Principles of flight

Principles of Flight – Modular ATPL(A) Course

1

PRINCIPLES OF FLIGHT

Contents:

• Review of subsonic aerodynamics

• Transonic aerodynamics

• Supersonic aerodynamics

• Airplane performance

• Airplane stability

Literature:

Richard Bowyer: AERODYNAMICS FOR THE PROFESSIONAL PILOT

Charles E. Dole: FLIGHT THEORY FOR PILOTS

A.C. Kermode: MECHANICS OF FLIGHT, revised by R.H. Barnard, D.R. Philpot

R.H. Barnard, D.R. Philpot: AIRPLANE FLIGHT

D. Stinton: THE DESIGN OF THE AEROPLANE

J.D. Anderson: FUNDAMENTALS OF AERODYNAMICS

W.N. Hubin: THE SCIENCE OF FLIGHT

H.C. Smith: THE ILLUSTRATED GUIDE TO AERODYNAMICS

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2

Review of Subsonic Aerodynamics

Properties of fluidState variables:• Temperature T [°C, °F, K]

• Pressure p [N/m2 = Pa, bar, atm]

• Density ρ [kg/m3]

Equation of state for perfect gas:

p = ρRT R = 287 J/kgK

const.=TpV

Properties:• Clasification: fluid – liquid

\ gas

• Continuum

• Speed of sound – alongitudinal wave motion

ρκ=κ= p

RTa vpv

p ccRc

c−===κ 1.4

a0 = 340 m/s = 1225 km/h = 1117 ft/s = 661 kts = 761 mph


3

Properties of fluid:• Viscosity

dynamic viscosity η

dydvη=τ

η = η(T) insensitive to changes in pressure

η0 ≈ 1.8⋅10-5 Pa⋅s air

η0 ≈ 1.1⋅10-3 Pa⋅s water

kinematic viscosity ν

ρη=ν

ν0 ≈ 1.46⋅10-5 m2/s air

ν0 ≈ 1.14⋅10-6 m2/s water

• Compressibility χ

volumespecific 1

1

ρ=υυ

υ−=χ

dpd

dpdρ

ρ=χ 1

dpd ρχ=ρ change in pressure dp results in change of density dρ

p

v + dv v

p + dp


4

Fluid mechanicsBuoyancy:The principle of Archimedes

Continuity equation:Physical principle: Mass can be neither created nor destroyed

streamtube a along const. =ρ= AVm n&

Momentum equation:Physical principle: Force = time rate of change of momentumMomentum equations for a viscous flow: Navier–Stokes equations

Momentum equations for an inviscid flow: Euler equations

After integration of Euler equations along a streamline for the inviscid andincompressible flow Bernoulli equation can be derived

const.21 2 =ρ+ρ+ gzVp

Energy equation:Physical principle:Energy can be neither created nor destroyed; it can only

change in form

Types of flow:• laminar flow

• turbulent flow

Reynolds number ν

= lV Re


5

Basic (two dimensional) airfoil theory• Airfoil terminology

• Lift generation

• Kutta-Joukowski condition

• Pressure distributionResultant aerodynamic forceCenter of pressureAerodynamic center

• Airfoil stallThin airfoil stallLeading edge stallRear stall

• Effect of Re, airfoil thickness, chamber

• High lift devicesTrailing edge flap: flapLeading edge flap: slat


6

Wing• 3-dimensional flow

Induced dragDownwashLift distribution along spanEffect of aspect ratio on lift and drag characteristicEffect of aspect ratio, sweep and twist on lift distribution along spanWinglets

Airplane

• Arrangement of surfacesTailless airplaneConventionalTandemCanard (tail first)

• Lift and drag characteristics

• Propulsion


7

Wake turbulence


8

Transonic Aerodynamics

• Speed of sound – a

ρκ=κ= p

RTa a0 = 340 m/s = 1225 km/h = 661 kts at 15°C

Average molecular velocity = RTπ8 ≈ 460 m/s = 1650 km/h = 890 kts = 1025 mph

Influence of temperature and altitudeH [m] T [K] a [m/s] a/a0 [%]

