethan at the tip. The weaker inboard trailing edgevortices quickly merge downstream with thestronger wingtip vortex.

Figure 3 suggests how the circulation generatedby the tip vortex adds to the downwash behindthe wing. The influence of the downwashactually extends ahead of the wing. The air aheadbegins to be pulled down in response to the flowbehind the wing, in proportion to the downwashvelocity, even before the wing arrives.Remember the upwash ahead of the wing, fromtwo-dimensional aerodynamics? The net result isa reduction in the upwash and a reduction in theeffective angle of attack.

Inward flow along the top of the wing

Figure 2 Trailing Edge Vortex Generation

Outward flow along the bottom

Relative effect ahead of the wing

Figure 3 Tip Vortex Flow Field

Downwash velocity profile behind a constant-cord wing

Air ahead of the wing begin descending in response to the vortex downwash.



The next few pages may be difficult going, but ifyou survive you’ll have some insight into wingstall patterns.

Figure 4 shows a common way of representingthe components of the bound vortex around agiven spanwise section of a finite wing, andFigure 5 shows what happens when the tipvortex is added to that circulation. Notice that thenet upwash/downwash at the aerodynamic centeris zero with the bound vortex alone. Adding thedownwash from the wingtip vortex increases thevertical velocities of the total downwash behindthe wing, and produces a decrease in upwashvelocities ahead of the wing, and a netdownwash at the aerodynamic center. (Theaerodynamic center can be quickly defined as thelocation along the chord where changes in lift areconsidered to act. It’s usually around 25 percentof the chord back from the leading edge. But

that’s an abbreviated definition.)

The wingtip and bound vortex together produce afinal, vertical downwash velocity, 2w, behind thesection, that’s twice the velocity, w, of thedownwash at the aerodynamic center. Adding thefreestream and downwash vectors together givesyou the downwash angle, ε, as shown at thebottom of Figure 5

Remember that the Figures 4 and 5 showcirculation around a section of a finite wing. Atanother section along the span the circulationcould be different. The tip vortex may havegreater or less influence due to distance orplanform, or the wing might be built with a twistor a change in section profile.

Upwash velocities of bound vortex only

Downwash velocities of bound vortex only

Figure 4 Bound Vortex Upwash/Downwash

Upwash/downwash is zero at the aerodynamic center.

2w

wε2w2εFreestream

Local relativewind

Figure 5Addition ofTip Vortex

Bound vortex only

Adding the tip vortex reducesupwash ahead of the wing and

creates a downwash at theaerodynamic center.

Downwash velocity, w, ataerodynamic center

Downwash angle, ε, at theaerodynamic center

Total downwash anglebehind wing: 2ε

Combinedvortices



Figure 6 shows how the downwash behind thewing influences the effective angle of attack of awing section. When you add the remote,freestream wind ahead of the section to thedownwash at the section’s aerodynamic center,the resulting vector is the section’s averagerelative wind. This average relative wind, whichis inclined to the freestream, is what the wingemploys to create lift. Its inclination to thefreestream is called the induced angle of attack,αi. Its inclination to the wing chord is the local,average, section angle of attack, αo. See Figure7.

Once again, we can’t talk about lift withouttalking about drag. Because the lifting force isperpendicular to the local relative wind, theinclination of the local relative wind, as shown inFigure 8, causes the lift vector to tilt back,opposite the direction of flight. The result isinduced drag, as demonstrated in the figure bybreaking the lift vector into horizontal andvertical components. Induced drag doesn’t occuron a two-dimensional wing section: only on areal, three-dimensional wing with a tip vortex.Note that the angle ε between the freestream andthe section relative wind is the same as theinduced angle of attack, αi, and also the same asthe backward tilt of the lift vector.

The induced angle of attack, αi, is directlyproportional to coefficient of lift: double one andyou double the other. But induced drag goes up

as the square of the lift coefficient: doubling theCL gets you four times as much drag.

Freestream

ε

Resulting average section relative wind

Figure 6 Downwash Angle Downwash at

aerodynamic center

ε is called the downwash angle and is equivalent to the induced angle of attack, αi.

Weight

Effectivelift, equalto weight

Average sectionrelative wind

Lift is perpendicularto relative wind.

ε or αi

ε

Induced drag: thecomponent of lift actingopposite to the directionof flight

Freestream

Figure 8Induced Drag

Freestream

Section relativewind

Cord line

α

αi

αo

Figure 7αo/αi

A wing’s angle of attack, α, is the sum of induced angle ofattack, αi, and section angle of attack, αo. αo generates lift; αi

tilts the lift vector and causes drag.



At this point, you may have lost your patiencekeeping α, αi, αo, and ε straight. Don’t worry;the important concept is simply that thedownwash behind the wing affects the nature ofthe upwash ahead, and thus the local angles ofattack along the span.

Figure 9 struggles to show that even when theangle of attack, α (angle between chord line andfreestream), of the wing as a whole remainsconstant, its component angles αi and αo can bedifferent at different spanwise section locations.That’s because the downwash can vary along thespan behind the wing, depending on planformeffects and on the relative influence of thewingtip vortex. Wing sections operating at

different local angles of attack, αo, and thus atdifferent coefficients of lift, can reach stallingangle of attack at different times.

A rectangular wing, like that of our trainers,produces a strong tip vortex and a totaldownwash that increases from root to tip (asFigure 9 illustrates). The greater downwash nearthe tip in turn reduces the outboard sectionangles of attack, αo, relative to the inboard, forthe reasons described above. Because the wingroot operates at higher section angles of attackthan the tip, the root is where the stall begins.

Long tip cord produces a strong tip vortex.

Final downwash (2w) increases from root to tip.

αo tip

αo root

α, the wing angle of attack, is the angle between the cord line and the freestream relative wind.

With no wing twist, α tip = α root.

αo , the section angle of attack, is the angle between the cord line and section relative wind. Because of vortex effects:

αo tip < αo root

αi is the angle between the freestream and the section relative wind, and is the same as the inclination of the lift vector, ε, that’s responsible for induced drag. Because of vortex effects:

αi tip > αi root

w is the downwash at the section aerodynamic center. Because of vortex effects:

w tip > w root

DI (Induced drag) root

DI (Induced drag) tip

αi tip

αi root

w tip

w root

Root

Section relative wind

Stall begins here.

ε root

ε tip

Freestream

Cord line

Figure 9 Rectangular Wing Planform

Section relative wind Cord line



You’ll observe this as you watch, and manipulatewith the control stick, the spanwise movement ofthe tufts on the trainer’s wing during stall entry.The tufts can’t show you the downwash directly,of course, or section relative wind. But you willsee the tufts responding to the accompanyingchanges in pressure pattern and to the expansionof the adverse gradient from trailing edge toleading edge and from root to tip, as sectionangles of attack increase and flow reversal andboundary layer separation start to occur.

Aspect Ratio

At the start, we mentioned the effect of aspectratio, AR, on the slope of the lift curve. Here’ssome additional explanation. The formula foraspect ratio is:

AR = wingspan2/wing area

Induced drag is inversely proportional to aspectratio. Doubling the aspect ratio, for example,cuts induced drag in half. The smaller the aspectratio (short wings) the faster induced drag willrise as we pull back on the stick and increase αand CL. That’s because as wingspan (and thusaspect ratio) decreases, the downwash from thewingtip vortex affects more of the total span.

Downwash distribution is the reason why lowaspect ratio wings stall at higher overall anglesof attack. Because the downwash from the tipvortex reduces the working, section angles ofattack, αo, over more of the wing, low aspectratio wings need to operate at higher overallangles of attack, α, than longer wings to createequivalent lift. Therefore the slope of the liftcurve in Figure 10 decreases with decreasingaspect ratio. Sweeping the wing also extends theinfluence of the vortex downwash inboard alongthe span, with similar effect.

- 0 Angle of Attack , α +

Coe

ffic

ient

of L

ift

High aspect ratio

Wing sweep

2-D wing/infinite aspect ratio

Sb

AR2

=

Aspect ratio = wingspan (b) squared, divided by the wing area (S). Wingspan is measured directly from tip to tip.

Lower aspect ratio

Figure 10 Lift Curve Slope Revisited



Planform Differences and StallCharacteristics

Different wing planforms can producesignificantly different downwash distributionsbehind the wing, and therefore different liftdistributions along the span. You find the liftdistribution by comparing section coefficients oflift, Cl, to the lift coefficient produced by thewing as a whole, CL. The lift distributiondetermines the stall pattern.

When the downwash behind a constant-section,untwisted wing is uniform along the span, allsections of the wing will operate at the samesection angle of attack, αo, and sectioncoefficient of lift, Cl. An elliptically shapedwing (like the one on your Spitfire) creates thissort of uniform downwash distribution.

Compared to a rectangular tip, the ellipticalwingtip produces less total lift because of itsreduced chord, and therefore a less intense tipvortex. The elliptical wing has a great advantagein generating the least induced drag compared toany other wing shape of the same aspect ratio.Since induced drag predominates at high CL, theplanform probably helped keep the Spitfire fromlosing energy in turns, where high g-loadsrequire high lift coefficients. Elliptical wings aresaid to be difficult to build. As an alternativewith nearly the same drag reductioncharacteristics, a tapered wing allows acompromise between drag and structuralrequirements.

Figure 11 shows how the ratio between thesection lift coefficient, Cl, and the coefficient oflift for the entire wing, CL, varies betweenplanforms. The elliptical wing has a constantratio of 1.0. The lift distribution is uniform. As αincreases, the sections all use up their liftpotential at the same rate, and therefore will stallat about the same time. That can mean a suddenstall break, with little warning and ineffectiveailerons.

The rectangular wing, however, starts with aCl/CL ratio higher than 1.0 at the root, where thesection coefficients are greater than the wing

Rectangular

Elliptical

Root

Cl / CL Ratio of section lift coefficient, Cl, to total wing lift coefficient, CL

Tip

0.5

1.5

Delta

Tapered

1.0

Semi-Span distance

Figure 11 Cl / CL

Swept

Figure 12Stall PatternsNo WashoutRise in local section Cl as α increases



coefficient as a whole. The ratio drops below 1.0about two-thirds out, as the section coefficientsbecome less than the wing’s, and then goes tozero at the tip. As wing angle of attack, α,increases, the straight rectangular wing, with itsskewed lift distribution, uses up its lift potentialfaster at the roots than at the tips. It stalls first atthe roots.

The swept wing does just the opposite. It stalls atthe tips because that’s where it uses up its liftfirst. Figure 12 shows the relationship betweenstall pattern and the increase in local section Cl asα increases.

Although you pay a penalty in higher induceddrag from the wingtips, the rectangular wing hasoptimal stall characteristics. The ellipticalplanform is the standard against which theefficiency of other wings is measured in terms ofdrag at subsonic airspeeds, but the rectangularwing sets the standard for behavior in stalls.Most of the gizmos that you find on other wingsare designed to give them the benign stallcharacteristics and high-α lateral control morelike that of a rectangular planform.

Stall warning can be better with a rectangularwing because the initial separation at the root canplace the horizontal stabilizer in turbulentairflow, producing a warning buffet. This buffetis very evident in our training aircraft. When yousee the wing root tufts start reversing you’llimmediately feel the effect on the tail. In someaircraft the stick will shake against your hand asthe elevator responds to the turbulence. That’sthe reversible control feedback that mechanicalshakers are meant to simulate.

Roll control is naturally better with therectangular wing as the stall approaches, becausethe ailerons work behind a lower section angle ofattack and so remain in attached airflow longerinto the stall entry. Geometric washout (twistingthe leading edge of the wingtip down) andaerodynamic washout (changing the airfoilsection toward the tip) are also used to adjust thelift distribution, keep the wingtips flying, andkeep lateral control within bounds. Stall stripsare used to adjust the spanwise stall pattern bytripping the root section into a stall at a lowerangle of attack than would otherwise occur.

In out trainers, you’ll be able to make aconnection between the stall patterns that thetufts allow you to see and the resulting changesin aircraft lateral control.



Swept-wing Characteristics

A tendency toward tip stall happens when youradically increase wing taper, sweep, or both,without also introducing a compensating wingtwist or a change in airfoil section along thespan. Taper or sweep shift the vortex and thedownwash inboard, causing the tips to work athigher section coefficients of lift, αo.

Aerodynamic stall warning can deteriorateseriously when the tips reach stalling angle ofattack before the rest of the wing, if theturbulence produced by the stalling tips passesoutside the span of the horizontal stabilizer,preventing a warning buffet.

Because the tip sections of a highly swept wingcan operate at higher section angles of attack(thus at lower upper-surface static pressures)than the inboard sections, static pressure over thetop of the wing decreases from root to tip. Theresulting spanwise pressure gradient produces anoutward, spanwise flow that intensifies withincreasing wing angle of attack. The geometry ofa swept wing encourages this tendency becauseinboard areas of higher pressure are directlyadjacent to outboard areas of lower pressure, asshown in Figure 14. The spanwise flow tends to

thicken the boundary layer toward the tips. Thethicker boundary layer transfers less kineticenergy to the surface, and this lowers airflowresistance to the adverse pressure gradient alongthe wing chord, encouraging separation. On aswept wing the combination of higher tip sectionangles of attack, αo, and a thicker, more easilyseparated boundary layer can cause the tips totend to stall first. Stall fences along the wingchord, between the ailerons and wing root, werean early and often-seen solution.

Obviously, tip stall is bad for roll control,because of the airflow separation over theailerons. And it’s not good for pitch control,either. Due to the sweep angle, loss of lift at thetips will shift the center of lift forward. This shiftcauses a nose-up pitching moment, which candrive an airplane deeper into a stall or deeperinto a high-g turn. The wing vortices also moveinboard as the tips stall, thus increasing thedownwash on the vertical stabilizer and thepitch-up tendency.

Spanwise gradient from higher to lower pressure

Figure 14 Spanwise Pressure Gradient

Resultant flow

Because section angle of attack, αo, is higher at the wingtips due to the inboard shift of the downwash, adverse pressure develops first at the wingtips. The tips stall first.

Longer arrows indicate lower surface pressures and higher section angle of attack.

Nose-up pitching moment as tips stall.

Figure 13 Surface Pressures


Flightlab Ground School4. Lateral/Directional Stability


Sideslips and Directional Stability, Cnβ

Most aerodynamics texts cover longitudinal(pitch axis stability) before tackling coupledlateral/directional behaviors. Since our flightprogram emphasizes those behaviors, we’ll dothings in our own order.

An aircraft is in a sideslip when its direction ofmotion (its velocity vector) does not lie on the x-z plane of symmetry. The top drawing in Figure1 defines the x-z plane, and in the bottomdrawing we’re looking down the z-axis. Theangle between the velocity vector, V, and the x-zplane is the sideslip angle, β (pronounced“beta”). In aerodynamics notation β is positive tothe right, negative to the left. (Just so there’s noconfusion, a -β sideslip to the left, for example,means that the nose is pointing to the right of theaircraft’s actual direction of motion.)

Rudder deflections, wind gusts, asymmetricthrust, adverse yaw, yaw due to roll, and bankangles in which the effective lift is less thanaircraft weight can all cause sideslips. Inresponse, sideslips typically create both yawingand rolling moments. A stable aircraft yawstoward the velocity vector, but rolls away. Thesemoments interact dynamically—playing out overtime, most notably in the form of thedisagreeable undulation called the Dutch roll.We cover the associated rolling moments a bitfarther on, but concentrate on yaw around the z-axis here, pretending for the time being that itoccurs in isolation.

The notation for the yawing moment coefficientis Cn (positive to the right, negative to the left).Remember that a moment produces a rotationabout a point or around an axis.

β is approximately equivalent to the AOA of the vertical tail. The actual sideslip angle at the tail depends on fuselage/tail interference effects, on fin offset and slipstream in the case of propeller-driven aircraft, and, especially at high angles of attack, on the influence of wing tip vortices or vortices shed by the forward part of the fuselage.

The side force produced by the tail, times the arm, generates an overall stabilizing yaw moment.

Fuselage center of pressure ahead of cg produces destabilizing yaw moment.

z-axis

X-Z plane is the surface of the paper.

x-axis

cg

arm

Right Sideslip

β

V

v

v is the Y-axis component of the aircraft’s velocity, V. v = V sin β

x

y-axis

Figure 1 Directional Stability

Lateral/Directional Stability


CNβ

Stable slope

+ β (sideslip to right)

+C n Nose-right yaw moment

-C n Nose-left yaw moment

Figure 2 Directional Stability Response

− β (sideslip to left)

An aircraft has static directional stability if ittends to respond to a sideslip by yawing aroundits z-axis back into alignment with the relativewind. Another way to put it is to say that adirectionally stable aircraft yaws toward thevelocity vector, returning it to the aircraft’s x-zplane of symmetry.

This is also called “weathercock” stability, inhonor of a much simpler invention. Figure 2shows that this stabilizing yaw moment is nottypically linear, but tends to decrease at high βangles. In the figure, a positive slope (rising tothe right) in the Cnβ curve indicates directionalstability. The steeper the slope the stronger is thetendency to weathercock.



Figure 4 World War I Fokker Dr1 rudder

Not all parts of the aircraft contribute todirectional stability. Alone, the fuselage isdestabilizing. In subsonic flight, the center ofpressure on a fuselage in a sideslip is usuallysomewhere forward of 25 percent of the fuselagelength. Since the aircraft’s center of gravity istypically aft of this point, the fuselage alonewould tend to turn broadside to the relative windin a sideslip. Notice in Figure 3 how thedestabilizing contribution from the fuselagelevels out as β increases.

Figure 3 breaks down the components ofdirectional stability. A sideslip to the right (+β)produces a nose-right, stabilizing yaw momentfor the entire airplane, but a destabilizing yaw tothe left (-Cn) for the fuselage alone.

Of course, the vertical tail contributes most todirectional stability. The yaw moment producedby the tail depends on the force its surfacegenerates and on the moment arm between thetail’s center of lift and the aircraft’s center ofgravity. (Therefore, a smaller tail needs a longerarm to produce a yaw moment equivalent to abigger tail on a shorter arm. That being said,changing the c.g. location for a given aircraft,within the envelope for longitudinal stability, haslittle effect on its directional stability.)

The rate of the increase in force generated by thetail as β increases depends on the tail’s lift curveslope (just as the rate of increase in CL withangle of attack depends on the slope of the liftcurve of a wing). Lift curve slope is itself afunction of aspect ratio. Higher aspect ratiosproduce steeper slopes. (See Figure 13, top.)

The Cnβ directional stability curve for thefuselage and tail together reaches its peak whenthe tail stalls. You can see in Figure 3 thatadding a dorsal fin increases the tail’seffectiveness (and without adding much weightor drag). Because of its higher aspect ratio andsteeper lift curve, the vertical tail properproduces strong and rapidly increasing yawmoments at lower sideslip angles, but soon stalls.But the dorsal fin, with its low aspect ratio andmore gradual lift curve, goes to a higher angle ofattack before stalling, and so helps the aircraftretain directional stability at higher sideslipangles. The dorsal fin can also generate a vortexthat delays the vertical tail’s stall.

The Fokker Dr1 triplane provides an extremeexample of a low-aspect-ratio tail (there’s arough approximation in Figure 4). Without afixed vertical fin, the aircraft had low directionalstability. The low-aspect-ratio rudder stalled atabout 30-degree deflection. The combinationgave the pilot the ability to yaw the nose aroundrapidly if necessary to get off a shot. But instraight-ahead flight the aircraft needed constantdirectional attention (a typical attribute of WW-Ifighters).

+β (sideslip to right)

+Cn Nose-right yaw moment

Tail alone

Fuselage alone

Fuselage and tail

Fuselage, tail, and dorsal fin

-Cn Nose-left yaw moment

Tail stalls here.

Figure 3 Contributions to Directional Stability

Dorsal fin

X

Z



Coming back to modern examples, it’sappropriate to note that the lift curve slope of thevertical tail tends to go down at high Machnumbers, taking directional stability with it. Thistendency is one reason why supersonic fightersneed to compensate with such apparently over-sized tails. Another reason is that the slope of theCnβ stability curve also tends to go down at highangles of attack as the fuselage begins tointerfere with the airflow over the tail. This isespecially so with swept-wing aircraft thatrequire higher angles of attack to achieve highlift coefficients. Directional stability is essentialto prevent asymmetries in lift caused by sideslipthat can lead one wing to stall before the otherand send the aircraft into a departure.

Propellers and Directional Stability

Propellers ahead of the aircraft c.g. aredirectionally destabilizing, mostly because ofslipstream effects and P-factor (Figure 5). OurAir Wolf is an example of an aircraft thatrequires lots of directional trimming (or justrudder pushing) to compensate for propellereffects as angle of attack and airspeed change. Inthis respect it’s quite unlike a jet, say, or anaircraft with counter-rotating propellers, whichtypically have no associated directional trimchanges.

Note that as an airplane slows down,asymmetrical propeller effects cause it to yaw. Ifthe pilot cancels the yaw rate, using rudder,while keeping the ball centered and the wingslevel, the aircraft will end up in a sideslip (to theleft to generate the side force required tocounteract the usual yawing effects due to aclockwise-turning propeller). Thus even a“straight-ahead” stall at idle power has a smallsideslip component that may affect its behavior.

Spiraling slipstream produces a side force at the tail. The resulting yaw moment is most apparent at low airspeeds and high power settings—for example, during a go-around or at the top of a loop.

Figure 5 Slipstream and P-factor

As aircraft α increases, P-factor causes the down-going blade to operate at a higher prop α than the up-going blade. The difference in thrust produces a yawing moment. A similar change in blade angle happens if the aircraft is in a sideslip, but produces a pitching moment. Left sideslip = pitch up; right sideslip = pitch down.

Slipstream

Prop cord

Plane of rotation

V∞

α

Down-going blade: higher prop α

Resultant

P-factor

Up-going blade Down-going blade

Thrust

V∞

α

Up-going blade: lower prop α

Moment

V∞



Dihedral Effect, Clβ

An aircraft with dihedral effect rolls away from asideslip (away from the velocity vector). Theterm describes a single behavior with more thana single cause. Dihedral effect was observed firstas resulting from actual geometric dihedral (wingtips higher than wing roots), but it’s alsoproduced by wing sweep, by a high winglocation on a fuselage, and by forces acting onthe vertical tail. For convenience, Figure 6 againillustrates sideslip angle, β, and sideslip velocity,v, velocity vector, V, plus the direction of roll.

During our flight program, we’ll do steady-heading sideslips to assess the presence ofdihedral effect. We’ll press on a rudder pedalwhile applying opposite aileron, so that theairplane will be banked but not turning. We’llnote the deflections necessary to keep the aircrafttracking on a steady heading, and we’ll see whathappens when we release the controls.

Steady-heading sideslips give test pilotsinformation about the rolling moments a slippingaircraft generates and its lateral/directionalhandling qualities. We use them to illustrate thenature of yaw/roll couple and to demonstrate theeffects of sideslip under various flapconfigurations, during aerobatic rollingmaneuvers, and during simulated controlfailures. As you’ll see, an aircraft can sideslip inany attitude—including upside-down.

The interaction between sideslip and dihedraleffect forms the basis of an aircraft’s lateralstability. Lateral stability can’t appear unless an

aircraft starts to sideslip first. An aircraft withpositive lateral stability rolls away from thesideslip (velocity vector) that results when awing drops, and that usually means back towardlevel flight (although an aircraft with dihedraleffect can go into a spiral dive if the bank angleis high and other moments prevail).

In the notation used in Figure 7, sideslip angle isβ (beta), and the rolling moment coefficient is Cl,so the slope of the curve of rolling moment dueto sideslip is Clβ (pronounced “C L beta”).Since it does roll off the tongue, if we lapse intothis terminology you’ll know what we mean. Thefigure shows that the slope must be negative(descending to the right) for stability when wefollow the standard sign conventions, whereaircraft right is positive, left is negative.

A laterally unstable aircraft tends to continue toroll toward the direction of sideslip (positiveslope). Sweeping the wings forward or mountingthem with a downward inclination so that the tipsare lower than the roots (anhedral) produces thistendency. Sometimes anhedral is used to correctswept-wing designs having too much positivelateral stability at high angles of attack. Toomuch lateral stability can cause sluggish rollresponse (especially if there’s also adverse yawpresent) and a tendency toward the coupledyaw/roll oscillation of Dutch roll.

β, Sideslip angle

Cl, Rolling moment coefficient

Left roll moment

Left

Right roll moment

Right

Unstable

Slightly stable

Stable slope Clβ

Figure 7 Lateral Stability

Left slip produces right roll.

Right slip produces left roll.

Figure 6 Sideslip Angle, β

V x-axis β

v is the y-axis component of the aircraft’s velocity, V. v = V sin β

v

y-axis

Roll Moment



Geometric dihedral effect is easy to understandbecause it’s easy to see how wing geometry andsideslip interact. Just stand on the flight line at adistance in front of an aircraft with geometricdihedral and pretend that you’re looking rightdown the path of the relative wind. You mayneed to stoop a little to approximate an in-flightangle of attack.

Maintain that eye height above the ground andmove back and forth in front of the aircraft,trying hard not to look too suspicious to possiblerepresentatives of the TSA. Notice how the angleof attack, α, of the near wing increases—you cansee more wing bottom—while that of the farwing decreases as you change your position, asillustrated at the top of Figure 8. With anhedral,you’d see just the opposite.

Figure 8 also presents the same idea in anotherway. In the lower figure, the y-axis componentof sideslip, v, is in turn broken down into twovector components projected onto the aircraft’sy-z plane, one parallel to and one perpendicularto the wing. On the upwind wing, theperpendicular component acts to increase theangle of attack. It does the opposite on thedownwind wing. The difference produces arolling moment. v

α decreasesα increases

v

y-axis

Dihedral angle, Γ

Rolling moment varies inapproximately a linear fashion withdihedral angle and sideslip angle.

Geometric dihedral, wing viewed from thedirection of a sideslip to the left (i.e., backdown the velocity vector)

z-axis

x-axis

v is the y-axiscomponent of thesideslip.

Figure 8Sideslip, DihedralAngle, and ResultingChange in α

Aircraft in a sideslipto its right



Again, dihedral effect can also result frominterference effects due to wing placement on thefuselage, from wing sweep, or from vertical tailheight. Flap geometry and angle of deploymentinfluence dihedral effect, as does propellerslipstream.

Figure 9 shows the contributions of wingposition, tail height, landing gear, and slipstreamangle to dihedral effect. Wing position guides thecross flow around the fuselage in a sideslip,altering the angles of attack on the near and farwings, and thus the relative lift. This isstabilizing on a high-wing aircraft. It’sdestabilizing on a low wing, which is why low-wing aircraft typically require more geometricdihedral. These fuselage effects are enhanced bysmooth airflow over the wing-body junction.They’re diminished by flow separation at thewing roots at the approach of a stall.

A vertical tail produces a side force during asideslip. If the tail is tall enough, so that itscenter of lift is a good distance above theaircraft’s center of gravity, the vertical momentarm can provoke a stabilizing roll response.Landing gear, below the c.g., is destabilizing.

The bottom illustration in Figure 9 shows howthe angle of the propwash during a sideslipcreates a destabilizing condition by increasingthe airflow, and thus the lift, over the downwindwing. This generates a rolling moment into thesideslip. The destabilizing effect increases withthe flaps down. It also increases at low airspeedsand high power settings, as the ratio of propwashvelocity to freestream velocity increases and thepropwash gains relatively more influence.

The propwash effect may vary somewhat,depending on the direction of the sideslip.Propeller swirl, as it’s sometimes called, createsan upwash on the left wing root and a downwashon the right, leading to a difference in angle ofattack between the wings and thus a rollingmoment. For the aircraft at the bottom of Figure9, clock-wise propeller swirl may initiallygenerate a rolling moment to the right, which cansuddenly reverse at high α, when the left wingstalls first because of its swirl-induced higherangle of attack. This is an important factor inspin departures, especially during the classic,career-ending skidding turn to final.

Stabilizing roll moment

+ AOA

- AOA

Destabilizing roll moment

+ AOA

- AOA

Figure 9 Sideslip-induced Roll

Propwash causes destabilizing roll moment toward sideslip.

v

v

Cross flow due to sideslip

v

Destabilizing roll moment caused by side force on landing gear



Figure 11 Geometric Dihedral Effect

Equal lift differences produce equal rolling moments.

Equal wing-to-wing α differences generated by a given sideslip angle at two different starting αs

α

CL

Left wing

Right wing

Propwash effects don’t occur in jets, but flapeffects do. Flaps shift the centers of lift inboardon the wings, as illustrated in Figure 10. Thisshortens the moment arms through which the liftchanges caused by sideslip act, and so sideslip-induced roll moments decrease.

We’ll explore this effect during steady-headingsideslips by raising and lowering the flaps andwatching the roll response. When the flaps godown, dihedral effect will diminish and theaircraft will start to roll in the direction of aileroninput. (This demonstration is important inunderstanding the concept of crossover speed.)

Propwash increases flap effects because of theadded airflow over the flap region of the up-going wing, but we can demonstrate with theprop at idle—it will just take more flapdeflection.

Because wing taper also shifts the centers of liftinboard on the wings, a high taper ratio (tipchord less than root chord) decreases lateralstability. High aspect ratios move the centers oflift outboard, increasing lateral stability.

Geometric Dihedral and Coefficient ofLift, CL

The strength of geometric dihedral effect doesnot depend directly on aircraft coefficient of lift(you’ll see the reason for the italic treatmentpresently). The CL/α curve for a cambered wingin Figure 11 is linear up to the stall, which meansthat for a given change in angle of attack(produced by a sideslip) there’s a givenincremental difference in coefficient, until theslope starts to decline near the stall. As a result, agiven sideslip angle combined with a givendihedral angle, will generate a given differencein CL. It doesn’t matter if you start at low orhigh CL, as long you stay on the straight line.That difference then produces a rolling momentthat varies directly with speed.

If you can tolerate even more confusion, imaginethat an aircraft with geometric dihedral is flyingat its zero lift angle of attack (maybe during apushover at the top of a zoom). If the airplanestarts to sideslip, it will begin to roll as the angleof attack changes on each wing and a spanwiseasymmetry in lift appears. Without geometric

dihedral, a purely swept-wing aircraft, at zerocoefficient of lift, won’t roll in the samesituation, because the sideslip has no influence iflift is not already being generated.

Centers of lift move inboard with flaps during a sideslip, reducing the moment arm through which dihedral effect operates. Roll moment decreases.

v

v

Wing center of lift Lift Distribution

Total lift is the same (lift=weight), but shifts inboard.

Resulting roll moment

Figure 10 Flap Effects



Swept-wing Dihedral Effect

Figure 12 shows the contribution of wing sweepangle (Λ) to dihedral effect. It’s almost enoughto say that in a sideslip, because of the angle ofintercept, the wing toward the sideslip “getsmore wind” across its span, while the oppositewing gets less. But we can gain a betterunderstanding of swept-wing characteristics byfirst breaking the airflow over the wing intonormal and spanwise vectors. It’s the normalvector (perpendicular to the leading edge on awing with no taper, or by conventionperpendicular to the 25% chord line on a wingwith taper) that does all the heavy lifting,because only the normal vector is accelerated bythe curve of the wing. There’s no accelerationand accompanying drop in static pressure in thespanwise direction, because there’s no spanwisecurve.

When a swept wing sideslips, the relativevelocities of the normal and spanwise vectorschange. The spanwise component decreases andthe normal component increases on the wingtoward the sideslip, and so lift goes up; just theopposite happens on the other wing, and therelift goes down. A roll moment results. Adirectionally stabilizing yaw moment alsoresults, because a difference in drag accompaniesthe difference in lift—but the effect is smallcompared to the stabilizing moment provided bythe tail.

For a swept wing, the roll moment coefficientdue to sideslip is directly proportional to thesideslip angle, to the sine of twice the sweepangle, and to the coefficient of lift.

The relationship between sideslip and sweepangles, and subsequent rolling moment can beanticipated just from looking at Figure 12, butthe variation in rolling moment with CL takesexplaining. The easiest approach is to think ofsideslip as changing the effective sweep angle ofeach wing, and thus the slope of their respectiveCL/α curves. Sweep angle and slope are relatedas shown at the top of Figure 13. In a sideslip, asshown on the bottom, a swept-wing aircraft hastwo CL/α curves: a steeper one than normal forthe wing into the wind, and a shallower one thannormal for the trailing wing. The differencebetween them creates the rolling moment. Notehow the difference at any given β increases withα, and therefore with CL.

Freestreamvector Normal

vector

Spanwisevector

Zero sideslip

Sideslip toright

Normal vectordecreases.

Normal vectorincreases.

Resulting dihedraleffect rollmoment to left

Stabilizing yaw momentcaused by unequal drag

25%cord

Λ

Less lift,less drag

More lift,more drag

β

Figure 12Wing Sweep

α

CL

Increasing the sweep angle (or decreasing the aspect ratio) decreases the slope.

CL

Aircraft in sideslip to the right

Normal, zero sideslip

Left wing—more sweep

Right wing—less sweep

α

Figure 13 Swept-wing Dihedral and CL

Greater lift difference at higher aircraft CL increases roll moment.



Back in Figure 12, right, note the difference inspanwise drag during a sideslip. That differenceis directionally stabilizing, and it’s the reasonwhy flying wing aircraft are swept.

Since wept-wing dihedral effect varies with liftcoefficient, so does lateral stability. Aircraft withhigh sweep angles can have acceptable dihedraleffect and lateral stability in normal cruise flightwhen CL is low, but excessive dihedral effect atlow speeds, or during aggressive turningmaneuvers, or at high altitudes, where in eachcase CL is necessarily high. Under thoseconditions, sideslips can produce strong rollingmoments. This can allow a pilot to accelerate aroll rate by forcing a sideslip with rudder, butalso increases the potential for Dutch rolloscillation and rudder misuse.

As mentioned, unlike a wing with geometricdihedral, a purely swept-wing will not roll inresponse to a sideslip unless it’s alreadygenerating lift. There’s no dihedral effectattributable to wing sweep at zero CL.

