Flight Mechanics - Preliminaries

Center for Aerospace Systems Design & EngineeringDepartment of Aerospace Engineering

IIT Bombay, Mumbai 400076

04/22/23 Dept of Aerospace Engineering, IIT-B 2

Aircraft Come in All Shapes

What makes them fly?

04/22/23 Dept of Aerospace Engineering, IIT-B 3

Contents

• Principles of Flight – Airfoil– Wing– Wing + Horizontal tail

• Flight Mechanics?

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Why Airfoil ?

V

Airfoil : Shape that offers very low drag

Drag

DragV

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Airfoil – Lift, MomentThickness, Camber

L = Lift

M = MomentSign convention

t

c

h

h > 0 M < 0V

V

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Lift & Moment

L = Lift

M = Moment

dL/d & dM/dare constantover a range of

Fixed & V

Some MRF

L h h=0

M

h

h=0

04/22/23 Dept of Aerospace Engineering, IIT-B 7

Watch out ! : CP and AC

L = Lift

M = Moment

L1 = Lift

M1 = Momentx1

L1 = L M1 = M - L x1 (dM1/d) = (dM/d) – (dL/d) x1

Center of pressure, M1=0xcp = M/L M & L depend on Xcp shifts with

Aerodynamic Center, dM1/d=0xac = (dM/d)/(dL/d)In linear range of xac does not depend on . Is fixed at 0.25% of C

04/22/23 Dept of Aerospace Engineering, IIT-B 8

Lift & Moment

Lift = 0.5 V2 C a Moment = 0.5 V2 C2 dMoment is about 0.25 C

V

CLift

Moment

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Flat Plate

V

Lift

Drag

Lift = 0.5 V2 C a

Moment = 0.5 V2 C2 d; d = 0

More than that for airfoil

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Lift & Moment

Lift = 0.5 V2 C a

Moment = 0.5 V2 C2 d; d > 0

V

Lift

DragMoment(Pitching)

04/22/23 Dept of Aerospace Engineering, IIT-B 11

Lift & Moment

V

Lift

DragMoment(Pitching)

Lift = 0.5 V2 C a

Moment = 0.5 V2 C2 d; d < 0

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Airfoil / Flat Plate

Moment does not change with Lift increases with

Moment is about = 0.25C

SymmetricM = 0

Camberedh > 0M < 0

Camberedh < 0M > 0

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Airfoil

SymmetricM = 0

Camberedh > 0M < 0

Camberedh < 0M > 0

Moment is about = 0.25C

Moment does not change with Lift increases with

04/22/23 Dept of Aerospace Engineering, IIT-B 14

Equilibrium & Stability

L

MVW

L

MV W

L

Stable

L

MVW

L

V

L

MW

Unstable

04/22/23 Dept of Aerospace Engineering, IIT-B 15

Aerodynamic Center

Point about which Moment does not change with

0.25 C for an Airfoil.CG w.r.t. Aerodynamic Center

Stability

Stable Unstable

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Flat Plate Strip of Paper

How to make a strip of paper fly?

AR is large Like a flat plate airfoil• h = 0 M0 = 0 X = 0• X = 0 Neutral

For stability • h < 0 M0 > 0 X < 0• X < 0 Stable

M0

L

W

L

W

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Lets Fly a Strip of Paper!

Stable

CG without ballast

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Lets Fly a Strip of Paper!

Stable

CG with ballast

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Lets Fly a Strip of Paper!

Stable

Hinge line of elevator

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Wing

Cr

Cr - Root chord

Ct

Ct - Tip chord = Ct / Cr = Taper ratio

2rmac 11C3

2C

macC

Aerodynamic Center

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Wing

Aerodynamic CenterStable

Unstable

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Wing

Aerodynamic CenterStable

Unstable

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Lets Fly a Wing!

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Wing + Horizontal Tail (No Fuselage)

w

w

w

w

w

w

wt

wt

tw

wtw

wt

twwacacNP

ARa2

dd;

AR21

2a;AR

212a

;areressionsexpsimpleSome

)dd1(q

qSSaaa

)dd1(q

qaa

cSlSXXX

acw acT

Sw

lT

ST

Stable Unstable

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Vertical Tail?

?

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Vertical Tail? Dihedral?

?

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Flight Mechanics?

),,X(FX

motionof.Eq

BXAX

:Linearise

LdLdLdLdLd

LoLoLoLoLo

UBXAX

UBXAX

:Decouple

Stability – Eigenvalues of AModes - Eigenvectors of A

Simulation Bifurcation analysis

Thank You

04/22/23 Dept of Aerospace Engineering, IIT-B 28

Equations of Motion

zyx

rqp

V

x;

a

r

e

t

• Rigid body dynamics• Aerodynamic forces & moments modeled

MFcoscosM

T)sinsincoscossincossinCoscossin(gV

),,X(FX),,X(FX

aerox

11

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Decoupled Equations

a

r

e

t

rp

q

V

rp

q

V

x

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Decoupled Equations

a

r

e

t

00000000

00000000

rp

q

V

0000000000000000

0000000000000000

rp

q

V

x

ALo

ALD

BLo

BLD

Lo = Longitudinal, LD = Lateral-Directional

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http://www.casde.iitb.ac.in

sudhakar@aero.iitb.ac.in

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Airfoil, Flat Plate Or Strip of Paper

L = WL * X + Mo = 0 ; X = - Mo/LCamber M0 X for equilibrium Stability because

of X0 0 0 Neutral

> 0 < 0 > 0 Unstable< 0 > 0 < 0 Stable

L

W

xL

W W

L

x

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Control Surfaces

AileronsElevators

Rudder

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Elevators - Pitch

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Ailerons - Roll

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Rudder - Yaw