Aircraft Flight Dynamics Robert F Stengel Lecture8 Aircraft Equations of Motion 1
Aircraft Flight Dynamics Robert F. Stengel Lecture8 Aircraft Equations of Motion 1
... Construct aircraft
moments and products of
inertia from components
using parallel-axis
theorem"
• Model in Pro/ENGINEER,
etc."
Aircraft Equations of Motion - 1
Robert Stengel, Aircraft ...
of inertia, I
xz
"
North American XB-70!
Nominal Configuration
Tips folded, 50% fuel, W = 38,524 lb
x
cm
@0. 218 c
I
xx
= 1. 8 10
6
slug-ft
2
I
yy
= 19 .9 10
6...
Aircraft Flight Dynamics Robert F. Stengel Lecture9 Aircraft Equations of Motion 2
... sin
γ
!
"
#
#
#
$
%
&
&
&
Relationship of Inertial Axes
to Velocity Axes"
Aircraft Equations of Motion - 2
Robert Stengel, Aircraft Flight Dynamics, MAE 3 31,
2 012
"
• Rotating frames of reference"
• Combined equations ... )
• Rate of change of Translational Velocity "
• Rate of change of Angular Velocity "
Mirro...
Aircraft Flight Dynamics Robert F. Stengel Lecture10 Linearized Equations and Modes of Motion
... a
23
a
31
( )
a
11
a
33
− a
13
a
31
( )
− a
11
a
23
− a
13
a
21
( )
a
21
a
32
− a
22
a
31
( )
− a
11
a
32
− a
12
a
31
( )
a
11
a
22
− a
12
a
21
( )
!
"
#
#
#
#
$
%
&
&
&
&
a
11
a
22
a
33
+ ... 0,t
f
!
"
$
%
! Analytical evaluation of partial derivatives"
∂
f
1
∂
x
1
= 0;
∂
f
1
∂
x
2
= 1
∂
f
2
∂
x
1
= 10 − 30x...
Aircraft Flight Dynamics Robert F. Stengel Lecture14 RootLocus Analysis of Parameter Variations
... ratio"
Root Locus Analysis of
Parameter Variations
Robert Stengel, Aircraft Flight Dynamics
MAE 3 31, 2 012 "
• Effects of system parameter
variations on modes of motion& quot;
• Root locus ... −
λ
1
( )
s −
λ
1
*
( )
= s −
µ
1
+ j
ν
1
( )
$
%
&
'
s −
µ
1
− j
ν
1
( )
$
%
&
'
= s
2
−
µ
1
− j
ν
1
( )
+
µ
1
+ j
ν
1
( )
$
%
&...
Aircraft Flight Dynamics Robert F. Stengel Lecture16 Aircraft Control Devices and Systems
... Normal load factor"
– Pitch-command/attitude-hold"
– Flight path angle"
USAF F- 15 IFCS!
Princeton Variable-Response Research Aircraft!
USAF AFTI /F- 16 !
United Flight 232, DC -10
Sioux ... selected
angles of attack"
• Effectiveness of low
mounting is unaffected by
wing wake at high angle of
attack"
• Effectiveness of high-mounted
elevator...
Aircraft Flight Dynamics Robert F. Stengel Lecture1 Introduction to Flight Dynamics
... Velocity"
Normal "
Velocity"
Phases of Flight& quot;
Flight of a
Paper Airplane
Flight of a Paper Airplane
Example 1. 3 -1, Flight Dynamics& quot;
• Red: Equilibrium
flight path"
• ... Aerodynamics of Airplane Configurations
! Cruising Flight Performance
! Gliding, Climbing, and Turning Performance
! Nonlinear, 6-DOF Equations of Motion
!...
Aircraft Flight Dynamics Robert F. Stengel Lecture2 PointMass Dynamics and Aerodynamic Thrust Forces
... F
aerodynamics
+ F
thrust
⎡
⎣
⎤
⎦
I
Rate of change
of position!
Rate of change
of velocity!
Vector of
combined forces!
Equations of Motion for a
Point Mass "
˙
x (t) =
dx(t)
dt
= f[ x(t) ,F]
• ... Frame"
C
X
C
Y
C
Z
⎡
⎣
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
B
=
axial force coefficient
side force coefficient
normal force coefficient
⎡
⎣
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
C
D
C
Y
C
L
⎡
⎣
⎢
⎢
⎢
⎤...
Aircraft Flight Dynamics Robert F. Stengel Lecture3 Aviation History Mythology to 1990
... H. Bryan (18 64 -19 28)!
– Longitudinal equations of motion
(with W.E. Williams, 19 03)!
– Full equations of motion and
linearized equations (19 11)
!
Comfort and Elegance by the End of the Decade!
• ... Panther
and F9 F-6 Cougar!
Toward Supersonic
Flight and Stealth
Fighter Jets of the 19 50s!
• Emphasis on supersonic speed!
Republic F- 10 5!
Lockheed F- 1...
Aircraft Flight Dynamics Robert F. Stengel Lecture5 Configuration Aerodynamics 2.
... Dihedral effect"
• Vertical tail effect"
Rolling Moment due to Sideslip Angle!
• Crossflow effects depend on
vertical location of the wing"
Example of Configuration and
Flap Effects!
NACA ... y z
f
x
f
y
f
z
= yf
z
− zf
y
( )
i + zf
x
− xf
z
( )
j + xf
y
− yf
x
( )
k
m =
yf
z
− zf
y
( )
zf
x
− xf
z
( )
xf
y
− yf
x
( )
#
$
%
%
%
%
&
'
(
(
(
(
=
rf =
0 −z y...
Aircraft Flight Dynamics Robert F. Stengel Lecture6 Cruising Flight Performance
... Cruising Flight Performance
Robert Stengel, Aircraft Flight Dynamics,
MAE 3 31, 2 012 !
Copyright 2 012 by Robert Stengel. All rights reserved. For educational use only.!
http://www.princeton.edu/ ~stengel/ MAE3 31. html!
http://www.princeton.edu/ ~stengel/ FlightDynamics.html!
• ... Flight
Reading
Flight Dynamics, 13 0 -14 1, 14 7 -15 5
Virtual Textbook, Parts 6,7...