(Lynn et al)Tail Rotor Design Part I Aerodynamics.pdf

8/10/2019 (Lynn et al)Tail Rotor Design Part I Aerodynamics.pdf

1/14

Tail

Rotor Design

Part

I:

Aerodynamics

R.

R. Lynn

Chief of Research an d D evelopment

F.

D. Robinson

Senior Research and Development Engineer*

N N

Batra

Research and Development Engineer

J.

M.

Duhon

Group Engineer. A erodynamics

Bell Helicopter Company

Fort Worth, Texas

This paper discusses the various aerodynamic conside~.ationr

involved in tail rotor design. Sizing criteria aye given, and the

contribu tion of gyroscopic precession in caw ing b lade st,nll dur-

ing fa d turn s is explained. Th e stall boundariex fo r severnl Bell

helicnpters are shown s a function of yaw rate and acceleration.

These acceleration an d r ate values are suggested ns n minimum

reqniremont

for

fu tur e designs.

T h e

effects

of

fin

inlerferencc for both the Lrectur and p11sI1c1.

configurations are disc~lssed n d t,he app aren t effects of direction

of rotation are noted. Considerat,ions ~ 1 c iscussed which in-

volve selecting a tail rotor's d h c loading, ti p speed, airfoil

s

tion, and design torque. I u e h ~ d e d re noise, efficiency, and str11r:-

tura l loading.

T h e direction al conLrn1 requ irem ents of n helicopter and simpli-

fied equations for yaw an d gust sensitivity, and yam damp ing a1 e

discussed. Some

o

the directional control prohlems encountered

by the indmtry a1.e descrihed along with steps taken

to

c o l ~ e e t

them.

NOTATION

lift curve slope a 5.73/wdian)

B tip loss factor; blade elements outboard of

radius BR are assumed to have profile

drag but no lift,

b

number of blades

C

damping coefficient,( - M / ) ft-lb/rad/scc

c blade chord,

ft

cl section lift coefficient

l rcsenre,l HL tlra 25th

A n n ~ t t l

utiamal lic~r11111f ~ I I B ~ ~ ~ r r i v i k l t

I lc li co p tc r S or ie tv , A l ~ sIRO

N o w Senior Stnif I.:ncito* er, Huaht\i 'l'ool Cnm,ral.s, Aircrtxft

Division, Cu lver City, Caiifornis

l

average lift coefficient of rotor aftefter trip los

correction h fiT/bp~ BR)~n~)

CT/a thrust coefficient/solidit,y C,/v T/bpcR3n

Fti fin force, lb

I

polar moment of inertia per blade for :I. t.a

rotor), slug ft2

I

helicopter yaw moment of inertia, slug ft.2

M moment, Ib-ft

R rotor radius, f t

S A

ratio of bloclced disc area t,o t,otal disc area

T tail rotor thrust, lb

T,

tail rotor thrust requircd t,o compeusate fo

main rotor torque, lb

V velocity, fps

X

distance bet.nreen maiu rotor axis and ta

rotor, ft

first harmonic flappiug augle bet,ween t,h

rotor disc and the control plane), radians

-y

Lock number; ratio of air forccs to mass force

Y

pR4ac/I,)

63

pitch-flap coupling positive a produccs nose

down pitch with up flapping)

0 blade pitch, rad

p air density, slugs/fta3

yaw rate, rad/sec

3; yaw acceleration, rad/sec2

rotor speed, rad/sec

Direction of rotation-Main rotor direction of rota

t.ion is assumed to be counterclockwise when viewe

from above.


2/14

OCTOBER 1970 TAIL ROTOR DESIGN PART I : 9EROOYNhMlCS 3

THE

LOW

DISC loading tail rotor is by far the most,

efficient approach t,o torque compensatio~land direc-

tional control for the single rotor helicopter. Experience

on a wide vaxiety of helicopters has shown that it is

fa r from a simple task t o develop a tail rotor installation

t,liat has completely acceptable co~itrol, tability, and

structural characteristics. In view of the tail rotor's

know11 advautages as a coutml and alltitorque device,

it is considered highly desirable t.o develop

it

thorougll

uuderstanding of its operating e~lviroilmetitand tlie

important co~~sidcratiotisor its design. This kuowledgc

is essential if successful, long life tail rotors are to be

designed wit.h conlideoce for future high performance

helicopters.

A tail rotor is often thought of, incorrectly, as a

propeller or a small main rotor. Unlike a propeller, t,he

tail rotor must produce thrust with t,he free air corniug

from all directions. Unlilce a main rotor, a tail rotor is

not trimmed for wind or flight velocities with cyclic

pitch.

It

operates in an extremely adverse aerodynamic

aud dynamic environme~it and must produce hot11

positive and negative t,l~rust.Despite the difficulty of

tlie design task, tail rotors have operated successfully

for the most part, which at,tests to t he fact that they

are very forgiving. However, as wit11 the design of

all mechanical equipment, concentrated effort and

attention can produce an improved product, aud i t is t,o

t,hat, ud tha t this two-part paper is dedicated.

111

tlie succeeding Part I1 of this paper, the struc-

tural dynamics aspects of stiff-inplane tai l rotor de-

signs are co~widered. this Part

I

the major aero-

dynamic aspect,sof tail rotor design are discussed.

Ef i IGN

CRITERIA

Critical Ambient Co?iditi o?~

A tail rotor should be desigried for one of the follow-

ing ambient conditions: ( a ) the aircraft's critical

hovering altitude and temperature, or

(b )

the engi~lc

critical altitude. Usually the most severe of those

c~ndit~ionshould be used; however, in certai~icases

where the rotorcraft has extreme altitude capability,

such as a crane-type machine at light gross weight, a

less severe hovering altitude-temperahre design condi-

t,ion \r.ould be adequate.

The use of eugine crit,ical altitude as the tail rotor

design condition covers the normal situation for rotor-

craft wit,h supercharged or flat-rated engines. Tlie

use of tlie aircraft's critical liover condition provides

for the spccial cases noted above and for rotorcraft

designed with sea level engines.

Tlie first step in designiiig a tail rotor is to establish

t,he required t,hrust and the conditions under which it

must be generated. In all fliglit regimes, the tail rotor

must produce sufficient net thrust to couuteract residual

main rotor torque and simultaneously maneuver the

aircraft in yaw and/or correct for disturbances. The

term net thrust is used to account for the effect of fin-

tail rot,or and other such interferences which are dis-

cussed in a later section. Residual main rotor torque is

used because of the ~iow ommon practice to unload the

tail rotor io forward flight with a cambered or canted

fin. Also, in sideward flight, static stability of t,he air-

frame affects the tail rotor thrust required.

