... or
the FtF discussion was held first. However, more
saggestions were offered on the arctic problem if it
was discussed in CC as ~e first problem, but more
in FTF discussion if the FTF was preceeded ... term for A, B, A x B
S/ABC=error term for C/AB
WG=Pooled error term
Table Value for F
1 and 76 df=3.97
*Significant
The nested design yields a significant difference be-
tween the FTF and ... Conditions. The FTF conditions
show a greater percent of their comments in category 3-
Agrees.
REFERENCES
Bales, Robert
1950 InteractionProcess Analysis; A Method for
the Study of Small Groups....
... you find
this information helpful in understanding how you can make these worksheets work for you.
Form Number Form Type
1.# Top level of Business Reference Model : defines the “frame of reference” ... information.
Form: Business Collaboration
Form ID
[Provide an ID for this form so other forms can reference it (Đ5.1.8)]
Identifier
[This is a unique identifier that follows the Business Process ... sequence of
processes that are combined to form the “value chain” of the given business area.
Form: Describe Process Area
Form ID
[Provide an ID for this form so other forms can reference it...
... amplify overlapping PCR
fragments of rat VRL-1 (yellow to obtain fragment A with 534 bp, green for fragment B with 656 bp, orange for fragment C with 836 b and cyan for
fragment D with 633 bp).
Fig. ... 4. RT-PCR of fragment A. RT-PCR with rat VRL-1 specic
primer for fragment A (34568 bp ẳ 534 bp) yielded not only a
product from RNA of F- 11 (F1 1) and rat brain (rb) but also of the F-
11 parental ... were made with pcDNA3.1/
rVRL-1-CT-GFP transfected F- 11 cells. Anti-GFP
(Fig. 8B) and anti-VRL-1 (Fig. 8C) Western blots of F- 11
cells show an analogous pattern of the rVRL-1 glycopro-
tein, when...
... vehicles.
!
Understanding of aircraft equations of motion,
configuration aerodynamics, and methods for analysis of
linear and nonlinear systems.
!
Appreciation of the historical context within which past
aircraft ... a sound
footing for the development of future aircraft.
More Learning Objectives"
! Detailed evaluation of the linear and nonlinear flight characteristics of a
specific aircraft type."
! ... and references at
http://blackboard.princeton.edu/"
Syllabus, Second Half
! Analysis of Linear Systems
! Time Response
! Root Locus Analysis of Parameter Variations
! Transfer Functions...
... Frame"
C
X
C
Y
C
Z
⎡
⎣
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
B
=
axial force coefficient
side force coefficient
normal force coefficient
C
D
C
Y
C
L
=
drag coefficient
side force coefficient
lift coefficient
ã Functions of ight ... =
v
x
v
y
v
z
⎡
⎣
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
F
I
=
f
x
f
y
f
z
⎡
⎣
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
I
= F
gravity
+ F
aerodynamics
+ F
thrust
⎡
⎣
⎤
⎦
I
Rate of change
of position!
Rate of change
of velocity!
Vector of
combined forces!
Equations ... "
q
Equations of Motion
for a Point Mass
Newtonian Frame of Reference"
ã Newtonian (Inertial) Frame of
Reference"
– Unaccelerated Cartesian frame
whose origin is referenced to an...
... doubled (F4 F
vs. F8 F)!
ã Use of aps means high power at
low speed, increasing relative
signicance of thrust effects"
ã Short-Takeoff-and-Landing (STOL)
aircraft augment takeoff/landing lift ... compressibility effects on drag!
ã Dramatic change in stability, control, and ying qualities!
ã North American FJ-1
and FJ-4 Fury!
ã Republic F- 84B Thunderbird
and F- 8 4F Thunderstreak!
ã Grumman F9 F-2 Panther ... F9 F-6 Cougar!
Toward Supersonic
Flight and Stealth
Fighter Jets of the 1950s!