0 288 340 100

1000 281.5 336 99

2000 275 332 98

3000 268.5 328 97

4000 262 324 95

5000 255.5 320 94

10000 223 299 88

11000 216.5 295 87

20000 216.5 295 87

• Mach numberFlight Mach number

avTAS=Ma a - local speed of sound

Local Mach number

L

LL a

v=Ma aL, vL - speed of sound and speed of flow at point

290

300

310

320

330

340

0 5000 10000

a [m

/s]


9

const. FL and VCAS

varying T } no change in Ma

given Mavarying altitude } VTAS = Ma⋅a

Variation of Ma at varying altitude in the standard atmosphere with constant VCAS and VTAS

VCAS = 100 m/s VTAS = 100 m/sH [m] T [K] a [m/s] p [Pa] ρ [kg/m3] ρ/ρ0 VTAS Ma Ma

0 288 340 101325 1.2259 1 100 0.294 0.2941000 281.5 336 89863 1.1123 0.907 105 0.312 0.2975000 255.5 320 53983 0.7362 0.601 129 0.403 0.312

10000 223 299 26397 0.4124 0.336 172 0.576 0.334

Tro

posp

here

11000 216.5 295 22594 0.3636 0.297 184 0.623 0.33915000 216.5 295 12015 0.1934 0.158 252 0.854 0.33920000 216.5 295 5456 0.0878 0.072 374 1.267 0.339

Stra

tosp

here

0.29

0.30

0.31

0.32

0.33

0.34

0.35

0 5000 10000 15000 20000

H [m]

Ma

(V

= 1

00 m

/S)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 5000 10000 15000 20000

H [m]

Ma

(V

= 1

00 m

/s)

0

70

140

210

280

350

420

490

V (

V =

100

m/s

)Ma

VTAS


10

• Compressibility χ

volumespecific 1

1

ρ=υυ

υ−=χ

dpd ⇒

dpdρ

ρ=χ 1

dpd ρχ=ρ change in pressure dp results in change of density dρ

Isentropic variation of density, pressure and temperature with Mach number

Ma = 1

11

2

0

Ma2

11

−κ−

−κ+=

ρρ 634.0

0

=ρρ∗

12

0

Ma2

11

−κκ−

−κ+=

pp 528.0

0

=∗

pp

12

0

Ma2

11

−

−κ+=

TT 833.0

0

=∗

TT

Isentropic variation of density Mach number

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Ma

ρ/ρ0

5% variation


11

• Subdivision of aerodynamic flow – distinction based on the Mach numberSubsonic (Ma < 0.8) – the airflow around the airplane is completely below the

speed of soundTransonic (0.8 < Ma < 1.2) – the airflow around the airplane is partially subsonic

and partially supersonicSupersonic (Ma > 1.2) – the airflow around the airplane is completely above the

speed of sound but below hypersonic speedHypersonic (Ma > 5) – the airflow around the airplane is at very high supersonic

speeds, leading to stronger shock waves and high temperaturesbehind it – viscous interactions and/or chemically reacting effectsbegin to dominate the flow

0 1 2 3Mach number (Ma)

Den

sity

cha

nges

unim

porta

nt

Den

sity

cha

nges

impo

rtant

Shoc

k w

ave

appe

ar

Shoc

k sy

stem

fully

deve

lope

d

Kin

etic

hea

ting

effe

cts

impo

rtant

SUBSONIC TRANSONIC SUPERSONIC


12

• Propagation of pressure waves

at at

at

Vt

Vt Vt = at

θ

a) b)

c) d)shockwave

shockwave

zone ofsilence

zone ofaction

a) body hardly moving Ma ≈ 0; b) Speed about Ma = 0.5; c) Speed Ma = 1.0

Body has caught up with its pressure waves; d) Body moving about Ma = 1.9

Angle θ related to Ma by θ=θ

= cosecsin

1Ma


13

• Shock wave formation on wingsincreasing flight Ma– transition point– flow breakaway– local Mach number MaL = 1.0– incipient shock wave – usually near the point of maximum chamber (max. speed)

– approximately normal to the surface– pressure and temperature rise, decrease of speed of flow– tendency for a breakaway and turbulent wake