There are no special high-speed tail rotor thrust

requirements. Experience lias shown that if the lom-

speed trail rotor thrust rcquirements discussed below are

met, the forward flight requiremeuts will be satisfied.

The tail rotor t,lirust capability should be checked,

however, for various forward flight maneuvers. This is

especially so when higli advance ratios or high ivlacl~

numbers are used.

In liover aud low-speed flight there are two condi-

t.ions which need to be evaluated to establish the maxi-

mum required tai l rotor thrust. These are:

1

thc critical

maximum sideward flight velocity, and

2

near zero

velocity yawing maneuvers.

It

is one of these condi-

tions in combination with maximum maiu rotor torque

that results in the maximum required tail rotor thrust.

In all cases investigated, the yawiug maneuver require-

ment lias been found to be critical.

During a low-speed yawing maneuver, tail rotor

thrust capability is required to:

1

compensate for main

rotor torque,

2

accelerate the aircraft in yaw, and

3

accommodate tail rotor precession effects at the yaw-

ing rate of the aircraft. For most tail rotors, these re-

quirements are of comparable magnitude. The first

two are usually well understood; the third require-

ment is not, and its origiu is explained in the following

section.

effe ts o Precession.

A tail rotor is a gyroscope

which must be precessed wlie~lever he helicopter has a

yawing rate. The moment required to precess a gyro-

scope is equal to

I,

and is applied

90

ahead of the

direction of precession. For a fan or propeller this

moment is carried structurally, but for a flapping tail

rotor it must be produced aerodynamically. As the air-

craft yaws, the tail rotor tip path plane axis lags the

tail rotor mast or co~ltrol xis. This produces an equiv-

alerlt cyclic feathering or differential blade angle of

:l,t,taclc from one side of tlie rotor to the other. As

IL

couscquence, olie side of the disc will be loaded more

highly than the other. If stall is encountered, tlie addi-

t,ioual precessional moment must be produced by t,lie

u~wtalled ide of the disc \vIiere it subtracts from the

basic thrust.. This significa~ltly reduces the thrust

capability of the tail rotor.

After subt,racting the tail rotor thrust required for

main rotor torque compensation, tlie stall boundary of

the tail rotor call be plotted as a function of yaw ac-


3/14

4

I,YNN, ROBINSON,

B A T I t l l

A N 0 DUHOS

Y W

RATE

Y W RATE

Tr~oun~. Tail

rotor

stall hountla13 n a ho~cl.ing u~ n

celeration and yaw rate as sliomn in Fig. 1.The limiting

rate and acceleration values indicated on Fig. 1 are de-

rived in tlie appendix.

When stall due to precession is encou~ltered, arge

flapping angles occur as the unstallcd side of tlie disc

attempts t,o create all of the required precessional

moment. This pl~euomenon s the principal reason for

the excessive hover and high speed maneuver flapping

mliich has been encountered during the development of

many helicopters.

Stall due t o precession is most likely to occur when-

ever there is a combinatio~l f high tail rotor thrust and

high yaw rate. This occurs when stopping a uose-

right hovering turn. The trail rotor thrust required for

main rotor torque compensat,ion s cssent,ially the same

in steady turns to the riglit or left as it. is in steady

hover. Therefore, changes in tail rotor thrust are pri-

marily dependent, on wliet,her or not the aircraft is being

accelerated in yaw. A nose-left yaw acceleration in-

creases the tail rotor thrust rcquired and occurs either

at the beginning of a lcf t tu rn or when stopping a rigbt

tunl. Thus, stall is most liicely to occur in stopping

:I

right turn when bot.11 t,he t,lirust,and yaw rate are maxi-

mum.

In forvard flight, thc situation is somewhat altered.

Although yam rates are generally lower than in liover-

ing maneuvers, the effect of precession is to increase thc

angle of attacli of the tail rotor s ret,reating blade when

the aircraft is turning lcft. This is dependent on tlie

JOURNAL 01 THE

A M E R I C A N

HELICOPTER SOCIETY

main rotor s direction of rotation and is independent o

the direction of rotmationf the t,ail rotor. Consequently

in fol ~vard flight, helicopters with main rotors tha

rotat,e counterclocliwise when viewed from above wil

be susceptible to precessional stall of t.he tail rotor when

turning or yawing left.

Precessional stall can be delayed by increasing th

airfoil

el

the blade Lock number, or the tail roto

tip speed. Pitch-flap coupling,

fig

does not affect stal

due to precession. It only increases the amount o

equivalent cyclic feathering produced by the blad

flapping, and thereby changes the magnitude and aei

muth of the resultant blade flapping.

Suggesled

Criteria

Figure 2 shows the tail roto

st,all boundaries for t l~ree ell helicopters calculated a

indicated in the appendix. In each case, the boundarjz

was determined for the critical altitude condition

noted. Two-dimensional NACA airfoil data were used

to determine el . and t.he tip loss factorB mas assume

to be (1-c/2R).

The st.all boundary sllown for the UH-1D is believed

to represent an acceptable minimum for future designs

Based on the UH-1D capability, the follomi~~griteri

are suggested: A rotorcraft should be able to perform

the following maneuvers at its critical ambient desig

condition:

(1)

Start a left hovering turn wit11 a

initial yaw acceleration of 1.0 rad/sec2, (2) Stop a righ

hovering turn ratme f 0.75 md/sec with an initia

deceleration of 0.4 rad/sec2.

The first of the above maneuvers is critical from tb

thrust standpoint. The second is critical due to tb

gyroscopic moment, required for high inertia, low 1,ock

number blades.

In the next seet,ion the major considerations involve

in

designing

a, ail rotor to meet these requirements a.r

discussed.

AT OGE HOVER

C E I L I N G S OR

E N G I N E

C R I T I C A L ALTITUDE

2 0 6 A @

2900 LB

UH-LD @ 8500 LB

47 G 38 @ 10,000 FT

0

5

1.0

YAW RATE, , RAD/SEC

F I O U ~ ~ ETypical caleulat~d

tall

boundaries at

nltitudc


4/14


5/14

5

LYNN, ROBINSONJ, BATRA A N D OUHON

JOURNAL OF THE A A IERICA N HElrlCOPTEH S O C I E T Y

AH 1G

S/A=.264

UH C

15

10

AH 1G

TRACTOR PUSHER

P I G ~ EENerl

of

fin-tail

ro tor

s l~nmtion

a significant increase in comparison to tlic model and

zero wind flight dat.a. Furthermore, the adverse

pressures extended over a la,rgcr portiou of the tai l

boom. Thus, wit,li an aft and left wind, a higher t,ail

rot,or tlirust is required to overcome the larger adverse

fin and boom forces. This increase in tail rotor tlirust

required can become significant under crit~icaloper-

ating condit,ions.