You can see that a wing possessing bothgeometric dihedral and sweep has a kind ofmultiple personality (and usually a yaw damper).

Straight Wings and Coefficient ofLift—Revisited

Despite the claim made earlier, straight-wingaircraft with geometric dihedral do exhibit aconnection between increased CL and increaseddihedral effect.1

If you go to the illustrations in our briefingmaterials on three-dimensional wings, you’lldiscover that the downwash caused by wing tipvortices alters the effective local angle of attackacross the span. The greater the downwash, thelower the local effective angle of attack on thewing ahead of the downwash. (The angle ofattack changes because the acceleration of airdownward by the vortices actually starts to occurahead of the wing. The air starts coming downeven before the wing arrives.)

In a sideslip the vortex flow shifts laterally, as inFigure 14. This changes the overall downwashdistribution, shifting it to the left in the case 1 Bernard Etkin, Dynamics of AtmosphericFlight, Wiley & Sons, 1972, p. 305-306.

illustrated, which in turn causes the averageeffective angle of attack of the left wing to belower than it would from dihedral geometryalone. The average effective angle of attack onthe right wing becomes higher. The result is arolling moment to the left (a moment that wouldtheoretically occur even if the wing had zerodihedral—as long as lift is being produced).

Since downwash strength is a function of CL,pulling or pushing on the stick will affect rollmoment due to sideslip in a manner similar tothe swept-wing example already described. (Ourtrainers’ rectangular planforms tend to promotestrong tip vortices. Other straight-wingplanforms with different lift distributions mightnot be as effective.)

Pushing and pulling on the stick during a sideslipalso causes the aircraft to pitch around its y windaxis (as opposed to body axis), which introducesa roll as described in Figure 19. The effect wouldbe in the same direction as the downwashphenomenon just mentioned, and the two mighteasily be confused.

From all the above, an under-appreciated yetnevertheless great truth of airmanship emerges:For a swept or a straight wing, pulling thestick back tends to increase rolling momentscaused by sideslip (and by yaw rate), pushingdecreases them.

β

Downwash shiftslaterally with β,increases with CL.

Downwash shiftcauses section anglesof attack to decrease.

Downwash shiftcauses section anglesof attack to increase.

Sideslip to right

Rolls left

Figure 14Vortex Effects



Sideslip and Roll Rate

With our particular emphasis on theaerodynamics of unusual-attitude recovery, hereare the behaviors we want to be sure youunderstand:

(1) Increasing CL (by pulling back on thecontrol) will increase rolling moment due tosideslip and yaw rate. Decreasing CL (by pushingforward) will decrease rolling moment due tosideslip and yaw rate. We’ll explore theimplications of this during our flight program.(See roll due to yaw rate, and y-wind-axis roll,farther on.)

(2) A laterally stable aircraft rolling with ailerontoward the direction of a sideslip/velocity vectorwill experience a decrease in roll rate inproportion to the opposing rolling moment thesideslip produces. An aircraft rolling with aileronaway from the direction of a sideslip/velocityvector will experience an increase in roll rate.You’ll discover this effect when we start rollingthe training aircraft through 360 degrees andbegin using rudder-controlled sideslips toaugment roll rates.

Figure 15 describes the link between sideslipdirection and roll rate at two points during a 360-degree roll to the left, and Figure 16 plots rollrate against time, given differences in rudder use,dihedral effect, and directional stability.

(When aircraft directional stability is greater than dihedral effect)

(When aircraft dihedral effect is greater than directional stability)

Coordinated rudder resulting in roll only

Insufficient rudder resulting in decreased roll moment caused by sideslip toward roll direction

Excess rudder resulting in increased roll moment caused by sideslip opposite roll direction

Rol

l Rat

e

Time

Figure 16 Dihedral Effect, Rudder Use, Roll Rate

Sideslip-induced roll momentopposes aileron roll momentand reduces roll rate.

Sideslip-induced rollmoment reinforces aileronroll moment and increasesroll rate.

Low directional stability,adverse yaw, or top ruddercould cause left sideslip.

Right sideslip could becaused by low directionalstability or by top rudder.

v

v

Aileronmoment

Figure 15Sideslip andRoll Rate

Sidewayscomponent ofrelative wind.



Aerobatic Aircraft and Dihedral Effect

High-performance aerobatic airplanes usuallyhave little or no geometric dihedral, and so verylittle lateral stability through dihedral effect. Onecan’t always know what the designer had inmind, but the absence of dihedral allows aircraftto roll faster in the presence of opposingsideslips, and makes them easier to fly tocompetition standards because roll rate andrudder deflection remain essentially independent.It’s possible to use the rudder to keep the nose upduring the last quarter of a slow roll (when anaircraft that’s rolling left, say, and going throughthe second knife edge is sideslipping to the right)without having to change aileron deflection tokeep the roll rate from accelerating.

These desirable characteristics for smoothaerobatic flying actually make an aircraft lesssuitable for unusual-attitude training. Mostaircraft do exhibit lateral stability, and theresulting characteristics are important tounderstand. For one thing, lateral stability allowsyou to roll an aircraft with rudder using normaldirectional input should you lose the primary rollcontrol—the ailerons.

Absent dihedral effect and unaccompanied byaileron, rudder deflection alone in someaerobatic aircraft will produce a roll opposite theexpected direction. For example, right rudder,instead of rolling the aircraft right by dihedraleffect (and roll due to yaw rate), slowly rolls it tothe left, as in Figure 17. Roll due to rudder iscaused by the vertical tail’s center of lift beingabove the aircraft’s center of gravity. A momentarm results. The effect could be particularlyevident in a zero-dihedral, low-wing aircraft,when a sideslip generated by rudder deflectionalso produces an accompanying, destabilizingroll due to cross flow. (Check back to Figure 9,top. Low wing is destabilizing.) The first timeyou try to unfold a map while using your feet tokeep the wings level in an aircraft that behaveslike this, you’re in for a surprise.

If you actually lost your ailerons you mightregain some positive dihedral effect and roll dueto yaw rate by slowing down and increasing thecoefficient of lift. Also, slowing down will raisethe nose, and so place the tail lower and decreasethe vertical distance between its center of lift andthe c.g., reducing the moment arm. Perhaps theaircraft would then respond in the normal way. Itmay be possible (as in the Giles G-200, for

example) to control an aircraft by using roll dueto rudder, but it’s not the sort of thing thathappens intuitively. Aileron failure is typicallycatastrophic in an aircraft without dihedral effect.That’s one reason why preflight inspection of thelateral control system in a zero-dihedralaerobatic aircraft (for integrity of the linkages,and for items that could cause jams like loosechange, nuts, bolts, screwdrivers, hotelpens—your mechanic has horror stories andprobably a collection of preserved examples) isso important. The same, of course, goes forelevator and rudder systems.

Here’s a related phenomenon: Next time you flythe swept-wing MiG-15, notice that rudderdeflection produces a roll in the expecteddirection until you get past about Mach 0.86, butthen the response reverses—left rudder causingthe right wing to drop, for example. A sideslip,as pointed out in Figures 12 and 13, reduces thesweep of one wing and increases the sweep ofthe other, relative to the free stream. Thereduction in the effective sweep of the rightwing, caused by pressing the left rudder, cansend the right wing past critical Mach number,causing shock airflow separation and a wingdrop. If you’re pulling g, the effect can happen ata lower speed because of the acceleration of theairflow over the wing caused by the higher angleof attack. Response to the rudder returns tonormal at about Mach 0.95.

Roll moment due torudder deflected to theright

c.g.

Verticaltail centerof liftabove c.g.

Figure 17Roll due toRudder, Cl

δr

No dihedral



Roll Due to Yaw Rate, Clr

When an aircraft yaws, the wing moving forwardhas higher local velocity than the wing movingback. The higher the yaw rate, or the longer thewingspan, the greater the velocity differencebecomes. Yaw rate produces a difference in liftand an accompanying roll moment, whichdisappears once yaw rate returns to zero. The rollmoment varies with the square of the differencein speeds across the span (since the lift producedby a wing varies with V2).

When you enter a sideslip by pressing therudder, some percentage of the roll momentgenerated is caused by dihedral effect, and someby roll due to yaw rate. Once a given sideslipangle is reached and held and yaw ratedisappears, dihedral effect provides theremaining rolling moment.

Like the dihedral effects described above, rolldue to yaw rate increases with coefficient of lift,CL. For rectangular wings, the value for therolling moment coefficient per unit of yaw rate,Clr, is about 0.25 times CL, on average. Wingtipwashout, and/or flap deployment, reduces Clr.

An aircraft in a banked turn has a yaw rate. Theoutside wing has to travel faster than the inside.This can create a destabilizing, “over-banking”tendency and force the pilot to hold outsideaileron during the turn. The situation gets worseas you slow down (or grow longer wings). For agiven bank angle, yaw rate varies inversely withairspeed. So as you slow down and increase CL,yaw rate also increases and roll due to yawbecomes more apparent. That’s why turning inslow-flight required so much opposite aileron tomaintain bank angle and felt so weird back inprimary training—and still does today.

An aircraft that requires lots of opposite aileronin response to yaw rate in a turn is likely to bespirally unstable if left to its free response. Whena wing goes down and an aircraft enters asideslip, dihedral effect will tend to decreasebank angle and roll the wing back up. But at thesame time the aircraft’s directional stability tendsto yaw the nose into the sideslip, generating ayaw rate and a rolling moment that increasesbank angle. If that moment wins the contest, aspiral begins.

x body axis

Figure 18Aircraft Yaw Around Z Wind Axis

Lift vector

z body axis

x wind axis

z wind axis

Aircraft yaw aroundtheir z wind axis. Arolling moment thatmay result occursaround the x windaxis.



Dutch Roll

Directional stability, dihedral effect, and roll dueto yaw rate all do battle in the dynamicphenomenon called Dutch roll. Dutch rolltendency appears in aircraft with high lateralstability as compared to directional stability. It’sparticularly a problem with swept-wing aircraft,in which lateral stability increases with angle ofattack (i.e. coefficient of lift), as alreadydescribed. Although not nearly as bad, ourstraight-wing Zlin has enough Dutch roll inturbulence to make the ride memorable.

In the Dutch roll, a disturbance in roll or yaw,whether pilot-induced or caused by turbulence,creates a sideslip. A sideslip shifting the velocityvector (relative wind) to the right, as in Figure20, for example, leads to an opposite rollingmoment to the left (through dihedral effect androll due to yaw rate). But the aircraft’sdirectional stability works to eliminate thesideslip by causing the nose to yaw to the right,back into the wind. However, momentum causesthe nose to yaw past center (past zero β), and thissets up a sideslip in the opposite direction, whichin turn sets up an opposite roll. The resulting out-

of-phase yawing and rolling motions woulddamp out more quickly if they occurredindependently. Instead, each motion drives theother. Note that Dutch roll is the result of thefundamental tendency of a stable aircraft to rollaway from but yaw toward the velocity vectorwhenever that vector leaves the aircraft’s planeof symmetry.

Without a yaw damper to do it for them, it’sdifficult for pilots to control a Dutch roll becauseits period is short. It’s hard to “jump in” with therequired damping input at the right time. Pilotsof swept-wing are frequently trained to keep offthe rudders, check the roll with temporary, quick,on-off applications of aileron, and then recoverto wings level. Another strategy is to use the

After initial disturbance, aircraft asshown wants to yaw right (directionalstability) but roll left (roll due tosideslip angle and dihedral effect). Asthe nose-right yaw rate increases, aright rolling moment due to yaw ratebuilds. Left-rolling dihedral effectdeclines as sideslip angle decreases.

Velocity vector

Yaw overshootsdecrease as motiondamps out. Rollsubsides.

Yaws past center and now wants toyaw left but roll right as sideslipangle changes sides. Yaw rate (andassociated roll moment) is highestas the nose passes through therelative wind. Roll moment due todihedral effect increases withsideslip angle, β.

Yaw

Roll

Yaw

Roll

Yaw

Roll

Figure 20Dutch Roll

Figure 19 Aircraft Pitch Around Y Wind Axis

V

x body axis

β

y body axis

y wind axis

Geometrically, pitching around the y wind axis also produces a roll. In a sideslip to the right, as above, pulling the control back will cause a roll to the left; pushing forward causes a roll to the right. This is easier to visualize if you try it with a hand aircraft model. Note that the rolling effect is consistent with (operates in the same direction as) the other sideslip/yaw-rate rolling moments described in the text.



rudder—not to combat yaw but to keep thewings level.

The tendency to Dutch roll increases at higherCL, because increasing the coefficient of liftincreases both dihedral effect (especially swept-wing) and roll due to yaw rate. Dutch rolltendency also increases at higher altitudes, whereaerodynamic damping effects diminish. Sinceaircraft must fly at high CL at high altitudes, theproblem compounds. Normally aspirated piston-engine aircraft upgraded with turbochargers forhigh-altitude flight sometimes end up needinglarger vertical tails for better damping.

Reducing dihedral effect will ease the Dutch rollproblem, but at the expense of reduced lateralstability.

Aircraft with greater directional than lateralstability tend to Dutch roll less, but also tend tobe spirally unstable. Traditionally, the designcompromise between Dutch roll tendency andspiral instability has been to suppress the formerand allow the latter, because spiral dives—whilepotentially deadly—begin slowly and are easierto control than Dutch roll.


Flightlab Ground School5. Longitudinal Static Stability


Longitudinal Static Stability

Stability is a subject that gets complicated fast.Many factors contribute, yet the aerodynamicsliterature lacks an accessible, lucid account. Theemphasis here—and in the Flightlab groundschool texts on maneuvering and dynamicstability—is to give information that allows apilot to observe an aircraft’s stabilitycharacteristics in a thoughtful way, and tounderstand how those characteristics may varyunder different conditions and from type to type.

An aircraft has positive longitudinal staticstability if its initial response in pitch, in 1-gflight, is to return to equilibrium around its trimpoint after displacement by a gust or by thetemporary movement of the elevator control.(The term longitudinal maneuvering stabilitydescribes behavior in more than 1-g flight.Dynamic stability refers to response over time.)

When you trim an aircraft to fly at a givencoefficient of lift, CL, but then push or pull onthe stick and hold it there in order to fly at adifferent CL (or the equivalent angle of attack orairspeed) you’re working against the aircraft’sinherent stability. The aircraft generates arestoring moment that’s proportional, if youdon’t retrim, to the force you feel against yourhand. The faster that force rises with stickdeflection, the more stable your aircraft.

Classical stability depends on the distancebetween the aircraft’s center of gravity and a setof neutral points farther aft along thelongitudinal axis—the larger the distancebetween c.g. and neutral point the higher thestability. We’ll get back to neutral points lateron.

An aircraft in trim is in an equilibrium statearound its pitch, or y, axis. All the competing upor down moments (see Figure 4) generated bythe various parts of the aircraft, and actingaround its c.g., are in balance. In aerodynamicsnotation, a pitch-down moment carries a negative

sign; pitch up is positive. In equilibrium, allmoments sum to zero.

Figure 1, top, shows the change in coefficient ofmoment in pitch, CM, which results from achange in coefficient of lift for a statically stableaircraft. The longitudinal static stability curvecrosses the CL axis at the trim point, where CM =0. If the relative wind is displaced by atemporary gust or a pull on the stick, so that the

CL

+ CM

Nose up

- CM Nose down

Pitching Moment Coefficient

Trim point CM = 0

Increase in CL past trim point causes nose-down pitching moment.

Figure 1 Pitching Moment versus CL

A

B

Pitch break at stall

+ CM

Nose up

- CM Nose down

Pilot puts stick forward and retrims at new CL. Curve shifts vertically but stability slope remains constant.

New trim point

CL

Pilot puts stick aft and retrims at new CL.

0



CL

+ CM

Nose up

- CM Nose down


Unstable

Stable

Figure 2 Curve Slope

Neutral Stability +CM at CL = 0

CL of the wing goes up to point A, a negativepitching moment results, B, which restores theaircraft to its trimmed angle of attack, α, andthus CL.

The bottom of Figure 1 shows how the stabilitycurve moves vertically when you changeelevator angle to fly at a different CL. Note thatthe aircraft’s stability remains the same (sameslope), but the trim point shifts.

The stability (or ΔCM/ΔCL) curve typically takesa downward turn to a more negative slope as theaircraft passes the stalling angle of attack(Δ, pronounced “delta,” means change). This isbecause the downwash at the tail decreases as thewing gives up lift (assuming a root-first stall anda receptive tail location), and because thepitching moment of the wing itself becomesmore negative as its center of pressure suddenlymoves rearward at the stall. The increase indownward pitching moment, -CM, is helpfulsince it aids stall recovery. If such a pitch break(or g-break) occurs at the stall, it must be in thestable direction throughout the aircraft’s c.g.envelope under the requirements of FAR Parts23.201and 25.201.

On the early swept-wing aircraft with a tendencyto stall at the wingtips first—causing the centerof lift to shift forward and the aircraft to pitchup—an initially negative, stable curve mightactually reverse its slope at high CL and producean unstable pitch break.

A negative slope (ΔCM/ΔCL < 0) is necessary forpositive static stability. The more negative theslope the more stable the aircraft. In addition,there must be a positive pitching moment, CM,associated with CL = 0.

The curve for a neutrally stable aircraft has azero slope; so no change in pitching momentresults from a change in angle of attack (Figure2).

The ΔCM/ΔCL curve for a statically unstableaircraft has a positive slope (ΔCM/ΔCL > 0). Fornormal certification, it must be necessary to pullin order to obtain and hold a speed below theaircraft’s trim speed, and push to obtain and holda speed above trim speed. A statically unstableaircraft doesn’t obey this (Figure 3). Instead, achange in angle of attack from trim leads to apitching moment that takes the aircraft farther

from equilibrium, and actually produces areversal in the direction of stick forces.

The result of moderate instability might still be aflyable aircraft, but the workload goes up. Lookat the positive, unstable slope in Figure 3. If youpulled back on the stick the aircraft would pitchup and slow. But if you then let go of the stickthe nose would continue to pitch up, since apositive pitching moment would remain. Itwould require a push force to maintain yourclimb angle, not the mandated pull. If youpitched down and let go, the nose would tend totuck under. You’d have to apply a pull force tohold your dive angle, not the mandated push.That’s how the Spirit of St. Louis behaved. (TheEAA’s flying replica provides a fascinatingexample of the original’s unstable flying

CL

+ CM

Nose up

- CM Nose down


Figure 3 Examples of Instability

In an unstable aircraft an increase in α creates a nose-up moment. Pilot has to push to hold a speed less than trim.

Otherwise stable aircraft with unstable pitch break at high α (typical of swept wings)



qualities. It’s laterally and directionally unstable,as well. But it’s not hard to fly—you just have tofly it all the time.)

Pilots experience longitudinal static stabilitymost directly through the control force (and to alesser extent the deflection) needed to change theaircraft’s equilibrium from one airspeed trimpoint to another. The steeper the slope of theΔCM/ΔCL curve, the more force needed.

High performance, competition aerobatic aircrafttend to be somewhere on the stable side ofneutral. Compared to other types, aerobaticaircraft can feel twitchy at first, partly becausethe light control forces associated with theirshallow ΔCM/ΔCL curves cause pilots to overcontrol. But compared to aerobatic types, morestable aircraft can feel stiff and reluctant. Itdepends on where your most recent musclememory comes from. FAR Part 25.173(c)requires that transport category aircraft have aminimum average stick force gradient not lessthan one pound for each six knots from trimspeed. FAR Part 23.173(c) takes things morebroadly, requiring only “that any substantialspeed change results in a stick force clearlyperceptible to the pilot.”

Figure 4 shows how the different parts of anaircraft contribute to longitudinal stabilitycharacteristics. The fuselage and the wing aredestabilizing. Static stability depends on therestoring moment supplied by the horizontal tailbeing greater than the destabilizing momentscaused by the other parts of the aircraft. If yourequire an aircraft with a wide center of gravityloading range, make sure to give it a powerfulenough tail (large area, large distance from c.g.,both) to supply the necessary restoring moments.

On conventional aircraft, once the design is set,static longitudinal stability and the control forcenecessary to overcome that stability are bothfunctions of aircraft center of gravity location.Both decrease as the c.g. moves aft. Figure 5shows how the ΔCM/ΔCL curve changes with c.g.position.

Figure 4 Stability Components

+ CM

Nose up

- CM Nose down

CL

Wing and fuselage

Tail

Wing

Entire aircraft

+ CM

Nose up

- CM Nose down

c.g. aft of neutral point

c.g. forward

CL

c.g. on static neutral point

c.g. moves aft

Figure 5 Stability versus c.g.



Figure 6 shows how the curve for control forcenecessary to fly at airspeed other than trim varieswith c.g. position. The forces necessary aregreatest at forward c.g. Note that we’reswitching from a ΔCM/ΔCL curve, which a pilotcan infer but can’t experience directly, to forcesand speeds that he can.

The tendency of an aircraft to return to trimspeed when the controls are released is frictionand c.g. dependent. As the c.g. goes aft and theforce returning the stick to the trim positionbecomes less powerful, friction effects becomemore apparent. The aircraft can appear to havenearly neutral stability within a given airspeedband when there’s appreciable friction. If youdisplace the stick, let the aircraft establish a newspeed, and then let go, friction may prevent theelevator from returning to its original positionand the aircraft from settling back to its originalspeed.

The speed it does settle on is called the freereturn speed, which for Part 23 certification mustbe less than or equal to ten percent of the originaltrim speed. To determine free return speeds, trimyour aircraft for cruise and then raise the nose,allowing speed to stabilize about 15 knotsslower. Then slowly, so as not to provoke thephugoid, release aft pressure to lower the noseback down to trim attitude and hold it there,gradually releasing aft pressure as necessary.(Don’t push, since this immediately wipes outthe friction—the effect of which you’re trying tomeasure.) When you’ve released all aft pressure,note the speed. Repeat the exercise with a push.First let the aircraft accelerate 15 knots, and thenrelease forward pressure to bring the nose slowlyback up to trim attitude. (Don’t pull—friction,again) Hold that attitude and note the speed atwhich the necessary push force disappears. Thenumbers show your free return trim speed band,and may explain why you’re always fussing withthe trim wheel! A wide band makes an aircraftdifficult to trim.

The trim speed band may become wider as thec.g. moves aft. Aft movement reduces stability,which in turn causes the slope of the controlforce curve to become less negative (Figure 6).Less return force is then generated to oppose thefriction within the system.

Con

trol F

orce

, FS

0

Pull

Push

Airspeed

Aft c.g.

Trim

Figure 6 Control force versus c.g.

Forward c.g.

Con

trol F

orce

, FS

0

Pull

Push

Airspeed

Figure 7 Free Return Speed

Original Trim Speed

Free Return Speed

Free Return Speed



Neutral Points

When the angle of attack of an aircraftchanges, the net change in lift generated by thewings, stabilizer, and fuselage acts at theneutral point. The neutral point is sometimesreferred to as the aerodynamic center of theaircraft as a whole, similar to the more familiaraerodynamic center of a wing. There’s nomoment change about the neutral point (or aboutwing aerodynamic center) as angle of attackchanges—only a change in lift force.

In order for an aircraft to be longitudinallystable, the center of gravity must be ahead ofthe neutral point. Given that condition, the topleft of Figure 8 shows what happens when a gustor a pilot input increases angle of attack, α,above trim. The increased lift, acting at theneutral point some distance from the c.g.,generates a stabilizing, nose-down pitching

moment around the c.g. A stabilizing, nose-uppitching moment occurs if α goes down.

The aircraft on the right shows the unstableresponse when the c.g. lies behind the neutralpoint.

Static stability decreases as the c.g. moves aft,toward the neutral point. The ΔCM/Δ CL curvebecomes increasingly flat. If you shift the c.g. allthe way back to the neutral point, there’ll be achange in lift whenever α changes, but nomoment change. With the c.g. at the neutralpoint, pitching moment, Cm, becomesindependent of α. The aircraft will have neutralstatic stability. Since the aircraft no longergenerates a stabilizing moment, the pilot feels noopposing force in the stick when he moves it tofly at a new CL.

The aircraft becomes statically unstable when theelephant finally gets loose and moves the c.g. aft

Stick-free (elevator allowed to float) Static Neutral Point: c.g. location for zero stick force required to hold aircraft from trim α (airspeed)

Stick-fixed (elevator-fixed) Static Neutral Point: c.g. location for zero stick movement required to hold aircraft from trim α (airspeed) Increasing stabilizer area moves point aft.

Aircraft c.g. Stability decreases as c.g. moves aft. Stability and control force curves become less steep. Distance between c.g. and neutral point is static margin.

Stick-fixed static margin remaining at most aft c.g. ← →

Permissible c.g. loading range

Stick-fixed static margin ← →

Stick-free static margin ← →

Leading edge

Increase in α produces destabilizing moment.

Increase in α produces stabilizing moment.

Neutral point

c.g.

Figure 8 Static Neutral Points

Most aft c.g.



of the neutral point. Once again there’s a changein moment around the c.g. when α changes, butnow it’s destabilizing.

On a statically stable aircraft, the distancebetween the most permissible aft c.g. and theneutral point (both of which are expressed aspercentages of the mean aerodynamic chord ofthe wing) is known as the static margin. Thegreater the static margin, the greater the stabilitybecomes (and thus the more negative the slope ofthe stability curve).

Actually, as Figure 8 indicates, there’re twostatic stability neutral points: stick-fixed (elevatorand trim tab held in the prevailing trim position),and stick-free (hands off, elevator allowed tofloat in streamline as the angle of attack at thetail changes). In flight-testing, stick-fixedstability determines the amount of control andelevator movement needed to change airspeed (orCL, or α) from trim. Stick-free stabilitydetermines the required force. We’ll amplify thisbelow.

Stick-fixed Neutral Point

With a powered, irreversible control system theelevator usually doesn’t float unless somethingbroke, and so only the stick-fixed stabilitynormally matters. (However, sometimes aprogrammed, artificial float is introduced to curestability problems. Also, a control system canrevert in case of hydraulic failure. The Boeing737 reverts to a reversible system followinghydraulic failure. Its predecessor, the 707, wasreversible to begin with.)

At a given center of gravity position, an aircraft’sstatic stick-fixed stability is proportional to therate of change of elevator angle with respect toaircraft lift coefficient (aircraft lift coefficientincludes the combined wing and fuselage lifteffects). In other words, the more stable theaircraft is (the larger the static margin) thefarther you have to haul back or push on thestick. As you bring the c.g. back, less stickmovement is needed to produce an equivalentchange in CL and airspeed—and less spinning ofthe trim wheel is necessary to trim out theresulting forces. If the c.g. is brought back to thestick-fixed static neutral point, the change in stickposition needed to sustain a change of airspeed iszero. Once you’ve moved the stick to attain a

new angle of attack, you can put it back to whereit was before.

Reportedly, the Spitfire has just about neutralstick-fixed static stability in all flight modes. TheDC-3 is stable in power-off glides or at cruisepower but unstable at full power or in a powerapproach at an aft c.g.

Stick-free Neutral Point

The stick-free static neutral point is the c.g.position at which the aircraft exhibits neutralstatic stability (slope of the ΔCM/ΔCL stabilitycurve = 0) with the elevator allowed to float. Inother words, it’s the position where pitchingmoment, CM, is independent of CL with the stickleft free.

Your intuition may tell you that stick-fixed staticstability is likely to be greater than the elevator-floppy situation of stick-free, because of thefixed elevator’s greater efficiency in producingrestoring pitching moments. The actualdifference between fixed and free in an aircraftwith reversible controls (with reversible controls,wiggling the control surface wiggles the stick)depends on elevator control system design, inparticular the control surface hinge moments.Aerodynamic balance used to reduce hingemoments, and thus reduce the force a pilot has toapply to deflect the elevator, also reducesfloating tendency—and therefore increases thestick-free static stability margin. The stick-freeneutral point usually lies ahead of the stick-fixedpoint. Just how far ahead depends directly onhow much the elevator tends to float.

Figure 6 showed how the longitudinal stickforce, FS, necessary to move an aircraft off itstrim point decreases as the center of gravitymoves aft. This is the logical result of theaccompanying decrease in static stability. Whenthe aircraft’s c.g. lies on the stick-free neutralpoint, no change in force is needed to changeairspeeds.

Conventional handling qualities require that theaircraft c.g. lie ahead of the stick-free staticneutral point. If c.g. moves behind the neutralpoint, control forces reverse. A pull forcebecomes necessary to hold the aircraft in a dive;a push force becomes necessary in a climb.


Flightlab Ground School6. Longitudinal Maneuvering Stability


Maneuvering Stability

Longitudinal maneuvering stability is really juststatic stability with an additional factor: pitchrate. An aircraft in accelerated (curved)flight—whether pulling up, pushing over, orturning—has a pitch rate. Figure 1 shows thesimple case of an aircraft in a pull-up. Theaircraft pitches about its c.g. The tail sweepsalong behind, on its arm, lT. The tail’s motioncreates a change in its relative wind and thus intail angle of attack, αT. The change in tail angleof attack due to pitch rate produces an opposingpitching moment, known as pitch damping.

The change in tail angle of attack, ΔαΤ, due topitch rate is shown in the formula below, whereq is pitch rate in radians per second (one radianequals 57.3o; and 0.1 radian/second isapproximately 1 RPM). lT is the distancebetween aircraft c.g. and the aerodynamic centerof the tail. VT is the velocity of the tail (takentangentially to the aircraft’s flight path).

Thus the faster you pitch, and/or the farther backyour tail, the greater the change in αΤ, but it’s allinversely proportional to speed, VT, as theformula shows.

The actual tail angle of attack will also dependon the increased downwash produced by thewing as its lift coefficient rises in the pull-up,and a proper formula would take that intoaccount.

Because of pitch damping, an aircraft is actuallymore stable in maneuvering flight than in flightat 1-g. Remember, we assess stability in terms ofthe force needed to displace the aircraft fromequilibrium (trim). We assess static stability interms of the push or pull on the stick necessaryto change the coefficient of lift, CL, and toproduce airspeeds different than trim, whileflying at 1-g. In maneuvering flight at more than1-g, pitch damping increases the stick force wehave to apply to displace the aircraft fromequilibrium. How rapidly stick forces willincrease as we increase g depends on themaneuvering characteristics for which theaircraft was designed, and its c.g. location. Wecan examine an aircraft’s stick-fixed (elevatorposition-per-g) and the really moregermane—since it’s what the pilot feels—stick-free (stick force-per-g) maneuveringcharacteristics.

Figure 2 shows how the gradient, or slope, ofstick force-per-g depends on the location of theaircraft c.g. Forward c.g. increases an aircraft’s

Tail arm, lT

cg

Figure 1 Pitch Damping

qlT (pitch rate times arm)

ΔαΤ, change in tail angle of attack

VT

Pitch rate, q

Tail’s aerodynamic center

VT

T

TT V

ql=Δα

+ g

Stick Force

Figure 2 Stick force- per-g gradient versus c.g.

+ g

Stick Force

Turning flight At aft c.g.

At forward c.g.

Wings-level pull up

1 g

Longitudinal Maneuvering Stability


maneuvering stability, and therefore stick forcesbecome heavier. As you move the c.g. back,stick forces required to pull g go down. (Thestick position-per-g curve behaves similarly. Asc.g. moves aft, the deflection required to pull ggoes down.)

Stick force-per-g also varies directly with wingloading (aircraft weight divided by wing area).Highly wing loaded aircraft may need the help ofa powered control system to keep forces incheck. Raising the wing loading has the sameeffect as moving the c.g. forward.

Stick force-per-g is a particularly importantparameter and one of the basic handling qualitydifferences between aircraft designed fordifferent missions. When we maneuver anaircraft, we tend to evaluate its response in termsof the force we apply to the stick rather than thechange in stick position. We know the stick hasreturned to the equilibrium trim position, forexample, when the force disappears (at leastideally—friction and other factors can get in theway). And when we move the c.g. well aft in anaircraft—or take that first aerobatic flight—it’sthe reduction in stick forces we probably noticefirst.

Fighters and aerobatic aircraft require lowerforces-per-g than do normal or transport categoryaircraft because their g envelopes are wider andthe total stick force necessary at high g wouldotherwise be too great for the pilot to sustain. Soa fighter operating at up to 9-g or more needs ashallower force-per-g gradient than a transportexpected to operate at no greater than the 1.5-gapproximately required for a 45-degree-banklevel turn. The fighter’s shallow force-per-ggradient would be devastating in a transportbecause the pilot could easily overstress theaircraft. The transport’s steeper gradient wouldhave the fighter pilot pulling with both handswhile pushing on the instrument panel with hisfeet.

The importance of stick force-per-g in fightersbecame apparent during World War II. It wasdecided that the upper limit should be about 8lb/g to keep the pilot from tiring in a fight, with alower limit of 3 lb/g to prevent overstressing theaircraft and losing by default.

Overstress is the big worry; so FAR Part 23.155specifies the minimum total control forcenecessary to reach an aircraft’s positive limit

maneuvering load factor (g limit). It’s based onaircraft weight and the type of control. For wheelcontrols the minimum force has to be at least 1%of the aircraft’s maximum weight or 20 pounds,whichever is greater, but doesn’t have to exceed50 pounds. For stick controls, minimum force formaximum g has to be at least max weight/140, or15 pounds, whichever is greater, but doesn’thave to exceed 35 pounds.

To figure out what that would mean in terms ofrequired average minimum control-force-per-ggradient, you can take the design load limit ofthe airplane (6-g’s for our trainers), subtract 1-gto get the maximum g-load actually applied, andthen divide that into the minimum total forcerequired by regulation. For the Air Wolf (6-g’sand 2900 lbs. maximum aerobatic weight):

forcestick allowable minimum lb/g 4.1 5

1402900

=

A Cessna 172’s yoke force is greater than 20lb/g.A wings-level, 1.7-g pull-up in a Boeing 777requires 135 pounds. The Boeing is certifiedunder FAR Part 25, which actually doesn’tcontain sustained maneuvering control forcerequirements.

The FARs doesn’t specify maximum stick-force-per-g, but the military does, depending on thetype of aircraft.