• Observation of shock waves– light travels more slowly through denser air– rays bending towards higher density– „schlieren method“

schlierennem = streaking, striationang� �QDUHGLWL�SURJH��þUWH��(UQVW�0$&+

• Critical Mach number Macr

various definition– flight Mach number at which the local airflow at some point

reaches the speed of sound– flight Mach number at which the first shock wave is formed– flight Mach number at which severe buffeting begins (buffet boundary)– flight Mach number at which the drag coefficient begins to rise– flight Mach number at which the pilot loses the control

Once Macr is exceeded, the airplane is flying in the transonic speed range.


14

Normal shock waves

1 2

Ma1 > 1 Ma2 < 1

p1

ρ1

T1

p2 > p1

ρ2 > ρ1

T2 > T1

V1 V2 < V1

sho

ck w

ave

( )[ ]( ) 2/1Ma

Ma2/11Ma 2

1

212

2 −κ−κ−κ+=

( )1Ma1

21 2

11

2 −+κκ+=

pp

( )( ) 2

1

21

1

2

Ma12Ma1

−κ++κ=

ρρ

( ) ( )( ) 2

1

212

11

2

Ma1Ma12

1Ma1

21

+κ−κ+

−

+κκ+=

TT

Ma1 Ma2 p2/p1 ρ2/ρ1 T2/T1

1 1 1 1 1

2 0.58 4.5 2.67 1.69

3 0.48 10.3 3.86 2.68

4 0.43 18.5 4.57 4.05

5 0.42 29.0 5.00 5.80

6 0.40 41.8 5.27 7.94

7 0.40 57.0 5.44 10.47

8 0.39 74.5 5.57 13.39

9 0.39 94.3 5.65 16.69

10 0.39 116.5 5.71 20.39

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 2 3 4 5 6 7 8 9 10

Ma1

Ma2

0

2

4

6

8

10

12

14

16

18

20

p2/

p1, r

2/r1

, T2/

T1

Ma2

p2/p1

r2/r1

T2/T1


15

Effects of shock wavesShock wave is an extremely thin region (order of 10-4 mm) across whichthe flow properties can change drastically.Shock wave is an almost explosive compression process.At the normal shock wave there is• a great rise in pressure

• a considerable rise in temperature

• a rise in density

• a decrease in speed

• V2 is always subsonic

• breakaway of the flow from the surface

This all adds up to a:

• sudden increase in drag (up to 10×)

• loss of lift of an airfoil

• change in position of center of pressure

• change in pitching moment

• severe buffeting behind the shock wave

Shock drag

• energy dissipated in the shock wave – wave drag• increase in profile drag due to breakaway of the flow – boundary layer drag

} SHOCK STALL


16

Behavior of Airplane at shock stall- high incidence stall- shock stall

• compressibility correction factor 2Ma1

1

−

• considerable changes in longitudinal trim (usually nose heavy – Tuckunder)

• large control forces

• buffeting

• aileron buzz

• loss of control

• stability problems: - snaking (yaw)- porpoising (pitch)- Dutch roll

Measures:• machmeter

• regions of higher temperature

• slow down or accelerate

• power controls

• air brake


17

Height & speed range• speed limitations: - high incidence buffet boundary

- shock stall boundary

• variations of speed limitations with height and weight

High incidence buffet boundarydifference between VEAS and VCAS

• “coffin corner” – coffin ang� �NUVWD��SRORåLWL�Y�NUVWR

Raising the Critical Mach Number

• supercritical wing section (Whitcomb)◊ higher Macr ⇒ higher Madiv (-1965, NACA 64 series)

◊ increment between Macr and Madiv ⇒ supercritical airfoils

+ relatively flat top – lover MaL

+ weaker shock wave

- flat top – forward 60% of airfoil has negative chamber ⇒ lowers lift

extreme positive chamber on the rearward 30%- high Cm a.c.