It is believed that tlic wind effect on the pusher fin

intcrference is related to the main rotor malce. Al-

though tlie exact mechanism has not becn dcfined,

model t,ests show that. when a tail rotor is operat,ing,

t,hc main rot,or wvalce is drawn toward the t.ail mtor and

fin. Thus, t,he main rotor walce affects the fin and tail

boom pressures. The changes duc to wind direct,ionseen

in tlic flight dat a suggest tallat he effect,s of main rotor

wake are sensitive to the wind. In addition, the main

rot,or flow field may determine tlie best tail rotor direc-

tion of rot,at.ion as discussed later. The individual

effect,s of fin-tail rotor, and maill rotor male-tail rotor,

are extremely difficult to isolatc.

The UH 1C pusher flight tests, with the longer t,ail

rotor mast mentioncd earlier, shon, that the wind sen-

sitivity effect persists even when the fin-tail rot,or sep-

aration distance is doubled. This gives rise to t,lie possi-

bility that tlie principal wind effect is related to the

main rotor wake and tail rotor's direction of mtat.ion

since thc effccts have not beenseparated. For reference,

t,he rotation of the UH 1C trail rotor is blade forward

nt t.he top of tlie disc. This mill be disc~ascd ater.

Because of this uncert,ainty, t,he puslrer should be ap-

proached ~vit,haut.ion.

The tractor configuration with the hladc moving aft,

has becn sho~vno be free from t,he adverse wind effects,

so it, can be used wwrith confidcncc. Thc inhcrent high fin

sidcload losses associated ~w~it~l~he t.ract,or are severe,

and efforts t o eliminate t,hc pushcr problems could well

be worthwhile.

Engine Ezlraust. It has bccn theorized t8hat n hover

and low-speed flight,, condit.ions might exist where tlie

hot exhaust from the powcr plant can flow through the

tail rotor, reducing the air density and thus the tail

rotor thrust. This possibility

was

invest,igated with a

UH 1 helicopter instrumented wit11 thermocouples ontlie

fin, boom, and tail rotor blade. It was found t,hat hot

gases from the engine are indecd in tlic vicinity of thc

tail rotor and pass through it. under certain conditions

while tlre aircraft is tied down. However, in '11 hover

or lowv-speed flight conditions invehgated, including a

long interval IGE t,ail rotor blade and fin tempera-

t,ures did not rise appreciably above ambient . Thus, for

t,his aircraft t.he exhaust gases do not pass through the

tail rot,or or affect its performance for t.lie crit,ical lev-

speed maneuvers. i\lot.ion pict,ures of a hovering UH 1

\vit,h a tail pipe smol\-egenerator, shown by the photo-

graph in Fig. 6 confirm this. In high-spccd flight, ex-

haust. gas impingement on the tail rotor has been ell-

countcred and is belicved to hnve caused mild yaw

oscillat,ions ~vliichwere corrected by a tail pipe changc.

Whether or not the engine exhaust effects on the

UH 1 t,ail rot,or represent the general case is not lcnown.

It

is believed that tlie abovc theorized low-speed

phenomenon could occur and that it call be investi-

gated qualitatively by smolce flow dies of models.

Sucli t,ests, and tlle provisio~i or exhaust angle change

by t,ail pipe design, are recommended approxches to

avoid possible interference due to enginc exhaust,.


6/14

O C T O B E R 1970

TAIL

ROTOR

DESIGN

Pf

LRT

I: AE R ODYNi IAI IC S

Rotor Pa7.aateters

Diameter and Disc Loading. Principal consider-

ations in establishing the tail rotor diameter, moment

arm, and disc loading are: 1) the overall size of t he air-

craft as limited by such requiremeuts a air trans-

portability or carrier operation; 2) ground clearance,

particularly for rotorcraft with low-mounted tail rotors;

and 3) t.he effect of tail rotor power required and weight

(including balance) on tlie overall performance of th e

helicopter.

To make t,he tradeoffs suggested by item 3, it is

necessary to estimate the weiglit changes in the air-

frame, drive syst.em, and tail rotor, as the tail rotor di-

ameter is varied. Both weight and power required can

be expressed in terms of payload to find the optimum

diameter (or disc loading) for a give11 design. I such a

study the tail rotor power considered should be bascd

on the critical hovering condition for the aircraft.

System weight should be based on tail rotor thrust and

torque resulting from the most critical paw strwt.ura1

requirement.

The t, rade study suggested here has often been

neglected because tlie effects are small. Under certain

critical hover condit,ions,ho~vever, mall changes in t,otal

power required, which might be obt,ained with proper

attention given t,o he tail rot,or, can result in significant

payload increments. For example, th e UH-1H at GOO0

ft, 95'F day, has a payload of 767 lb. If tlie total power

required were reduced by 2 , tlle payload would in-

crease to 887 Ib, or 14.7 . I n many cases a 2 total

power reduct,io~lmay be obt,ained by careful at,tent.ion

to the tail rotor design.

The performance aspects of such an approach are

easily shown by considering disc loading. Typical tail

rotor disc loadings for present-day helicopters are

to 12 psf for main rotor torque compensation. Tliesc

values can easily double momeut,arily during a critical

maneuver. Fig. 7 shows th e effect of disc loading 11 t,he

rot,or power, expressed in terms of percent total power

required.

T i p Speed; N ~ n b e r f Blatles.

Factors which must,

be considered in select,ing t,lie t,ail rotor t,ip speed in-

clude noise, profile power, blade stall a t high advance

ratio, drive system torque, weight, and control forces.

I n comparison to a low-tip-speed design, biglier-tip-

speed tail rotors are relatively light, permit a lomer-

torque drive system, are less suscept,ible to blade stall

at high advance ratio and yawing maneuvers, and are

less sensitive to gusts. However, higher t, ip speeds

result in illcreased profile power, compreesibility

effects, and noise. In the past, noise was [lot considered

of primary importauce. This is no longer true.

