Flight Mechanics - Preliminaries
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Flight Mechanics - Preliminaries
Center for Aerospace Systems Design & EngineeringDepartment of Aerospace Engineering
IIT Bombay, Mumbai 400076
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04/22/23 Dept of Aerospace Engineering, IIT-B 2
Aircraft Come in All Shapes
What makes them fly?
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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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04/22/23 Dept of Aerospace Engineering, IIT-B 4
Why Airfoil ?
V
Airfoil : Shape that offers very low drag
Drag
DragV
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04/22/23 Dept of Aerospace Engineering, IIT-B 5
Airfoil – Lift, MomentThickness, Camber
L = Lift
M = MomentSign convention
t
c
h
h > 0 M < 0V
V
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04/22/23 Dept of Aerospace Engineering, IIT-B 6
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
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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
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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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04/22/23 Dept of Aerospace Engineering, IIT-B 9
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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04/22/23 Dept of Aerospace Engineering, IIT-B 10
Lift & Moment
Lift = 0.5 V2 C a
Moment = 0.5 V2 C2 d; d > 0
V
Lift
DragMoment(Pitching)
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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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04/22/23 Dept of Aerospace Engineering, IIT-B 12
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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04/22/23 Dept of Aerospace Engineering, IIT-B 13
Airfoil
SymmetricM = 0
Camberedh > 0M < 0
Camberedh < 0M > 0
Moment is about = 0.25C
Moment does not change with Lift increases with
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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
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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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04/22/23 Dept of Aerospace Engineering, IIT-B 16
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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04/22/23 Dept of Aerospace Engineering, IIT-B 17
Lets Fly a Strip of Paper!
Stable
CG without ballast
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04/22/23 Dept of Aerospace Engineering, IIT-B 18
Lets Fly a Strip of Paper!
Stable
CG with ballast
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04/22/23 Dept of Aerospace Engineering, IIT-B 19
Lets Fly a Strip of Paper!
Stable
Hinge line of elevator
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04/22/23 Dept of Aerospace Engineering, IIT-B 20
Wing
Cr
Cr - Root chord
Ct
Ct - Tip chord = Ct / Cr = Taper ratio
2rmac 11C3
2C
macC
Aerodynamic Center
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04/22/23 Dept of Aerospace Engineering, IIT-B 21
Wing
Aerodynamic CenterStable
Unstable
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04/22/23 Dept of Aerospace Engineering, IIT-B 22
Wing
Aerodynamic CenterStable
Unstable
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04/22/23 Dept of Aerospace Engineering, IIT-B 23
Lets Fly a Wing!
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04/22/23 Dept of Aerospace Engineering, IIT-B 24
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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04/22/23 Dept of Aerospace Engineering, IIT-B 25
Vertical Tail?
?
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04/22/23 Dept of Aerospace Engineering, IIT-B 26
Vertical Tail? Dihedral?
?
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04/22/23 Dept of Aerospace Engineering, IIT-B 27
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
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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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04/22/23 Dept of Aerospace Engineering, IIT-B 29
Decoupled Equations
a
r
e
t
rp
q
V
rp
q
V
x
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04/22/23 Dept of Aerospace Engineering, IIT-B 30
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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04/22/23 Dept of Aerospace Engineering, IIT-B 32
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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04/22/23 Dept of Aerospace Engineering, IIT-B 33
Control Surfaces
AileronsElevators
Rudder
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04/22/23 Dept of Aerospace Engineering, IIT-B 34
Elevators - Pitch
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04/22/23 Dept of Aerospace Engineering, IIT-B 35
Ailerons - Roll
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04/22/23 Dept of Aerospace Engineering, IIT-B 36
Rudder - Yaw