18

• slimness◊ smaller increase of local airflow velocity

+ formation of shock wave is delayed– increasing Macr

+ reduced intensity of shock wave+ reduced boundary layer separation+ reduced drag+ improved longitudinal handling and stability- reduced total lift- structural problems

• sweepback◊ component of velocity along span has no effect on the flow across the wing

◊ only the component of the velocity across the cord of the wing is responsible

for the pressure distribution and so for causing the shock wave (shock wavelies parallel to the span of the wing)

+ higher Macr

+ lower drag slope and peak drag

- swept wing has lower CL comparing to straight wing of same chord and α- tip stall, pitch-up and high induced drag- high minimum drag speed- additional wing torsion due to lift- aeroelastic effects


19

• area rule (Whitcomb)◊ the area of cross-section should increase gradually to maximum and then

decrease gradually

• vortex generators◊ make the boundary layer turbulent

+ reduced boundary layer drag+ weaken the shock wave and reduce shock drag+ vorticity can prevent buffeting


20

Supersonic Aerodynamics

Mach angle

Ma1

sin ==θVa

• the greater the Mach number, more acute the angle θ• compressible flow through convergent-divergent nozzle (Laval nozzle)

In a Contracting Duct In an Expanding Duct

Subsonic FlowFlow acceleratesAir rarefies slightlyPressure falls

Flow deceleratesAir is compressed slightlyPressure rises

Supersonic FlowFlow deceleratesAir is compressedPressure rises

Flow acceleratesAir is rarefiedPressure falls

at

Vt

θ

shockwave

directionof flight


21

• supersonic flow over wedge – compressive flow- shock wave angle- change of direction and speed of flow- effect of change of Ma- effect of change of wedge angle

• supersonic flow over convex corner – expansive flow

V1 Ma1

V2 Ma2

w2

w1u1

u2

β

θ

V1

V2

w1 = w2

Oblique shock geometry


22

• supersonic flow over airfoil

• boundary layer and supersonic flow- boundary layer is relatively unimportant in supersonic flow- supersonic flow can turn sharp corners

• relation between supersonic flow over wedge and cone

• supersonic wing shapes – plan form- at subsonic speeds the airfoil is more important than the plan form of thewing- but at supersonic speeds the plan form of the wing is more important- sweepback increases Macr

- leading edge of the wing lies inside the Mach cone- structural disadvantages of sweepback- tip stalling- rectangular wing at high Ma

• supersonic airfoil sections

• control surfaces

• supersonic engine inlets

• aerodynamic (kinetic) heating


23

Airplane StabilityDefinitions:EquilibriumA body is in static equilibrium when it is in a state of rest of uniform motion in a straightline and the forces acting on it are balanced out.The definition can be extended to cover those bodies in uniform motion in a curved path.There is, in these cases, a resultant force and an acceleration towards the centre of thecurved path, but they can be considered as cases of dynamic equilibrium.Stability is property of the equilibrium state and there are two types of stability to consider,static stability and dynamic stability.

Static stabilityStatic stability is concerned with the forces and moments produced by a small disturbancefrom the condition of equilibrium. It determines whether or not the body will initially tendto return, of its own accord, towards the equilibrium condition, once the disturbance isremoved.

• a body is statically stable when it tends to return to the equilibrium position

• a body is statically unstable when it tends to diverge further away from the equilibrium position

• a body possesses neutral static stability when it remains in the disturbed position

Degree of static stability possessed by a body:

edisturbanc theof Magnitudeedisturbanc theofresult a as producedeffect Restoring


24

Dynamic stabilityDynamic stability is concerned with the subsequent behaviour of a body which possessesstatic stability. The motion consists of either oscillations about the equilibrium position oraperiodic motion. There are once again three possibilities:

• a body is dynamically stable when the amplitude reduces with time

• a body is statically unstable when the amplitude increases with time

• a body possesses neutral when the amplitude remains constant

Airplane stability• airplane is designed mainly from performance considerations, but it must also posses

acceptable handling characteristics, if necessary achieved by artificial methods

• motion of rigid airplane can be represented as translation along and rotation about threemutually perpendicular axes

• airplane must be controllable

• stability and control are closely related

Assumptions- rigid airplane- conventional arrangement of surfaces


25

System of axes

C.G.