For nearly all flight condit,ions, t,he tail rotor is the

predominant noise source for single rotor iielicopters.

Tlle perceived noise occurs at discrete harmonics which

are multiples of the blade passnge frequency. The

T A I L ROTOR D I S C L O A D I N G

(PSP)

FIGURE Effect of tail rotor disc loading an nntitorque powcr

required

sound pressure energy levels of a tail rotor are usually

slightly lower t,hau those of a main rotor; however, due

to their frequencies being more within the audible

range, they sound louder to the observer.

Tail rotor rotational uoise is a funct,ion of t,he total

aerodynamic forces ac ti~ ig n the blades, the number

of blades, and th e tip speed. Of these, t ip speed is t.he

most important. Lower thrust, per blade reduces noise,

and this is frequently the primary aerodynamic con-

sideration in selecting the number of blades. Compressi-

bility increases the noise directly by its effect on the

related forces, and indirectly by increasing the more

easily perceived Irigher frequency components.

A great deal of effort is being made to reduce rotor

noise. Recent i~~vestigationsy Bell and o t l~ e rs ~ , ~ave

shown that significant reductions are possible 4 t.o 8

db) by altering th e blade tip loading and/or by reduc-

iug the compressibility effects. In any eveut, future

rotorcraft designed with noise as a primary consider-

ation will probably feat,ure mult,ibladed designs 1vit11

tip speeds be be en 575 and 650 fps.

Some degradation of performance will have to be

accepted to achieve a significant reduction in noise

level. Since there is a laclc of valid noise criteria, or even

definition, it is hoped that both the customer and the

regulatory agencies mill exercise caution in est,ablishing

rest,rictive noise limitations.

I ,tuist.

Negative values of blade twist have been

used for the tail rotor, as for the main rotor, t o improve

the spanmise load distribution. In hover and low specd

flight, twist is helpful in reducing the tail rot,or torque

required at. lhigh t,hrusts. In high-speed flight, the in-

flow can be from either side of the disc so negative twist

is not advautageous. This is especially true when the

tail rotor is unloaded by a fixed surface. Increases in

oscillatory blade moments have bee11 observed ~vhich

were attributed to increased twist,. However, for low-

speed lielicopt,ers, t~ vi st liould be considered because

of t,he higlrcr hovcring efficiency.


7/14

JOURNAL

O F

THE

A M E R I C A N

HELICOPTER

SOCIETY

T I G I ~ ~ E1Jppel.

sul face

of IJH-l tail ro tor

a1

hi h tl>l.,nstin

flight.

Airfoil

Section

A primary parametcr in tail rotor

design is the blade airfoil section. This is generally

realized, but has often bccn neglected due to conccnt,ra-

tion in other areas. Many t,imes airfoil shape has beell

i~d uc nced sig11ificant.ly by structural, dynamic, or

manufacturing considerat,ions.

A

good airfoil section

has often been degraded acrodynamicallg by a thick

abrasion &rip placed around the leading edge. Such

considerations am important,, but tlic so lutio~~so de-

sign problems should not violate the basic aerodynamic

requirements. Airfoil selection is important because the

blade airfoil section is one of only three means available

to the designer to minimize the adverse characteristics

of a tail rotor that is designed for high thrust (i.e.,

increased gust sensitivity, high design torque, added

weight). The other two means available to the designer

are to make the blade as light as possible (delays pre-

cessional stall) and to increase the t ip speed.

The principal feature desired of

a

tail rotor blade

airfoil section is a high maximum lift coefficient at t11e

operating Mach and Reynolds numbers. Low minimum

drag cocfficients are desircd but. are secondary in im-

portance to t,he stalling characteristics. Zero or Ion.

pitching moment,s in thc past have been tliougl~t csir-

able; ho~vever, t is believed that the design can be

such that section pitching moments are not a problem.

Compressibilit,y effects, of course, me significant for

all of the parameters associated witah the airfoil. For

example, the cl . of a n NACA

15

airfoil at a Mach

number of

0.6

is only about

2 s

of its CI,,,, a t low Mach

nu mb ers .TT s effect, plus th e fact th at inflo , reduces

the angle of attack a t the tip less than it does inboard,

makes the typical untwisted tail rotor quit,e suscept,ible

to tip st,all. The id ight photograph in Fig.

8

sho~vs

11

examplc of this. Radial locations for the calculated

critical, drag divergence, and shock stall R4acb num-

bers are indicated. Compressibility also produces

pitching moments and t,orquc increases due to drag

divergence.

t

is expccted tha t a great dcal more attenti011will be

givcn tail rotor airfoil

selection

in the future and opti-

mum airfoils, including those nrit,h camber, will be

used. The results of recent BHC experiment,alwork~vith

tail rot,or airfoil sect,ions support this. Recent,l.v, a lavge

increase in maximum thrust was achieved by adding

leading edge camber to a symmetric~l ect.ion and

eliminatting t,he abrasion strip discontinuit,y. For this

case, the helicopter flight envelope and t,ai1 rotor t,ip

speed allowed the use of a large amount of fo~~var

camber. Figure

9

illustrates the combined effect. of

droop and elimination

of

the abrasion strip.

Ch o ~ d

Wit11 the other dcsign parameters defined,

the blade chord required can bc calculated using the

following expressioli which is derived in t.he appendix

To satisfy the maneuver criteria suggest,ed in n pre-

vious section,

= 0.75

and

II

0.4

can be substituted

into the above for the critical ambient condition. For

helicopters with large fins, an additional margin should

be allowed for interfercnce.

In deriving the foregoing expression, and in t, I~eol-

Ionring control section, linear theory has been em-

ployed for clarity and simplicity. In somc cases, more

det,a.iled analyses would be appropriate.

FORWARD

CAMBER

SYMMETRICAL WITH

A B R A S I O N S T R I P

COL L E CT IVE P IT CH DE G)

FIGURE

Effect of

leading

e ge

camber

and

abrasion strip elimi-

nation


8/14

OCTOBER

1970

TAIL

HOTOR

DESIGN PART :

AE R ODYNAMIC S

9

Pitcl~.

ange.

Select,ion of the correct t,a.il otor pitch

range as controlled by the rudder pedals has impo~-tant

effects on directional handling qualities. Maximum

posit,ive tai l rotor collective pitch is required a t the

maximum right sideward flight speed for the critical

combination of power, design altitude, and tempera-

ture. This condition requires the higllest pitch travel

due primarily to the inflow velocity in sideward flight,.