Aircraft with shallow stick force-per-g gradientscan feel dramatically sensitive if your musclememory expects greater forces. Evenexperienced aerobatic pilots stepping up tohigher performance aerobatic aircraft usuallyfind themselves pulling too hard, detaching theboundary layer, and buffeting theaircraft—especially in the excitement ofaerobatic competition. This is seen from theground as an abrupt flattening in the arc of aloop, and from the cockpit as a sudden g-break.But after one becomes accustomed to thoseshallow gradients, the lower performanceaerobatic aircraft one trained in can seemdisagreeably reluctant to maneuver. The physicaleffort now feels out of proportion to the result.

On the other hand, pilots of early swept wingfighters had to worry about “g-limit overshoot”because of the forward shift in the center of liftas the tips began to stall. The F-86E SabreAircraft Operating Instructions cautioned pilots



against “A basic characteristic towardlongitudinal instability under conditions of highload factor, which … results in a tendency toautomatically increase the rate of turn or pull-upto the point where the limit load factor may beexceeded.” Fortunately, this was preceded bylots of warning buffet.

As noted, pitch damping depends on pitch rate.Pitch rate depends not just on how hard you pull,but also on the kind of maneuver you’re pullingin. At a given load factor, n, (where n =lift/weight) a level turn actually requires a higherpitch rate than a wings-level pull-up.

For a level (constant altitude) turn at a givenvelocity, pitch rate is a function of n - 1/n, butfor a wings-level pull-up it’s the smaller functionof n - 1. That greater pitch rate in the level turnmeans more pitch damping. As a result a 2-gturn, for example, requires more stick force thana 2-g pull-up. Accordingly, a high-performanceturn takes more pilot muscle than a loop entry atthe same load factor. See the dotted versus thesolid lines in Figure 2.

Our trainers have reversible controls (wiggle anelevator by hand and the stick wiggles as well).In aircraft with reversible controls, at any givenaltitude and c.g., the gradient of the stick force-per-g curve is independent of airspeed. Figure 3shows how the gradient remains constant asairspeed shifts from trim. The figure also showshow the absolute stick force needed to obtain agiven g will depend on the relationship betweentrim speed and actual airspeed. For example,when the aircraft is flying slower than trim, staticstability leads to a nose-down pitching moment,which adds to the pull force a pilot has to hold tomaintain a given g. But when flying faster thantrim, static stability leads to a nose-up pitchingmoment that decreases the pull force necessaryto maintain a given g. Because of the change inabsolute stick force necessary to hold a given gat speeds slower or faster than trim, test pilots tryto maintain trim speed when examining stick-force-per-g in “windup turns.” Otherwise thedata would plot an inaccurate stick force-per-ggradient.

The stick force needed to pull a given g remainsthe same at any trim speed. Say the trim speedrises. Because the elevator’s effectivenessincreases with airspeed, you don’t have to deflectit as much to produce a given pitch rate and loadfactor as you do at lower speeds. Less deflection

would mean lower forces, except that controlsurface hinge moments—which are what thepilot feels through the control systemgearing—also increase with airspeed. Thedecrease in required deflection is canceled out bythe increase in hinge moment, and the stick forcerequired for a given g load is the same at all trimvelocities (at a constant altitude and c.g.). Thisholds as long as compressibility effectsassociated with high Mach numbers don’tbecome a factor. Compressibility tends toproduce an increase in stick force-per-g.

g

Stick Force, Pull

Figure 3 Stick force- per-g gradient is constant at constant cg and altitude.

Velocity > Trim

Velocity = Trim

Stick Force, Push

1-g

Velocity < Trim



Damping versus Altitude

While static stability is not a function of altitude,maneuvering stability is. Stick force-per-g goesdown as you go up. That’s because dampingdecreases along with the decrease in air densityas you climb.

At least that’s the short explanation. Actually, inresponding to a given control input an airplanedoesn’t care about altitude, it cares aboutairspeed. Compressibility effects aside, for agiven input it will generate the same pitching (orrolling or yawing) moment at a given EAS(equivalent airspeed, meaning calibrated airspeedcorrected for compressibility) regardless ofwhether it’s flying down low or up high. But thedamping this moment has to overcome is afunction of altitude, because damping is afunction of TAS (true airspeed, or equivalentairspeed corrected for density altitude), as Figure4 explains. TAS goes up as altitude increases.

The figure shows that for a given pitch rate, q,the velocity component generated by themovement of the tail, qlT, is the same regardlessof altitude. But since true airspeed is higher ataltitude, the vectors add up to less change in tailangle of attack, and so less damping.

This is why an airplane will feel more responsiveand less stable at altitude, or perhaps even lowerdown on a hot, high-density-altitude day. Thereduction in damping also applies to an aircraft’sdirectional and lateral stability. Stabilityaugmentation systems, like yaw dampers, earntheir keep up high.

Tail Volume

Stability depends on the restoring momentsupplied by the horizontal tail being greater thanthe destabilizing moments caused by the otherparts of the aircraft. One factor is the tail-volumecoefficient, V . This is the product of thedistance between the aircraft c.g. and the tail’saerodynamic center, lT, times the tail area, ST.The result is then divided by the meanaerodynamic chord of the wing, c , times thewing area, S.

ScS

V TTl=

In other words, the tail volume coefficient relatesthe area of the tail and its distance from the c.g.

to the chord and area of the wing. It suggestshow effective the tail is going to be at producingpitching moments. You can achieve a given tailvolume for a wing of a given size either byhaving a small tail on a long fuselage, or a largetail on a short fuselage (Figure 5).

Tail arm, lT

c.g.

qlT

ΔαΤ, change in tail angle of attack

True Airspeed, TAS

Pitch rate, q

qlT

TAS goes up as altitude increases.

ΔαΤ, Change in tail angle of attack is less than above.

Figure 4 Damping and TAS

Figure 5 Tail Volume Coefficient

Same tail volume coefficient as above, but shorter lT. Less pitch damping makes the aircraft more maneuverable.

lT



Since pitch damping is a function of the squareof the tail’s lever arm, lT

2, the farther back yourtail is the greater the opposing aerodynamicdamping generated when you start pitching itaround to maneuver. The design criterion forrapid maneuvering is a big tail on a shortfuselage—a hallmark of modern fighter design.Transports have proportionately smaller tails onlonger fuselages.

Neutral Points Again

Figure 6 adds the stick-fixed maneuver neutralpoint and the stick-free maneuver neutral point tothe stick-fixed and stick-free static neutral pointsdiscussed in the ground school briefing“Longitudinal Static Stability.” The aft shift ofthe corresponding maneuver points reflects thestabilizing effect of pitch damping. Becausedamping goes down with altitude, the maneuverpoints actually sneak forward as you climb.

The stick-free maneuver point is the c.g. positionat which the gradient of stick force-per-gbecomes zero. The more rearward stick-fixed

maneuver point is the c.g. position at which stickmovement-per-g becomes zero.

If we had a weight on rails and could move thec.g. rearward during flight, the first thing we’dnotice is a reduction in control force necessary tochange α and thus airspeed from trim (staticstability), accompanied by a reduction in stickforce needed to pull g (maneuvering stability).Short of shifting the c.g., a knowledgeableinstructor can simulate this for a student bymanipulating the trim.

As tail volume increases, the neutral points moveaft. This in turn increases the aft c.g. loadingrange.

Stick-free Maneuvering Point: c.g. location for zero stick-force-per-g gradient

Stick-fixed Maneuvering Point: c.g. location for zero stick movement to hold g

Stick-free Static Neutral Point: c.g. location for zero stick force gradient to hold airspeed from trim

Stick-fixed Static Neutral Point: c.g. location for zero stick movement required to hold airspeed from trim

Aircraft c.g.

Figure 6 Stick-fixed and free Neutral Points

←Permissible c.g. Loading Range → →

Typically for inherent stability and good handling qualities for an aircraft with reversible controls, maximum permissible aft c.g. must be ahead of all static and maneuvering neutral points, and forward of the point for minimum allowable stick-force-per-g. Maximum forward c.g. is determined by control authority need to raise the nose to CLmax, or by the maximum allowable stick-force-per-g.


Flightlab Ground School7. Longitudinal Dynamic Stability


Introduction to Stability

Stability is the general term for the tendency ofan object to return to equilibrium if displaced.

Static stability is an object’s initial tendencyupon displacement. An object with an initialtendency to return to equilibrium is said to havepositive static stability. For those blessed with aconventional pilot’s education, the concept ofstability normally evokes the textbook image ofa marble rolling around in something like ateacup, as shown in Figure 1.

An airplane can’t be trimmed unless it haslongitudinal (around the y axis) staticstability—in other words, unless pitching forcestending to equilibrium are present. But thegreater an aircraft’s static stability (thus thegreater the forces tending to equilibrium) themore resistant the aircraft is to the displacementrequired in maneuvering. For a given aircraft, themost important factor in determininglongitudinal static stability is c.g. position.Moving the c.g. aft reduces static stability.

Dynamic stability, our real subject here, refers tothe time history that transpires followingdisplacement from equilibrium, as shown inFigures 1and 2.

Aircraft can either have inherent aerodynamicstability (the typical case), or de-facto stability,in which stability requirements are met with theaid of a control system augmented with sensorsand feedback. For example, in order to achievemaximum maneuverability, the F-18 lacksinherent stability, and can’t be flown withoutsome operational brainpower on board inaddition to the pilot. The Boeing 777 has relaxedinherent longitudinal static stability, whichproduces efficiencies in cruise from a morerearward c.g. and a physically lighter tailstructure than otherwise possible. Boeingtransport aircraft have conventional downward-lifting tails that, like all such tails, in effect addweight to the aircraft by virtue of the “down-lift”

they generate (and also drag, the by-product ofthat lift). The main wing has to produceadditional lift in compensation, and consequentlyproduces more drag itself, which costs money atthe gas truck. Moving the c.g. aft reduces thenecessary down-force. The 777’s digital flightcomputers make up for the resulting longitudinalstability deficit—but the aircraft still has to havesufficient inherent stability to be flown safelyand landed should the digital augmentation gobust. The monster Airbus A380 employs an aftcenter of gravity for the same reason. It canpump fuel aft to shift the c.g.

Positive: Quick to return, hard to displace

Neutral: Stays put

Negative: Quick to displace, hard to return

Figure 1 Static Stability

Positive: Slower to return, easier to displace

Negative: Slower to displace, easier to return

Time

Dis

plac

emen

t

Time

Dis

plac

emen

t

Time

Dis

plac

emen

t

Time

Dis

plac

emen

t

Longitudinal Dynamic Stability


Dynamic Stability: Short Period andPhugoid

Figure 3 illustrates positive longitudinal dynamicstability: a series of damped oscillations ofconstant period, or frequency, and diminishingamplitude, that bring the aircraft back to thetrimmed condition after a displacement.

Period is time per cycle. Frequency, which isinversely proportional to period, is cycles perunit of time. Amplitude is the difference betweenthe crest or the trough and the originalequilibrium condition.

Damping is the force that decreases theamplitude of the oscillation with each cycle. Thedamping ratio, ζ, is the time for one cycledivided by the total time it takes for theoscillation to subside. The higher the dampingratio, the more quickly the motion disappears.

Damping defines much about the character of anaircraft. If damping is too high, an aircraft mayseem sluggish in response to control inputs. Ifdamping is too low, turbulence or control inputscan excite the aircraft too readily; its behaviorappears skittish.

There are two modes of pitch oscillation: theheavily damped short period mode (dampingratio about 0.3 or greater), followed by the

lightly damped, and more familiar, long period,phugoid mode. When you maneuver an airplanein pitch by moving the stick forward or back,you initially excite—and essentially just ridethrough—the short period mode. If you werethen to let go or to return the stick back to thetrim position, the aircraft would enter thephugoid mode. Instead, you normally hold thepressures necessary to prevent a phugoid fromoccurring.

Short Period

The short period mode is excited by a change inangle of attack. The change could be caused by asudden gust or by a longitudinal displacement of

Dis

plac

emen

t fro

m T

rim

Positive Static Stability and Positive Dynamic Stability

Figure 2 Dynamic Stability

Positive Static Stability and Neutral Dynamic Stability

Positive Static Stability and Negative Dynamic Stability

Time

Figure 3 Positive Dynamic Stability

Dis

plac

emen

t

Time →

Period

Amplitude

Period/Time to subside = damping ratio, ζ

Time to subside

Equilibrium



the stick. Figure 4 shows the variation in angle ofattack, α, over time. The aircraft quicklyovershoots and recovers its original angle ofattack, or its new angle of attack in the case of anintentional pilot input and a new stick position.The motion of the tail causes most of thedamping, although other parts of the aircraft cancontribute to damping (or to oscillation). There’snegligible change in altitude or airspeed by thetime the mode subsides. During the short periodoscillation the aircraft pitches around its c.g.

Positive damping of the short period is importantbecause catastrophic flight loads could quicklybuild from a divergent oscillation—suddenly theairplane has oscillated into parts. The shortperiod mode is also an area in which pilot-induced-oscillations, PIO, can occur, because thetypical lag time in pilot response is about thesame as the mode’s period (approximately 1-2seconds). As a result, by the time a pilotresponds to an oscillation his control input is outof phase, and he ends up reinforcing rather thancounteracting the motion he’s trying to correct.

At some point during our flights, we can performa frequency sweep with the stick to try to isolatethe aircraft’s short period natural frequency, ωn.(As a child you pumped a swing in rhythm withits natural frequency to make it go higher andterrify your mother.) We’ll do this by moving thestick back and forth over a constant deflectionrange of perhaps three or four inches, but fasterand faster until we find the input frequency thatplaces us 90 degrees out of phase—meaning thatthe stick is either forward or back when the noseis on the horizon (although it can be hard to tell).We’re then at the undamped short period natural

frequency—undamped because we’re driving itwith the stick. Then we’ll abruptly return thestick to neutral when the aircraft is at its trimattitude, and observe the damping of the shortperiod oscillation. It subsides very quickly, as inFigure 4.

The frequency sweep is not occupant friendly,but it’s a good way to assess an aircraft’s pitchacceleration, or “quickness.” The high pitchacceleration—the ability to quickly change angleof attack—is one of the first things you’ll noticewhen transitioning to high-performanceaerobatic aircraft. You can think of an aircraft’snatural frequency in terms of its ability to“follow orders”—how rapidly you can tell it todo one thing, then tell it the opposite, and stillhave it respond. The higher the naturalfrequency, the more response cycles you cancoax from it per unit of time. As we do oursweep, you’ll notice that past a certain point youcan’t coax any more. Then the faster you movethe controls back and forth the less the aircraftresponds. It’s as if the aircraft figures that youcan’t make up your mind, and that you need tobe ignored.

An aircraft with a low natural frequency mayseem initially unresponsive to control input. Apilot may then over control, using a large initialinput to get things going, only to find that theaircraft’s final response is excessive. If thenatural frequency is too high, the aircraft willfeel too sensitive in maneuvering and tooresponsive to turbulence.

Aircraft with low short period damping ratiostend to be easily excited by control inputs andturbulence, and the resulting oscillations takelonger to disappear. Aircraft with high shortperiod damping can be slow to respond—they’resluggish, and the control forces seem high.

(We’ll also look at our trainer’s quickness in roll.The notion of a natural roll frequency doesn’treally apply, because an aircraft isn’t supposed tooscillate in roll. Oscillatory response ischaracteristic of “second-order” systems. First-order systems, like a rolling aircraft, areexponential and non-oscillatory. We’ll do some“roll sweeps,” anyway. You’ll discover a similarfall-off in response.)

Trim α

α +

α -

Time (seconds)

Figure 4 Short Period

1 2



Long Period—Phugoid

The lightly damped, long period, or phugoid,oscillation can take minutes to play out. But itdoesn’t get to very often. Unlike the short mode,the phugoid period is long enough that the pilotcan intervene easily and return the aircraft toequilibrium. We typically demonstrate thephugoid by pitching the nose up (thus excitingthe short period mode) and allowing the aircraftto decelerate and stabilize some 15-20 knotsbelow trim. Then we positively return the stickto its original trimmed position. The positivereturn overcomes any friction in the elevatorsystem, and this keeps us from imposing anoverall descent or a climb onto the phugoid.Usually it doesn’t matter if you then hold thestick or let it go, since the difference betweenstick-fixed and stick-free is minor in the longperiod mode. But for consistency in response wewant to keep the wings level. By using rudder forthat job, we can avoid inadvertent pitch inputs.(On our flights we’ll often enter a phugoid moretheatrically, perhaps as the recovery from a spiraldive.)

From the nose-high attitude, the nose will beginto drop through the horizon into a descent, thenpitch up and climb back up as speed increases. Itthen repeats the cycle, overshooting its original,trimmed airspeed/altitude point by less and lesseach time. During the phugoid the aircraftmaintains essentially a constant angle of attack,α, while cyclically trading altitude and airspeed(potential and kinetic energy) until it againregains equilibrium as in (Figure 3). The pitchrate and the variation in maximum pitch attitudewill diminish with each oscillation. Pitch attitudeat the very top and bottom will be approximatelythe same as the original pitch attitude at trim.Minimum airspeed will occur at the point ofmaximum altitude, and maximum airspeed willoccur at the point of minimum altitude.

The phugoid oscillation is typically damped andconvergent, but it can be neutral, or evendivergent, and the aircraft will still be flyable,because of the ease with which the pilot canbring the long period under control (you’recontrolling the phugoid whenever you holdaltitude). But poor damping does increase theworkload and complexity of the scan forinstrument pilots when flying by hand, becausethe effort needed to hold altitude increases. Poordamping also makes it harder to trim an aircraft.

The undulating lines back in Figure 3 suggesthow the phugoid would appear to a stationaryobserver. Figure 5 shows the same from thepoint of view of another pilot flying level information, watching a “phugoidal”(“phugoiding?”) wingman. The aircraft appearsto rise and fall as airspeed changes produce liftchanges. Excess airspeed at the bottom produceslift greater than weight and a resulting upwardforce. Diminished airspeed at the top produceslift less than weight and a resulting downwardforce. Remember, α stays the same.

As a result of the airspeed changes an aircraft inthe phugoid would also appear to move back andforth, falling behind at the top of the cycle andscooting forward at the bottom, but less and lesseach time as the motion damps out.

Drag effects, rather than tail movement, dampthe phugoid. Raising parasite drag increasesdamping. With both the short period and thephugoid mode, an aft shift in c.g., close to theneutral point, will begin to produce an increasein period and a decrease in damping (for neutralpoint, see ground school “Longitudinal StaticStability”).

Propellers add a damping factor absent with jets.If brake horsepower is constant, propeller thrustincreases as airspeed decreases, and vice versa.This adds a forward force at the low-speed top ofthe phugoid and a restraining force at the high-speed bottom. This changing thrust/airspeedrelationship helps reduce the speed variationfrom trim and thus helps damp the motion.

Figure 5 Phugoidal Wingman

Lead pilot’s position and velocity

High speed at bottom

Low speed at top



The phugoid is sensitive to coefficient of lift, CL.At slow speeds, thus at high CL, both the periodand the damping decrease. At high speeds, thusat low CL, both period and damping increase.

Regulations

FAR Part 23.181(a) requires that the short periodoscillation must be “heavily damped” with thecontrol free and fixed. FAR Part 23.181(d)requires that “Any … phugoid oscillation …must not be so unstable as to increase the pilot’sworkload or otherwise endanger the aircraft.”

Part 25.181, for large aircraft, says the samething about the short period, but leaves thephugoid unmentioned.

The common element in the regulations is therecognition that a pilot can readily control thelong phugoid mode, and it’s not a crucial factorin flying qualities.

In regulatory practice, “heavily damped” meansin no more than two cycles. Test pilots for theRaytheon Premier I took the aircraft to 35,000feet to evaluate short period behavior in gusts.After pitching up and releasing the controls(stick-free), they found that the aircraft tookapproximately 2.5 cycles and 5 seconds to returnto level flight. The FAA agreed that thispresented no safety issues, but refused to wavetheir criteria (2 cycles and 4 seconds). Thedesigners fixed things by adding wedges to thetrailing edge of the elevator to change the hingemoments, making the elevator’s response tovertical gusts more neutral and bringing theaircraft into line with FAA requirements. All ofthis happened after an earlier modification hadslightly reduced the friction in the elevatorcontrol system, which in turn reduced thedamping ratio. The strange protuberances yousee on aircraft often have complex histories.


Flightlab Ground School8. Maneuvering Loads, High-G Maneuvers


Maneuvering Loads and the V-n Diagram

The V-n, velocity-versus-load diagram, Figure 1,describes the relationship between an aircraft’sspeed, its longitudinal (pitch axis) maneuveringcapability, and its structural strength. Thepositive-g, maximum lift line indicates howaggressively, at any airspeed, we can apply aftpressure to pitch an aircraft to change its flightpath without stalling the wings or doing damagethrough excessive loads. The maximum lift lineshows how our excess margin of nose-up pitchcontrol (in other words, the load factor, or g,available in reserve) diminishes as we slowdown, disappearing finally at the 1-g stall. Atthat point, in a normal aircraft, we can only pitchdown.

The limits represented by the parabolicmaximum lift line are also physiological, and

dramatically so. If you pull too hard, climb thelift line too high, and stay there too long, theblood starts leaving your brain. Your facebecomes strikingly woeful in the video; yourvision collapses from gray to black. Thenconsciousness shuts down. When the bloodreturns and the lights come on, your short-termmemory is an empty hole. Amnesia is commonenough in centrifuge trials that the USAFbelieves that many fighter pilots who experienceg-induced loss of consciousness (G-LOC) neverrealize it.

Each V-n diagram is for a specific aircraftweight and wing configuration (lift devices in orout): see Figure 2. Indicated airspeed is generallyused. Calibrated airspeed is sometimes usedsince it corrects IAS for position errors causedby the placement of the pitot and static sources,and by gauge errors within the airspeed indicator

Pos. Ultimate Load (Structural failure)

-3

-2

-1

0

6

5

4

3

2

1

Pos. Limit Load

Neg. Ultimate Load

Neg. Limit Load

Airspeed

Maneuvering speed or Corner speed (at max takeoff weight) VA, VC

G, o

r Loa

d fa

ctor

(n)

Maximum positive lift line and 1-g stall speed at reduced weight

Maximum positive lift line at maximum takeoff weight

1-g stall speed, max takeoff weight

VA, VC, reduced weight

VD

ive

Stall speeds above 1-g go up as the square root of the load factor.

Figure 1 V-n Diagram

2-g stall speeds

(Structural damage possible)

Maneuvering Loads, High-G Maneuvers


itself. An aircraft will stall at the same calibratedairspeed regardless of altitude. If the gauge errordepends only on airspeed, the aircraft will stall atthe same indicated airspeed, regardless ofaltitude.

The maximum lift line, or CLmax boundary, takesits parabolic shape from the fact that lift is afunction of velocity squared (because lift isproportional to dynamic pressure, q, which isitself proportional to V2). You can draw the liftline based purely on an aircraft’s 1-g stall speedat a given weight. At least you can for speeds toabout Mach 0.3. Above that, compressibilityeffects take over, CLmax declines, and the slope ofthe curve decreases.

Load factor, n, (n = Lift/Weight) is what’s readon the g meter. In normal, 1-g equilibrium flight,lift equals weight. In 2-g turning or loopingflight, the aircraft produces lift equal to doubleits weight. Some of that extra lift goes togenerate a centripetal force that accelerates theaircraft toward the center of an arc. Flight atmore than 1 g is always associated with a pitchrate.

As you increase your pitch rate at a givenairspeed, your g-load increases until you reachthe maximum lift line and stalling angle ofattack. Actually, before you hit the lift line youusually hit a buffet boundary, as airflowseparated from the wing and fuselage starts

belaboring the tail. In aircraft with personalityissues, the buffet boundary might be severe, orthe aircraft might have a pitch-up tendency or awing rock before reaching maximum coefficientof lift, CLmax, in which case the operationalboundary is defined by those characteristicsrather than by an actual stall break.

The lift line represents the maximum load factorobtainable at the corresponding velocity. In aconventional aircraft you can’t fly to the left ofthe line because the wing will stall first. Theaircraft unloads itself. You might exceed the liftline briefly by a quick charge, since dynamiceffects can allow airfoils to sustain liftmomentarily at greater than normal stalling angleof attack, if angle of attack is increased at a highrate per second. But then you’d just fall back intothe envelope as the momentary, extra liftdisappears.

Stall speed goes up by the square root of theload factor. So at 2 g, for example, stall speedgoes up by a factor of 1.4 (since √2 = 1.4).

-2

-1

0

4

3

2

1

Pos. Limit Load at max takeoff weight

Neg. Limit Load

Airspeed

VA, VC

G, o

r Loa

d fa

ctor

(n)

Flaps down at max takeoff weight

Figure 2 V-n Envelopes Flaps Down, Over Gross

Flaps extended speed

Over gross

Over gross reduces envelope.



Maneuvering Speed, VA

As defined by the V-n diagram, maneuveringspeed, VA, is the maximum speed at which anaircraft in symmetrical flight at the specifiedflight weight and configuration will stall(unload) before exceeding limit load andsustaining possible structural damage. Aircraftare therefore aerodynamically g-limited by thelift line up to maneuvering speed, andstructurally g-limited by the load line above it.Maneuvering speed is also the maximum speedfor turbulent air penetration, although a speedsomewhat less—fast enough to avoid stall yetslow enough to diminish the loadsexperienced—is usually recommended. (In anaircraft subjected to a sharp vertical gust of givenintensity, the increase in structural load—andthus the acceleration the pilot feels—variesdirectly with airspeed.)

At speeds above roughly Mach 0.3, CLmax beginsto decrease. Mach number depends on altitude,so indicated VA increases with altitude becauseyou have to go faster to generate equivalent liftat the lower CLmax.

Symmetrical flight means the aircraft isn’trolling and isn’t yawed. The load is symmetricalacross the span. That’s not the case in a rollingpull-up, however, where the rising wingexperiences a higher load than the wing goingdown (the rising wing is lifting more because ofthe camber change; the descending wing liftingless). The g meter in the fuselage reads only theaverage load, as in Figure 3.

Rolling pull-ups became a problem with the F4UCorsair gull-wing fighter in World War II.Reportedly, pilots would roll with aileron as theypulled out after a ground attack run, hoping toplace the aircraft’s protective armor platingbetween them and the answering ground fire.They sometimes went past limit load in the rolland came home with bent wings along with theusual shell holes.

VA and limit load (as measured at the fuselage)therefore decrease if the aircraft is rolling. Therolling motion could come from ailerondeflection, or from aggressive rudder inputcausing a roll couple (as in a snap roll). Aircraftflight manuals that specify a maximum limit loadfor rolling pull-ups typically place it at two-thirds to three-quarters of the symmetrical limitload. If you settle on a conservative two-thirds, a

6-g aerobatic aircraft has a rolling pull-up (andsnap roll) limit of 4 g. To keep things in roundnumbers, the “rolling” VA, as calculated for theaircraft weight, would be about twenty percentless than the symmetrical VA.

By the same logic a large aircraft certified underFAR 25.337(b) with the minimum allowed limitload of 2.5 would be restricted to a 1.65-g rollingpull-up, assuming that Mach buffet, caused bythe transonic acceleration of the airflow over thewing as angle of attack is increased, doesn’toccur first.

Unload before rolling if you’re in a high-gsituation and need to level the wings.

The above not withstanding, maneuvering speedis usually defined—without regard toasymmetrical loads—as the maximum speed atwhich full or abrupt combined controlmovements can be made without damaging theaircraft. The FAA’s AC 61-23C, “Pilot’sHandbook of Aeronautical Knowledge,” saysthat “any combination of flight control usage,including full deflection of the controls, or gustloads created by turbulence should not create anexcessive air load if the airplane is operatedbelow maneuvering speed.” According to theNavy, “Any combination of maneuver and gustcannot create damage due to excess airload whenthe airplane is below the maneuver speed.”1

1 Hurt, H. H. Jr., Aerodynamics for NavalAviators, Aviation Supplies & Academics, Inc.1965. p. 339. I understand that the FAA copiedHurt.

Asymmetrical Load during Rolling Pull-up

7 g’s

5 g’s

3 g’s

Figure 3 Asymmetrical Loads



The NTSB has pointed out that this broaderdefinition, although widespread among pilots, isincorrect. Engineers consider each axisseparately in designing for the air loadsaccompanying an abrupt, full control input atmaneuvering speed. “Full inputs in more thanone axis at the same time and multiple inputs inone axis are not considered in designing for these[VA] flight conditions.”2

The particular “multiple inputs” that promptedNTSB comment were the rudder reversalsleading to a yaw over swing followed by a finalreversal that destroyed the vertical tail ofAmerican Airlines Flight 587 on November 12,2001. (Under FAR 25.351, rudders are tested forsudden displacement in a single direction at atime, and then returned to neutral, at speeds upto design dive speed.)

So here’s a conservative, inclusive, legalisticmouthful: Maneuvering speed, VA, is themaximum speed, at a given weight andconfiguration, at which any one (and only one)flight control surface can be abruptly and fullydeflected—not to include rapid control surfacereversals—without causing aircraft damage.

Simple Formulas

These formulas help define the relationshipsbetween aircraft weight, speed, and load.

(1) 1-g Stall Speed vs. Aircraft Weight:Knowing the 1-g stall speed, VS, at any weightgives you the 1-g stall speed for any otherweight:

( ) SS V NewVKnown htKnown Weig

WeightNew=×

(2) Stall Speed and Load Factor: Stall speedgoes up as the square root of the load factor, n.To find the accelerated stall speed, VSacc, for agiven load factor:

n factor, LoadV V SSacc =

(3) Maneuvering Speed, VA. Given the 1-g stallspeed, to determine an aircraft’s maneuvering

2 NTSB Safety Recommendation, November 10,2004.

speed at maximum takeoff weight for uprightflight in its category, use the formula above andsubstitute VA for VSacc. Insert a load factor of:

• 3.8 for Normal & Commuter but seeFAR Part 23.337(1).

• 4.4 for Utility• 6 for Aerobatic• FAR Part 25.337(b), 2.5 minimum

(4) Maximum Aerodynamic Load Factor for aGiven Airspeed: The highest load factor youcan pull at a given airspeed is based on the 1-gstall speed, VS, at the aircraft’s actual weight.You can use this to plot the lift line in the V-ndiagram:

n factor, Load V

Airspeed2

S=

(5) Maneuvering Speed vs. Aircraft Weight:Like other V speeds calculated on the basis ofaircraft weight, maneuvering speed, VA, goesdown as aircraft weight goes down. If the aircraftis under max gross takeoff weight, the allowablelimit and ultimate limit loads don’t change (sointerpret the g meter as usual). Only thecorresponding V speeds change as the maximumlift line shifts toward the left. Although the totallift force that the wing has to develop at limitload is less at lower weights, and the stress onthe wing is less, individual aircraft componentsstill weigh the same. Things like engine mounts,battery trays, luggage racks, chandeliers (ithappens), and landing gear up-lock systems maynot be designed to withstand more than theircomponent weight times limit load. At lowergross weights that load can be reached at lowerspeeds because the wing doesn’t have to produceas much lift. Since it doesn’t have to work ashard, it won’t stall until after the limit load isexceeded.

To calculate VA at reduced aircraft weight:

( ) AA V NewV TakeoffMax WeightTakeoffMax

WeightNew=×



Corner Speed

VA is also known as corner speed, VC, especiallyby fighter pilots, for whom it has tremendoustactical significance. VC is the speed formaximum instantaneous turn performancewithout exceeding structural limits.“Instantaneous” is used because an aircraft mightnot have the thrust necessary to sustain VC underthe elevated induced drag of maneuvering at highangle of attack. Sustained corner speed has alower value.

Turn rate goes to maximum at corner speed.

That’s because turn rate is proportional to n/VT(n is load factor; VT is true airspeed).Combinations of high g and low airspeed favorturn rate. Corner speed is the lowest airspeed atwhich maximum structural g is possible. Flyingat maximum structural g at any speed in excessof VC causes turn rate to decrease.

A high turn rate is obviously important to fighterpilots because it allows them to achieve firingsolutions in a turning fight.

Turn radius goes to minimum at corner speed.

Turn radius is proportional to VT 2/n. Thereforeradius is minimized by high g and low airspeed.Again, corner speed is the lowest speed for thehighest allowable structural g.

The top of Figure 4 suggests how the radiusdecreases as load factor rises. It decreasesquickly at first, but then the rate of change per gslows down. Note that flying at maximumstructural g at any speed in excess of VC causesthe turn radius to increase.

Low wing loading (aircraft weight/wing area)favors maneuverability. At a given CL, minimumturn radius and maximum rate come when theaircraft is light. Higher air density (thus loweraltitude) also favors maneuverability.

Pull-ups

Corner speed is spoken of in discussions ofturning flight, but remember that turning isn’tlimited to the horizontal plane. The pull-up youmay find yourself in during a nose-low unusual-attitude recovery is a vertical turn. Here,achieving minimum radius may be crucial.Figure 4 shows the relationship between cornerspeed and turn radius in a pull-up.

The strategy for a low-altitude, maximum-performance, minimum-radius, limit-load pull-up is to pull to and maintain CLmax (indicated byinitial buffet, angle of attack indicator, stickshaker, fly-by-wire g limiter, unacceptable wingrock) until reaching corner speed, then remainat limit load until recovery.

The problem is blasting through VC, (or startingthe recovery past VC) so you’ll want to have thedrag devices out, pending approval from thePOH/AFM. In propeller aircraft, that includespower back and flat pitch for more drag.Lowering the landing gear might blow off thedoors or lead to a partial extension, but thatcould be a good trade. In a jet, what you do withpower could depend on the pitching momentassociated with power change. With fuselage-mounted engines, throttles would normally comeback. But retarding power on an aircraft with

Figure 4 Pull-up Turn Radius versus Corner Speed

Corner Speed, VC

Ver

tical

Tur

n R

adiu

s →

Load

Fac

tor →

Airspeed

Limit Load



wing-pylon-mounted engines creates a nose-down pitching moment. Some speed brakes dothe same. The POH/AFM is the guide. At lowaltitude, Mach buffets and Mach-related trimeffects presumably would not be a factor.