N, R

M, Q

L, P

z, Z, w

y, Y, v

x, X, u

vrtenje okrog:Y]GROåQH�RVL�valjanje (ang. roll; nem. rollen)RNURJ�QDYSLþQH�RVL�sukanje (ang. yaw; nem. gieren)SUHþQH�RVL��"��DQJ��SLWFK��QHP��QLFNHQ�

axis Linearvelocities

Aerodynamicforces

Angularvelocities

Aerodynamicmoments

Moment ofinertia

Angulardisplacement

s

Ox u X p L Ix φ

Oy v Y q M Iy θ

Oz w Z r N Iz ψ


26

Stability and control are analysed in three planes:

MOTION STABILITY

Pitch Longitudinal

Yaw Directional

Roll Lateral

Airplane longitudinal static stability• pitch motion

e

d

Cm0

Cm

α 0

Unbalanced andunstable

Unbalanced andstablea

bCm0

Cm

c0

A B

C

α

Balanced andstable

Balanced butunstable


27

Possible arrangement of wing and tail surfaces

pozitivna ukrivljenost

Cm0 < 0

simetriþQL�SURILOCm0 = 0

negativna ukrivljenost

Cm0 > 0

Krilo s pozitivno ukrivljenostjo pri CZ=0

Krilo s pozitivno ukrivljenostjo pri CZ=0

a)

b)

Višinski rep s CZ>0

Višinski rep s CZ<0

MS

MS

Wing contributionZk

αk

M0k

XklSAT

aerodinami

� � �

center SAT

srednja aerodinami

� ��

tetiva krila – SAT


28

αk

Zk

XkM0kMS

V

Aerodinami

��

center SAT

Srednjaaerodinami

��

tetiva krilahnk lSAT

hlSAT

lSAT

zlSAT

sinαk ≅ αk , cosαk ≅ 1

( )( )....

....

cacammk

caZcammk

hhaCC

hhCCC

−α+=−+=

Fuselage contribution

Vsinα

a)

b)


29

Tail contribution

V

αkt

MS

V

V’ ε

zh

αh

Zh

Xh

Mach

ih

αkt-ε

Srednja aerodinami

� tetiva višinskega repa

Aerodinami

� ��

srednje aerodinami

�

tetive višinskega repa

xh

Srednja aerodinami

�

tetiva krila (SAT)

( )hkhhhhhmh iiaVaVC +ε−−αη−=αη−=

Pitch moment of complete airplane

( ) ( ) DmFmhkhhcaamfusmm CCiiaVhhaCCC ...c. +++ε−−αη−−α++=

Balance or equilibrium: Cm = 0

Static stability: 0<∂∂

z

m

CC

or 0<α∂

∂ mC

Neutral point: N0 = hn

( )nm hha

C −=α∂

∂


30

Cm

α

Cm0

0

masno središþHzadaj

masnosredišþH�VSUHGDM

h = hn

h > hn

h < hn

Cm = Cm0 + a(h-hn)α

9SOLY�OHJH�PDVQHJD�VUHGLãþD�QD�JUDGLHQW�NROLþQLND�PRPHQWDPitch control

Višinskistabilizator

Višinskokrmilo

Šarnirna oskrmila lb

lhk TrimerŠarnirna ostrimerja

yh

A

A

Šarnirna oskrmila

Šarnirna ostrimerja

lb lhk

lh

b)

a)


31

višinski stabilizator

δh

a)

b)

c)

0

Cm

za

��

αuravnote

��

δh = 0

δh > 0kon

� � �

αuravnote

��

α

CZ

δh > 0

δh = 0za

��

to

� ��

kon

� � �

RT∆CZ

0 α

višinsko krmilo

Vpliv odklona višinskega krmila na Cm in CZ: a) pozitiven odklon krmila,b) diagram Cm - α, c) diagram CZ - α


32

višinskistabilizator

višinskokrmilo

šarnirna oskrmila V

V

α

δh

b)

a)

Porazdelitev normalne sile na višinskem repu pri:a) spremembi vpadnega kota α ob δh = 0; b) odklonu krmila δh ob α = 0