The maximum negat,ive pitch is usually based on the

negative t,hrust required to trim and maneuver the

rotorcraft in autorotation. This requiremeut is strongly

influenced by a canted or cambercd fin uscd to unload

the tail rotor in forwad flight. In certain cascs, side-

ward fliglit to the left may define this value.

Convelitio~lal are applicable in esti-

mat.ing the required tail rotor collective pitch values.

Some of the problems and peculiarities associated with

tail rotor control in sideward flight are discussed in a

later sect,ion.

I'atu

Acceleration Se~rsitiuitu. Reference 7 defines

the acceptable pedal travel for aircraft design as 3 n.

Wit,h the control travel fixed at the cockpit and a t the

tail rotor, the pitch change per inch of pedal travel is

established. With t,he tail rotor sized to prevent blade

stall, t,his determines the minimum y a ~cceleration

per inch of pedal travel. Neglecting the change in ill-

duced velocity, and letting (Acl)/in. = a(AO)/in., the

instanta~ieous a ~cceleration sensitivit,y ( /in.) of t,he

aircraft is:

1

M,,,/in.

=

abcp(BRJ3S12

e)

6

m.

I

Actually, the change in induced velocity is not negli-

gible. For severe maneuvers, it can reduce the yaw ac-

celeration per inch by 50% or more. Therefore, the

preceding expression should be used for comparat,ive

purposes only and not t o correlate with flight test data.

I'azu

Dampiny; Rate Sensitivity.

When a rotorcraft

has a yaw rate, the airflow through the tail rotor changes

the elemental angle of attack on the blades. This alters

the tail rotor thrust so as to oppose the yax7 rate.

Neglecting the change in induced velocity and 1ett.ing:

X a 1

atl

= nd AT = J- ~p(rSl)~(AC~)cZr,

1 n 2

an approximate expression for tail rotor damping, ref-

erenced to the aircraft's yaw inertia, is:

As with the y a ~cceleration sensitivity, meeting the

maneuver criteria tends t o establish the minimum yaw

damping for a given design. For small and medium size

F r o u n ~

10

Typical test

vnlucs of

yaw dnmping acceleration.

and rate

sensitivities.

helicopters, the valuc of the inherent damping will only

be about one-half tha t required by Rcf.

8

By combining the damping expressioll rnit.11 that. for

control se~isitivity rom t,he preceding paragraph, the

steady (final) rate of yaw per inch of pedal call be ex-

pressed as:

It

can be sho~vnhat about

2 3

of this rate is obtained

after a time equal to I,,/C, following an abrupt pedal

displacement. Figure 10 gives typical flight tes t values

of yaw damping, acceleration sensitivity, and rate

sensitivity for several helicopters.

The pitch change per inch of pedal is dictated by the

sideward flight and human factors requirements; the

tail arm, X by geometric considerations; and the tip

speed by the considerations listed earlier. Therefore,

the designer is not left with a great deal of freedom to

alter the yaw rate sensitivity.

Gust

Response.

In th e expression for yaw damping,

S

is the sideward velocity of the tail rotor due to a

given yaw rate. If the velocity of a side gust,

V...

is

substituted into the expression in place of

S ,

the

following expression for gust response is obtained:

This means that there are no basic parameters, other

than tail length, which the designer can usc to change

the ratio of the gust. response to yaw damping. This

ratio, which is important mith respect to the aircraft's


9/14

10 LYNN,

ROBINSON

BA TH A

A N D

DUHON

JOURNAL O F THE A n I E R I C A N HELICOPTER SOCIETY

WITH VORTEX

R I N G E F F E C T S

WINDMILL

BRAKE

STATE

L E F T 0 RIGHT

SIDEWARD FLIGHT VEIDCITY

FIGURE1. Tail rotor pitch in

sideward

flight.

flying qualities, can only be varied for a given machine

by adding artificial damping.

Tho consequences of t,his are that as the inherent

damping

C/I,,)

of the tail rotor is increased, the ma-

chine will become more susceptible to gusts. In-

creasing the inherent damping of tlie tail rotor will im-

prove a helicopter's no mind handling characteristics

in a hovcr, but it will make it more gust sensitive and

less accept,able to the pilot.

Thc consequences of a gust are largely dcpcndent on

tlie reaction timc available to the pilot for corrective

action. This can be altered favorably if the damping,

and

therefore

the gust sensitivit,~,nn be reduced for a

given maximum thrust capability. The lower the gust

sensit,ivit,y, he slower and less severe will be the yaw

resulting from a gust,. The gust response is redefined

below in terms of the maneuver thrust requirement and

related parameters:

t is seen that the gust response can be reduced by in-

creasing the t ip speed or maximum lift coefficient of th e

blade or by lowering the maximum tbrust/inertia ratio.

To explain this physically, increasing the

cl ..

or

lowering the maximum thrust/inertia ratio allows the

required maximum thrust to be produced with less

blade area. Thus, a given gust will produce the same

change in blade anglc of attack but less change in

thrust. Increasing the tip speed also reduces gust re-

sponse, but not by its reduction in blade area required,

since this is accompanied by a corresponding increase in

dynamic pressure. For this case a given gust velocity

combined with the higher t.angentia1velocity produces

a smaller change in thc blade angle of attack and hence,

less change in tlirust.

For a given configuration, with a required maneuver

capability and normal restrictions on tip speed, the

only variable left that will reduce gust response is an

increase in

C

Yaw gust response effccts are also

discussed in Ref. 9

Sideward

Flight

The major aerodynamic tail rotor problems en-

countered have occurred in left, sideward flight. As

noted earlicr, thc problems

generally

relat,e primarily to

the aircraft's yaw control charact,eristics.

In

the

following paragraphs, the principal peculiarities as-

sociated with sideward flight are discussed.

T ortex Rin g Sla te. Tlic Bell i\~Iodel47 and many

ot,her helicopters experieiice a not.iceable difficulty in

establishing pedal trim in left sideward flight from 5

to 15 knots. Trim pedal posit,ion vs sideward flight

speed is extremely difficult to define in flight test. The

pedal-speed gradient appears to be flat or with a slight

reversal. When flight under these conditions must be

maintained, the characteristic is annoying; if possible,

pilots change heading t,o avoid it,. This is caused by

operation in the vortex ring state.