Critics of the use of corner speed as part ofrecovery procedure point out that the speedvaries with aircraft weight, and there’s the“potential that pilots could fixate on obtainingand maintaining corner speed, while delaying oroverlooking implementation of other recoverytechniques, and result in [sic] unnecessary loss ofaltitude during a nose low recovery. Exposingpilots to the concept of corner speed and radiusof turn as a basis for understanding why it maybe necessary to increase speed in order torecover from a nose low, low altitude upset isbeneficial. However, incorporating a cornerspeed into recovery procedure, we feel isinappropriate.”3 Sounds like a sensible objection.

Student behavior suggests that the most commonerror is to be too gentle on the aircraft in theinitial part of a dive recovery. For fear ofoverstressing the aircraft, pilots are reluctant toadd normal acceleration (g’s) to longitudinalacceleration (the aircraft’s increasing speed), sothey bring in the g slowly. But the induced dragcreated by the increased lift necessary for normalacceleration also acts as a brake on longitudinalacceleration. Pull smoothly—no yanking intoan accelerated stall that actually lowers pitchrate—but if ground avoidance is at stake don’thesitate in getting to the maximum g (i.e.,maximum pitch performance and minimumradius) the flight condition allows.

Rolling is a limiting flight condition. Ifnecessary, level the wings before a pull up. Theasymmetrical load caused by aileron deflection,added to a pull-up load, can overstress thewing. Again, an aircraft’s VA and g-meter limitload decrease when rolling. And as pilotsgenerally don’t recognize, high adverse yawgenerated by large aileron deflection whilepulling could lead to high sideslip angles andbending stresses on the vertical tail. 3 Attachment H, Correspondence from AirplaneManufacturers to American Airlines andResponse. Exhibit Items from the Public Docket,NTSB Public Hearing American Airlines Flight587 Belle Harbor, New York, October 29-November 1, 2002. (Link atwww.ntsb.gov/events/2001/AA587/exhibits)

A wings-level pull-up is also more efficient,since the entire load is applied to lifting the noseto the horizon, and not partly to turning.

Pull-ups and Phugoids

The hands-off phugoids we fly at the beginningof our flight program demonstrate that alongitudinally stable aircraft will try to pull outof a dive by itself. The altitude consumed willdepend on the true airspeeds and load factorsattained.

At a given g at any instant, the radius of either apilot-induced or a pure phugoid-induced pull-upvaries with the square of the airspeed. As aresult, for example, if you enter twice as fast, butyour load factors remain identical, you’llconsume four times the altitude.

(The g that actually matters in maneuveringperformance is “radial g,” explained farther on.Radial g depends both on the load factor seen onthe g meter and on aircraft attitude.)

The phugoid-generated load factor depends onthe design and balance characteristics of thecontrol system, but more essentially on thedifference between the airspeed attained and thetrim speed. Remember that during the phugoidthe aircraft maintains a constant angle of attack.At a constant angle of attack, lift goes up as thesquare of the increase in airspeed. For example,if we trim for 100 knots in normal flight (1 g)and reach 200 knots in a phugoid dive recovery,airspeed will be double the trim speed and theload factor will hit a theoretical 4 g. If weaccelerate to 140 knots, it’s a 1.4 increase inairspeed over trim. 1.42 = 2; thus a load factor of2 g.

A pilot can overstress an aircraft in a dive by apull on the stick in addition to the aircraft’snatural phugoid. Again, the load generated by thephugoid depends on trim speed versus airspeed.The required pull, or g-limiting push, depends onhow this load compares to limit load.

The classic disaster pattern consists of thehorizontal stabilizers failing downward first ifthe pilot pulls too hard. When they fail, theaircraft suddenly pitches nose down, and thewings fail downward because of the suddennegative load.



Lift Vector, Radial G, and the Split-s

In a level turn, as shown at the top of Figure 5,the tilted lift vector has two vectoralcomponents, a vertical one equal to and oppositeaircraft weight, and a horizontal one pointingtoward the center of the turn. While the pilotfeels (and the g meter reads) loads in thedirection of the tilted lift vector, the horizontal,centripetal force that’s actually turning theaircraft—its radial g—has a lower value.

As bank angle increases in coordinated, constant-altitude flight, radial g grows. Past 90 degrees ofbank, the lift vector starts pointing toward theearth, and radial g gets a boost from gravity. Theresult can be up to a 1-g gain in radial g ininverted flight at the top of a loop.

For a given load factor (g on the meter),pointing the lift vector above the horizondecreases radial g and pitch rate; pointing itbelow the horizon increases radial g and pitchrate. The increased radial g available in invertedattitudes can help win dogfights, but it’s a trapfor untrained pilots. It’s why, at a given airspeedand applied g, positive (nose toward your head)pitch rates when flying inverted are higher thanpositive pitch rates when flying upright, and whypulling back on the stick as a reaction to theconfusion of inverted flight so quickly brings thenose down and the airspeed up. The resultingsplit-s entry (half loop from inverted), especiallyif provoked by an inexperienced pilot whoreleases his aft control pressure out of contritiononce the nose starts down, then changes heartand pulls some more, can quickly take theaircraft outside the envelope of the V-n diagram.That’s when it rains aluminum.

In a nose-down, inverted unusual-attituderecovery, the most important thing is to get thelift vector pointed back above the horizon.Except at extreme nose-down attitudes, thatmeans rolling upright rather than pulling throughin a split-s. In brief: When inverted, push tokeep the nose from falling further. Roll the liftvector skyward with full aileron while removingthe push force as you pass through knife-edge.Then raise the nose.

Just so you know, maximum structuralinstantaneous turn performance happens whilepulling maximum g, at corner speed, inverted.

Resultant Lift = Weight

Radial g or centripetal force.

Lift Vector and load factor (n) indicated on g meter.

Weight

Weight

Radial g or centripetal force.

Lift Vector and load factor (n) indicated on g meter.

Radial g = load factor + 1. Pitch rate increases; radius decreases.

Radial g = load factor

Radial g = load factor

Figure 5 Radial G

Radial g

Load factor

Theoretical constant-speed loop with a constant g on the meter.

Radial g = load factor - 1. Pitch rate decreases; radius increases.

But actual speed variation in constant-g loop makes it look more like this.


Flightlab Ground School9. Rolling Dynamics


The Aircraft in Roll

The dynamics of an aircraft in roll aresurprisingly complex, given the apparentsimplicity of the maneuver. Of course, oneperson’s complexity is just another persongetting started. At the U.S. Navy Test PilotSchool, for instance, “The classic roll mode is aheavily damped, first order, non-oscillatorymode of motion manifested in a build-up of rollrate to a steady state value for a given lateralcontrol input.”1 Well, ok, that sounds right.

Our Maneuvers and Flight Notes training guidedescribes piloting technique during aerobatic orunusual attitude rolling maneuvers. Here theemphasis is on the general characteristics ofaircraft response.

A roll starts with the creation of an asymmetriclift distribution along the wingspan. In the caseof aileron roll control, deflecting an aileron downincreases wing camber and coefficient of lift;raising the opposite aileron reduces camber andcoefficient of lift. The resulting spanwiseasymmetry produces a rolling moment.

As the aircraft begins to roll in response to themoment produced by the ailerons, the liftdistribution again begins to change. The rollingmotion induces an angle of attack increase on thedown-going wing, and an angle of attackdecrease on the up-going wing (Figure 1). Thiscreates an opposing aerodynamic moment, calledroll damping (or rolling moment due to roll rate,Clp). Roll damping increases with roll rate (andvaries with other factors we’ll get to). When thedamping moment produced by the roll rate risesto equal the opposing moment produced by theailerons, the roll rate becomes constant.

1 U.S. Naval Test Pilot School Flight TestManual: Fixed Wing Stability and Control,USNTPS-FTM-No. 103, 1997. p. 5.55.

In Figure 1 you can see that as the airplane rolls,the lift vector tilts to accommodate itself to thenew direction of the relative wind, creating newvectors of thrust and drag. As a result, the rollingmotion produces adverse yaw all by itself, ayawing moment that goes away when the rollstops. This yaw due to roll rate, Cnp, is inaddition to the adverse yaw created by thedisplaced ailerons, and increases with coefficientof lift. Depending on wing planform, at aspectratios above 6 or so, adverse yaw due to roll rateactually becomes more significant than that dueto aileron deflection.

Roll Helix Angle

Resultant lift

Resultant lift

Path of down-going tip: α increases.

Path of up-going tip: α decreases.

Figure 1 Roll Damping, Clp Yaw due to Roll Rate, Cnp

Flight velocity

Roll Direction

Change in α caused by rolling motion produces an opposite damping force, Clp.

Resultant drag yaws wing backward.

Resultant thrust yaws wing forward.

Rolling Dynamics


Adverse Yaw, Cnδa

Aerodynamic coupling effects keep rolling frombeing a one-degree-of-freedom proposition.Rolling moments come with yawing momentsattached, and those yawing moments affect rollbehavior.

Induced drag increases when an aileron goesdown, decreases when an aileron goes up. Theresult is usually an adverse yawing moment,opposite the direction of roll. In the absence of asufficient counteracting yaw moment—suppliedin part by the aircraft’s inherent directionalstability, in part by aileron design, and in theremainder by coordinated rudder—the aircraftwill begin to sideslip. The velocity vector willshift from the plane of symmetry toward the rolldirection if too little coordinating rudder isapplied, and shift opposite the roll direction ifthe rudder gets too emphatic an in-turn boot. In aperfectly coordinated, ball-centered roll and turn,with adverse yaw properly countered by rudderdeflection, the “instantaneous” velocity vectorremains on the plane of symmetry, as Figure 2describes.

The rudder deflection necessary to handleadverse yaw depends on the ratio of yawmoment to roll moment the ailerons produce.While the ratio is basically a function of theaileron system design, it increases withcoefficient of lift, CL. This means that asairspeed goes down, the need for ruddercoordination becomes greater. The nature ofinduced drag rise at high angles of attack is themajor reason, since induced drag increases as thesquare of the coefficient of lift. As the drag curvebecomes steeper, a given aileron deflectionproduces a greater difference in induced dragacross the span, and the yaw/roll ratio increases.Differential or Frise ailerons, initially designedto reduce aileron forces, also reduce adverse yawby increasing the drag of the up-going aileron.

Another factor is the reduction in directionalstability caused by the disrupted fuselage wake atangles of attack approaching stall. Becauseenergy is removed from the free stream, morerudder deflection is needed as weathercockstability goes down in the tired-out air.

Configuration is also important. Partial-spanflaps cause an aircraft to fly at a more nose-downangle for a given overall coefficient of lift. As a

result, the aileron portion of the wingexperiences a relative washout (leading edgedown) and generates a lower local coefficient oflift than when the flaps are up. That lower localcoefficient translates into less adverse yaw. Flapsalso reduce dihedral effect, so the sideslip thatdoes occur has less effect on roll.

Spoilers

Spoilers are generally thought to produceproverse, roll-direction yaw, but they can causeadverse yaw. Spoilers increase profile drag. Theyalso decrease induced drag, since they kill lift.When the increase in profile drag predominates,as it does at high speed, spoilers can generateproverse yaw. At low speeds, when induced dragis more important, they can generate adverseyaw, since the induced drag on the wing goingdown, the one with the deflected spoiler killinglift, is less than on the wing going up, where thespoiler remains tucked away.

Spoilers are useful in situations when aeroelasticaileron reversal could have been a problem (B-52, and just about all of the swept-wing, highaspect ratio transports that followed), or whenit’s necessary to extend the wing area availablefor flaps. They have an advantage over aileronsof producing powerful rolling moments at highangles of attack, but the disadvantage of lessermoments at low angles. The classic problem withspoilers is a possible nonlinear response as theirlocation moves forward on the wing. Smalldeflections may generate no roll, or even atemporary reversed roll response. (As the spoilerfirst rises, the tripped airflow can reattach to thewing. This results in an effective increase incamber and therefore in lift. Spoiler movementhas to be nonlinear with control wheel or stickmovement—so that the spoilers can quickly popup high enough to defeat any tendency for theairflow to reattach.) Many designs use spoilersand ailerons in combination, with the aileronsproviding both rolling moment and control feel,and a possible way of overcoming nonlinearspoiler response.

If you’re stuck in coach, the most entertainingwindow seat on a Boeing is just back of thetrailing edge, where you can watch the slot-lipspoilers being used for bank control when theflaps are extended. When the spoilers rise, theslots above the flaps open up. The change inpressure pattern reduces the lift gained from flap

Rolling Dynamics


deployment and causes the aircraft to roll.Deployed symmetrically, the spoilers provideaerodynamic braking.

A pilot who looks up to find himself flyinginverted in a spoiler-equipped aircraft has aquandary, since spoilers become more effectiveat higher coefficients of lift (higher α). Does thatmean the pilot should pull while inverted, toincrease roll response, at the risk of altitude lossand airspeed gain from the resulting nose-lowattitude? It’s hard to find someone with asatisfactory answer. Aggressive use of the ruddermight be warranted to help roll the aircraft usingdihedral effect and roll due to yaw rate.

Turn Coordination

Usually, we roll in order to turn. Steep turnsdeserve to be regarded as unusual attitudes, notjust because of the high bank angles but also thehigh-gain response those angles require whenyou’re trying to be perfect. The concentrationlevel goes up when you fly a steep (45-degreeplus), coordinated turn, while holding altitude.

We’ve defined coordination during roll in termsof keeping the velocity vector on the plane ofsymmetry. While the ailerons are deflected, thatmeans using rudder to correct for adverse yawand yaw due to roll rate—companion phenomenawhose relative magnitudes can be difficult tofigure out, but then you don’t have to figure: justpush the rudder to center the ball.

Once the bank is established, the ailerons moveto the position necessary to maintain the bankangle. Rudder into the turn is often needed tocounteract yaw damping, Cnr, caused by thefuselage and tail resisting the yaw rate and by theoutside wing moving faster than the inside wingand producing more drag. That might be thepredicament shown in the center aircraft at thebottom of Figure 3. An over-banking tendencyrequires aileron deflection against theturn—possibly causing proverse yaw (since theinside aileron is down), which of course modifiesthe rudder requirement.

The gyroscopic precession of the propellercreates a force parallel to the vertical turn axis.Therefore, precession causes the nose to moveperpendicularly to the horizon, regardless ofbank angle. For a clockwise propeller as seenfrom the rear, that means nose down turning

right, nose up turning left. At high bank angles,when the aircraft’s y-axis approaches alignmentwith the turn axis, more rudder deflection may beneeded to counter precession. Step on the ball.

Banked turns are combinations of yaw and pitch(Figure 2). Coordination (keeping the velocityvector on the plane of symmetry) meansestablishing both the yaw rate and the pitch rateappropriate for the bank angle.

As bank angle increases, pitch rate becomesincreasingly sensitive. Pitch rate controls loadfactor, and for a constant-altitude turn, therequired load factor goes up exponentially withbank angle. Getting the pitch rate/load factorright at high bank angles is difficult because theload requirements change so rapidly with evensmall changes in bank angle. Because the loadfactor goes up exponentially, so do the stickforces, at least in aircraft with reversible elevatorcontrols.

As bank increases, pitch rateincreases, yaw ratedecreases.

Turn ratearound turnaxis

Pitch rate

Yaw rate

Figure 2Relative Yaw andPitch Rates.Constant-Altitude Turn

Rolling Dynamics


Figure 3Coordinated Yaw Rate

Ball stays centered when the acceleration toward the outsideof the turn due to yaw rate and velocity equals the accelerationto the inside due to bank angle and gravity.

32.2 (sine φ) = Vr

“Stepping on the ball” controls yaw rate.

Bank angle φ (inradians)

Yaw rate, r

Acceleration due to gravity, g,(32.2 ft/sec2) times the sine ofthe bank angle (radians)

g(sine φ)

Velocity (ft/sec) times yawrate (radians)

Vr

g

Left. Coordinatedturn, velocity vectoron the plane ofsymmetry

x-axis

+β-β

In a turn thevelocity vector(arrow) is tangentto the flight path atany instant.

Flight path

Right. Too much rudder: Too muchyaw rate. Aircraft slips to the right ofthe plane of symmetry. Turn radiusdecreases because resulting sideforce caused by the relative windcoming from the right of the fuselagepushes aircraft toward the center ofthe turn.

Center. Too little rudder: Too little yaw rate. Aircraft slips to the leftof the plane of symmetry. Turn radius increases because resultingside force caused by the relative wind coming from the left of thefuselage pushes aircraft away from the center of the turn.

Note that for a given bank angle,coordination requires that as velocitydecreases yaw rate must increase.

x-axis

Rolling Dynamics


Roll Helix Angle

As an airplane rolls, its wingtips follow a helicalpath through the sky, like the shape of astretched spring. You see the helix at airshowswhen the pilot fires up the tip smoke. The anglebetween the resultant flight path of the wingtipand flight path of the aircraft is called the rollhelix angle (Figure 4). The roll helix angleincreases with increasing aileron displacement.Maximum attainable helix angle depends onaircraft design and mission. But on a givenaircraft a given aileron deflection always buildsto a given roll helix angle.

For any aileron deflection (roll helix angle),coordinated roll rate, p, varies directly with trueairspeed. “Coordinated” means there’s nosideslip affecting the rate. For the statement to betrue, there must also be no aero-elastic effects(wing bending caused by aileron deflection athigh speeds).

As the aircraft’s forward velocity increases, itwill maintain the helix angle—by virtue ofrolling faster. As a result, for a given helix anglean aircraft will complete a roll in the sameforward distance traveled, regardless of airspeed.Slippage aside, the helix angle is like the pitch of

a screw of given length. Regardless of rpm, ittakes the same number of turns to fasten it down.

When you know the helix angle, wingspan, andaircraft velocity, you can solve the formula inFigure 4 for roll rate. The helix angle provides away of establishing minimum acceptable rollrates for different aircraft (about 0.09 minimumfor fighters; 0.07 for transports). But it doesn’taccount for roll inertia, so it’s only a partialdescription of rolling character and is no longerused as a certification or acceptance measure.

Timed bank changes are used instead. TheFAA’s requirements are listed in FAR Parts23.157 and 25.147 (e).

Figure 4Roll Helix Angle

At a given helix angle,the distance to completea roll remains constantregardless of forwardspeed.

Roll HelixAngle ( )( )

( ) Vpb2sec. per. ft.in velocity 2

ft.in wingspan secondper radiansin rate rollanglehelix Roll ==

The helix angle is the ratio of tip velocity in roll,pb/2, to the aircraft’s forward velocity, V.

2pb

b

Rolling Dynamics


Roll Acceleration, Time Constant

Roll acceleration (and thus how quickly theaircraft reaches the final roll rate for a givenaileron deflection) depends on how much rollingmoment the ailerons produce versus the momentof inertia about the roll axis the ailerons have toovercome. We’re assuming the necessary ruddercoordination, and thus no inadvertent momentsdue to sideslip:

Rolling momentdue to ailerondeflection = Rolling accelerationMoment of inertiaabout the roll axis

The moment of inertia about the roll axis, Ixx,depends on how mass is distributed in theaircraft. If there’s lots of fuel in the wings, someengines hanging out there, and maybe full tiptanks, roll inertia will be higher than if most ofthe mass were confined to the aircraft’s fuselage.

Figure 5 shows the effect of inertia on rollacceleration and deceleration. Span, wingplanform, and the rolling moment due to theaileron “step” deflection are the same for bothcurves. Only the moment of inertia, Ixx, isdifferent. Notice the difference in initial slopebetween the two curves, and how maximum rollacceleration (not rate) happens at the initialcontrol input, before damping forces have achance to build. Notice the difference in the timerequired for reaching the steady rate in the two

inertia cases, and for the roll to stop when theailerons are neutralized.The roll mode time constant, τR, is the time ittakes to achieve 63.2 percent of the final rollrate, in seconds, following step input. If youcould maintain the initial acceleration (i.e. nodamping to slow things down) the airplanewould reach the target roll rate in only 63.2percent of the time actually required. In theory,the rolling aircraft “remembers” this constant.Because of damping, it takes the same amount oftime to achieve the next 63.2 percent of the finalroll rate, then the next 63.2 percent after that, andso on. At least theoretically, the asymptotic curvekeeps trying but never flattens out. After fivetime constants the roll rate will be at 99.5% ofthe final value. Close enough.

The greater the moment of inertia versus theaileron authority, the longer the time constantwill be. Two aircraft may have the samemaximum roll rate, but the one with the greatertime constant will take longer getting to it andlonger to stop rolling when the ailerons arereturned to neutral. Therefore inertiacharacteristics, and not just maximum roll rates,need to be taken into account when comparingthe rolling performance of different aircraft. In agiven aircraft, roll rate can magically increasewith increasing change of angle. Roll ratemeasured from a 45-degree bank to an opposite45-degree bank may be lower than if measuredfrom, say, 60 degrees to 60 degrees. That’sbecause the time spent accelerating is a smallerfraction of the total.

Low inertia

High inertia

“Steady” rollrate

63.2%

+

0

-

Slope indicates initialroll acceleration.

High inertia

Low inertia

Time

Roll Mode Time Constants, τR

Ailerons deflected:step input

Figure 5Time to ReachRoll Rate

Ailerons returnedto neutral

Rolling Dynamics


It’s difficult for a pilot to measure the timeconstant without special equipment, becausethere’s no easy visual reference on roll initiation,and it’s usually less than a second (andimperceptible for a fast roller). Since the timeconstant is the same to stop a roll as it is to startone, and the visual references are clearer, youcan try to measure the time to stop instead. (Ithelps if there’s minimal freeplay in the controlsystem.) Begin with a 45-degree bank angle andmake a coordinated roll to upright using animmediate, step aileron deflection (the amount ofdeflection doesn’t matter, since the time constantis the same, see Figure 6). Hold that aileron inputuntil the wings become level with the horizon,then instantly neutralize the controls and watchfor any additional roll. 63.2 percent of the timeit takes for any remaining roll to subside is thetime constant due to roll inertia. You might thinkthat the more aileron you use and the faster youroll to upright the greater your overshoot pastlevel. But it doesn’t work that way, because thefaster you roll the greater the aerodynamicdamping available to stop things when youneutralize the controls.

The idea that an aircraft that accelerates quicklyinto a roll can stop just as quickly takes aerobaticstudents by surprise. In performing 360-degreerolls, most will start out leading the recovery bytoo much and stopping short of wings-level.(That’s normal, but students who over-roll andstop past wings level are obviously behind theaircraft.)

At a given altitude, roll mode time constantvaries inversely with true airspeed (TAS). That’strue to experience—the faster you go, thequicker you can accelerate into a roll. But at aconstant TAS, the time constant increases withaltitude. The air is less dense, and for a givenTAS there’s less dynamic pressure available toovercome inertia. There’s also less damping asaltitude increases, so it takes longer for the rollrate to settle.

Airplanes with noticeable time constants (ascaused by high roll inertia and/or low rolldamping, and limited aileron control power)require that pilots learn to “shape” their controlinputs, first using large initial deflections formaximum acceleration and then reducing thedeflection once the desired rate is achieved. Thenthey have to check the airplane’s roll motionwith opposite, anticipatory aileron inputs whencapturing a bank angle or returning to level

flight. The wheel or stick becomes anacceleration controller. Pilots can adapt, but theworkload increases. Because of its huge x-axisroll inertia, the B-52 has this kind of response.

On the other hand, aircraft with short timeconstants tend to feel quick and responsive.Because they accelerate quickly, the stickbecomes essentially a rate controller. Withinbounds, that’s what pilots prefer.

The FARs don’t specify time constantrequirements, but, for the military, MIL-STD-1797A 4.5.1.1 sets the maximum τR between 1and 1.4 seconds, depending on aircraft missionand phase of flight.

In an aerobatic aircraft, because of the rapid rollacceleration, you can sometimes get theimpression that the aircraft’s steady roll rate isfaster than it really is. We feel acceleration muchmore profoundly than rate, especially as passiverecipients. Studies have shown that pilots tend toestimate ultimate roll rate based on initialacceleration. One of the malicious joys ofinstructing from the backseat in a true high-performance tandem aerobatic trainer iswatching your student’s head snap sidewayswhen you demonstrate maximum accelerationpoint rolls. A given roll rate can seem muchfaster (and not such great fun) when you’re thepilot-not-flying, because you’re not performingthe initiating control inputs that prepare the restof your body for the ride.

Identical time to reach steady roll rate following step input

Time constant at a given airspeed

Time

Rol

l Rat

e

Full aileron deflection

2/3 deflection

1/3 deflection

Figure 6 Time to Reach Roll Rate

Rolling Dynamics


Roll Rate

Figure 6 shows a time history, from the initialacceleration to the point where acceleration stopsand a constant rate is achieved, for rolls usingthree different aileron instantaneous stepdeflections at the same airspeed. One thing itreveals is that at a given airspeed it doesn’t takean airplane any longer to reach its highest, full-deflection roll rate than it does to reach lesserrates using lower deflections.

Figure 7 shows the effects of sideslip on roll rate.Roll moments caused by sideslip are a functionof effective dihedral and of both sideslip angleand angle of attack. (See Flightlab GroundSchool, Lateral/Directional Stability) The twodashed lines in Figure 7 show an uncoordinated,aileron-only bank, with adverse yaw allowed todo its worst. In a laterally stable aircraft, sideslipproduced by adverse yaw reduces roll ratebecause of the opposing rolling moment fromdihedral effect. Rolling in one direction whileyawing in another can also set off Dutch rolloscillation, seen in the figure as an oscillation inroll rate over time. Note that the worse case,when rolling without coordinating rudder, comeswhen dihedral effect is high and directionalstability is low.

For geometrically similar airplanes, roll ratevaries inversely with span (cutting the span inhalf gives twice the rate). The reason is that rolldamping varies directly with span. At any givenroll rate, the longer the span the faster the

wingtip moves, and therefore the greater thedamping caused by the larger roll-inducedchange in angle of attack. This explains the shortwingspans of aircraft designed to roll fast.

Roll damping is also an inverse function of trueairspeed. Because TAS increases with altitude,roll damping decreases as you climb—as doesdirectional and longitudinal damping. (SeeDamping versus Altitude in “LongitudinalManeuvering Stability.”)

At high angles of attack approaching CLmax, rolldamping begins to decrease as the wing’s CLcurve begins to level out (Figure 8). Turbulenceor yaw rate causing a wing to drop can then forcethe angle of attack of the tip section past thepoint of stall. Now the coefficient of lift, insteadof rising as it normally does as the wingdescends, starts falling down the post-stall sideof the lift curve, and damping disappears. Thetransformation of damping into autorotation isthe essence of spin departure. Quickly reducingthe angle of attack usually restores roll damping,and lateral control, before a real spin can getunderway.

Muscle Versus Roll Rate

Aileron systems are designed primarily in termsof the lateral control required at speeds nearstall—a function of aileron size. At high speeds,roll rate is a function of the available ailerondeflection.

(Directional Stability > Dihedral Effect)

(Dihedral Effect > Directional Stability)

Coordinated rudder resulting in roll only

Insufficient rudder resulting in decreased roll moment caused by sidesliptoward roll direction: Roll rate oscillates due to Dutch roll response.

Excess rudder resulting in increased roll moment caused by sideslip opposite roll direction

Time

Figure 7Dihedral Effect,Rudder use,Roll rate

Rolling Dynamics


As mentioned earlier, for a given ailerondeflection (thus roll helix angle), coordinatedroll rate, p, varies directly with true airspeed.Roll rate also depends on how big a gorilla isdriving. In an aircraft without boosted orpowered flight controls, the control force felt bythe pilot increases as the square of the trueairspeed. As a result, aileron forces go up fasterthan roll rates, and ultimately the force requiredfor maximum deflection can exceed the pilot’smuscle power.

For example, a Spitfire had a maximum roll rateof around 105 degrees per second at about 175knots EAS. A clipped-wing Spitfire made it toabout 150 degrees per second at the same speed.A P-51B Mustang’s roll rate peaked at onlyabout 90 degrees per second at around 260 knotsEAS. When these airplanes went slower,maximum-performance roll rates decreased dueto the slower TAS. When they went faster, rollrates decreased because the pilot couldn’t fullydeflect the controls, as Figure 9 illustrates. Theroll rate of the Japanese Zero went down

drastically at high speed because of aileronreversal caused by wing twisting (see below).

By way of comparison, if a contemporary, high-performance aircraft designed for top aerobaticcompetition rolls less than 360 degrees persecond, at maximum sustained level flight speed,it’s considered a slug.

Angle of Attack

In the roll-dampingregion, when thewing rolls downand α increases, liftand dampingincrease.

On the backside of thecurve, in the autorotationregion, when the wing rollsdown and α increases, liftdecreases and dampingdisappears.

Figure 8Loss of RollDamping past Stall

Damping begins to decreaseas slope changes aroundCLmax.

Max force pilot can sustainwith reversible controls

Fa ∼ EAS2

Pilot maintains max force butdeflection starts going down asairspeed increases.

Symbol ∼ meansproportional.

p ∼ TAS

P∼ 1/TAS

Roll rate decreases withreversible controls becausepilot can’t hold deflection.

Airspeed

Airspeed

Airspeed

Airspeed for max roll ratewith reversible controls

Figure 9Roll Rates versusAirspeed, Muscle-Powered ReversibleControls

Rolling Dynamics


In testing for certification under FAR Part23.157, aircraft are required to roll from a thirty-degree banked turn to a thirty-degree bank in theopposite direction within time limits specifiedfor aircraft weight and configuration. Under FARPart 25.147 (e), “Lateral control must be enoughat any speed up to VFC/MFC to provide a peakroll rate necessary for safety, without excessivecontrol forces or travel.”

Aeroelastic Aileron Reversal

At high speeds, aeroelastic deformation also putsa cap on roll rates. The down aileron produces atwisting moment on the wing, which forces theleading edge to deflect downward, reducing theangle of attack (Figure 10). This reduces lift andconsequently rolling moment. Roll rate thenstarts going down and at a certain speed, VR,when the decrease in lift due to twisting equalsthe increase in lift due to aileron deflection, theailerons will no longer create a normal rollingmoment. Beyond this speed “aileron reversal”occurs. A down-going aileron then produces adown-going wing.

One of the cures for aileron reversal, notsurprisingly, is to increase the torsional stiffnessof the wing (at the expense of added weight). Onswept wings it’s necessary to increase thebending stiffness because the geometry of aswept wing causes it to twist as it bends. Movingthe ailerons inboard or extending their spaninboard also helps raise VR on a swept wing.Spoilers are another option, as mentioned.

Comparing Roll Performance

You first need to specify flight regime in order tomake useful roll performance comparisonsbetween our aerobatic training aircraft and largertransports—for example the roll rates atapproach speed and configuration versus cruise.Because of yaw/roll coupling, you also need toconsider sideslip and yaw rate contributionsbased on aircraft dynamics and pilot technique.The question is complicated by all of thederivatives that have to be plugged in.

The people who create simulation algorithmshave the derivatives plugged in. Comparisons ofroll rates (and control forces) made between youraircraft and our trainers based on theperformance of your aircraft’s simulator should

be useful—especially if the simulation occurswithin the boundaries of the angle of attack, α,and sideslip, β, envelopes supported by youraircraft manufacturer’s flight-test data. Rollsthrough 360 degrees can be modeled reliably, aslong as they happen within α/β boundaries, evenif the subject aircraft has never been tested in fullrolls itself. Combined high angles of attack andhigh sideslip angles may not be well supported,however, because they’re usually not flight-tested for aircraft not receiving spin certification,and their nonlinear effects make reliablemodeling difficult. During the unusual-attitudeportion of your simulator training (if indeedthere is such), ask to observe roll rates atdifferent airspeeds, configurations, andaltitudes—and especially with differentcontributions from the rudder. Then, assumingyou passed the check and won’t be called atroublemaker, go ahead and ask where the testdata stops and the extrapolation begins.

Figure 10Aileron Reversal

Aileron deflection causeswing to twist. Roll momentreverses.


Flightlab Ground School10. Spins


A Short Sermon

There’s a distinction between feeling safe andbeing safe. Unfortunately, we can experience theformer without actually achieving the latter.Most of the decisions people make about safetyrely on the feeling of protection—a feeling thatcomes from the sense of a buffer betweenthemselves and any dangers likely to occur. It’sbeen pointed out that the reason some peopleprefer sport utility vehicles, despite the pooraccident record, is that being surrounded by allthat metal and padding simply feels safer. Theimpression is that an accident will be survivable.The fact is that an SUV accident will also bemore likely because of poor handling qualities.Drivers are less likely to get into accidents insmaller cars that are more easily maneuvered outof danger. In the SUV case, people apparentlyassume that accidents are inevitable andtherefore seek a physical buffer. In the small-carcase, people accept more responsibility for theirown welfare. They don’t really feel safe in theirsmaller cars, but the absence of that feelingmakes them drive more safely, anticipantpotential trouble sooner, and so actually be saferin the end. Their skill is the buffer.

The problem of feeling safe versus being safeobviously applies to flying in general and to spintraining in particular. Airplanes, even giant ones,are like small cars. They aren’t designed to makeyou feel comfortable about the notion of hittingthings. They’re meant to be maneuvered back tosafety. People who argue against spin trainingusually do so by relying on statistics showingthat most stall/spin accidents start too close tothe ground for recovery. In such cases, knowinghow to recover from a spin wouldn’t help. Theconclusion they draw is that flight trainingshould rely on stall avoidance as the way to spinavoidance—that stall avoidance is the buffer.Aerodynamically, they’re right: stall avoidanceis the way to spin avoidance. But spin training isitself the best way to produce unswerving loyaltyto stall avoidance, because it’s the only way for apilot to experience what happens when you takethe buffer away. Its real purpose is to reinforce

the buffer and render emergency spin recoveriesunnecessary. Spin training shouldn’t make apilot feel complacent while maneuvering anaircraft—or, for that matter, feel safe. It shouldmake him better at anticipating the trouble instore if airspeed gets low and the precursors ofautorotation appear (perhaps during anemergency landing following engine failure).Not feeling safe is what motivates people to actsafely. Training shows them when to be waryand how to behave. An otherwise well-schooledpilot who hasn’t experienced spin training mightfeel safe, but have less real ability to look aheadand refrain from doing the wrong thing—lessability to keep the buffer intact.