αh

δleb

V

Floating elevator


33

Longitudinal manoeuvring stability

Effect of thrust on

Effect of elasticity of structure on longitudinal stability

Lt

∆αh = -kZh

Sprememba vpadnega kota višinskega repa pri deformaciji trupa

The aft C.G. limitThe permissible aft C.G. limit is determined by the stability considerations. It is based onthe location of the stick-free neutral point h’n when manual controls are employed, and onthe stick-fixed neutral point hn if the elevator control is irreversible. Conservative practice isto keep the aft limit a small distance forward of the computed relevant neutral point due tothe effects of wing flaps, the propulsive system, aeroelastic deformation and to provide safehandling characteristic.


34

The forward C.G. limitAs the C.G. moves forward, the stability of the airplane increases and larger control

movements and forces are required to maneuver the airplane. The forward C.G. limit istherefore based on the control considerations and may be determined by one of thefollowing requirements:

1. the stick-force per g should not exceed a specific value,2. the stick-force gradient at trim, dP/dV, shall not exceed a specified value,3. the stick-force required to land, from a trim at the approach speed, shall not exceed a

specified value and4. the elevator angle required to land shall not exceed maximum up elevator.

Airplane directional static stability

Sideslip

0>β∂

∂ nC

V

N

y

x β


35

Airplane lateral static stability

G

Vzgon

φ

L

y

MS

z γ

Sile na letalo v nagibu

Ravnina tetive krilay

Vx

Vy

Vz

Vn

xz

Komponente

hitrosti letala

β γ

Vpliv diedra oz. V-loma krila na vpadni kot krila


36

Vβ

Nizkokrilnik

Visokokrilnik

9SOLY�WUXSD�QD�XþLQHN�GLHGUD��Clβ

V V

Vn Vn

Λ

β

V

9SOLY�SXãþLFH�NULOD�QD�XþLQHN�GLHGUD

V

MS

zv

aerodinami

! "# $ ! % $&

smernega repa

Vpliv smernega repa na Clβ


37

Rigid Airplane Dynamic Stability

Equations of motion for rigid airplane (6 DOF)

• for inertial reference frame

dtvd

mF cv

v

=dthd

Gv

v

=

• for airplane-fixed reference frame

ωx

z

y

iv

kv

jv

P

ivdtid

P

vvv

v

×ω==

ω

cc vmtv

mF vvv

v×ω+

δδ= h

dthd

Gvv

vv

×ω+=

Symmetrical airplane assumption

• longitudinal dynamic stability (pitch)

• lateral-directional dynamic stability (roll-yaw)


38

Small disturbance theory

vv

vv

FFu

uF

uuF

F δ∆

δ∆∂

∂+δ∆

δ∆∂

∂++

∂∂+

∂∂=∆ &&

&&&

&L&

&0000

Stability derivatives

KKK

KKK

1

1

1

1

1

1

000

000

∂∂=

∂∂=

∂∂=

∂∂=

∂∂=

∂∂=

rN

IN

wM

IM

pL

IL

wZ

mZ

vY

mY

uX

mX

zr

yw

xp

wyu

Linearised system of equations:

• eigenvalues, eigenvectors

Aperiodic motion

• first order linear differential equation

Oscillatory motion

• second order linear differentialequation

0=++ xmk

xmd

x &&&

02 200 =ω+δω+ xxx &&&

• PIOTime

Am

plitu

de

Time

Am

plit

ud

e


39

Airplane Longitudinal Dynamic Stability – 2 oscillatory modesPhugoid mode

u1 ≈ 0.85 θ1

α1 ≈ 0.02 θ1

(ni viden)

θ1

Re

Im

ω

Vector diagram of phugoid mode

x’

x

x

x' – u0t

a)

b)

Phugoid motion path in (a) fixed reference frame (b) moving reference frame


40

Phugoid mode• change of angle of attack is negligible (∆α ≈ 0) – velocity of airplane is approximately

tangent to the path

• the motion is approximately one of constant total energy, the raising and fallingcorresponding to an exchange between the kinetic and the potential energy

• long period (T ≈ 2min) and lightly damped mode (Nhalf = 2)