I sideward flight to the left, the vortex ring state is

entered at 5-10 knots and extends up to 15-35 knots

depending on tail rotor disc loading. This flow state

produces strong vortex formations which increase t.he

rotor power and effective induced velocity at. the rotor

plane and produce nonuniform flow through tlie rotor

disc. In the higher speed range of the vortex ring sta te

there is a tendency for the f l o ~o be unstable as tlie

voltices are carried away from the blades.

References 10 and 11, for example, give experimeutal

data ~ h i c han be used in calculating the steady state

power and control angles throughout the sideward

flight speed range, including the vortex ring state. This

has been done for several cases for a free tail rotor and

tlie effects of t,he vortex ring statc are illustrated in

Fig. 11. Test data for the Bell Model 47 and other

helicopters substant,iate these trends.

The vortex ring state causes a reversal tendency in

the steady-statc tail rotor blade pitch vs sideward

flight velocit,y plot. For higher thrust,s and disc load-

ings, the vortex ring state, and consequently the re-

versal, occurs at a higher speed due to the increase in

tail rotor induced velocity.

Main Rotor Torque T ariation. When in ground

effect during steady-st,ate sideward flight, just as the

LEFT

0

RIGHT

SIDEWARD

FLIGHT VELOCITY

FIGURE2.

Effcct

of main ro tor

torque

Q,,,,)variation


10/14

helicopter "loses its ground cusl~ion," llcrc is an in-

crease in main rotor power required.

This requires

addit,ional t,ail rotor thrust,, and hence, more left pedal.

This effect increases t.lie pedal reversal in left sideward

flight as shown by Fig.

12,

which is based on Model 47

flight data.

Other phenomena affect the pedal reversal ttendency,

but are usually of minor impo~l.ance. Under certain

condit,ions, liowevcr, such effects as t,lie aircraft's

weathervaning characteristics a.nd sideload produced by

the main rotor wake act,ing on t,he boom must be con-

sidered in evaluat,ing t,lie pedal reversal.

Stall a71rl Con~bi~iedf e e t s .

Any phenomenon that

causes a dissymmetry of angle of

attack across the tail

rotor disc reduces the maximum thrust capabilit,~ f

the rotor. The vortex ring state a ~ idin and main rotor

\ralce interferences are examples.

If a tail rotor is operated at its maximum thrust

capability a~idhen subjected to one of the above, its

thrust \\rill be reduced due to the stall produced by the

dissymmet,ry. Under such a condition, t,lie applica-

tion of additional pitch will aggravate the situation.

3Ianifestations of this t,ype of plienome~lon re loss of

control, high torque, and reduced thrust. Also, n.lien

operat,io~~s at full engine power available, the incre-

ment in t,ail rotor power can cause loss of Rlt,it,udeor

"settling."

A

similar situat.ion might occur mit,liout t,he stall and

h i ~ l iorque if the phenomenon produci~ig ,he dissym-

met,ry were more effect,ive

ii

reducing t,ail rotor t,hrust

t,han the pitcli is in increasing it,.

hIai11rot,or wake and

vortex effects may be t,11ispowerful.

When problems such as described here occur, usually

they result fromacombinat,ion of effects.

It

is not surpris-

ing to find many explanations as to the cause. In t,he

follo~ving aragraphs, several problems of this t,ypc are

recorded.

Pa vtic t~l av Pvobleins E ncout~tererl.

During informal

discussions with representatives of several helicopter

manufacturcrs from this connt,~ynd abroad, a problem

in left sideward flight was noted. As far as can be de-

tcrmincd, all aircraft, were of the pusher tail rotor con-

figuration with tlie direction of the tail rot,or rotat,ion

such that tlie blades moved forward at the top of tlie

disc.

With each of the aircraft, yaw control cliaracterist,ics

became unsatisfactory to the pilot in low spccd, left,

sideward flight. Some describe tlie phenomenon as a

static instability, where the ship feels to the pilot as

thougli the tail rotor were "falling in a hole to the left

Others emphasize the inability to stabilize or control

t,he heading, more like an accentuat,ion of t,he yaw trim

difficult,^

experienced by the 3Iodcl 47. In one case,

the control difficult,^, mas rcpoitcd as follows: "At a

speed range between 8 and 8 knots when passing

tlirough the vortex ring st,at,eof tlie tail rot,or, t, l~ere as

a dist,inct shudder of the tail, causi~ig iolent reaction of

the pilot's pedal movement^. For one of the aircraft,

it is stated tha t t,he problem occurred only in t,rue left

side~va,rdlight. I t disappeared when a small component

of forward or aft speed was present. Details are missing;

however, it is uilderstood that tlie instability was not

accompa.nied by excessive flapping or tail rot,or ttorqne.

Comments mit,h respect t,o t,he cause indicate that the

Row aroillid the hi1 fin or pylon, t,he t.ail rotor speed,

and the direction of tail rotor rotation were significant.

In most cases, multiple changes to t,he aircraft were

made simultaneously i n an cffol-t to correct t,he problem.

However, in three cases t,he reversal of direction of rot,a-

tion of the tail rotor (from moving formard to aft at

tlie top of the disc) is credited with changing the un-

acceptable characterist.ics to a~cept~able,ven though

ot,her changes were made a t tlie same timc. In tlie fourth

case, the problem is said to have been eliminated by

only the clii~ngen direction of rotation.

A similar problem was e~lcountercdwit.11 t,he AH-1G

Cobra helicopter when configured with a pusher tail

rotor, rotating blade for\va.rd at the top of the disc.

With a118-15 knot,1vi11d coming from the aft left quarter

a left pedal input would have little or no effect,. The

characterist,ics were similar to a static divergence in

yaw to the riglit. The most adverse situatio~iwas when

tlie aircra.ft was heavily loaded, on a hot day or a t

alt.itude. Under such conditions, ~vhen eft pcda.1 was

applied to a.rrest a right turn for instance, the ship

somet,imes would swing around to the right momen-

tarily. As left pedal was applied, a rise in tail rotor

torque occnrrcd, sugge~t~ivef blade stall. 17lapping

cha~iges ere not noted. Tests showed tha t t,he problem

was diminatfed by repositioning the t,ail rotor to the

opposite side of tho fin (from pusher to t,metor) and

simultaneously, cl~anginghe direction of rot,at,ionof t,he

tail rotor t,o blade t.ip moving aft a t the top of the disc.

Diveclio~a f R olatio t~.

The above problems and their

reported solutions have resulted in considerable coli-

jecture as to the combined effects of direction of rota-

t,ion of the tail rotor, main mtor wake, and ~vind. n

an attempt to define these effects, some simple model

and flight tests were conducted at Bell. To this point,

t,he cause-effect relationships have not been est,ablislied;

l~owever, some pertinent informati011 has been ob-

tained and is reported.