We cover spin theory in this briefing, andexamine some of the characteristic differencesbetween aircraft types.

A Little History

Lieutenant Wilfred Parke, of the Royal Navy,made the world’s first spin recovery, on August25, 1912. We’ll note here that while Parke wasdesperately improvising, Geoffery de Havillandwas watching anxiously from the ground.Sometime between late April and late Novemberof 1914, de Havilland became the first to enteran intentional spin, recovering using thetechnique Parke had discovered of rudderopposite the spin direction. That this plannedattempt only occurred some two years after“Parke’s Dive,” as it came to be called,underscores the wariness that remained. UntilParke’s nick-of-time revelation, pilots hadalways held rudder into the direction of a turn toprevent sideslip—a practice mistakenly carriedover into spins. 1 Parke died in the unexplainedcrash of a Handley Page monoplane soon afterhis pioneering spin recovery. Geoffery de

1 Wing Commander Norman Macmillan, articleson the early history of spins, Aeronauticsmagazine, July, December 1960, September1961.

Spins


Havilland went on to build the series ofpioneering aircraft that carry his name.

Of course, spins went on to become standardcivilian training maneuvers—and then not, atleast not in the U.S. after 1949, once theregulators changed their minds. We’ll jumpforward some decades after Parke and begin atthe point where “jet-age” spin history begins.This will help us place the spin characteristics ofour training aircraft in better context—since ouraircraft are pre-jet-age, if you will, at least in afunctional if not a chronological sense.

Wing Planform and Aircraft MassDistribution

After World War II, a new generation of jetfighter aircraft appeared with swept wings andwith their mass distributed more along thefuselage axis, and less along the span (fuselageloaded). This changed for the worse thegoverning aerodynamic and inertial relationshipsthat determined their stall/spin behavior. Moderncorporate jets are the descendents of these earlyfighters; just as modern jet transports are thedescendents of early swept-wing bombers.

Swept wings allowed the early jets to achievehigh speeds by delaying transonic drag rise. Butthe swept-wing solution for high-speed flightintroduced problems in the high-α regime, wherecontrol was jeopardized by the swept wing’stendency to stall first at the tips. This caused aforward shift in the center of lift and a pitch-up.It also destroyed aileron authority. If one swepttip stalled before the other, the resultingasymmetry could send the aircraft into adeparture leading to a spin.

The hefty-looking chord-wise stall fences yousee on early swept-wing fighters, like the KoreanWar MiG-15, were an attempt to control thespan-wise airflow that encourages tip stall.(Fences are still used to manage spanwiseairflow and stall pattern.) During itsdevelopment the rival North American F-86Sabre was given leading-edge slats to improveits high-α behavior, and the horizontal stabilizerwas re-positioned away from the downwash ofthe high-α wing wake to improve nose-downpitch authority.

Figure 1 shows that swept wings stall at higherangles of attack than straight wings. There’s

typically also a more gradual change in slopearound the peak of the lift curve, and so the stallis less defined. Figure 1 suggests that when aswept-wing aircraft stalls asymmetrically, itswings reaching different angles of attack, the liftdifference, and thus the autorotative rollingmoment, is small. But because induced drag risesquickly with angle of attack, asymmetrical yawmoment may be large. If directional stability isweak, this can produce mostly yaw accelerationon departure in swept-wing jets. (However, athin airfoil with a sudden, leading-to-trailing-edge stall pattern will typically accelerate in roll.The lift curve peak is sharp, and differences inwing contour or surface texture usually causeone wing to stall first. See “Two-DimensionalAerodynamics.”)

Departure yaw can come from aileron deflection.Adverse yaw was a big problem on the NorthAmerican F-100-series swept-wing jets.Deflecting the ailerons could cause roll reversalat high α. Instead of rolling away from it, theaircraft could yaw toward the wing with thedown aileron—the resulting sideslip and roll dueto yaw rate sending it into a departure against theailerons. At high α, aircraft had to be rolled withrudder to prevent aileron-induced “lateral controldeparture.”

The redistribution of mass toward the fuselagewas also important. Once departure occurs and aspin develops, in a fuselage-loaded aircraftinertial characteristics can cause the spin attitudeto flatten or tend toward oscillation. Anti-spinaerodynamic yawing moments generated byrudder deflection can be insufficient forrecovery. To break the spin, the pilot (or flightcontrol computer more recently) often needs todeflect the ailerons into the spin to generate anti-spin inertia yawing moments to help the rudder

Coe

ffic

ient

of L

ift, C

L

Swept wing

Figure 1 Lift Curve

Larger lift difference for a given α difference produces more roll.

Lft. Wing

Rt. Wing

Angle of Attack, α

Straight wing

Spins


along. (Described farther on, inertia momentsoperate on the same principle as the propellergyroscopics you’re familiar with, but the rotatingmass is the aircraft itself.)

The piston-engine fighters of World War IIbehaved differently than the new jets. They hadstraight wings, with stall patterns often morefavorable for aerodynamic warning and lateralcontrol (but not always—there were manyaircraft that announced a stall by suddenlydropping a wing). The lift curves for straightwings typically have well-defined peaks (Figure1). This can help promote well-defined stalls andprompt recoveries. But there can be strongrolling moments if the wings stallasymmetrically, and therefore predominantly rollacceleration on spin departure. Usually the pistonfighters departed to the left because of enginetorque and local airflow differences produced bythe slipstream. You can observe departurecharacteristics by watching the old training films.(Sociologically entertaining, as well. Times weredifferent. For an informative collection ofvideos, see www.zenoswarbirdvideos.com/)

Our trainers exhibit straight-wing spin behavior.The rectangular-wing Zlin’s departurecharacteristics are dominated by wing-root-firststall patterns at high α—patterns you’ll see whenwe stall a tufted wing. The tapered-wing SF260’sstall pattern is shifted outboard, which makes theaircraft more susceptible to a sudden wing drop.Their inertial characteristics come from a fairlyequal distribution of mass in fuselage and wings(pitch inertia only a little higher than rollinertia—close to the Iyy/ Ixx =1.3 neutral valuediscussed later). They need a bit of yaw to shiftthe stall pattern asymmetrically, respondpositively in autorotative roll, and then pick upthe yaw rate as the spin gets organized. In thedeparture and early incipient stage, before theyaw rate begins to develop and while spinmomentum remains low, neutralizing thecontrols is often all that’s necessary to recoverlift symmetry and break autorotation.

Training: What’s Possible

The spin training available to civilian pilots islimited to aerobatic, straight-wing, piston-enginesingles, like ours. This raises the obviousquestion of how such training corresponds to thekind of spin behavior a pilot might experience inan aircraft with a different wing planform or

distribution of mass. (Corporate jets are oftenswept-wing and fuselage-loaded, for example.)Does a stick-pusher make the issue irrelevant, orcan it fail and suddenly reveal the reasons it wasinstalled in the first place? In addition, whenaircraft are not flight tested for spins, on theassumption that a spin is a very unlikely event intype, their behavior can only be predicted.Prediction is complicated because the relevantaerodynamic stability derivatives, which arelinear when the aircraft experiences smallperturbations (the engineer’s term) from steadyflight, become nonlinear when perturbations arelarge. They can’t be extrapolated from staticconditions in a wind tunnel; they depend toomuch on the history of the unsteady airflow thatprecedes them. Dynamic wind tunnel testing ispossible,2 but only flight tests can really confirmspin characteristics and recovery techniques.

As a result of training in aircraft possibly quitedifferent from their own, pilots taking spintraining have to think in general terms. This isreasonable, however, because generic departureawareness—focused on the general principles ofspin avoidance rather than on the peculiarities ofa specific aircraft—works across the board:Aircraft depart into spins when lateral and/ordirectional stability break down in the stallregion, the wings develop asymmetrical lift anddrag along the span, and the asymmetry drawsthe aircraft into autorotation. The solution toavoidance is to deprive this combination of itskey ingredient—operation in or near stall,especially in uncoordinated flight, when theaircraft takes on a yaw rate and sideslip that canprovoke lift/drag asymmetry.

In recovery from a spin departure, rudderapplication is also generic: Always, full rudderopposite the spin direction. You can learn this inany spin-approved aircraft. Following therudder, stick neutral or forward of neutral isnearly generic, although the timing, amount ofdeflection past neutral, and the elevator stickforce necessary can vary among airplanes. Thedetails should always be determined from thePOH/AFM before first-time spin practice. Foraircraft with lots of their mass in the wings, theelevator can actually be a more effective anti-yaw recovery control than the rudder, as we’llsee.

2 Visit www.bihrle.com

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Spin-recovery technique depends on the abilityof these two primary anti-spin control surfaces,rudder and elevator, to generate large enoughaerodynamic anti-spin moments. Sometimes theycan’t, and that’s when recovery procedures needto generate persuasive anti-spin inertia momentsto help the aerodynamics along. This iscomplicated stuff in the telling (and predictiverather than proven for aircraft not spin-tested)but it essentially boils down to how the pilothandles the ailerons. In addition to anti-spinrudder and elevator, fuselage-loaded aircraftmay require aileron into the direction of thespin.

Check the aileron instructions for your aircraft. Ifan aircraft has not been certified for spins,there’s no requirement to list a hypotheticalprocedure in the handbook.

Regulations and Recoveries

The flight testing of both military and civilaircraft is done according to intended use andlikely user—the user being a pilot who isassumed to have only average skills in aircrafttype and who might be slow to react or mightmisuse controls (the guy test pilots refer tosolicitously as “your average Joe-Bag-of-Donuts”). In other words, testing is for intendeduse with some abuse. For uniformity, both themilitary and the FAA prefer standardized spinrecovery techniques, but neither actually requiresa specific set of inputs.

FAR Part 25, for large aircraft, doesn’t includespin certification, because spins are not intendeduse and aircraft are expected to behave in amanner making them very unlikely. The militaryechoes this. Under the military acceptancestandards (MIL-STD), “All classes of airplanesshall be extremely resistant to departure fromcontrolled flight, post-stall gyrations, and spins.The airplane shall exhibit no uncommandedmotion which cannot be arrested promptly bysimple application of pilot control.”3 Onlytraining aircraft that might be intentionally spunand Class I and IV aircraft undergo spin tests.(Class I includes small airplanes such as lightutility, primary trainer, light observation. ClassIV includes high-maneuverability airplanes suchas fighters, interceptors, attack, and tacticalreconnaissance.) 3 MIL-F-8785C, 3.4.2.2.1

Appendix 3-D in the Airplane Upset RecoveryTraining Aid4 shows the α/β flight-testingenvelope for a number of transport aircraft. Youcan see the variation in tested parametersbetween aircraft. In no cases are high angle ofattack and high sideslip conditions exploredsimultaneously. Stall tests are done at zerosideslip to prevent spins.

Back to smaller aircraft: Our ground school text,“Certification Requirements,” contains the civilaircraft FAR Part 23.221 spin requirements. Inaddition, “The Flight Test Guide forCertification of Part 23 Airplanes” (FAAAdvisory Circular AC-23-8A)5 providesinterpretation and procedures. Together theydescribe the minimum acceptable spincharacteristics for each aircraft category. For thenormal category, in particular, meeting therequirements actually means leaving much aboutthe aircraft’s spin characteristics still unknown.The normal-category, one turn spin recoveryrequirement is intended to address recovery froman abused stall, meaning a stall in which controlsare held in the pro-spin position and recoveryinputs are delayed, not recovery from adeveloped state with higher angular (rotary)momentums needing greater aerodynamicmoments to counteract. Consequently, meetingthe requirement does not clear an aircraft forintentional spins.

According to the “The Flight Test Guide forCertification of Part 23 Airplanes,” for aircraftcertified for spins under FAR Part 23.221,“Recoveries should consist of throttle reduced toidle, ailerons neutralized, full opposite rudder,followed by forward elevator control as requiredto get the wing out of stall and recover to levelflight, unless the manufacturer determines theneed for another procedure.”

What the Part 23 flight test guidance has in mindare aircraft with approximately neutralwing/fuselage mass distributions, and enoughrudder and elevator authority to do the job. Theuseful PARE acronym for recovery inputs,promoted by flight instructor Rich Stowell(Power off, Ailerons neutral, Rudder opposite,Elevator forward) follows this preferred recoveryformat. But the acronym is also adaptable tofuselage-loaded aircraft, because the ailerons are

4, 5 Available on the Internet, search the title.

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still taken care of in the propersequence—although deflected in the spindirection (for upright spins) rather than setneutral.

For certification purposes, the recovery controlsdescribed above are applied after one turn (or athree-second spin, whichever takes longer) fornormal category aircraft, and after six turns forspin-approved utility or aerobatic category. Atthat stage, PARE-input usually produces thequickest recovery.

Although PARE input is never inappropriate incertified aircraft (unless the manufacturer saysotherwise), it’s by no means uniformly essentialin all aircraft at the very beginning of a spindeparture, when autorotation first takes effectand a wing begins to drop. At that early stage,forward pressure to break the stall on thedropping wing is usually sufficient to endautorotation, even if spin-provoking rudder andaileron are still being held. In reality, by the timea pilot not current in spins remembers the PAREacronym, a PARE-input recovery is probablynecessary. Beyond the initial wing drop, once areal yaw rate begins to develop, pushing the stickforward out of the PARE sequence canaccelerate the spin, for reasons we’ll describe.

Autorotation

Spins feed on autorotation, which can follow astall if for some reason (sideslip, yaw rate, windgust, inherent asymmetry in response, pilotinput) the wings begin to operate at differentangles of attack. Figure 2 shows what happens.During our practice spins, for example, if wekeep the ball centered as we slow down andsimultaneously increase α, both wings shouldarrive at their maximum coefficient of lift, CLmax,more or less together.

If we then press hard left rudder, the right wingwill begin to move faster than the left. Theairplane will roll to the left in response (roll dueto yaw rate, plus dihedral effect). Because thewing’s rolling motion adds a vector to therelative wind (Figure 3), the left wing will see anincrease in α as it descends, but a decrease inlift, since the wing is past CLmax. Because of theincrease in α there will also be an increase indrag (as you’ll note in Figure 5).

The right wing will see a decrease in α as it rises,but still more lift than the left wing. Because ofthe decrease in α there will also be a decrease inthe right wing’s drag.

As a result, the coefficients of lift and drag willvary inversely in relation to one another alongthe span. The outcome is a self-sustainingautorotation.

Wing going upproduces downwardwind component.

Wing going down producesupward wind component.

Figure 3Roll-induced Angle of Attack

Decreased effective angle of attackdue to free stream plus roll rate

Increased effective angle of attackdue to free stream plus roll rate

Freestream

Free stream

Figure 2Autorotation

CLmax

Symmetrical stall atCLmax, left ruddersends wings todifferent α/CL.Autorotation begins.

Ascending Rt. Wing

DescendingLft. wing

Angle of Attack, α

Spins


Although yaw typically leads to roll and thus toautorotation, sometimes departure happens inroll initially, even if the aircraft is in coordinatedflight with zero yaw rate or sideslip. One wingmight be rigged differently than the other, andstall first. Because of their sensitivity to anyasymmetry along the span, wings that producesudden leading edge stalls—or that generatesudden trailing-to-leading-edge stalls—tend toroll off. The down-going wing receives anincrease in α, which leads to an increase in drag.The up-going wing gets the opposite. Theasymmetry in drag sets the airplane off in yaw,which in turn reinforces roll.

Autorotation is roll damping reversed (Figure 4).Consider a wing operating normally on the leftside of the CL/α curve, before the stall region. Ifthe wing goes down, perhaps because of a gustor an aileron deflection that the pilot thenremoves, it doesn’t continue to roll, but stops.The downward rolling motion adds a vector tothe relative wind, which produces a geometricalincrease in α.The resulting increase in CLopposes the roll. This damping, rolling momentdue to roll rate, Clp, subsides as the roll ratereturns to zero.

If a wing operates on the right side of the CL/αcurve, past stall, a downward roll still producesan increase in α, but now accompanied by adecrease in CL, as we’ve seen. There’s nodamping effect. Just the reverse—the wingcontinues to fall. Roll damping turns unstablewhen the slope of the CL/α curve turns negativepast CLmax. A rolling motion kicks off a self-sustaining rolling moment.

Again consider a wing operating on the left sideof the CL/α curve, below the stall region, butnow rolling upward. An upward rolling motionwill induce a decrease in α (Figure 4) and a lossof lift—therefore generating roll damping. If thatwing were operating on the post-stall, right sideof the CL/α curve, an upward roll would stillinduce a decrease in α, but an increase in CL.The wing would continue to rise—again nodamping.

For autorotation to occur, at least one wing hasto operate on the right side of the curve, past themaximum coefficient of lift. Watching wing tuftsin a departure, you’ll typically see completeairflow separation on the inside wing (indicatinglow lift and high drag), while the outboard tufts

on the outside wing remain attached (more lift,less drag). Once autorotation gets going, inertialdynamics can take both wings to post-stallangles of attack, as they drive the nose up andthe spin attitude flattens. Spin recovery involvesgetting both wings back into the roll-dampingregion on the left side of the CL/α curve.

(If you remain a glutton for complication, notethat the derivative yaw-due-to-roll, Cnp,reverses sign at autorotation.)

Figure 4Roll Damping, Clp

Descending wingincreases α,decreases lift.

Ascendingwing decreasesα and lift.

Descendingwing increasesα and lift.

Ascending wingdecreases α,increases lift.

Damping No Damping

Angle of Attack, α

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Figures 5 and 6 show how the yaw component ofautorotation is generated by the rise in thecoefficient of drag, CD, as α increases. As wingsget shorter (smaller aspect ratio), or wing sweepincreases, the slope of the lift curve decreases.This reduces the divergence in lift coefficientwhen the left and right wings operate at differentα. In such cases, CL might not vary much overwide values of α, but CD will. Asymmetric dragthen dominates autorotation. That means moreyaw. One consequence is that spin attitude has atendency to go flat (nose up), especially in afuselage-loaded aircraft with flat-spin inertialcharacteristics.

Figure 6Swept-WingLift & Drag

Drag Curve

Drag differencebetween wings

Lift differencebetween wings

Angle of Attack, α

Descendingwing

Ascendingwing

Figure 5Straight-WingLift &Drag

Drag Curve

Lift differencebetween wingspromoting rollmoment.

AscendingWing

Descending wingproduces more drag thanascending wing.

Drag differencebetween wingspromoting yawmoment.

Angle of Attack, α

Spins


Spin Phases

Spins are typically described as passing throughphases: departure, post-stall gyration, incipientspin, developed spin, and recovery. Thedeveloped spin may achieve steady rates ofrotation and a consistent nose angle against thehorizon, or the rates may oscillate—often withthe nose bobbing up and down accompanied byfluctuations in roll and yaw. The notion thatspins pass through identifiable phases is more astudied analytical observation than a factimmediately gladdening to pilots. If you’re newto spins, or new to the quirks of a particularaircraft, one moment can blur awfully quicklyinto another as a spin revs up; the chief sensationbeing that things are simply getting worse. Untilthe developed state, spin phases themselves aretransitional in nature, with uncommandedchanges in roll, pitch, yaw, and sideslip—oftengoing on all at once and difficult to sort intoseparate components. This is especially soduring the incipient phase, which ends quitedifferently than it begins. Some aircraft will passthrough the phases quickly, particularly duringintentional spins if control deflections generatestrong aerodynamic pro-spin forces and there’snot much inertia to overcome (strongaerodynamics and weak inertias are also theformula for good recovery characteristics).Others take longer to get going and finallystabilize, if indeed they do stabilize.

Departure

The military uses the term “departure” in thesense of a boundary between controlled anduncontrolled states, a boundary between linearand nonlinear aerodynamics. Within thisdefinition, an aircraft might depart and enter apost-stall gyration or a deep stall, but notnecessarily a spin. In initial spin training, we usepro-spin control inputs to bring the aircraftquickly through departure and “shape” the post-stall gyration so that the aircraft immediatelyenters the incipient phase. In a training situation,the pilot knows (or quickly learns) what theaircraft is doing. However, accidental departurescan come as a surprise, and the pilot might havedifficulty tracking aircraft motion. The militarytrains its student pilots to return the controlsquickly to neutral (and reduce power asappropriate) to try to prevent the aircraft frompassing beyond departure and into a developing

autorotation. If the aircraft has sufficient anti-spin stability characteristics it may then end upin an unusual attitude, but not in a spin. If a spindoes develop, the military pilot uses instrumentreferences (altimeter, AOA indicator, airspeed,turn needle) to determine the spin type and thecorrect recovery input. The military teaches“heads-in” recovery, it’s suspicious of outsidevisual references.6

Early in our Wide-Envelope training flights,you’ll observe directional stability and lateralstability (dihedral effect). You’ll evaluate thedeterioration of control effectiveness as αincreases, and you’ll find yourself introducingcorrective rudder inputs as the aircraft’sdirectional stability diminishes. You’ll see thetransformation of airflow over the tufted wingand the disappearance of roll damping asautorotation begins. These are lessons in thecomponents of departure.

Static directional stability usually decreases asaircraft angle of attack increases and the airflowover the tail slows down and becomes disruptedby the fuselage wake. As a result, anything thatcauses a disturbance around the aircraft’s z-axis

6 Naval Air Training Command, “Out-of-ControlFlight, T-34C,” 2006.

Recovery Controls

Developed Phase

Recovery

Autorotation begins.

Figure 7 Spin Phases

Incipient Phase

Departure/post-stall gyration

Spin axis

Helical path of aircraft cg

Spins


can start a yaw that may be slow to correct, thusallowing the aircraft to go to a higher sideslipangle, β, and remain there longer. If dihedraleffect is present, the aircraft will tend to rollaway from the sideslip. The rolling motionimposed on wings at high α can send them intothe angle of attack disparity necessary forautorotation.

With American-turning engines, propeller effectsyaw an aircraft to the left as α rises and speeddecreases. Even if the pilot dutifully arrests theyaw rate with right rudder and keeps the ballcentered, the spiraling slipstream willnevertheless tend to increase the angle of attackon the left wing and decrease it on the right. Asaircraft angle of attack goes up, the left wingtherefore stalls first and the aircraft departsaccordingly.

Some aircraft will depart due to aileron adverseyaw. (We mentioned swept-wing fightersearlier.) The phenomenon is referred to as lateralcontrol divergence, or simply “aileron reversal.”It can happen when adverse yaw introduces asideslip that in turn produces a rolling momentopposite to and greater than the momentgenerated by aileron deflection. The airplanethen yaws and rolls toward the down aileron, notaway.

All the factors that lead to lateral controldivergence increase with α. The disturbed,lower-energy air generated by the fuselageand/or wing wake causes directional stability togo down, which allows a larger sideslip angle.And adverse yaw goes up, which promotes thatsideslip angle. Dihedral effect also goes up, atleast to stall, although more for swept than forstraight wings. The only thing that goes down isthe ability of the ailerons to generate an opposingroll rate.

Pilot lore often attributes a departure caused byaileron reversal to an increase in local angle ofattack as the aileron goes down. The idea is thatif you lower an aileron the angle between thewing chord line (as drawn from leading totrailing edge) and the relative wind increases.

This sudden increase in angle of attack issupposed to produce a local, sudden stall—thedecrease in lift causing the wing to go down. Inground school, you’ll see a wind tunnel film thatshows what can happen when a control surface isdeflected down on a wing already operating at ahigh angle of attack. There can indeed be asudden separation if airflow is unable to followthe abrupt change in camber. The effect dependsin part on the shape of the hinge line. Airflowtends to stay attached if the hinge design allowsa smooth curve. If the change is abrupt (pianohinge joining the top of the aileron to the top ofthe wing, for example), flow may separatesooner. That separation is accompanied by alarge increase in profile drag, as our film reveals.

Figure 8 uses a constant chord-line reference forangle of attack and shows how deflecting anaileron down shifts the lift curve to the left—andcan indeed bring a wing past stall angle of attack.But the lift curve also rises, and the lift of thestalled section actually increases (as does drag,even more). Notice the effect of a 20 deg. ailerondeflection at 14 deg. α: An aileron deflecteddown places the corresponding wing area outside

No ailerondeflection

20 deg.up

20 deg. down

30 deg.aileron down

0

1

2

Angle of Attack

Figure 8. Aileron deflection shiftslift curve. (LS(1)-0417 wing)

-4 0 4 8 12 16 20

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the region of roll damping. The lift of the areaincreases, but its contribution to damping—itsresistance to autorotation—drops out!

It’s usually difficult to persuade most airplanesto play along and depart into a down aileron bysuddenly deflecting that aileron just before astall. Typically, the aircraft has to start yawingdue to aileron-provoked adverse yaw (drag) first;a coupled roll leading to autorotation in thedirection of the down aileron then follows. If youuse active rudder inputs to counter theasymmetric drag and to prevent a yaw rate fromdeveloping, an aircraft with a well-manneredtrailing-to-leading-edge, root-to-tip stall typicallywon’t depart, no matter where the ailerons are.

Planforms (wing shape as viewed from above)that tend to stall initially outboard over theailerons, and that lack a compensating washout,might more easily misbehave following ailerondeflection (bad design). The trailing wing in asideslip is also, in effect, swept with regard tothe freestream. This could cause a thickening ofthe boundary layer outboard, which in turnencourages separation. By generating lowerpressures outboard, and creating a suction, adown aileron can definitely increase the rate ofstall propagation from root to tip on the insidewing during a cross-controlled skidding-turn-to-final. (We’ll show you this with a tufted wing inflight; so don’t worry if you can’t quite picturethings now.)

When we practice intentional spins, we force thedeparture issue by pressing the rudder in theintended spin direction. We deliberately producea yaw rate that leads to a rolling moment inresponse to the outside wing moving faster thanthe inside wing, and in response to dihedraleffect. This rolling moment sets up theconditions for autorotation.

You’ll notice that in all our upright spins,however we provoke them, the aircraft willalways depart in the direction opposite the ball inthe turn indicator or coordinator. The airplanefalls “into the hole,” as the arrow belowindicates. So “step on the ball to prevent thefall.”

The ball tells us the general direction of therelative wind or velocity vector (from/to theright, as illustrated above), and therefore of the

presence of a sideslip angle (see Figure 4 in theground school text “Rolling Dynamics”). Anaircraft that’s rigged fairly symmetrically (noneis perfect except by accident), that doesn’t sufferfrom extreme prop effects, and that tends to stallstraight ahead without dropping a wing won’tdepart into a spin if the ball is centered (zero β)and the velocity vector is thus on the plane ofsymmetry. The adventure starts when high α andhigh β combine. (Actually, an aircraft can be in asideslip even when the ball is centered. A twinon one engine is in a sideslip when the pilot usescorrective rudder but keeps the wings level. Thispoor technique creates more drag than when thepilot reduces the sideslip by banking a fewdegrees into the good engine. A power-on stall ina single-engine aircraft may involve a slightsideslip. Propeller slipstream and p-factorusually require right rudder to prevent yaw.Zeroing the yaw rate puts the aircraft in asideslip to the left. The ball will be centered ifthe wings are level.)

The displaced ball is predictive. It tells youwhich direction a departure will go. During aspin it’s an unreliable indicator of spindirection—unlike a turn needle, which is reliableupright or inverted. The aircraft symbol in a turncoordinator is reliable only in upright spins.

Since geometric dihedral causes an angle ofattack change in a sideslip—the angle of attackgoing up on the wing toward the slip—whydoesn’t dihedral cause that wing to stall and dropfirst during a sideslip (into the ball rather thaninto the hole)? It’s because the aircraft rolls awayfrom the slip as dihedral takes effect, the rollcausing a decrease in α on the upwind, up-goingwing. Because it rolls to lower α, it doesn’t stall.The down-going wing rolls past stalling α,however.

In our Zlin aircraft, if you’re carrying power andsimply hold the rudder neutral and continue tohold the stick full back after the stall, P-factorand spiraling slipstream will set up the necessaryyaw for a departure to the left. If you’re at idlepower (and depending on rudder trim, c.g., orturbulence), usually the airplane will oscillatearound its axes (in a post-stall gyration, seebelow) until it eventually trips into a divergentroll and autorotation takes over. Very polite,elevator-limited, directionally and laterally stableaircraft often won’t spin if you do nothing morethan hold the stick back with the rudder neutral

Spins


or free, because they can’t generate the necessarycombinations of angle of attack and yaw withoutpilot intervention.

Post-Stall Gyration

A post-stall gyration is defined as anuncontrolled motion about one or more axesfollowing departure. The motions can becompletely random, and the angle of attack canwander significantly, as well. The militaryincludes snap rolls and tumbles as uncontrolledpost-stall gyrations. The term post-stall gyrationhas particular application to the behavior ofaircraft with the characteristics of fuselage-loaded, swept-wing fighters, as described at thestart. In a ready-and-willing straight-wingtrainer, if you do a standard entry, with stickback and full rudder at or just before stall in theintended spin direction, autorotation beginsimmediately and no post-stall gyrations may beevident. The aircraft goes directly to the incipientstate.

Incipient Spin

The rate at which an aircraft decelerates into astall is important. Certification flight-testing todetermine stall speed (and thus a collection ofnumbers derived from stall speed) is done at aone-knot-per-second rate of deceleration. If youincrease the rate of deceleration just a bit bybringing the stick back faster, you can oftendrive the stall speed down by virtue of the lag inthe change of pressure distribution over thewings. If you overdo it however, and start to pullg, the load factor goes up and stall speedincreases. You can also decrease stall speed byentering the stall nose-high, power on.

Stall speed affects the ballistic track of theincipient phase. Higher speeds mean that theaircraft travels a longer path over the groundbefore the spin axis becomes vertical, and issubject to higher aerodynamic forces at thebeginning of the phase. The forces createoscillations in roll, pitch, and yaw as the aircraftchanges orientation to the flight path, as shownin Figure 9.

Figure 9Incipient PhasePitching and Yawing Momentsdue to Ballistic Track

At 1-1/2 turns, relative windapplies a nose-down pitchingmoment.

At 1/2 turn, the horizontalcomponent of relative windapplies a nose-up pitchingmoment toward the horizon.

Decreasing horizontal component ofrelative wind as spin axis becomesvertical

At 1 turn, relative wind applies nose-uppitching moment.

At 3/4 turns, relative wind applies nose-upyawing moment.

As yaw rate builds, aircraftalso experiences anincreasing nose-up inertialcouple. See Figure 15.

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For example, after an aircraft departs and nearsinverted at 1/2 turn, the nose tends to stopfalling, even if the stick is held back, because therelative wind hits the bottom of the horizontalstabilizer. As the aircraft approaches the 3/4-turnpoint, the nose may yaw upward, the relativewind having shifted to the vertical tail. At theone-turn point, the horizontal stabilizer againtakes over, tending to hold the nose up. As theaircraft continues to the 1-1/2-turn point, thenose pitches down as the relative wind hits thestabilizer from beneath. These gyrationstypically decrease in intensity as entry stall speedgoes down and the horizontal wind componentbecomes less.

This, essentially weathervane, behavior is onlypart of the story. During the incipient phase theairflow can detach and reattach to the fuselage,wings, and tail surfaces, creating varyingmoments around the aircraft’s axes. This isparticularly evident on the outside wing on ourtrainers, as the wing tufts will show.

Judging from the training materials, the P-51grabbed a pilot’s attention during the incipientstage: “Upon entry in a power-off spin, the planesnaps 1/2 turn in the direction of the spin. Nosedrops nearly vertical. After one turn, the noserises to or above the horizon and spin almoststops. Snaps 1/2 turn again and nose drops 50 to60 degrees below horizon. Upon application ofcontrols for recovery, nose drops to near verticaland spin speeds up, then stops in one to 1-1/4turns. Approximately 1000 feet altitude lost perturn.”

Note that in half a turn the nose went from down“nearly vertical” up to “above the horizon.”That’s pretty frisky, but not unique. Note alsothat initially the “spin speeds up” after theapplication of recovery controls. That’s verytypical, for reasons we’ll see.

An aircraft’s mass distribution and its resultinginertial characteristics play an important roll inincipient spin behavior. In the case of the P-51,the interactions going on between propellereffects, inertias, and nonlinear aerodynamicswould challenge simulation even today. Ingeneral, an aircraft with low moments of inertiaaround its axes will be more susceptible to thechanging aerodynamic forces and easier toinfluence in the manner described above.

An aircraft with higher inertias might initially beharder to boss around aerodynamically. Once itstarts rotating, however, inertial characteristicsbecome increasingly influential as the spin axissettles down to vertical. Inertia moments (whichare not the same as moments of inertia!) can thenstart to define spin behavior. We’ll see this later.

Spins


Developed Spin

In a steady, developed spin, aerodynamic andinertia forces come into balance. Yaw, roll andpitch rates settle down to constant values. Angleof attack, descent rate, and pitch attitude do thesame. In the case of oscillatory developed spins,which never settle down, the rates may fluctuatearound average values, with aerodynamicmoments in ascendance at one instant, inertiamoments at another. Dynamic equilibrium in adeveloped spin can take longer to reach thanmany realize. The aerobatic certificationrequirement of six turns before recovery inputsare applied doesn’t guarantee the aircraft hasreached equilibrium.

Spin Attitudes

Spins consist primarily of roll and yaw, with theairplane center of gravity following a helical patharound, and displaced from, the spin axis, asshown in Figures 7, 10, and 11. If the wings aretilted, relative to the helical path (Figure 10,bottom) the wing tilt angle introduces acomponent of pitch.

Flat spins are mostly yaw, while steep spins aremostly roll. Spins at 45-degrees nose down areequal parts roll and yaw. You can see why this isso by holding a model aircraft wings-level at a45-degree nose down angle and yawing it aroundits z-body axis. The nose is 45-degrees above thehorizon after half a turn. You need to roll as youyaw in order to keep the nose down. If you playwith other angles, you’ll see how roll and yawinteract. If you can figure out how to move themodel on a helical path and tilt the wing asillustrated, you’ll discover the need for a pitchrate, as well.