Short-period mode

Reu2

(ni viden)θ2

α2

ω2

Im

Vector diagram of short-period mode

• negligible speed variation (∆u ≈ 0)

• the motion is approximately pure oscillatory pitch motion of the airplane

• short period (T ≈ 3sec) and highly damped mode (Nhalf = 0.2)


41

Short-period motion path

• Root locus plot

Puš

' ()* +, -* ./ 01 * 23 2* 1 ( + , 4* 5*

korenov kratkoperiodi

'6 * / 7 4 ( +* 3 2 (

pomikanju masnega središ

' , 4* 8 , 4 , 6 ,9 , .Root locus plot of short-period motion

Puš

: ;<= >? @= AB

smer pomika legekorenov fugoidneoblike pripomikanju masnegasrediš

: ? C= D ? C ? E?F ? A

Tretja oscilatorna oblika

Root locus plot of phugoid motion


42

Phugoid motion summary:• the motion is approximately one of constant total energy, the raising and falling

corresponding to an exchange between the kinetic and the potential energy

• change of angle of attack is negligible – velocity of airplane is approximately tangent tothe path

• long period and lightly damped mode

• moving CG back lowers static stability and consequently reduces frequency of thephugoid mode

• increase in equivalent airspeed reduces frequency of the phugoid mode

• at higher altitude the damping of the phugoid mode is reduced

Short-period motion summary:• the motion is approximately pure oscillatory pitch motion of the airplane

• negligible speed variation, short period and highly damped motion

• as for the phugoid mode, shifting the CG back lowers static stability (aerodynamicstiffness) and therefore reduces frequency of the short-period motion

• damping and frequency of the short-period mode are proportional to the equivalentairspeed

• with increasing altitude the damping of the short-period mode is reduced

• motion should be considerably damped in order to prevent PIO


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Airplane Lateral–Directional Dynamic Stability

– 2 aperiodic modes and oscillatory mode

Roll mode• very heavily damped, almost pure single DOF rolling motion

• damping is reduced with decrease in airspeed and increase in altitude

• CG position has no effect on roll motion

• it is very important to determine the roll response characteristic of the airplane

Time

p

Variation of roll rate p with time for pure rolling motion

Spiral motion• usually weakly damped motion in bank and yaw, with negligible sideslip

– approximately a correctly banked turn of increasing radius; the airplane flies along aslightly curved path and approaches initial heading

• often this mode is unstable; the path of motion of the airplane is then a tightening spiral– approximately a correctly banked turn of decreasing radius (graveyard spiral)

• due to large time to double/half the amplitude, there is no quantitative standard of spiralstability; however, time to double the amplitude should exceed 20 sec


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• effect of fin and dihedral

• increase in airspeed (decrease of AOA) increases stability of the spiral mode

• CG position does not effects the damping of the mode

• spiral divergence vs. directional divergence

ψ

divergentna

spiralna oblika

asimptota

y’

x’

Dutch Roll oscillation• Dutch Roll motion consists of a relatively short period oscillations, which may be either

damped or divergent, involving rolling yawing and sidesliping motions

• roll/yaw ratio is important characteristic of Dutch Roll because it affects the pilot‘sassessment of the handling qualities

• snaking – the motion consists mainly of yawing


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Re

ψ

φ

β

Im

ω

Vector diagram of Dutch Roll mode

Sketch of Dutch Roll motion

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• Increase in equivalent airspeed increases frequency of Dutch Roll motion

• At higher altitudes damping of the Dutch Roll motion reduces considerably (yaw damper)

Effects on Dutch Roll motion

• Increase in dihedral stability

G

slightly increase frequency

G

decrease damping

G

increase roll/yaw ratio

• Increase in weathercock stability

G

increase frequency

G

increase damping

G

decrease roll/yaw ratio


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Control balance

• aerodynamic balance of controls

• mass balance of controls

Modification of directional stability characteristicsdorsal (zgoraj) fin – increase in fin stall angleventral (spodaj) fin – increase in fin area effects stability in stall characteristics

Inertial coupling

Principles of flight

Engineering

Transcript of Principles of flight