The testsinvolved hoverand sideward flightwith a Bell

47-G. The tests were then repeated with the tail rotor

rotating in the opposite direction. Since this liclicoptcr

s

no fin in t,lie tail rotor flow field, the fill-tail rotor

interference discussed earlier is avoided. The tail rot,or

blade surface was instrumented to mcasure local air-

flow velocitjr at 86% radius and 37 chord. Additional

qualitative smolte tests of t he main rotor flow in t,hc

vicinity of a thrust,ing tail rotor were carried out with a


11/14

12

TIYNN,ROBINSOT B A T R A AN11 DUHOK JOUHShIl OF THE AAIE HICAN HElrlCOFTER S O C I E T Y

VELO ITY

90

FIGURE

3. Airflow rrelocity variation

over

tail rotor

blade

model.

Wind-tunnel tests of tlie

main and tail rotor

combination are needed.t

Figure 13 shows typical airflow velocity over the

blade as measured during the flight tests. During these

tests the wind velocity was measured at about 4 knots.

The data indicate that tlie local velocity is a function

of tail rotor azimuth, main rotor height above ground,

and tail rotor direction of rotation. These variations of

air-flow velocity are also present, in varying degrees,

during sideward flight, botli in- and out-of-ground

effect. To date the effect of these local flow variations on

tail rotor thrust lias not been show conclusively.

Figure 14 shows a typical model smoke flow test.

Notc thc position of thc main rotor t ip vol%ices. Thc

observed patterns of these tip vortices are given by

Fig. 15. They are shown with and without tail rotor

t,lirust and for tlie casc with a ground plane. It is seen

that the main rotor walce is drawn toward the t.lirust,ing

t.ail rotor, and as expected, the main rotor ~valce s

marlccdly altered in thc presence of

a

ground plane.

Because of this, ground tests are not considered 60 be

conclusive in est~ablishing he effect of tail rotor direc-

tion of rot,ation.

From tlle work to dat,e, many I~ppot,hescs r specula-

tions can be developed to explain tlie observed effccts.

At, this point, it can only be concluded positively that

there are main rotor walce-tail rotor interactions; and,

that t,hey are a function of rotor height above t,hc

ground, t,ail rot,or position, and relative mind.

Work is bcing conti~~uedo define t,he causal re-

lationships. Until these have been cstablished, it is

See paper by Huston and Morris in

t his

irw

of the Journal

suggested,

based on the experie~lces escribcd in the

prior section, that the direction of t.ail rot,or rot.ation,

blade aft at. the top of t,he disc, be uscd.

A tail rotor drive system is different from most

others becanse there is no rest,riction on the available

po\vcr or torque. It is a demand system in that whatcver

torque it requires mill be supplied by the power plant

or main rotor. As a consequence, either the system

must be designed for the maximum torque that can be

encountered, within reasonable flight restrictions, or

means must be found to limit tlie ability of the pilot or

aircraft, to enter situations wlicre excessive torque can

be obtained.

If tlie approacll is talcen to limit tlie pilot or aircra.ft,

then the design of tlie trailrotor geaxing and antifriction

bearings should be based on fatigue considerations at

the maximum steady state torque. That torque will

usually occur a t the maximum sideward fight speed at

the critical ambient design condit,ion. Use of tlie maxi-

mum torque is justified since structural loading cycles in

the tail rotor drive build up rapidly. With contemporary

gear design and technology, this approach should result

in gear tooth scuffing and st.at,ic orque limit,s of about

2 or

3

times tlie fatigue design value.

If it is elected t,o design tlie system for the maxinrum

torque tha t can be

encountered,

in addition to the above

fat,igue crit,eria, the structural loads must

be established and the system designed statically to

t.hat value. Yor aircraft designs using flat-rated engines,

the static design condition is the application of full

tail rotor pitch

11

the ground or in flight at sea level.

This is justified by the recent experience with botli

the Bell Model 47 and UH-1 helicopters. Flight mall-

euver and ti cd ow ~tatic evaluation of tail rotor pomer,

thrust., and blade pitch show that for all practical pur-

F l o m r ~ 4 Typical n l n i t ~ olol. make

in

the vicinity

of

the tml

mlor

OGE).


12/14

OCTOBER

1970 *TAIL H O TO R DESIGN~PART

I : AERODYNAMICS

13

poses, near zero airspeed, maximum tail rotor torque is

defined by the maximum blade pitch.

The impact of the static requirement can be quite

adverse from the weight and balance standpoint, not

only for the drive system, but also for the tail boom.

If the pitch is available, homever, it probably mill be

used by the pilot a t some point during th e life of the air-

craft. Since the consequence of not providing for this

can be static failure, the system must be designed to

withstand full pedal input, or the pedal must be re-

stricted.

Pedal rate limiting has been used but this approach

is not considered satisfactory because with it, the yam

maneuver capability is reduced. Other approaches

should be developed. Presently, altitude-compensated

pedal stops and rate limiting are being investigated.

Plapping

Magnitude

The tail rotor flapping range and boom

clearance are establislied by the detail design of the

rotor and the configuration of the aircraft. Early in the

design, maximum flapping values should be estimated to

assure tha t tbe flap stops \\,ill not be contacted in flight.

Excessive blade-hub structural loading has occurred due

to bitting the stops in hover and high-speed maneuvers.

If the tail rotor is designed to the maneuver criteria

suggested to prevent stall during hovering turns, then

maximum flapping will most probably occur at high

speed and thrust with a yawing rate to the left. During

structural demonstrations, and also during normal

operation, rapid pedal inputs are occasionally required

at high forward flight speeds. When the helicopter is

turning or yawing in fornrard flight, the precessional

flapping (derived in the appendix) adds to the forward

flight flapping.

Normal flapping does not significantly affect the

pcrfolmance of a tail rotor but t can be an important

parameter in determining structural loads. Fuselage,

fin, engine exhaust, and main rotor effects reduce the

accuracy \\.it11 which flapping can be estimated. Addi-

VORTEX

CORES

W I TH O U T TA I L

/

ROTOR THRUST

WITH

Z ab

ITH TAIL ROTOR

THRUST OGE

TAIL ROTOR

THRUST IGE

~ouno

15

Main rotor

make

distortion due to thrusting tail

rotor and ground plane.