From the cockpit, spins often appear as mostlyyaw, even past the 45-degree nose-down angle,when roll rate is actually taking over. As thepitch attitude becomes steeper, roll rate increasesand roll perception starts to dominate. With thenose down it can be difficult for the pilot torecognize that he’s actually entered a spin andnot a vertical roll, or that he’s still in a spin witha yaw rate that has yet to be stopped.

Velocity vector

Figure 10 Spin Helix

Local wind axis (aircraft velocity vector) is tangent to helix at any moment. In this drawing the aircraft’s plane of symmetry and the velocity vector are coincident. Spin consists of roll and yaw.

Aircraft viewed from the bottom. Spin axis is some distance behind.

x axis

Velocity vector

Wing tilt angle introduces a pitch rate, also a sideslip.

Helix angle, γ: Angle between velocity vector and spin axis

Reference line perpendicular to velocity vector

y axis

y axis

Helix

Spin axis

CG follows helical path.

Spin axis

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Figure 11 shows some of the characteristics offlat versus steep spins. In the example shown,for simplification the spin consists of roll andyaw only—no pitch rate. In an equilibrium state,the aerodynamic pitching moments, which arenose down, are opposite to and equal the noseup inertia moments (more about this later).

As the angle of attack, α, increases and the spinbecomes flatter, the coefficient of drag, CD,increases. Because of the drag rise, the descentrate decreases. Lift goes down. The distance, r,from the aircraft center of gravity—riding thehelix—to the spin axis also decreases.

The figure shows the balances of forces in asteady spin. The resultant aerodynamic force(vector sum of lift and drag) balances theresultant of weight (the acceleration of a massby gravity) and centrifugal force. As aircraftangle of attack increases, and lift consequentlydecreases, the aerodynamic resultant tilts moretoward the vertical, or clockwise in theillustration. The resultant of weight andcentrifugal force tilts clockwise as well. Sinceweight stays the same, this means centrifugalforce decreases. As it does, the radius of thehelix, r, around the spin axis decreases. As theaircraft c.g. moves closer to the spin axis, spinrate, ω, increases. In an aircraft with the c.g.behind the cockpit, the axis can pass behind thepilot; the spin accelerating and becoming“eyeballs out.” Not fun, says those who havebeen there.

Whether the spin is steep or flat will depend onthe attitude necessary to balance themoments—aerodynamic versus inertial—aroundthe aircraft’s axes. As we’ll see, an aircraft withits mass predominately in its fuselage will tendto spin more nose-up. An aircraft with its masspredominately in its wings will spin more nose-down.

Flatter Spin:Higher αMore yaw than rollSmaller spin radiusHigher drag meanslower descent rate.

Weight = Drag

Drag = Weight

Figure 11Spin Attitudes,Steady Spin Balance ofForces

Spin axis rotation, ωFlatter attitude =faster rotation

Spin rate

Roll rate

Yaw rate

ω

Inertial pitchingmoment

Aerodynamicpitching moment

Resultant

Spin axis

Minimum spin rotationrate happens at 45-degree pitch attitudewhen the spin axis isvertical.

Resultant

Lift = mrω2Centrifugal Force, mrω2 = Lift

Spinradius, r

Steeper Spin:Lower αMore roll than yawGreater spin radiusLess drag meanshigher descent rate.

ω

ωω

Spins


Spin Practice

Spin practice should build anti-spin and spin-recovery responses that will stick with youthroughout your flying career. A good flightinstructor lays the groundwork by unravelingspins in stages you can absorb, not with asudden, multiple-turn baptism. (Teaching spinsis not for instructors with lingering personalityissues.) Since you will likely be in survivalmode, concentrating on the plan for recovery,there’s a limit to how much real motioninformation you’ll be able to take in the first fewtimes. The initial blur factor is high, and spinsbecome increasingly difficult to follow as therotations accelerate and your tracking reflexesbreak down.

When practicing spins with an instructor the firsttime, READ THE AIRCRAFT Pilot’s OperatingHandbook or AFM. Don’t go flying until youhave. If you’re experienced with spins, butspinning an unfamiliar aircraft for the first time,READ THE POH/AFM. Don’t makeassumptions based on other aircraft. Assumptionsfail. When it comes to spins, the voice of cautionshould be the one in charge of the plans. Or youcan listen to the voice of Murphy, The Lawgiver,who actually was a flight-test engineer, “If it cango wrong, it will.”

Always run a weight-and-balance on anunfamiliar aircraft or a suspicious loading. A c.g.shifted aft of the approved envelope can cause aspin to flatten out due to diminished nose-downelevator authority. A c.g. shift measured ininches may not seem like much as a percentageof the distance (or arm) between the c.g. and theaerodynamic center of the elevator, but that’s notthe distance that matters. It’s the distancebetween the c.g. and the aircraft’s neutral pointthat makes the difference. (See “LongitudinalStatic Stability.”)

As you do before any aerobatic flight, clear thecockpit of all foreign objects. (Things hide—thewriter, now more vigilant, once brained hisaerobatic instructor with a quart-size can of fueladditive.) Search the manual for and askknowledgeable pilots about any characteristicsdifferent from those you’ve experienced. Andcheck for stretch in the elevator cables: Havesomeone hold the stick full forward while youlook for play by pulling up on the trailing edgeof the elevator. Do you have full down elevatorfor recovery?

Some aircraft require power to enter a spin. Ifyou’re accustomed to entering practice spinspower-off, you’ll have to remember to pull thepower once autorotation begins, both inconsideration of propeller gyroscopic effects andfor speed control during recovery. Simple detailslike the settings for trim and mixture control areeasy to forget, but can be important. Rememberthat an aircraft reluctant to enter a spin can alsohave limited aerodynamic authority for recovery.The aircraft may be asking you not to force theissue. “Spin-proof” aircraft can enter spins ifimproperly rigged and their control surfacesexceed design deflection, but might not berecoverable.

Practice Spin Entry

Unless an aircraft is reluctant to spin, andrequires the encouragement of a specialdeparture technique endorsed by themanufacturer, the following is typical for apractice spin.

Altitude. (Adequate if planned recovery isdelayed? The FAA says recovery from anintentional spin must be able to occur nolower than 1,500 AGL.)

Cockpit check. (Seatbelts, loose objects?Trim, engine controls, fuel valves set asspecified in the POH/AFM?)

Clear Airspace.

Power to idle. (But some, like the Cessna150 and 172 series, may need aid from theslipstream to enter a spin.)

Stick back for standard 1-knot-per-second deceleration. (This is thedeceleration rate used in certification todetermine the “book” stall speed. Just bringup the nose as necessary to hold altitude orclimb slightly as airspeed bleeds.)

Ailerons Neutral. (Although some aircraftmay require that the stick be held oppositethe intended spin direction. In that case theaileron deflected down contributes anadditional yawing moment—from adverseyaw—in the same direction as the rudder.)

Spins


Rudder deflected fully toward intendedspin direction just before the stall. (Theaircraft might not enter a spin, or entrymight be delayed if a stall break occurs andthe aircraft dumps the necessary angle ofattack before the rudder is applied.Smoothest entries come from applying therudder first.)

Hold full rudder deflection.

Stick full back as aircraft departs.

Spin or Spiral?

Spin-reluctant aircraft will often reward you witha spiral departure, until you figure out the trickof getting them to spin (rudder timing, blast ofpower, rapid deceleration leading to a higherangle of attack). You’ll immediately recognize aspiral departure, because the roll-off happensslowly. A spin departure will roll you faster.Opposite aileron will recover a spiral, but theresulting adverse yaw may aggravate a spindeparture. Airspeed and z-axis load factor willincrease in a spiral, and the ball will respond toyour feet in the normal ways, remaining centeredif your feet are off the rudders.

Recovery Controls

Neutral rudder and aileron, and neutralelevator (or perhaps stick forward of neutral)are all that’s required for recovery from theimmediate departure stage in a typical trainer.Responding quickly to a wing drop in thismanner is usually enough to breakautorotation. PARE-sequence recovery controlsbecome more critical as angular momentumstarts to grow and the spin heads toward adeveloped state. To recover from an upright spin:

Power to idle. (Reduces propellergyroscopic effects and slipstream-inducedyaw.)

Ailerons neutral. (Removes any inadvertentdeflection that may delay recovery. In afuselage-loaded aircraft the ailerons gotoward the yaw direction—toward the turnneedle whether upright or inverted—toproduce anti-spin inertia moment in yaw.)

Rudder opposite yaw direction. (Providesanti-spin aerodynamic yaw moment.)

Elevator forward to neutral or pastneutral. (Unstalls the wings; for wing-loaded aircraft generates anti-spin inertiamoment in yaw.)

When the spin stops, pull out with therudder neutral. (If the recovery rudder isstill deflected and you pull too hard, aircraftcan snap roll into a spin in the oppositedirection.)

In the following, we refer to inertia moments andgyroscopic effects that depend on how the massof the aircraft is distributed around its three axes.For simplicity in presentation we’ll just makereference to them now; try to explain them later.

Power

Power goes back to idle to reduce gyroscopicand slipstream effects. In an aircraft with aclockwise turning propeller as seen from thecockpit, power in an upright spin to the left tendsto raise the nose due to the gyroscopic forcesillustrated in Figure 14. Spiraling slipstreamtends to increase in-spin yaw moment. In a spinto the right, gyroscopics can bring the nose downand the slipstream can supply anti-spin yawmoment. Properly timed, power application in aright-hand spin can help damp the oscillations ofthe incipient phase shown in Figure 9. But that’san advanced spin technique; just bring the powerto idle in an emergency recovery.

In jets, power to idle is typically recommended.Although modern fighters designed to operate athigh angles of attack have capable fuelcontrollers, earlier jets or less robust designshave trouble handling the unsteady inlet flowsaccompanying spin departures. Compressorstalls and flameouts are common. In spin tests ofthe T-38 supersonic trainer, there were threeflameouts of both engines and eighteen singleflameouts in twenty-one upright spins. Someonegot good at restarts!

Note that power often isn’t mentioned in theaircraft handbook recoveries reproduced fartheron.

Spins


Ailerons

Aileron deflection works in the normal rollingsense during a spin, even if both wings arestalled. At spin attitudes, aileron deflectioncauses a span-wise difference in drag. Thisproduces a component of roll as well as yaw. Aglance back at Figure 11 shows how the dragvector tilts toward the aircraft’s z-axis and thustoward roll effectiveness in a spin. Out-spin stickdeflection lowers the inside aileron. In a typicalspin trainer, this tends to drag the inside wing up,and bring up the nose, causing the spin to flatten.

Ailerons go to neutral for a recovery in anaircraft with broadly neutral mass distribution.Sometimes ailerons are hard to hold in neutral,because they have a tendency to float with thespin. Aircraft that recover more slowly if theailerons are deflected often have a line paintedon the instrument panel. The pilot uses this as anaim point to be sure that the ailerons are centeredwhen the stick goes forward.

As we’ll explain later, a roll moment canproduce a yaw moment, depending on theaircraft mass distribution. In a fuselage-loadedaircraft, aileron deflection into the spintypically produces an anti-spin yaw inertiamoment that helps recovery.

This anti-spin yaw moment generated by in-spinaileron in a fuselage-loaded aircraft tends to raisethe outer wing and increase wing tilt. Greaterwing tilt increases the nose-up pitch rate. This inturn causes an increase in both anti-spin rollingand anti-spin yawing inertia moments. (Relax.You’re not supposed to understand this yet.)

The standard recommendation for aircraft thatrequire aileron into the spin is aileron first, thenrudder and elevator.

Aileron deflection could make it difficult tofigure out when the spin has stopped, however. Ifheld, aileron will cause the aircraft to continue toroll after it ceases autorotation. Look at the F-4recovery procedure given later. You’ll see thatthe pilot is instructed to “Neutralize controlswhen rotation stops.” You have to wonder if itwould stop. Since the purpose of ailerondeflection is the creation of anti-spin yawmoment, and since the nose would go down asyaw rate decreases, pitch attitude would likely bean important cue in an aileron-assisted recovery.

In a wing-loaded aircraft (Ixx>Iyy) aileron into thespin can increase spin yaw rate and bring up thenose. Aileron against the spin will produce anti-spin yaw moment, but a pro-spin, acceleratingmoment in roll, the dramatic opposite of what thepilot’s instincts are suggesting. Since wing-loaded aircraft generally spin nose down, with ahigh apparent roll rate seen from the cockpit, thetemptation to use aileron against the spin can bestrong. Neutral ailerons are usuallyrecommended for spin recovery in wing-loadedaircraft.

Rudder

Stopping a spin requires slowing down therotation in yaw to the point where angle of attackcan be decreased, the wings returned to the pre-stall side of the lift curve, and roll dampingreestablished. The primary anti-spin recoverycontrol in most aircraft is opposite rudder. Fullrudder opposite the spin direction is alwaysappropriate.

Opposite rudder decreases the yaw rate, which inturn decreases the inertial couple driving thenose-up pitching moment. (Figure 15 willexplain this nose-up couple.) The rudder’seffectiveness will depend on the surface areaexposed to the relative wind at spin attitudes(perhaps the airflow to the rudder is partlyblocked by the horizontal stabilizer andelevator), by the additional available yawdamping effect of the fuselage, and by theposition of the center of gravity. Aft c.g. reducesthe arm and thus the available anti-spinaerodynamic moment.

Take a look at the wing tilt angle illustrated atthe bottom of Figure 10. During spin recovery,with recovery rudder deflected, the outside wingtends to rise. This increases the wing tilt angle,which reduces any outward, pro-spin sideslip,and introduces a positive, nose-up pitch rate. Infuselage-loaded aircraft, the pitch rate precessesto an anti-spin yaw inertia moment, assistingrecovery.

Elevator

After applying opposite rudder, apply forwardstick. (In the case of an inverted spin, the stickcomes back.) The sequence of rudder-then-elevator is important, since, once the yaw rate

Spins


begins to develop, leading with the elevator canaccelerate the spin rate gyroscopically, makingthe rudder’s task more difficult. As justmentioned, elevator deflected down may alsodecrease the rudder surface exposed to therelative wind, limiting its effectiveness. In manyinstances, even aircraft designed for spins maynot recover if anti-spin rudder is applied whilethe stick remains too far forward (for example,after an instructor demonstrates an acceleratedspin but then fails to bring the stick all the wayback in a Pitts). Recovery from a developed spinshould start with full back elevator.

Once the yaw rate begins to build andgyroscopics come into play, a nose-down pitchproduces a pro-spin inertia moment in roll.You’ll feel the roll rate increase as the nosecomes down. This is always the case, once theaircraft begins to develop angular momentumabout the yaw axis, regardless of wing/fuselagemass distribution or spin direction. With thecontrols applied in the proper opposite-rudder,elevator-forward sequence, the roll accelerationmeans that recovery is on the way, but it’s adisconcerting sensation. It appears that the spinis getting ready to become nasty, when it’sactually getting ready to stop. The gyroscopicmechanism at work is a pitching moment thatprecesses 90 degrees around the yaw axis,producing a rolling moment. The initial anti-spinrudder will slow down the yaw rate (z-axisangular momentum) so that when the stick thencomes forward less spin-direction rollacceleration will occur.

Down-elevator can be the most effectiverecovery control with an aircraft with a wing-loaded mass distribution, because it produces ananti-spin inertia moment in yaw. That could becrucial if the rudder is too weak to produceenough aerodynamic anti-spin yawing momenton its own. The amount of forward sticknecessary may increase at aft c.g. loadings.

Our trainers actually behave as if they werewing-loaded as the spin just gets started. Theirroll acceleration is initially high; their yaw ratepicks up more slowly. As a result, angularmomentum is greater initially in roll than in yaw.Pushing the stick forward causes gyroscopicprecession around the roll axis that leads to ananti-spin moment in yaw. Plus, pushing gets theangle of attack back down, out of autorotation.But once the aircraft’s yaw rate and angularmomentum about the yaw axis has begun to

build, forward stick will cause the momentaryacceleration described above, even when itfollows the rudder in proper sequence.

If you hold pro-spin rudder while holding thecontrol forward, the aircraft typically will stay inan accelerated spin. Decelerate the spin bybringing the control all the way back, and thenrecover in the normal way: use full anti-spinrudder followed by forward stick.

Flaps

Flap recommendations are inconsistent, as youcan see in the pilot-handbook recoveries listedfarther on. With the exception of flaps usedduring practice slow-flight, flap deploymentimplies an aircraft flying close to the ground. Inthat case, unless the manufacturer directs,emphasis should be on the primary anti-spincontrols. During flight testing under Part23.221(a) iv, an aircraft is required todemonstrate spin recovery in the flaps-extendedcondition: “…the flaps may be retracted duringthe recovery but not before rotation has ceased.”Thus, by design, flaps at very least cannot delayrecovery beyond the maximum turns allowed bycertification. Retraction after rotation stops willreduce the chance of overstressing the wingswhile returning to level flight. Limit load usuallydrops to 2g when the flaps are fully deployed.

Pull Out

Spin students sometimes remind instructors thatthe game isn’t over once the spin stops. Groundrush, the sensation that the closure rate with theplanet is accelerating, can lead inexperiencedpilots to start yanking. The aircraft then goes intoa heavy buffet, and the pilot loses the nose-uppitch authority he’s desperate for. Pilots can alsofind themselves holding recovery rudder. If thepilot pulls too aggressively while holding rudderdeflection, the aircraft can depart into a rapidrotation in the direction opposite the originalspin. This is one of those scenarios in which anaircraft answers a pilot’s fearful response bygiving him even more to worry about. Thesolution is to neutralize the rudder andmomentarily decrease the aft pressure on thestick.

Spins


Inverted Spins

Inverted spins present unusual motion clues.Pilots are accustomed to seeing aircraft yaw androll in the same direction, a visual paringreinforced whenever entering an ordinary turn.But in an inverted spin the aircraft appears to rollone way while yawing the opposite. (If you weresitting upright on the belly of the invertedaircraft, however, the yaw/roll relationshipwould appear normal.) The aircraft’s motion pathrelative to the landmarks below also takes gettingused to. Until you’ve had some practice, it’s hardto count the turns in an inverted spin.

In upright and inverted spins, one thing remainsthe same: In a standard intentional entry, ruddercauses the corresponding wingtip to fall.Imagine an aircraft beginning an intentionalupright spin to the left. The left wing falls towardthe earth when you press the left rudder withyour left foot. The same thing happens flyinginverted when you press your left foot during anintentional inverted spin entry: the left wing fallstoward the earth. Anti-spin rudder application isidentical in both the intentional upright andinverted cases. Use the foot opposite the fallingwing. If you press the left rudder to enter aninverted spin, the spin will be to the right as seenfrom outside. But the outside direction onlymatters in aerobatic competitions. Think of yourintroductory inverted spins in simple cockpitterms, as left- or right-footed.

Recovery from an inverted spin follows the samePARE sequence as recovery from upright, exceptfor the direction of elevator deflection. The stickcomes back in an inverted spin recovery.

An intentional inverted spin entry may lookweird from the cockpit at first, yet with practiceit’s easy to initiate or react to correctly, if youremember your feet. But an intensifying invertedspin entered by surprise is a different matter. Ifyour thoughts were elsewhere, or if the spin ishighly coupled and oscillatory or unexpectedlytransitions from upright to inverted, determiningyaw direction can take a while. Since spinrecovery technique depends on yaw direction,recognition is critical. Again, a turn needle willshow you the correct yaw direction, whetherupright or inverted. A turn coordinator, however,only works upright. In the absence of a turnneedle, look directly over the cowling to pick upthe yaw direction. Peripheral cues tend to bedistracting since they correspond more strongly

to roll. Looking back, behind the spin axis, givesyou a false yaw direction.

Inverted spins usually respond quickly to anti-spin rudder. With conventional tails (as opposedto T-tails), more unshielded rudder area isexposed to the relative wind in an inverted spinthan when the aircraft is upright. The aircrafthandbook tells you how far back to bring thestick after applying opposite rudder.

The possible difficulty of recognizing spin typeand direction is reflected in military recoveryprocedures. Check the procedures for the T-34Cand F-4, farther on. When there’s confusion, theturn needle and angle of attack indicator dictatepilot response, not the view outside. (Althoughanti-spin control inputs can be easier todetermine from instrument reference, identifyingthe recovery and regaining orientation is mucheasier using external cues.)

During spin recovery, less experienced aerobaticpilots sometimes unintentionally tuck-underfrom an upright into an inverted spin by pushingtoo aggressively while holding recovery rudder.As viewed from outside, the spin directionremains constant as the aircraft switches toinverted. The transition is hard for the pilot tosee. Another way to tuck into an inverted spin isby applying too much forward stick during theyawing transition to the descending line of ahammerhead. Aerobatic spin training doesn’thave to exhaust the complete spin matrix, butdual instruction that cautiously points to suchdangers is invaluable.

Spins


Müller-Beggs Recovery

With the above in mind, aerobatic pilots shouldlearn the Müller-Beggs method, used forrecovery from unintended spin departures whenthe direction and mode is unclear.

The steps are:

• Power to idle.• Let go of the stick.• Establish the yaw direction by looking

directly over the nose (or at the turn needle).• Apply opposite rudder, and recover from the

dive when the rotation stops.

Look at the rudder pedals if you can’t figure outspin direction. In an aircraft with reversiblecontrols, the rudder will float trailing-edge-toward the spin. This will set the rudder pedalsso that the recovery rudder will be the one closerto you when the cables are taut. In a dim cockpitthe pedals might be hard to see. The recoverypedal is the one that offers the most resistancewhen you press.

This release-the-stick technique works well withcertain aerobatic aircraft, but not always withothers, a point that usually unleashes claims,counter-claims, and a certain amount ofposturing when aerobatic pilots start makingcomparisons. Spins are very sensitive to massdistribution, to c.g. location, and to the timehistories of complex, nonlinear airflows.Different examples of even the same aircraftmodel can behave in different ways, dependingon the inevitable differences in rigging. Pilots dothings differently without knowing it. Thereaction of an aircraft to control inputs candepend on how far a spin has developed and onits current oscillatory phase. So take thesuggestions of experienced pilots concerningMüller-Beggs seriously, but beware those whomake messianic pronouncements unsupported byevidence. You might be listening to theaforementioned Joe-Bag-of-Donuts. Neither theDecathlon nor the Zlin 242L nor the DeHavilland Chipmunk should be consideredMüller-Beggs recoverable.

The procedure of letting the stick go assumes thepilot is too confused to perform the aircraftmanufacturer’s recommended recovery, andcan’t identify the spin mode as upright orinverted. It releases any impulsive out-spin stickdeflection that might tend to flatten the spin, but

it usually also accelerates the roll rate throughinertial effects generated when the nose pitchesdown. The roll acceleration could delay recoverycompared to the recommended procedure.

Training in the Müller-Beggs technique isessential if you plan to fly or instruct aerobaticsin aircraft that depart quickly and can quicklyshift between upright and inverted modes ifmishandled—characteristics that can make visualtracking difficult. Fly with a qualified instructorin an aircraft with a known, positive Müller-Beggs response. Start with upright spin entries ataltitudes allowing delayed recovery. When yourelease the stick, watch where it goes in responseto the float angles of elevator and ailerons. Notethe force required to move it. The stick can feelalarmingly stiff. (In a tandem trainer, you mightthink the other pilot has frozen the control.)

Practice and familiarization are important so thatdifferences in aircraft motion and recovery timebetween the recommended and Müller-Beggsprocedures don’t come as a surprise during anemergency. If they do, you may be tempted tochange control inputs before they have time towork, delaying recovery even more. Duringtraining, be prepared if necessary to return thecontrols to the initial full stick-back, in-spin-rudder, spin entry position before beginning themanufacturer’s recommended recovery. Thisshould return the aircraft to a known recoverablestate.

Spins


Handbook Recoveries

The following are directly from the respectiveaircraft handbooks, unless indicated. For foreignaircraft, the translation is from the manufacturer,including the original spelling and syntacticalcharm. Format follows the original as much aspossible.

All specify full rudder against the spin, asexpected. Elevator recommendation varies fromneutral to forward of neutral. Except for theFalcon and the F-4, ailerons remain neutral.Most remind the pilot to pull out of the dive, justin case:

Falcon 20 Business Jet

Intentional spins are prohibited. This aircraft hasnot been spin tested in flight. However, results ofwind tunnel tests have shown that the followingprocedure should be applied:

Configuration CleanRoll Same direction of rotationYaw Opposite direction to spin

rotationElevator Neutral

AT-6C (Army) and SNJ-4 Navy Trainers

Spins should not be made intentionally withflaps and landing gear down. Should aninadvertent spin occur, recovery can be effectedafter 1-1/2 or 2 turns by first applying fullopposite rudder and then pushing the controlstick forward to neutral. The ailerons are held inthe neutral position. Centralize the rudder assoon as the airplane is in a straight dive toprevent a spin in the opposite direction. Bringthe airplane out of the dive and return the controlstick to neutral.

Zlin 242L Single-engine Trainer

Mixture Max richThrottle IdlingRudder Full deflection

opposite to directionof rotation.

Elevator Immediately after fullcounteraction ofrudder push smoothlycontrol stickminimally to half ofthe travel betweenneutral and fullforward within 1-2sec. Ailerons inneutral position.

After rotation is stopped:Rudder Neutral positionElevator Pull steadily control

stick to recoveraircraft from diving.

Spins


National Advisory Committee for AeronauticsTechnical Note No. 555, “Piloting Technique forRecovery From Spins,” W. H. McAvoy, 1936.

The recommended operation of the controls forrecovery from a spin, which presupposes that theailerons are held in neutral throughout therecovery, is as follows:

1. Briskly move the rudder to a positionfull against the spin.

2. After the lapse of appreciable time, sayafter at least one-half additional turn hasbeen made, briskly move the elevator toapproximately the full down position.

3. Hold these positions of the controlsuntil recovery is effected.

(The recommended delay in applying elevatoraddressed fact that in many aircraft the elevators,when deflected down, reduced the efficiency ofthe rudder by blocking its airflow.)

PZL M-26 Iskierka (Air Wolf)

Be sure of the direction of the aircraft’s rotation.Rudder Set vigorously

opposite the self-rotation.

Elevator Slightly forward,beyond neutralposition.

Ailerons Neutral PositionAfter stopping rotation:Rudder NeutralFlaps UpControl stick Smoothly backward

(recover the aircraftfrom dive withoutexceeding theairspeed and loadlimits).

Engine power Increase smoothly

Cessna Model 172P

1. Retard throttle to idle position.2. Place ailerons in neutral position.3. Apply and hold full rudder opposite

to the direction of rotation.4. After the rudder reaches the stop, move

the control wheel briskly forward farenough to break the stall. Full downelevator may be required at aft center ofgravity loadings to assure optimumrecoveries.

5. Hold these control inputs until rotationstops. Premature relaxation of thecontrol inputs may extend the recovery.

6. As rotation stops, neutralize the rudder,and make a smooth recovery from theresulting dive.

F-4 Phantom

TA-4F/J NATOPS Flight Manual

• Neutralize flight controls and physicallyhold the stick centered (visually checkposition of the stick).

• Retard throttle to idle.• Determine type and direction of spin.• Apply and maintain recovery controls.

Aileron: Full with turn needle if spin iserect. Full opposite turn needle if spin isinverted.Rudder: Full opposite turn needledeflection.Stick: Neutral to slightly aft.

• Neutralize controls when rotation stops andrecover from the ensuing dive at a maximumof 18 to 20 units angle of attack.

• PSG recovery procedures: Neutralize allcontrols.

Spins


T-34C Turboprop Trainer

Naval Air Training Command, “Flight TrainingInstruction, T-34C Out-of-Control Flight,” Q-2A-0017, 1993.

1. Landing gear and flaps – Check “up”2. Verify spin indications by checking

AOA, airspeed and turn needle.Warning – Application of spin recovery controlswhen not in a steady state spin (as verified byAOA, airspeed and turn needle) MAY furtheraggravate the out-of-control flight condition.

3. Apply full rudder OPPOSITE the turnneedle.

4. Position stick forward of neutral(ailerons neutral).

Warning – “Popping” down elevator CAN resultin the spin going inverted in some airplanes. A“smooth” forward movement of the stick is bestfor most light aircraft during spin recovery.

5. Neutralize controls as rotation stops.6. Recover from the ensuing unusual

attitude.

(Note that the recovery procedures areinstrument-based in the two military examplesabove. Angle of attack indicator and airspeedverify the spin. The turn needle determinesrecovery rudder and aileron deflection if calledfor. The recovery procedure for the T-37Btrainer—a side-by-side jet twin built byCessna— reproduced in part below, takes anunusual approach. The pilot first attemptsrecovery from an inverted spin. If that doesn’twork, he tries to recover from an upright spin.)

T-37B Trainer

One procedure which will recover the aircraftfrom any spin under all conditions:

1. THROTTLES – IDLE.2. RUDDERS AND AILERONS –

NEUTRAL.3. STICK – ABRUPTLY FULL AFT AND

HOLD.a. If the spin is inverted, a rapid and

positive recovery will be affected[sic] within one turn.

b. If the spinning stops, neutralizecontrols and recover from theensuing dive.

c. If spinning continues, the aircraft mustbe in an erect normal spin (it cannotspin inverted or accelerated if thecontrols are moved abruptly to thisposition). Determine the direction ofrotation using the turn needle andoutside references before proceeding tothe following steps.

4. RUDDER – ABRUPTLY APPLY FULLRUDDER OPPOSITE SPIN DIRECTION(OPPOSITE TURN NEEDLE) ANDHOLD.

5. STICK - ABRUPTLY FULL FORWARDONE TURN AFTER APPLYINGRUDDER.

6. CONTROLS – NEUTRAL AFTERSPINNING STOPS AND RECOVERFROM DIVE.

L-39 Albatross Jet Trainer

Note

Spin character is stabile during the first turn,with increasing instabilities typical for jet aircraftin continuous turning. Unregular [sic]longitudinal oscillations develop with increasingamplitude and shudder. Rudder bounces andincreasing varying pedal forces must beovercomed [sic]. Unadequate [sic] control inputscan lead to inverted spin development (especiallywith extreme forward stick position), or to thechange in turning sense (ailerons against spinturning).

Upright Spin Recovery

Recovery is initiated with rudder and elevatorcentering. The aircraft stops turning and passesto steep dive with maximal one turn overturning.Ailerons remain held in neutral position. Moreaggressive turning stop can be initiated withrudder deflected against turning first, withsubsequent all controls centering.

Spins


Aircraft Gyroscopic InertialCharacteristics

We’ve referred to pro-spin and anti-spin inertiamoments without defining what we mean ordescribing how they work. The following maynot be entirely easy going, but give it someeffort—especially if you’re headed for your CFI.You won’t go into (or remember) this muchdetail with your primary students, but you doneed to get a sufficient handle on things toanswer some tough questions without leadingyour students too far astray. You should takeyour eventual CFI students to as high a level ofunderstanding as you both can manage. Don’tshirk your responsibility! And get a toygyroscope to play with. It will help you figurethings out.

Some definitions:

A moment causes rotation about an axis.

The moment of inertia, I, of a rigid bodyabout a given axis is a measure of itsrotational inertia, or resistance to change inrate of rotation. It equals the sum, ∑, of thebody’s various masses, m, multiplied by thesquares of their respective distances, r, from thataxis:

Moment of inertia, I = ∑ (mr2)

The greater its moment of inertia about an axis,the greater the applied moment or torque (forceapplied x lever arm) needed to change therotational motion of the body around that axis.

Aircraft have moments of inertia around eachinertial, or principal axis, which are normallyclose to the body axes.

IxxRoll Moment

of InertiaA

Predominantly the massof the wings.

IyyPitch Moment

of InertiaB

Predominantly the massof the fuselage.

IzzYaw Moment

of InertiaC

Mass of wings andfuselage.

Izz is always greatest.

If Ixx > Iyy, then wing mass > fuselage mass.

If Ixx < Iyy, then wing mass < fuselage mass.

(A, B, C are symbols used in Great Britain.)

Since it comprises all the aircraft’s mass, yawmoment of inertia, Izz, is always greatest. Pitch orroll inertia are greater, respectively, dependingon the aircraft’s distribution of mass betweenfuselage and wing. An aircraft with puny wingsand a heavy fuselage, so that Ixx < Iyy, has rollinertia < pitch inertia, for example.

The pitch/roll, Iyy/ Ixx inertial ratio is important tothe character of an aircraft’s spin and recovery.Iyy/ Ixx =1.3 is approximately the neutral value.Above that number, when Iyy/ Ixx >1.3, aircraftare considered fuselage-loaded in their behavior.Below that number, when Iyy/ Ixx < 1.3, aircraftare wing-loaded in behavior.

An aircraft’s external shape determines itsaerodynamics. Pilots are accustomed to lookingat the external shape and anticipating aircraftbehavior (often unsuccessfully). But aircraft alsohave an “internal shape,” as determined by thedistribution of mass. Aircraft stability andcontrol is a contest between the two. That’salways so, and especially so in spins, when theinternal shape starts to take on angularmomentum.

Pitch Inertia Iyy

Yaw Inertia Izz

Roll Inertia Ixx

Spins


Angular Momentum

Momentum is inertia in motion. A rotatingbody’s angular momentum, Iω, is its momentof inertia, ∑ (mr2), about a given axis times itsangular velocity, ω, around that axis.

Angular momentum = ∑ (mr2 ) ωor

Angular momentum = Iω

Angular momentum is also referred to as rotarymomentum.

Angular velocity

Angular velocity, ω, just referred to, is the rateof change of angular displacement. Consider aflat, rotating disk with a line drawn from centerto circumference, as below. The axis of rotationis perpendicular to the page. As the disk rotatesthrough an interval of time, the displacedreference line forms an angle with its originalposition. Angular velocity is typically stated inradians-per-second (and in aerodynamicsdenoted by the symbols p, q, and r, for roll,pitch, and yaw).

