This preview shows pages 1–3. Sign up to view the full content.
Equations of Aircraft Motion
Force Diagram Conventions
Definitions
V
≡
flight speed
≡
θ
angle between horizontal & flight path
≡
α
angle of attack (angle between flight path and chord line)
≡
W
aircraft weight
≡
L
lift, force normal to flight path generated by air acting on aircraft
≡
D
drag, force along flight path generated by air acting on aircraft
≡
M
pitching moment
≡
T
propulsive force supplied by aircraft engine/propeller
T
≡
angle between thrust and flight path
To derive the equations of motion, we apply
∑
=
a
m
F
K
K
(1)
Note:
we will not be including the potential for a yaw force.
Applying (1) in flight path direction:
dV
Fm
am
dt
==
∑
&&
and examining the force diagram
cos
sin
T
FT
DW
=−
−
∑
&
cos
sin
T
dV
TD
W
m
dt
αθ
⇒−
−
=
(2)
Chord line
Flightpath
θ
α
T
α
θ
V
M
W
D
T
Horizontal
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentEquations of Aircraft Motion
16.100
2002
2
Now applying (1) in
−
⊥
direction to flight path
2
c
V
Fm
a
m
r
⊥
⊥
==
∑
where
c
r
≡
radius of curvature of flight path
sin
cos
T
FL
T
W
α
θ
⊥
=+
−
∑
2
sin
cos
T
c
V
LT
W
m
r
αθ
⇒+
−
=
(3)
Equations (2) & (3) give the equations of motion for an aircraft (neglecting yawing
motions) and are quite general.
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '03
 willcox
 Dynamics, Aerodynamics

Click to edit the document details