-ROTOR

PLANE

BLADE SPAN

\

A X I S

ONTROL

FIGUR 6 Eff~ct f on tail

mtor

flapping

tional work is needed to develop an understanding and

representation of these effects.

Delta Three Efects Pitch-flap coupling, a 8 , is used

in many tail rotor designs to reduce the first harmonic

flapping. First harmonic flapping is the tilt of the rotor

plaue relative to the control plane.

Various analytical methods have been used in the

literature to account for the effects of

63

on flapping.

These methods seem unnecessarily complex and un-

wieldy when trying to visualize or calculate the result-

ing magnitude and phase lag of forward figh t or pre-

cessional flapping. It is believed tha t an easier and more

direct method is to considcr only the maximum equiva-

lent cyclic feathering required, the resultant flapping

produced, and the phase angle between them.

This can be visualized by considering the blades to be

whirling in the rotor plane ~vllile he ends of their pitch

horns are whirling in the control plane (plane of no

feathering), With first harmonic flapping, the ends of

the pitch horns are moving back and foi-th relative to

the rotor plaue (see Fig. 16) thus producing an equiva-

lent cyclic feathering of the blades. This is true witb or

without

a3

(Equivalent cyclic feathering is uscd here to

denote a cyclic change in the blade angle of attack and

not necessarily a rotation of t he pitch change bearings.)

The equivalent cyclic feathering produced is maximum

when the end of the pitch born is a t that azimuth posi-

tion ~vhere he separation between the rotor plane and

the control planc is greatest. The relative travel of the

pitch horn end is equal to tho flap angle times the

arm (y). The equivalent feathering produced is equal to

this travel divided by the pitch horn arm about the

blade span axis (u cos a 3 . Letting t,he equivalent feath-

ering required equal the flap angle without

83

results in

the following:

Thus, the flap angle with

8a

present cquals the flap angle

reauired without

8 .

multi~liedby cos

S3.


13/14

14 LYNN, OBINSON,ATRA AND DUAON

Since the maximum

feathering

occurs when the pitch

horn end is at the 'zimuth positioii where the separation

between the rotor plane and cont,rol plane is greatest,

it then follows that thc phasc augle between maximum

feathering and maximum flapping is tlie angle between

t,he blade span axis and the pitch horn end, or (90 3)

degrecs.

The aa shown in Fig. 16 is defiued as positive (up

flapping produces anose down change in angle of attack).

If negative a8 (trailing edge pitch liorns) is used, i t can

be seen from the figure tha t the magnitude of the flap-

ping would still be reduced by cos 8%; o~vever,he phase

angle between the maximum flapping and the maximum

feathering rvould be (90

+

J3) degrees.

An interesting difference bet.n.een positive and negac

tive 83 is tha t with positive aa the addit,ion of flap hinge

offset further reduces first harmoilic flapping. Con-

versely, with negative present, the addition of flap-

lringe offset actually increases flapping.

To visualize this, consider a rotor in forward flight

where the higher relat,ive velocity of the advancing

blade produces a moment on the rotor disc, causing it to

tilt aft, thus producing the necessary feathering for

equilibrium. With positive

a3,

this til t of the rotor plane

occurs less than 90 past

the advancing side. With flap

hinge offset, the tilt of the rotor plane produces a cen-

trifugal couple on the rotor hub; t,he rotor hub in turn

prnduces an opposite reaction moment on the rotor disc.

Since the reaction moment on the disc is less than 90'

past the advancing side and is in the opposite direction,

it has a component which subtracts from the aero-

dynamic moment produced by the advancing blade aild

thus, reduces the flapping required. With negative as

the phase lag is greatcr than 90 ; therefore, the offset

hinge reaction moment increases the flapping required.

This is also true for precessional flapping and for hubs

with other types of hinge restraint.

Two-bladed tai l rotors frequent.1~ ave their flap

hinge axes coclced by the same angle as the

as

of their

pitch liorns. Tliis prevent,^ l/rev cycling of the pitch

change bearings as the tail rotor flaps. Cocking tlie flap

hinge does not affect the pitch-flap coupling described

above, and the S3angle is still the angle between the end

of the pitch horn and a line normal to tlie blade span

axis. With this arrangement,, t,he angular travel about

the cocked hinge is increased over the t,rue flapping by

l/(cosine of cocked hinge angle). In flight testing, flap-

ping is usually measured about the coclced hinge; there-

fore, the correction to obtain true flapping should not be

overlooked.

APPENDIX

Deriwation of Tail Rotor Thrust and Precession Capability

The aerodynamic moment required to precess a tail

rotor during a turn can be derived as follo~vs:

JOURNAL OF

THE AMERICAN

HELICOPTER

SOCIETY

For any gyroscope, the precessioiial moment equals:

J I 01,. For a tiail rotor this becomes: OI,b.

As the tail mtor flaps, an equivalent cyclic feathering

is produced. This provides t,he cliange in lift from one

side of tlie disc to the other required to precess the

rotor.

Letting

Acl

ap

thc aerodynamic moment. produced

equals:

The /, in front of thc integral is because a blade is

producing moment only /, of the t,ime as it rotates.

Setting the aerodynamic momeilt equal to tlic preces-

sional moment, required gives:

The flap a.ugle required to precess the rotor is:

For rotors with

by referring to the section on Delta

Three Effects, t,he flap angle required for precessioii is:

To determine the tail rotor's susceptibility to stall

in a hovering tunl , i t is necessary to find the maximum

combined c . The combined cl is the sum of t.he follonr-

ing :

AZ for main rotor torque

compensation

(TQ)

AZI for yaw acceleration (6)

AZI for precession (4)

Letting the combined

CI

= c~ . for determining the

stall boundary and noting that:

G =

GT

b ~ p ( B R ) ~ 0 ~

ndI,,6 = XT,

the follon~ing xpression is obtained:

To determine and plot the stall boundaiy for a given

tail rotor on a graph of vs 6:


14/14

O C T O R E R 1 J T O

T. I I L H O T O R D E S I G N P A R T I : A E R O D Y N h l l l C S 15

-

YAW

RATE

T h c t e r m s c a n b e a r r a n ge d t o s o lv e d i re c tl y f o r t h e

n u n i m u n ~ h o rt l r e q u ir e d a t a g i v en an d :

REFEREN ES

1. McI

(Lynn et al)Tail Rotor Design Part I Aerodynamics.pdf

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Transcript of (Lynn et al)Tail Rotor Design Part I Aerodynamics.pdf