(Inpounds)

Moments of Inertia (in slug-ft2) Source:www.jsbsim.sourceforge.net/MassProps.html

Aircraft Weight IxxRoll

IyyPitch

IzzYaw

F-16C(BLK30)

18,588 6,702 59,143 63,137

F-4Phantomw/2 AIM-7, 20%fuel

33,196 23,668 117,500 133,726

C-5w/220,000lb. Cargo,20% fuel

580,723 19,100,000 31,300,000 47,000,000

X-15w/zerofuel

15,560 3,650 80,000 82,000

CherokeePA-28

2,100 1,070 1,249 2,312

C172Skyhawk 1,700 948 1,346 1,967

LearjetEmptyweight

7,252 3,000 19,000 50,000

B-727Emptyweight

88,000 920,000 3,000,000 3,800,000

B-747 636,600 18,200,000 33,100,000 49,700,000

T-38Emptyweight

7,370 14,800 28,000 29,000

F-15 26,000 22,000 182,000 200,000

SchweizerSailplane 874 1,014 641 1,633

Twin Otter 9,150 15,680 22,106 33,149

Change in angle, θ ω = change in time

S = arc length

r

θ

Every point on the line has the same angular velocity. Its tangential velocity is proportional to its distance from the axis.

θ = s/r θ = Angular displacement in radians per second 1 radian = 57.3 deg.

ω = angular velocity

Spins


Gyroscopes

A spinning aircraft is a system of gyroscopes.The rotating mass of a gyroscope has twoimportant features. The first is rigidity inspace—as the spin rate of the rotor increasesaround its axis, it takes increasing force to tilt theaxis in a new direction.

The second feature is precession: An applied“input” will precess (go forward) and generate an“output,” 90 degrees ahead in the direction ofrotation. This is shown in the simplest andprobably easiest-to-visualize way in the drawingon the left, in Figure 12.

The same input is occurring in Figure 12, right,but presented in terms of moments. Thegyroscopic rotation is around the z-axis. If youapply a moment (or torque) around the y-axis, asshown, it will precess, causing a resulting inertiamoment around the x-axis. The inertia momentis our output.

Think of the drawing in Figure 12, right, in termsof the axis system of an airplane. If the aircraft isyawing around the z-axis (in a spin, perhaps) andyou apply a pitching (y-axis) moment withelevator, you’ll end up getting a rolling inertiamoment (x-axis), as well.

Because inertia moment = angular momentum xapplied angular velocity, the higher the appliedpitching angular velocity (i.e., greater the appliedpitching moment), the greater the resultingrolling inertia moment.

Aircraft Gyroscopics

The basic gyroscopic relationships in a spinningaircraft are easy to imagine once you get thetrick. If an aircraft is already rotating around anaxis, and thus acting like the rotor of a gyroscopearound that axis, a moment applied around asecond axis results in a moment produced aroundthe remaining third. Therefore:

Pitching into a yaw rotation gives a roll.

Pitching into a roll rotation gives a yaw.

Yawing into a pitch rotation gives a roll.

Yawing into a roll rotation gives a pitch.

Rolling into a pitch rotation gives a yaw.

Pitch Precession is 90 deg. in direction of rotation.

Input

Direction of gyroscopic rotation

Input push

Output tilt

Gyroscopic precession is the result of the conservation of angular momentum.

Figure 12 Gyroscopic Precession Direction of gyroscopic

rotation: Z-axis has angular momentum, Iω (moment of inertia times angular velocity).

Resulting precessed inertia moment

Applied moment (torque) produces an applied angular velocity, ωY.

X-axis

Z-axis

Y-axis

Inertia moment = Angular Momentum x Applied Angular Velocity (Moments of inertia and inertia moments are two different things. The former resist changes in angular velocity, the latter produce changes in angular velocity as the result of gyroscopic effects.)

Yaw

Roll

Output

Spins


Rolling into yaw rotation gives a pitch.

Somewhere before the end of the list, youprobably got the point. It’s not so simple inpractice, however, because in an actual spinningaircraft a moment around one axis precessesaround two “gyroscopes” simultaneously. Forinstance, the applied angular velocity following apilot’s pitch input works both the yaw-axis androll-axis gyroscopes. The resulting inertiamoments generated depend on the relativeangular momentums (angular momentum =moment of inertia x angular velocity) aroundthose axes. Thus for a given applied angularvelocity around the first axis, the second axiswith the highest angular momentum will“precess” the highest inertia moment into thethird.

Take, for example, pitch inertia moment.Imagine an aircraft rolling and yawing in a spinto the right, as in Figure 13, top. It has an angularmomentum in roll (equal to Ixx times angularvelocity in roll, p). Since it’s also yawing to theright, it has an applied angular velocity aroundthe yaw axis. The yaw precesses 90 degrees inthe direction of roll, and produces a nose downpitching moment. This is an anti-spin moment.

At the same time, the aircraft also has angularmomentum in yaw (equal to Izz times the angularvelocity in yaw, r), as in the bottom drawing. Inthis case the applied angular velocity is providedby the roll rate. The applied roll precesses 90degrees in the direction of yaw, and produces anose-up pitching moment. This is a pro-spinmoment.

This nose-up moment will be larger than thenose-down moment already described, becausethe moment of inertia around the z-axis, Izz, isalways greater than the moment of inertia aroundthe roll axis, Ixx. The net effect of the gyroscopicinterplay between roll and yaw is always a nose-up, thus pro-spin, pitch inertia moment.

What if the pilot steps in and imposes a pitch rateaerodynamically, by moving the elevator?Because yaw moment of inertia, Izz, is alwayshigher than roll moment of inertia, Ixx, roll ismore likely to be affected than yaw. The rollinginertia moment generated will be higher, and themass it has to accelerate will be less. In a spin, apitch down always produces a pro-spin rollinertia moment. A pitch up always produces ananti-spin roll inertia moment. If a spin oscillates

in pitch, its roll rate will vary as it pitches up anddown.

OK, you deserve a break.

x-axis roll direction

y axis

z-axis yaw direction

y axis

A roll to the right precesses through yaw 90 deg. into a pitch up inertia moment.

Right yaw input (an applied angular velocity around the z axis)

Right roll input (an applied angular velocity around the x axis)

Spin is vector sum of roll and yaw

Pitch down output

Pitch up output

Net inertia pitch moment is up (pro-spin), because Izz is always greatest.

Figure 13 Pitch Inertia Moment

Yaw Gyro

x axis

z axis Roll Gyro

A yaw to the right precesses through roll 90 deg. into a pitch down inertia moment.

Spins


Propeller Gyroscopics

There’s a fourth gyroscope to consider, and it’sthe one you actually learned about first inprimary ground school—the propeller.

The effects of propeller gyroscopics are mostevident in aircraft with heavy props and ratherlow directional and longitudinal stabilities,whenever the aircraft yaws or pitches rapidly athigh prop rpm and low airspeed. It also helps ifthe prop is a substantial distance from the aircraftcenter of gravity and can exert some leverage.High rpm gets the gyroscope’s angularmomentum going, and low airspeed reduces theaircraft’s stabilizing aerodynamic moments tothe point where prop gyroscopic effects canbecome apparent. Gyroscopic precession (notjust prop but also aircraft mass) is the essentialdriving force behind the aerobatic tumblingmaneuvers derived from the Mother of Tumbles,the lomcovak.

Gyroscopic effects acting through the propellercause yaw to produce a secondary pitchresponse, and pitch to produce a secondary yawresponse, as Figure 14 describes. With aclockwise prop, yawing to the left causes thenose to precess up. A spin to the left can go flatwith power, and possibly refuse to budge untilpower is reduced and the prop’s angularmomentum decreased.

In a spin to the right, power increases thegyroscopic tendency to bring the nose down andalso generates an anti-spin slipstream effect overthe tail. That may assist recovery (the gyroscopicpart may also increase the tendency for a spin togo inverted if the pilot applies forward stick tooaggressively). Many flight manuals—as well asthe usual generic recovery procedures—specifypower off at the start of spin recovery regardlessof direction. The idea is to prevent the prop fromcontributing anything harmful during the ensuingconfusion, and to prevent excessive airspeedduring the recovery pull out.

Unlike other propeller-induced effects,gyroscopic precession occurs only in thepresence of pitch or yaw rates, and depends ontheir magnitude. Precession tends to hold anaircraft’s nose up in a turn to the left and to forceit down in a turn to the right. Precession occursthroughout looping maneuvers and actuallydecreases the amount of rudder input thatcompensating for p-factor and spiraling

slipstream would otherwise require (right rudderin positive maneuvers).

In jets, the rotating masses of compressors andturbines supply the fourth gyroscope. Aclockwise rotating engine, as seen from behind,produces a faster spin to the right. Remember themovie The Right Stuff, when Chuck Yeager tookthe rocket boosted F-104 above 100,000 feet andlost control? Aerodynamic damping wasinsignificant at that altitude. The air-breathing jetengine had been throttled back, but its rotationstill produced a significant yaw couple.According to a well-placed authority, this tookYeager by surprise, because he hadn’t flown theflight profile in the simulator like everybody wassupposed to and was therefore late getting on theyaw thrusters.

Aircraft yaws right.

Pilot pitches up.

Pilot yaws right.

Aircraft pitches down. Pilot pitches down.

Aircraft yaws left.

Pilot yaws left.

Propeller rotation as seen from the cockpit

Pilot’s input

Precession causes output 90o in direction of rotation.

Figure 14 Prop-induced Gyroscopic Response

Aircraft pitches up.

Propeller rotation

Spins


Dumbbells

Figure 15 shows the fuselage and wing of anaircraft represented as dumbbells possessing theequivalent inertial characteristics. Rotationproduces centrifugal forces that tend to drive themasses apart. In this situation, equal andopposite forces, acting along different lines,produce a rotary inertial couple.

By itself the fuselage couple tends to drive thenose up, flattening the spin attitude (a pro-spinpitch couple).

The fuselage couple also tends to yaw the noseopposite the spin direction (anti-spin yawcouple), as in the bottom drawing. Thedumbbells in the wings, however, tend to yawthe aircraft in the pro-spin direction. Theultimate inertial couple in yaw depends on theaircraft’s mass distribution. Yaw couple is pro-spin when the wings are the dominant mass (Ixx >Iyy). Yaw couple is anti-spin when the fuselage isthe dominant mass (Ixx < Iyy).

Fuel load affects spin behavior by shifting thebalance. Filling the outboard or tip tanks isusually prohibited before intentional spins inaerobatic aircraft that have them, partly forweight concerns and partly because the buildupof greater angular momentum in roll and thegreater pro-spin yaw couple have to be overcomeduring recovery.

Note that the rotary inertial couples have thesame effect (the same positive or negative sign)as the gyroscopic inertia moments we’ve beendiscussing.

Figure 15 Inertial Couples in Pitch and Yaw

Anti-spin yaw inertial couple dominates.

Pro-spin yaw inertial couple dominates.

Nose-up, pro-spin pitch couple

Spin to the left Aircraft is seen from the top.

Spins


Axis InertiaMoment

AngularVelocity

Momentof Inertia

AircraftComponent

xRoll

Li(positive

right,negative

left)

Roll rate, p(positive right,negative left)

IxxRoll

Inertia

Predominantlythe mass of the

wings.

yPitch

Mi(positive

up,negativedown)

Pitch rate, q(positive up,

negativedown)

IyyPitch

Inertia

Predominantlythe mass of the

fuselage.

zYaw

Ni(positive

right,negative

left)

Yaw rate, r(positive right,negative left)

IzzYaw

Inertia(alwaysgreatest)

Mass of wingsand fuselage.

Positives and Negatives

In the three simplified moment equations on thefollowing page, the relative magnitudes of Ixx,Iyy, and Izz determine whether an inertia momentgenerated by precession will be pro-spin or anti-spin. This is key to understanding how thedistribution of mass in an aircraft affects spinrate and attitude, and how control inputs affectrecovery.

Remember that in the aerodynamics sign systempositive values are up and/or to the right,negative values are down and/or to the left.(Remember from algebra that a negative times anegative equals a positive; a negative times apositive equals a negative; and a positive times apositive equals a positive.)

In the case of the inertia moment in pitch, Mi,imagine an airplane is spinning to the positiveright. Roll, p, and yaw, r, are both positive in thiscase. Since Izz is always the greatest moment ofinertia, (Izz - Ixx ) is also positive. Since a positivetimes a positive times a positive equals apositive, the inertia moment in pitch, Mi, ispositive. That means nose up, pro-spin. Thesame goes for spinning to the negative left, sincea negative times a negative (-p times -r) againequals a positive.

Look at inertia moment in roll, Li: (Iyy - Izz) isalways negative, because Izz is always greatest.In a spin to the left, a negative (Iyy - Izz) times anegative yaw, r, times a positive or zero7 pitch, q,equals a positive. When spinning to the negativeleft, a positive (rightward) inertia moment in rollis anti-spin. In a spin to the positive right, theinertia moment in roll would be negative, againanti-spin.

In the last equation, the direction of the inertiamoment in yaw, Ni, may be anti- or pro-spindepending on which is greatest, Ixx or Iyy. Inother words, on whether the aircraft carries moreof its mass in the wings (Ixx > Iyy), or in thefuselage (Ixx < Iyy).

7 Zero is neither negative nor positive.

Figure 16 Iyy / Ixx Ratio

Ixx > Iyy Roll moment of inertia greater than pitch moment

Ixx < Iyy Roll moment of inertia less than pitch moment

Spins


If the aircraft is wing loaded, and thus Ixx isgreater than Iyy, the value in the brackets will bepositive. In a spin to the positive right, p ispositive, q is positive or zero, and so the appliedinertia moment in yaw will be positive and pro-spin. In a spin to the negative left, p is negative,q is positive or zero. A negative times a positivetimes a positive is a negative, thus again causingpro-spin yaw. (Note how this also corresponds tothe dumbbell illustration.)

Wing-loaded, Ixx > Iyy, aircraft generate pro-spinyaw inertia moments.

If the aircraft is fuselage loaded, and thus Ixx isless than Iyy, the value in the brackets will benegative. In a spin to the negative left, p isnegative, q is positive or zero. The result of allthree is positive, thus anti-spin in a spin to thenegative left. It’s also anti-spin in a spin to thepositive right.

Fuselage-loaded, Ixx < Iyy, aircraft generate anti-spin inertia yaw moments.

Aircraft become spin resistant, in terms of theirinertia moments, roughly when the ratio Iyy/ Ixx =1.3 or greater; in other words, when they leantoward the fuselage-loaded, with more pitchmoment of inertia than roll moment of inertia.

Once they get going, however, spins in fuselage-loaded aircraft may be more oscillatory or have atendency to go flat, due in part to their powerfulinertia moment in pitch, Mi. Anti-spinaerodynamic moments generated by the ruddermay not be sufficient for recovery against theangular momentum built up in yaw. Soadditional anti-spin yaw inertia moments, Ni,may be necessary for rescue. In this case, togenerate those moments, recovery may requireaileron into the spin direction in addition to out-spin rudder. This accelerates the roll rate, p,which precesses into a resulting anti-spin yawinertia moment (when Ixx < Iyy). The adverse yawprovoked by the aileron going down on theoutside wing might also provide some helpfulanti-spin aerodynamic yaw moment (onecertainly easier to visualize and understand thanconvoluted gyroscopic moments—and aperfectly good way to remember the recoveryaction), but generating that anti-spin yaw inertiamoment is the main idea.

Note from the third formula that when massshifts to the wings and roll moment of inertiabecomes higher than pitch moment of inertia, thesign in the brackets becomes positive. Aileroninto the spin now produces a pro-spin moment inyaw.

After this, is your head spinning? It’s not easy.

Ixx < Iyy Inertia moment in pitch = (yaw axis moment of inertia – roll axis moment of inertia) times roll rate times yaw rate .

( )prIIM xxzzi −=

Inertia moment in pitch, Mi, is nose-up, pro-spin. (Izz always > Ixx; sign in brackets always positive) Inertia moment in roll = (pitch axis moment of inertia – yaw axis moment of inertia) times pitch rate times yaw rate

( )qrIIL zzyyi −=

Inertia moment in roll, Li, is anti-spin. (Iyy always < Izz; sign in brackets always negative)

Inertia moment in yaw = (roll axis moment of inertia – pitch axis moment of inertia) times roll rate times pitch rate

( )pqIIN yyxxi −=

Inertia moment in yaw, Ni, may be pro-spin if roll inertia, Ixx , is greater than pitch inertia, Iyy (Ixx > Iyy; sign in brackets positive), or anti-spin if roll inertia is less than pitch inertia, (Ixx < Iyy; sign in brackets negative).

Spins


Moments in Balance

As already noted, in a steady spin, rotary andgyroscopic inertia moments about the aircraft’saxes and aerodynamic moments about those axesbalance (or sum to zero, since they have oppositesigns). Take the example, in Figure 17, of theinertia moments in pitch, which are always nose-up. An aerodynamic, nose down moment,generated mostly by the horizontal stabilizer,balances this. (Even if you’re holding back-stickin a practice spin, the aerodynamic moment isnose down.)

Likewise, the inertia moment in roll, which isalways anti-spin, will be balanced by the pro-spin aerodynamic roll moments generated bysideslip and autorotation.

The situation around the yaw axis is morecomplicated, since the inertia moments in yaware affected by the ratio Iyy/ Ixx. They tend to bepro-spin in wing-loaded aircraft, as describedabove. In that case the balancing aerodynamicmoment is the damping moment generated bythe fuselage and tail. If the aircraft is fuselage-loaded, the inertia moments are anti-spin andbalanced by the aerodynamic moments drivingthe spin (pro-spin yaw moments generated byautorotation and by rudder deflection if the spinis intentional).

Nose up inertial moments

Nose down aerodynamic moment

Relative wind

Figure 17 Moments in Balance

=

Spins


Inertia Pitching Moment in Particular

Figure 18a shows a curve of inertia pitchingmoment plotted against angle of attack for adeveloped steady spin. It’s always greatest at 45degrees for a given angular velocity, andincreases overall with angular velocity, ω (spinrate), as shown. Although inertia pitchingmoment is always positive (nose up), in this caseit’s plotted in the negative direction. Note thatthe curves each represent a different but constantangular velocity.

Figure 18b shows aerodynamic pitchingmoment, which is always nose down, plottedagainst angle of attack. Note the increase inaerodynamic moment as angle of attackincreases and/or as the stick moves from aft toforward.

Both moments appear in Figure 18c. The pointof intersection, where inertia pitching momentand aerodynamic pitching moment are equal andopposite, shows the angle of attack at which astabilized spin can occur.

Finally, Figure 18d shows what happens whenthe stick is moved from aft to the forwardposition. Angle of attack decreases as theincreased aerodynamic moment forces the nosedown. At the new angle of attack, the line ofincreased aerodynamic moment intersects a newinertia moment curve. The aircraft stabilizes at afaster spin rate.

The figures underscore the importance of stickposition and timing during spin recovery.Applying forward stick, before opposite rudder,can accelerate a spin rate. This increases thenose up inertia moment and actually makes theelevators less effective in reducing the angle ofattack and breaking the spin—since they havemore to work against. Holding the stick backdecreases the aerodynamic moment and thereforethe inertia moment as the system restoresbalance. Opposite rudder applied first allows thespin rate to decelerate to the point where forwardstick can be applied and the elevator will havesufficient authority to decrease the angle ofattack and break the spin. In practice, forwardstick following opposite rudder typically leads toa momentary acceleration, but anti-spinaerodynamic moments quickly prevail.

Angle of Attack

Iner

tial M

omen

t

(

Nos

e-up

tow

ard

arro

w)

0o 45o 90o

Angle of Attack

Aer

odyn

amic

Mom

ent

(N

ose -

dow

n to

war

d ar

row

)

0o 45o 90o

Angle of Attack

Aer

odyn

amic

Mom

ent (

Nos

e-do

wn)

. In

ertia

l Mom

ent

(Nos

e -up

)

0o 45o 90o

Angle of Attack

Aer

odyn

amic

Mom

ent (

Nos

e-do

wn)

. In

ertia

l Mom

ent

(Nos

e-up

)

0o 45o 90o

Increasing spin rate, ω

Aft Stick

Steady state: moments are equal and opposite.

Forward Stick

Neutral Stick

Aft Stick

Forward stick decreases α, equilibrium reestablishes at a higher spin rate.

b

d

c

a

Figure 18 Pitching Moments

Spins



Flightlab Ground School11. Some Differences Between Prop Trainers and Passenger Jets


As we work through our flight test and upsetmaneuvers, keep in mind the possible differencesbetween our aircraft and the one you normallyfly. Below is a quick review of some of thedifferences between typical aerobatic proptrainers and passenger jets.

Although they are different in quickness and inattainable rates of roll, pitch, and yaw, differentin stability versus maneuverability, and differentin control forces and gradients, aerobatictrainers and passenger aircraft still follow thesame set of rules. If you exclude prop effects forour trainers and various inlet and thrust effectsfor jets, each “calculates” the same basic matrix,constantly working out a balance between theforces of lift, weight, thrust, and drag, andbetween the opposing moments generated aboutthe aircraft’s axes. One can observe these basicforces and moments in any aircraft.

However, that doesn’t mean that they actuallyhave been observed during flight test toanywhere near the same extent in all aircraft. Forexample, flight-test requirements for an FAAspin approved trainer take it to much highercombinations of angle of attack, α, and sideslip,β, than required for passenger jets. Thedemonstrated ability to recover from a six-turnspin is required of the former. Adequate stallwarning and the demonstrated ability to recoverfrom a stall without needing extraordinary pilotskill are required of the latter. Between the oneobligation and the other lies plenty of unexploredterritory.

Accordingly, when we do our maneuveringexercises in our trainers at high α and β, we’ll bein a regime where the behavior we observe willnot be the same for all aircraft. That won’tinvalidate our observations, or the principles ofaerodynamics they illuminate, but it will make usthink.

What happens if you simply scale up an aircraft,keeping the proportions and the wing loadingconstant? Aerodynamic moments increaseapproximately as the third power of aircraft

dimension. But moments of inertia increase asthe fourth power—which slows down aircraftresponse.

Maneuvering

If you normally fly a people-hauler, you’llimmediately notice a livelier feeling in ouraerobatic trainers:

In pitch, short period response will be faster thanyou’re accustomed to (your instructor willdemonstrate short period response, and we’llcover it in ground school). For our purposes,short period response is essentially a measure ofaircraft quickness—how rapidly an airplane canrespond to a control deflection in pitch. Ouraircraft have high short period frequencies, andare also quick to respond in roll and yaw. Thesignificance is that you’ll be learning maneuversin an airplane that’s more instantaneouslyresponsive (higher initial accelerations) aroundits axes than the one you normally fly, and canbuild up higher rates of rotation about thoseaxes, as well. As a result, you may tend toovercontrol at first.

But once you get accustomed to the trainingaircraft, your response expectations may thenbecome unrealistic in terms of what your ownaircraft can do. Your own aircraft might also feelsomewhat out of phase during upset maneuverscompared to the trainer. It might respond to thecontrols at different rates around each axis.Control forces may not be as nicely harmonized,which can make it more difficult to coordinateunusual-attitude control inputs in a smoothmanner.

Stability and maneuverability mark the oppositeends of a continuum. Passenger aircraft designedwith the geometry and mass distribution for highlongitudinal stability (or equipped with controlsystems that produce high stability artificially)are reluctant to maneuver. As the center ofgravity shifts aft, stability relaxes,maneuverability increases, and required elevator

Some Differences Between Prop Trainers and Passenger Jets


deflection and control forces diminish. An aftcenter of gravity also means that less down forcehas to be generated by the horizontal stabilizer totrim the aircraft, and there’s less accompanyingdrag. Any down force at the tail in effectincreases the weight of the aircraft, and so morelift is required of the main wing, which then hasto operate at a higher angle of attack, againadding to the total drag necessary to trim.Transports designed with “relaxed” longitudinalstability can take advantage of lower drag, butrequire control systems that augment stability. Ifstability augmentation fails at aft loadings, thepilot needs to keep control movements in check,since response will be livelier.

Maneuvering produces loads. While our trainersare designed for maneuvering and built for thehigh g-loads that maneuvering entails, passengeraircraft are designed for a narrower maneuverenvelope. Because aggressive maneuveringcould produce excessively high structural loads,low-g passenger aircraft require higher controlforces and steeper gradients of stick-force-per-gto discourage the pilot from exceeding structurallimits. Aircraft stressed for higher g need lowerpitch control forces and shallower gradients toavoid exceeding a pilot’s strength during highlyaccelerated maneuvers. A 2-g pull in our aircraftwill require much less force than in yours.

Propeller Effects

Propeller effects include spiraling slipstream, p-factor, precession, and torque. These tend tomake the nose wander on an aerobatic aircraft inresponse to changes in power (slipstreameffects), changes in angle of attack and sideslip(p-factor), and changes in pitch and yaw rates(precession), and can introduce rolling moments(torque). Lacking such annoyances, jet’s trackstraighter and require much less attention torudder for yaw control during normal aerobatics.In fact, the most-welcome discovery in thetransition from aerobatics in a propeller aircraftto aerobatics in jets is the absence of thefootwork associated with a prop, and the lack ofdirectional trim change due to speed change thatpropeller effects require.

On the other hand, the least-welcome discoveryis the loss of on-command airflow associatedwith a prop. At low speeds, prop-inducedslipstream over the wing and tail surfaces helpsmaintain longitudinal and directional control.

The enhanced airflow over the wing can decreasepower-on stall speed by a considerable amount,and by decreasing effective angle of attack overthe wing roots tends to increase the overall deckangle at which stalls occur. The effects of powerincrease on stall speed and recovery control aremore immediate and pronounced for propeller-driven aircraft than for jets, which don’t see amarked induced airflow with power applicationbut instead have to accelerate to build up thedynamic pressure necessary to reestablish liftand control authority. And propellers providealmost immediate thrust, while jets spool up andgenerate thrust and aircraft acceleration moreslowly. These differences are especiallyimportant during the approach phase of flight,when speed control and engine rpm managementbecome critical in jets. Excessive sink rates thatrequire only a power increase for immediatecorrection in a prop aircraft take more time tocorrect in a jet.

Lift and Drag

Lift curve slope affects stall behavior. Wingsweep has the result shown in Figure 1. Whenslope is reduced, CL varies less rapidly withangle of attack, α. For a straight wing, smalldifferences in angle of attack produce notablechanges in lift and potentially a quicker stallrecovery when the nose goes down. Swept wingsstall at higher angles of attack, and the stall andrecovery may not be so well defined—more amush than a break. Induced drag is also higher inthe stall region with swept wings.

At idle, a propeller creates substantial drag,while a jet still manages a small amount ofthrust. The ability to produce parasite drag withthe prop one moment, and thrust the next makesspeed control an easier matter. In a jet, with itsrelative lack of parasite drag to slow things down

Coe

ffic

ient

of L

ift, C

L

Figure 1 Lift Curve

Angle of Attack, α



and its delay in thrust to speed things up, plusgreater inertia to overcome, speed control usingthrottle requires more anticipation and planning

Because of the high induced drag at low speed,shallower lift curve peak, greater aircraft inertia,and longer spool-up time, stall recovery withminimum altitude loss can be touchy in jets. Themethod usually taught is to set the nose close tothe horizon, add full power, and regain flyingspeed at as high a coefficient of lift aspossible—CL then being gradually reduced asairspeed builds. However, high-altituderecoveries may require putting the nose down tocompensate for deficiencies in thrust. Transportpilots have been known to apply power during arecovery at altitude, but attempt to hold the noselevel, allowing the stall to persist, even throughrepeated pitch breaks and buffet, until theairplane loses lateral control before hitting theground. (Airborne Express, Douglas DC-8-63,Narrows Virginia, 12/22/96.)

The Rudder

On jets, the rudder is secondary to aileron andelevator. Without the various propeller effects totame, rudders are used for counteringasymmetrical thrust during engine failure and fordirectional control in crosswind landings. Pilotsotherwise tend to keep their feet on the floor andlet the yaw damper maintain turn coordination,especially in swept-wing aircraft that Dutch rollin response to sideslip. As a result, jet pilotsoften have to rediscover the rudder whenlearning unusual-attitude skills in aerobatictrainers (just as prop pilots have to learn to stopplaying with their feet when transitioning theother way). In transferring those rudder skillsback to their normal flying, jet pilots need toconsider that the vertical fin and rudder structureand the rudder limiting system in their ownaircraft may not be designed for the loads thatpoorly executed or maximum performancerecoveries might generate or require. They’ll alsoneed to remember that, compared to a straight-wing trainer, in a large, high-yaw-inertia swept-wing aircraft it can be difficult to apply therudder in phase to augment roll rate. Possibly, atfirst nothing happens, then too much happensand the aircraft over-rotates and begins a Dutchroll cycle. We’ll need to keep this in mindthroughout our flights, as we think about how (orif) specific techniques learned in the trainershould be transferred to other aircraft.

Speed and Altitude

Other differences between aerobatic trainers andjets include the latter’s greater speed and altitudeenvelopes. Our trainers can’t go fast enough andclimb high enough to become involved withMach-induced buffet and trim effects, or with thenarrowing speed band between Mach buffet andlow-speed stall (the “coffin corner”). Nor canthey climb high enough to experience the changein stability and flying qualities caused by thereduction in aerodynamic damping due todecreased atmospheric density.

Finally, because of their lower speeds, at a giveng-load our trainers will fly much tighter radiithan jets during looping maneuvers or pull-uprecoveries from nose-down attitudes. They canpull to higher limiting g-loads than passengerjets, as well. For a given g the radius of a turn (orof a pull-up) at any instant varies directly withthe square of the true airspeed. Double the speedmeans four times the altitude consumed. As aresult, the altitude required during maneuvers inthe vertical plane will be much less in anaerobatic trainer than in a jet. The latter needsexponentially more sky.


Flightlab Ground School12. Vortex Wake Turbulence


Vortex Characteristics

The wake generated behind an aircraft has twosources. The first is turbulence caused by profiledrag and engine thrust—a disorganized motionthat diminishes to a harmless level severalwingspans behind the aircraft. The second sourceis the vortex pair. The vortices are highlyorganized and decay only slowly, persisting formiles behind the generating aircraft.

The FAA publications do a good job ofdescribing the typical behaviors of aircraft vortexwakes, and in describing the appropriateavoidance techniques for aircraft followingbehind. But the graphics used (often a wideningspiral) tend to give a misleading impression of

vortex structure and therefore of aircraftresponse. We’ll address that here. In addition, inground school you’ll see wind tunnel filmsshowing how the vortex rolls up around awingtip, and also videos from NASA that showvortex structure and encounter dynamicsdownstream. The NASA videos reveal howmobile the vortex core is in turbulent conditions,and how abruptly it can change position inresponse to penetration by a large aircraft.

Figure 1 shows vortex structure in terms of thetangential velocity at increasing distance fromthe core.

Flow field

Vortex core

Tangential velocity within the core increases directly with radius.

Figure 1 Vortex Velocity Profile

Tangential velocity in the flow field is generally inversely proportional to the square of the distance from the core.

Distance

Velocity

r

v

Vortex Wake Turbulence


Core size depends on vortex intensity. The coresfrom transport aircraft have been estimated to beanywhere from two to five feet in diameter. Coresize is believed to be of minor importance in avortex encounter, as long as the ratio of thewingspan of the follower aircraft to corediameter is large. The radius of influence of thevortex flow field surrounding the core istypically twenty-five to fifty feet, according tothe FAA.

The vortex pair descends behind the generatingaircraft because of the mutual induction betweenthe two fields of circulation—each vortex pushesthe other down. The rate of descent dependsdirectly on vortex strength, and on wingspan: fora given vortex strength, the greater the wingspanthe slower the descent. It also depends ontemperature stratification in the atmosphere (adescending vortex pair heats up due to adiabaticcompression and becomes buoyant). Crosswindscan reduce sink rates, sometimes more on onevortex than the other, causing the pair to tilt.Vortices formed close to the runway have beenobserved to “bounce” back to higher altitude,indicating that the recommendation given in theAeronautical Information Manual that pilots flyabove the glide path of the preceding aircraftmay not always ensure protection.

Circulation is a measure of the angularmomentum of the air in the surrounding flowfield, and defines the strength of a vortex. Thatstrength is directly proportional to the weight ofthe generating aircraft and inversely proportional

to its velocity and wingspan (speed and spanreduce the vortex).

Size and strength of the flow field determine therisk to the follower. A hazardous situation canoccur when the leading aircraft is landing at itsmaximum landing weight, and the followeraircraft is operating at minimum weight—andtherefore with minimum roll inertia.

When the follower aircraft has a large span, theencounter forces are distributed over a greaterlateral distance. The induced rolling momentsbuild up more gradually and are less intenserelative to the aircraft’s aileron control power.

Studies have shown that a follower aircraft withthe same span as the generating aircraft willtypically have enough maximum aileron controlpower to handle wake-induced rolling moments.Pilots, however, consider the need for maximumcontrol inputs as unacceptably hazardous.



Simulations, wind tunnel studies, and in-flightresearch demonstrate that penetrating a vortexcore is unlikely. Depending on the followeraircraft’s intercept angle, speed, and inertia, theflow field tends to roll the aircraft away from thevortex. In a more serious encounter, the aircraftcan be carried over the core and through thedownwash between the generator’s wingtips(Figure 3, right).

Because penetrating, let alone staying within, thevortex core is unlikely, pilots shouldn’t concludefrom an initial, rapid roll acceleration (or fromupset training) that continuing to roll the aircraftthrough 360 degrees in the vortex directionconstitutes an automatic recovery procedure.Although that type of recovery could becomenecessary when a small aircraft follows a heavyone, the probability is low that a roll excursionwill go that far.

Pilots often inadvertently reinforce the rollingmoments generated by a vortex encounter. Forexample, an aircraft entering the right-handvortex from the outside will experience an abrupt

rolling moment to the right, as in Figure 3.Responding with left aileron will reinforce thevortex-induced rolling moment once the leftwing passes the core and enters the downwasharea.

The interaction between the vortex flow field andthe aircraft’s vertical tail produces yawingmoments that often result in Dutch rolloscillation, especially with swept-wing aircraft.Pilots trying to settle the aircraft down tend toget their control inputs out of phase and insteadamplify the oscillation.

According to the Flight Safety Foundation, theespecially bad news is that more than two-thirdsof all wake vortex accidents and reportedincidents happen over the runway threshold.

Upwash rolls aircraft right; pilot applies left aileron, reinforcing encounter effect.

Lateral penetration angle too shallow. Upwash rolls and carries aircraft away from vortex.

Downwash area

Vortex cores

Aircraft passes through vortex flow field.

Perpendicular vortex penetration can produce dangerous structural loads.

Figure 3 Follower Aircraft/Flow Field Interaction


Flightlab Ground School13. A Selective Summary of Certification Requirements

FAR Parts 23 & 25


The Federal Aviation Regulation Part 23Airworthiness Standards covers normal, utility,aerobatic, and computer category airplanes.According to section 23.3:

“(a) The normal category is limited to airplanesthat have a seating configuration, excluding pilotseats, of nine or less, a maximum certificatedtakeoff weight of 12,500 pounds or less, andintended for nonacrobatic operation.Nonacrobatic operation includes:

(1) Any maneuver incident to normal flying;

(2) Stalls (except whip stalls); and

(3) Lazy eights, chandelles, and steep turns, inwhich the angle of bank is not more than 60degrees.

(b) The utility category is limited to airplanesthat have a seating configuration, excluding pilotseats, of nine or less, a maximum certificatedtakeoff weight of 12,500 pounds or less, andintended for limited acrobatic operation.Airplanes certificated in the utility category maybe used in any of the operations covered underparagraph (a) of this section and in limitedacrobatic operations. Limited acrobatic operationincludes:

(1) Spins (if approved for the particular type ofairplane); and

(2) Lazy eights, chandelles, and steep turns, orsimilar maneuvers, in which the angle of bank ismore than 60 degrees but not more than 90degrees.

(c) The acrobatic category is limited to airplanesthat have a seating configuration, excluding pilotseats, of nine or less, a maximum certificatedtakeoff weight of 12,500 pounds or less, andintended for use without restrictions, other thanthose shown to be necessary as a result ofrequired flight tests.

(d) The commuter category is limited topropeller-driven, multiengine airplanes that havea seating configuration, excluding pilot seats, of19 or less, and a maximum certificated takeoffweight of 19,000 pounds or less. The commutercategory operation is limited to any maneuverincident to normal flying, stalls (except whipstalls), and steep turns, in which the angle ofbank is not more than 60 degrees.

(e) Except for commuter category, airplanes maybe type certificated in more than one category ifthe requirements of each requested category aremet.”

FAR Part 25 contains the airworthiness standardsfor transport category airplanes.

We’ve reproduced some of the regulations thatpertain to maneuvers we fly in the course, andthat set the baseline for aircraft behavior. You’llsee that the standards are not always the same inboth parts. If you really want to enter the belly ofthe beast, Parts 23 and 25 are available online.

Certification Requirements


Far 23

Controllability and Maneuverability

§23.147 Directional and lateral control.

(a) For each multiengine airplane, it must be possible,while holding the wings level within five degrees, tomake sudden changes in heading safely in bothdirections. This ability must be shown at 1.4 VS1 withheading changes up to 15 degrees, except that theheading change at which the rudder force corresponds tothe limits specified in §23.143 need not be exceeded,with the --

(1) Critical engine inoperative and its propeller in theminimum drag position;

(2) Remaining engines at maximum continuous power;

(3) Landing gear --

(i) Retracted; and

(ii) Extended; and

(4) Flaps retracted.

(b) For each multiengine airplane, it must be possible toregain full control of the airplane without exceeding abank angle of 45 degrees, reaching a dangerous attitudeor encountering dangerous characteristics, in the eventof a sudden and complete failure of the critical engine,making allowance for a delay of two seconds in theinitiation of recovery action appropriate to the situation,with the airplane initially in trim, in the followingcondition:

(1) Maximum continuous power on each engine;

(2) The wing flaps retracted;

(3) The landing gear retracted;

(4) A speed equal to that at which compliance with§23.69(a) has been shown; and

(5) All propeller controls in the position at whichcompliance with §23.69(a) has been shown.

(c) For all airplanes, it must be shown that the airplaneis safely controllable without the use of the primarylateral control system in any all-engine configuration(s)and at any speed or altitude within the approvedoperating envelope. It must also be shown that theairplane's flight characteristics are not impaired below alevel needed to permit continued safe flight and theability to maintain attitudes suitable for a controlledlanding without exceeding the operational and structural

FAR 25

Controllability and Maneuverability

§25.147 Directional and lateral control.

(a) Directional control; general. It must be possible, with thewings level, to yaw into the operative engine and to safelymake a reasonably sudden change in heading of up to 15degrees in the direction of the critical inoperative engine. Thismust be shown at 1.4Vs1 for heading changes up to 15degrees (except that the heading change at which the rudderpedal force is 150 pounds need not be exceeded), and with --

(1) The critical engine inoperative and its propeller in theminimum drag position;

(2) The power required for level flight at 1.4 VS1, but notmore than maximum continuous power;

(3) The most unfavorable center of gravity;

(4) Landing gear retracted;

(5) Flaps in the approach position; and

(6) Maximum landing weight.

(b) Directional control; airplanes with four or more engines.Airplanes with four or more engines must meet therequirements of paragraph (a) of this section except that --

(1) The two critical engines must be inoperative with theirpropellers (if applicable) in the minimum drag position;

(2) [Reserved]

(3) The flaps must be in the most favorable climb position.

(c) Lateral control; general. It must be possible to make 20°banked turns, with and against the inoperative engine, fromsteady flight at a speed equal to 1.4 VS1, with --

(1) The critical engine inoperative and its propeller (ifapplicable) in the minimum drag position;

(2) The remaining engines at maximum continuous power;

(3) The most unfavorable center of gravity;



is safely controllable without the use of the primarylateral control system in any all-engine configuration(s)and at any speed or altitude within the approvedoperating envelope. It must also be shown that theairplane's flight characteristics are not impaired below alevel needed to permit continued safe flight and theability to maintain attitudes suitable for a controlledlanding without exceeding the operational and structurallimitations of the airplane. If a single failure of any oneconnecting or transmitting link in the lateral controlsystem would also cause the loss of additional controlsystem(s), compliance with the above requirement mustbe shown with those additional systems also assumed tobe inoperative.

[Doc. No. 27807, 61 FR 5188, Feb. 9, 1996]

§23.155 Elevator control force in maneuvers.

(a) The elevator control force needed to achieve thepositive limit maneuvering load factor may not be lessthan:

(1) For wheel controls, W/100 (where W is themaximum weight) or 20 pounds, whichever is greater,except that it need not be greater than 50 pounds; or

(2) For stick controls, W/140 (where W is the maximumweight) or 15 pounds, whichever is greater, except thatit need not be greater than 35 pounds.

(b) The requirement of paragraph (a) of this sectionmust be met at 75 percent of maximum continuouspower for reciprocating engines, or the maximumcontinuous power for turbine engines, and with the wingflaps and landing gear retracted --

(1) In a turn, with the trim setting used for wings levelflight at VO; and

(4) Landing gear (i) retracted and (ii) extended;

(5) Flaps in the most favorable climb position; and

(6) Maximum takeoff weight.

(d) Lateral control; airplanes with four or more engines.Airplanes with four or more engines must be able to make 20°banked turns, with and against the inoperative engines, fromsteady flight at a speed equal to 1.4 VS1, with maximumcontinuous power, and with the airplane in the configurationprescribed by paragraph (b) of this section.

(e) Lateral control; all engines operating. With the enginesoperating, roll response must allow normal maneuvers (suchas recovery from upsets produced by gusts and the initiationof evasive maneuvers). There must be enough excess lateralcontrol in sideslips (up to sideslip angles that might berequired in normal operation), to allow a limited amount ofmaneuvering and to correct for gusts. Lateral control must beenough at any speed up to VFC/MFC to provide a peak rollrate necessary for safety, without excessive control forces ortravel.

[Doc. No. 5066, 29 FR 18291, Dec. 24, 1964, as amended byAmdt. 25-42, 43 FR 2321, Jan. 16, 1978; Amdt. 25-72, 55 FR29774, July 20, 1990]



flight at VO; and

(2) In a turn with the trim setting used for the maximumwings level flight speed, except that the speed may notexceed VNE or VMO/MMO, whichever is appropriate.

(c) There must be no excessive decrease in the gradientof the curve of stick force versus maneuvering loadfactor with increasing load factor.

[Amdt. 23-14, 38 FR 31819, Nov. 19, 1973; 38 FR32784, Nov. 28, 1973, as amended by Amdt. 23-45, 58FR 42158, Aug. 6, 1993; Amdt. 23-50, 61 FR 5189 Feb.9, 1996]

[TOP]§23.157 Rate of roll.

(a) Takeoff. It must be possible, using a favorablecombination of controls, to roll the airplane from asteady 30-degree banked turn through an angle of 60degrees, so as to reverse the direction of the turn within:

(1) For an airplane of 6,000 pounds or less maximumweight, 5 seconds from initiation of roll; and

(2) For an airplane of over 6,000 pounds maximumweight,

(W+500)/1,300

seconds, but not more than 10 seconds, where W is theweight in pounds.

(b) The requirement of paragraph (a) of this sectionmust be met when rolling the airplane in each directionwith --

(1) Flaps in the takeoff position;

(2) Landing gear retracted;

(3) For a single-engine airplane, at maximum takeoffpower; and for a multiengine airplane with the criticalengine inoperative and the propeller in the minimumdrag position, and the other engines at maximum takeoffpower; and

(4) The airplane trimmed at a speed equal to the greaterof 1.2 VS1 or 1.1 VMC, or as nearly as possible in trim forstraight flight.



straight flight.

(c) Approach. It must be possible, using a favorablecombination of controls, to roll the airplane from asteady 30-degree banked turn through an angle of 60degrees, so as to reverse the direction of the turn within:

(1) For an airplane of 6,000 pounds or less maximumweight, 4 seconds from initiation of roll; and

(2) For an airplane of over 6,000 pounds maximumweight,

(W+2,800)/2,200

seconds, but not more than 7 seconds, where W is theweight in pounds.

(d) The requirement of paragraph (c) of this sectionmust be met when rolling the airplane in each directionin the following conditions --

(1) Flaps in the landing position(s);

(2) Landing gear extended;

(3) All engines operating at the power for a 3 degreeapproach; and

(4) The airplane trimmed at VREF.

[Amdt. 23-14, 38 FR 31819, Nov. 19, 1973, as amendedby Amdt. 23-45, 58 FR 42158, Aug. 6, 1993; Amdt. 23-50, 61 FR 5189, Feb. 9, 1996]

Stability

§23.171 General.

The airplane must be longitudinally, directionally, andlaterally stable under §§23.173 through 23.181. Inaddition, the airplane must show suitable stability andcontrol "feel" (static stability) in any condition normallyencountered in service, if flight tests show it isnecessary for safe operation.

§23.173 Static longitudinal stability.

Stability

§25.171 General.

The airplane must be longitudinally, directionally, andlaterally stable in accordance with the provisions of §§25.173through 25.177. In addition, suitable stability and control feel(static stability) is required in any condition normallyencountered in service, if flight tests show it is necessary forsafe operation.

[Doc. No. 5066, 29 FR 18291, Dec. 24, 1964, as amended byAmdt. 25-7, 30 FR 13117, Oct. 15, 1965]§25.173 Static longitudinal stability.




Under the conditions specified in §23.175 and with theairplane trimmed as indicated, the characteristics of theelevator control forces and the friction within thecontrol system must be as follows:

(a) A pull must be required to obtain and maintainspeeds below the specified trim speed and a pushrequired to obtain and maintain speeds above thespecified trim speed. This must be shown at any speedthat can be obtained, except that speeds requiring acontrol force in excess of 40 pounds or speeds above themaximum allowable speed or below the minimum speedfor steady unstalled flight, need not be considered.

(b) The airspeed must return to within the tolerancesspecified for applicable categories of airplanes when thecontrol force is slowly released at any speed within thespeed range specified in paragraph (a) of this section.The applicable tolerances are --

(1) The airspeed must return to within plus or minus 10percent of the original trim airspeed; and

(2) For commuter category airplanes, the airspeed mustreturn to within plus or minus 7.5 percent of the originaltrim airspeed for the cruising condition specified in§23.175(b).

(c) The stick force must vary with speed so that anysubstantial speed change results in a stick force clearlyperceptible to the pilot.

[Doc. No. 4080, 29 FR 17955, Dec. 18, 1964, asamended by Amdt. 23-14, 38 FR 31820 Nov. 19, 1973;Amdt. 23-34, 52 FR 1828, Jan. 15, 1987]

§23.177 Static directional and lateral stability.

(a) The static directional stability, as shown by thetendency to recover from a wings level sideslip with therudder free, must be positive for any landing gear andflap position appropriate to the takeoff, climb, cruise,approach, and landing configurations. This must beshown with symmetrical power up to maximumcontinuous power, and at speeds from 1.2 VS1 up to themaximum allowable speed for the condition beinginvestigated. The angel of sideslip for these tests mustbe appropriate to the type of airplane. At larger anglesof sideslip, up to that at which full rudder is used or acontrol force limit in §23.143 is reached, whicheveroccurs first, and at speeds from 1.2 VS1 to VO, the rudderpedal force must not reverse.


Under the conditions specified in §25.175, the characteristicsof the elevator control forces (including friction) must be asfollows:

(a) A pull must be required to obtain and maintain speedsbelow the specified trim speed, and a push must be required toobtain and maintain speeds above the specified trim speed.This must be shown at any speed that can be obtained exceptspeeds higher than the landing gear or wing flap operatinglimit speeds or VFC/MFC, whichever is appropriate, or lowerthan the minimum speed for steady unstalled flight.

(b) The airspeed must return to within 10 percent of theoriginal trim speed for the climb, approach, and landingconditions specified in §25.175 (a), (c), and (d), and mustreturn to within 7.5 percent of the original trim speed for thecruising condition specified in §25.175(b), when the controlforce is slowly released from any speed within the rangespecified in paragraph (a) of this section.

(c) The average gradient of the stable slope of the stick forceversus speed curve may not be less than 1 pound for each 6knots.

(d) Within the free return speed range specified in paragraph(b) of this section, it is permissible for the airplane, withoutcontrol forces, to stabilize on speeds above or below thedesired trim speeds if exceptional attention on the part of thepilot is not required to return to and maintain the desired trimspeed and altitude.

[Amdt. 25-7, 30 FR 13117, Oct. 15, 1965]

§25.177 Static lateral-directional stability.

(a)-(b) [Reserved]

(c) In straight, steady sideslips, the aileron and rudder controlmovements and forces must be substantially proportional tothe angle of sideslip in a stable sense; and the factor ofproportionality must lie between limits found necessary forsafe operation throughout the range of sideslip anglesappropriate to the operation of the airplane. At greater angles,up to the angle at which full rudder force of 180 pounds isobtained, the rudder pedal forces may not reverse; andincreased rudder deflection must be needed for increasedangles of sideslip. Compliance with this paragraph must bedemonstrated for all landing gear and flap positions andsymmetrical power conditions at speeds from 1.2 VS1 toVFE, VLE, or VFC/MFC, as appropriate.



pedal force must not reverse.

(b) The static lateral stability, as shown by the tendencyto raise the low wing in a sideslip, must be positive forall landing gear and flap positions. This must be shownwith symmetrical power up to 75 percent of maximumcontinuous power at speeds above 1.2 VS1 in the take offconfiguration(s) and at speeds above 1.3 VS1 in otherconfigurations, up to the maximum allowable speed forthe configuration being investigated, in the takeoff,climb, cruise, and approach configurations. For thelanding configuration, the power must be that necessaryto maintain a 3 degree angle of descent in coordinatedflight. The static lateral stability must not be negative at1.2 VS1 in the takeoff configuration, or at 1.3 VS1 inother configurations. The angle of sideslip for these testsmust be appropriate to the type of airplane, but in nocase may the constant heading sideslip angle be lessthan that obtainable with a 10 degree bank, or if less, themaximum bank angle obtainable with full rudderdeflection or 150 pound rudder force.

(c) Paragraph (b) of this section does not apply toacrobatic category airplanes certificated for invertedflight.

(d) In straight, steady slips at 1.2 VS1 for any landinggear and flap positions, and for any symmetrical powerconditions up to 50 percent of maximum continuouspower, the aileron and rudder control movements andforces must increase steadily, but not necessarily inconstant proportion, as the angle of sideslip is increasedup to the maximum appropriate to the type of airplane.At larger slip angles, up to the angle at which full rudderor aileron control is used or a control force limitcontained in §23.143 is reached, the aileron and ruddercontrol movements and forces must not reverse as theangle of sideslip is increased. Rapid entry into, andrecovery from, a maximum sideslip consideredappropriate for the airplane must not result inuncontrollable flight characteristics.

[Doc. No. 27807, 61 FR 5190, Feb. 9, 1996]

§23.181 Dynamic stability.

(a) Any short period oscillation not including combinedlateral-directional oscillations occurring between thestalling speed and the maximum allowable speedappropriate to the configuration of the airplane must beheavily damped with the primary controls --

VFE, VLE, or VFC/MFC, as appropriate.

(d) The rudder gradients must meet the requirements ofparagraph (c) at speeds between VMO/MMO and VFC/MFCexcept that the dihedral effect (aileron deflection opposite thecorresponding rudder input) may be negative provided thedivergence is gradual, easily recognized, and easily controlledby the pilot.

[Amdt. 25-72, 55 FR 29774, July 20, 1990; 55 FR 37607,Sept. 12, 1990]

§25.181 Dynamic stability.

(a) Any short period oscillation, not including combinedlateral-directional oscillations, occurring between 1.2 VS andmaximum allowable speed appropriate to the configuration ofthe airplane must be heavily damped with the primarycontrols --



(1) Free; and

(2) In a fixed position.

(b) Any combined lateral-directional oscillations("Dutch roll") occurring between the stalling speed andthe maximum allowable speed appropriate to theconfiguration of the airplane must be damped to 1/10amplitude in 7 cycles with the primary controls --

(1) Free; and


(c) If it is determined that the function of a stabilityaugmentation system, reference §23.672, is needed tomeet the flight characteristic requirements of this part,the primary control requirements of paragraphs (a)(2)and (b)(2) of this section are not applicable to the testsneeded to verify the acceptability of that system.

(d) During the conditions as specified in §23.175, whenthe longitudinal control force required to maintainspeeds differing from the trim speed by at least plus andminus 15 percent is suddenly released, the response ofthe airplane must not exhibit any dangerouscharacteristics nor be excessive in relation to themagnitude of the control force released. Any long-period oscillation of flight path, phugoid oscillation, thatresults must not be so unstable as to increase the pilot'sworkload or otherwise endanger the airplane.

[Amdt. 23-21, 43 FR 2318, Jan. 16, 1978, asamended by Amdt. 23-45, 58 FR 42158, Aug.6, 1993]

Stalls

§23.201 Wings level stall.

(a) It must be possible to produce and to correct roll byunreversed use of the rolling control and to produce andto correct yaw by unreversed use of the directionalcontrol, up to the time the airplane stalls.

(b) The wings level stall characteristics must bedemonstrated in flight as follows. Starting from a speedat least 10 knots above the stall speed, the elevatorcontrol must be pulled back so that the rate of speedreduction will not exceed one knot per second until astall is produced, as shown by either:

(1) Free; and


(b) Any combined lateral-directional oscillations ("Dutchroll") occurring between 1.2 VS and maximum allowablespeed appropriate to the configuration of the airplane must bepositively damped with controls free, and must becontrollable with normal use of the primary controls withoutrequiring exceptional pilot skill.

[Amdt. 25-42, 43 FR 2322, Jan. 16, 1978, as amended byAmdt. 25-72, 55 FR 29775, July 20, 1990; 55 FR 37607,Sept. 12, 1990]

Stalls

§25.201 Stall demonstration.

(a) Stalls must be shown in straight flight and in 30 degreebanked turns with --

(1) Power off; and

(2) The power necessary to maintain level flight at 1.6 VS1(where VS1 corresponds to the stalling speed with flaps in theapproach position, the landing gear retracted, and maximumlanding weight).



stall is produced, as shown by either:

(1) An uncontrollable downward pitching motion of theairplane;

(2) A downward pitching motion of the airplane thatresults from the activation of a stall avoidance device(for example, stick pusher); or

(3) The control reaching the stop.

(c) Normal use of elevator control for recovery isallowed after the downward pitching motion ofparagraphs (b)(1) or (b)(2) of this section hasunmistakably been produced, or after the control hasbeen held against the stop for not less than the longer oftwo seconds or the time employed in the minimumsteady slight speed determination of §23.49.

(d) During the entry into and the recovery from themaneuver, it must be possible to prevent more than 15degrees of roll or yaw by the normal use of controls.

(e) Compliance with the requirements of this sectionmust be shown under the following conditions:

(1) Wing flaps. Retracted, fully extended, and eachintermediate normal operating position.

(2) Landing gear. Retracted and extended.

(3) Cowl flaps. Appropriate to configuration.

(4) Power:

(i) Power off; and

(ii) 75 percent of maximum continuous power.However, if the power-to-weight ratio at 75 percent ofmaximum continuous power result in extreme nose-upattitudes, the test may be carried out with the powerrequired for level flight in the landing configuration atmaximum landing weight and a speed of 1.4 VSO, exceptthat the power may not be less than 50 percent ofmaximum continuous power.

(5) Trim. The airplane trimmed at a speed as near 1.5VS1 as practicable.

(6) Propeller. Full increase r.p.m. position for the poweroff condition.

[Doc. No. 27807, 61 FR 5191, Feb. 9, 1996]

landing weight).

(b) In each condition required by paragraph (a) of this section,it must be possible to meet the applicable requirements of§25.203 with --

(1) Flaps, landing gear, and deceleration devices in any likelycombination of positions approved for operation;

(2) Representative weights within the range for whichcertification is requested;

(3) The most adverse center of gravity for recovery; and

(4) The airplane trimmed for straight flight at the speedprescribed in §25.103(b)(1).

(c) The following procedures must be used to showcompliance with §25.203;

(1) Starting at a speed sufficiently above the stalling speed toensure that a steady rate of speed reduction can be established,apply the longitudinal control so that the speed reduction doesnot exceed one knot per second until the airplane is stalled.

(2) In addition, for turning flight stalls, apply the longitudinalcontrol to achieve airspeed deceleration rates up to 3 knots persecond.

(3) As soon as the airplane is stalled, recover by normalrecovery techniques.

(d) The airplane is considered stalled when the behavior of theairplane gives the pilot a clear and distinctive indication of anacceptable nature that the airplane is stalled. Acceptableindications of a stall, occurring either individually or incombination, are --

(1) A nose-down pitch that cannot be readily arrested;

(2) Buffeting, of a magnitude and severity that is a strong andeffective deterrent to further speed reduction; or

(3) The pitch control reaches the aft stop and no furtherincrease in pitch attitude occurs when the control is held fullaft for a short time before recovery is initiated. [Doc. No.5066, 29 FR 18291, Dec. 24, 1964, as amended by Amdt. 25-84, 60 FR 30750, June 9, 1995]



§23.203 Turning flight and accelerated turningstalls.

Turning flight and accelerated turning stalls must bedemonstrated in tests as follows:

(a) Establish and maintain a coordinated turn in a 30degree bank. Reduce speed by steadily andprogressively tightening the turn with the elevator untilthe airplane is stalled, as defined in §23.201(b). The rateof speed reduction must be constant, and --

(1) For a turning flight stall, may not exceed one knotper second; and

(2) For an accelerated turning stall, be 3 to 5 knots persecond with steadily increasing normal acceleration.

(b) After the airplane has stalled, as defined in§23.201(b), it must be possible to regain wings levelflight by normal use of the flight controls, but withoutincreasing power and without --

(1) Excessive loss of altitude;

(2) Undue pitchup;

(3) Uncontrollable tendency to spin;

(4) Exceeding a bank angle of 60 degrees in the originaldirection of the turn or 30 degrees in the oppositedirection in the case of turning flight stalls;

(5) Exceeding a bank angle of 90 degrees in the originaldirection of the turn or 60 degrees in the oppositedirection in the case of accelerated turning stalls; and

(6) Exceeding the maximum permissible speed orallowable limit load factor.

(c) Compliance with the requirements of this sectionmust be shown under the following conditions:

(1) Wing flaps: Retracted, fully extended, and eachintermediate normal operating position;

(2) Landing gear: Retracted and extended;

(3) Cowl flaps: Appropriate to configuration;

§25.203 Stall characteristics.

(a) It must be possible to produce and to correct roll and yawby unreversed use of the aileron and rudder controls, up to thetime the airplane is stalled. No abnormal nose-up pitchingmay occur. The longitudinal control force must be positive upto and throughout the stall. In addition, it must be possible topromptly prevent stalling and to recover from a stall bynormal use of the controls.

(b) For level wing stalls, the roll occurring between the stalland the completion of the recovery may not exceedapproximately 20 degrees.

(c) For turning flight stalls, the action of the airplane after thestall may not be so violent or extreme as to make it difficult,with normal piloting skill, to effect a prompt recovery and toregain control of the airplane. The maximum bank angle thatoccurs during the recovery may not exceed --

(1) Approximately 60 degrees in the original direction of theturn, or 30 degrees in the opposite direction, for decelerationrates up to 1 knot per second; and

(2) Approximately 90 degrees in the original direction of theturn, or 60 degrees in the opposite direction, for decelerationrates in excess of 1 knot per second.

[Doc. No. 5066, 29 FR 18291, Dec. 24, 1964, as amended byAmdt. 25-84, 60 FR 30750, June 9, 1995]



(4) Power:

(i) Power off; and

(ii) 75 percent of maximum continuous power.However, if the power-to-weight ratio at 75 percent ofmaximum continuous power results in extreme nose-upattitudes, the test may be carried out with the powerrequired for level flight in the landing configuration atmaximum landing weight and a speed of 1.4 VSO, exceptthat the power may not be less than 50 percent ofmaximum continuous power.

(5) Trim: The airplane trimmed at a speed as near 1.5VS1 as practicable.

(6) Propeller. Full increase rpm position for the poweroff condition.

[Amdt. 23-14, 38 FR 31820, Nov. 19, 1973, as amendedby Amdt. 23-45, 58 FR 42159, Aug. 6, 1993; Amdt. 23-50, 61 FR 5191, Feb. 9, 1996]

§23.207 Stall warning.

(a) There must be a clear and distinctive stall warning,with the flaps and landing gear in any normal position,in straight and turning flight.

(b) The stall warning may be furnished either throughthe inherent aerodynamic qualities of the airplane or bya device that will give clearly distinguishableindications under expected conditions of flight.However, a visual stall warning device that requires theattention of the crew within the cockpit is not acceptableby itself.

(c) During the stall tests required by §23.201(b) and§23.203(a)(1), the stall warning must begin at a speedexceeding the stalling speed by a margin of not less than5 knots and must continue until the stall occurs.

(d) When following procedures furnished in accordancewith §23.1585, the stall warning must not occur during atakeoff with all engines operating, a takeoff continuedwith one engine inoperative, or during an approach tolanding.

(e) During the stall tests required by §23.203(a)(2), thestall warning must begin sufficiently in advance of thestall for the stall to be averted by pilot action taken afterthe stall warning first occurs.

§25.207 Stall warning.

(a) Stall warning with sufficient margin to prevent inadvertentstalling with the flaps and landing gear in any normal positionmust be clear and distinctive to the pilot in straight andturning flight.

(b) The warning may be furnished either through the inherentaerodynamic qualities of the airplane or by a device that willgive clearly distinguishable indications under expectedconditions of flight. However, a visual stall warning devicethat requires the attention of the crew within the cockpit is notacceptable by itself. If a warning device is used, it mustprovide a warning in each of the airplane configurationsprescribed in paragraph (a) of this section at the speedprescribed in paragraph (c) of this section.

(c) The stall warning must begin at a speed exceeding thestalling speed (i.e., the speed at which the airplane stalls or theminimum speed demonstrated, whichever is applicable underthe provisions of §25.201(d)) by seven percent or at any lessermargin if the stall warning has enough clarity, duration,distinctiveness, or similar properties.

[Doc. No. 5066, 29 FR 18291, Dec. 24, 1964, as amended byAmdt. 25-7, 30 FR 13118, Oct. 15, 1965; Amdt. 25-42, 43 FR2322, Jan. 16, 1978]



stall for the stall to be averted by pilot action taken afterthe stall warning first occurs.

(f) For acrobatic category airplanes, an artificial stallwarning may be mutable, provided that it is armedautomatically during takeoff and rearmed automaticallyin the approach configuration.

[Amdt. 23-7, 34 FR 13087, Aug. 13, 1969, asamended by Amdt. 23-45, 58 FR 42159, Aug.6, 1993; Amdt. 23-50, 61 FR 5191, Feb. 9,1996]

Spinning

§23.221 Spinning.

(a) Normal category airplanes. A single-engine, normalcategory airplane must be able to recover from a one-turn spin or a three-second spin, whichever takes longer,in not more than one additional turn after initiation ofthe first control action for recovery, or demonstratecompliance with the optional spin resistant requirementsof this section.

(1) The following apply to one turn or three secondspins:

(i) For both the flaps-retracted and flaps-extendedconditions, the applicable airspeed limit and positivelimit maneuvering load factor must not be exceeded;

(ii) No control forces or characteristic encounteredduring the spin or recovery may adversely affect promptrecovery;

(iii) It must be impossible to obtain unrecoverable spinswith any use of the flight or engine power controlseither at the entry into or during the spin; and

(iv) For the flaps-extended condition, the flaps may beretracted during the recovery but not before rotation hasceased.

(2) At the applicant's option, the airplane may bedemonstrated to be spin resistant by the following:

(i) During the stall maneuver contained in §23.201, thepitch control must be pulled back and held against thestop. Then, using ailerons and rudders in the properdirection, it must be possible to maintain wings-levelflight within 15 degrees of bank and to roll the airplanefrom a 30 degree bank in one direction to a 30 degreebank in the other direction;

§25.351 Yaw maneuver conditions.

The airplane must be designed for loads resulting from theyaw maneuver conditions specified in paragraphs (a) through(d) of this section at speeds from VMC to VD. Unbalancedaerodynamic moments about the center of gravity must bereacted in a rational or conservative manner considering theairplane inertia forces. In computing the tail loads the yawingvelocity may be assumed to be zero.

(a) With the airplane in unaccelerated flight at zero yaw, it isassumed that the cockpit rudder control is suddenly displacedto achieve the resulting rudder deflection, as limited by:

(1) The control system on control surface stops; or

(2) A limit pilot force of 300 pounds from VMC to VA and 200pounds from VC/MC to VD/MD, with a linear variationbetween VA and VC/MC.

(b) With the cockpit rudder control deflected so as always tomaintain the maximum rudder deflection available within thelimitations specified in paragraph (a) of this section, it isassumed that the airplane yaws to the overswing sideslipangle.

(c) With the airplane yawed to the static equilibrium sideslipangle, it is assumed that the cockpit rudder control is held soas to achieve the maximum rudder deflection available withinthe limitations specified in paragraph (a) of this section.

(d) With the airplane yawed to the static equilibrium sideslipangle of paragraph (c) of this section, it is assumed that thecockpit rudder control is suddenly returned to neutral.

[Amdt. 25-91, 62 FR 40704, July 29, 1997]



stop. Then, using ailerons and rudders in the properdirection, it must be possible to maintain wings-levelflight within 15 degrees of bank and to roll the airplanefrom a 30 degree bank in one direction to a 30 degreebank in the other direction;

(ii) Reduce the airplane speed using pitch control at arate of approximately one knot per second until the pitchcontrol reaches the stop; then, with the pitch controlpulled back and held against the stop, apply full ruddercontrol in a manner to promote spin entry for a period ofseven seconds or through a 360 degree heading change,whichever occurs first. If the 360 degree heading changeis reached first, it must have taken no fewer than fourseconds. This maneuver must be performed first withthe ailerons in the neutral position, and then with theailerons deflected opposite the direction of turn in themost adverse manner. Power and airplane configurationmust be set in accordance with §23.201(e) withoutchange during the maneuver. At the end of sevenseconds or a 360 degree heading change, the airplanemust respond immediately and normally to primaryflight controls applied to regain coordinated, unstalledflight without reversal of control effect and withoutexceeding the temporary control forces specified by§23.143(c); and

(iii) Compliance with §§23.201 and 23.203 must bedemonstrated with the airplane in uncoordinated flight,corresponding to one ball width displacement on a slip-skid indicator, unless one ball width displacementcannot be obtained with full rudder, in which case thedemonstration must be with full rudder applied.

(b) Utility category airplanes. A utility categoryairplane must meet the requirements of paragraph (a) ofthis section. In addition, the requirements of paragraph(c) of this section and §23.807(b)(7) must be met ifapproval for spinning is requested.

(c) Acrobatic category airplanes. An acrobatic categoryairplane must meet the spin requirements of paragraph(a) of this section and §23.807(b)(6). In addition, thefollowing requirements must be met in eachconfiguration for which approval for spinning isrequested:

(1) The airplane must recover from any point in a spinup to and including six turns, or any greater number ofturns for which certification is requested, in not morethan one and one-half additional turns after initiation ofthe first control action for recovery. However, beyondthree turns, the spin may be discontinued if spiralcharacteristics appear.



characteristics appear.

(2) The applicable airspeed limits and limitmaneuvering load factors must not be exceeded. Forflaps-extended configurations for which approval isrequested, the flaps must not be retracted during therecovery.

(3) It must be impossible to obtain unrecoverable spinswith any use of the flight or engine power controlseither at the entry into or during the spin.

(4) There must be no characteristics during the spin(such as excessive rates of rotation or extremeoscillatory motion) that might prevent a successfulrecovery due to disorientation or incapacitation of thepilot.

[Doc. No. 27807, 61 FR 5191, Feb. 9, 1996]

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