ã Emphasis on supersonic speed!
Republic F- 105!
Lockheed F- 104!
Convair F- 102!
McDonnell F- 101!North American F- 100!
Fighter...
... page)"
Interference
Effects
Interference
Effects
Wing
Aerodynamics
Fuselage
Aerodynamics
Tail
Aerodynamics
Interference
Effects
ã NASA 30 x 60 Tunnel"
Full-scale aircraft on balance"
– ... Airfoil section may vary from tip-to-tip"
Chord length"
Airfoil thickness"
Airfoil prole"
Airfoil twist"
ã Lift of a 3-D wing is found by integrating 2-D lift
coefficients ... D
y
( )
c y
( )
q dy
−b/2
b / 2
∫
Effect of Aspect Ratio on Wing
Lift Slope Coefcient
(Incompressible Flow)"
ã Airfoil section lift
coefficients and
lift slopes near
wingtips are lower
...
... Axes"
f
B
=
X
B
Y
B
Z
B
!
"
#
#
#
$
%
&
&
&
m
B
=
L
B
M
B
N
B
!
"
#
#
#
$
%
&
&
&
Force Vector"
Moment Vector"
r ì f =
i j k
x 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 ... Dihedral effect"
ã Vertical tail effect"
Rolling Moment due to Sideslip Angle!
ã Crossow effects depend on
vertical location of the wing"
Example of Configuration and
Flap Effects!
NACA ... S
=
C
L
C
D
Lift-Drag Polar for a
Typical Bizjet"
ã Lift-Drag Polar: Cross-plot of C
L
() vs. C
D
()"
Note different scaling
for lift and drag!
ã L/D equals slope of line
drawn from the origin"
– ...
... 0
ã Satisfy necessary condition for a maximum"
ã Lift-to-drag ratio"
ã Lift coefcient for maximum L/D
and minimum thrust are the same"
Airspeed, Drag Coefficient, and
Lift-to-Drag ... V
cruise
C
L
C
D
!
"
#
$
%
&
1
c
T
!
"
#
$
%
&
ln
W
i
W
f
!
"
#
#
$
%
&
&
! V
cruise
as fast as possible"
!
ρ
as small as possible"
! h as high as possible"
C
L
MR
=
C
D
o
3
ε
: Lift Coefficient for Maximum Range
Maximum Range of a Jet Aircraft
Flying at ...
tubes on Fouga
Magister"
Cessna 172 pitot tube"
X-15 Q Ball"
Flight Testing Instrumentation"
ã Air data measurement far from
disturbing effects of the aircraft"
z...
... Glide"
Climbing Flight
Gliding, Climbing, and Turning
Flight Performance
Robert Stengel, Aircraft Flight Dynamics,
MAE 331, 2012
!
Copyright 2012 by Robert Stengel. All rights reserved. For educational ... stall"
ã Flow-separation buffet"
Angle of attack"
– Local shock waves"
Piper Dakota Stall Buffet"
http://www.youtube.com/watch?v=mCCjGAtbZ4g
!
Boeing 787 Flight
Envelope ... maneuver"
The Flight Envelope
Flight Envelope Determined by
Available Thrust"
ã Flight ceiling defined by
available climb rate"
– Absolute: 0 ft/min"
– Service: 100 ft/min"
Performance:...
... Measurement of Position in
Alternative Frames - 1"
ã Two reference frames of interest"
– I: Inertial frame (fixed to inertial
space)"
– B: Body frame (xed to body)"
ã Differences ... sequences of 3 rotations can be chosen; however,
once sequence is chosen, it must be retained
"
Effects of Rotation on Vector Transformation
from Inertial to Body Frame of Reference"
Yaw ... 22.1ì10
6
slug-ft
2
I
xz
= 0.88 ì10
6
slug-ft
2
Angular Momentum
of a Particle
!
ã Moment of linear momentum of differential
particles that make up the body"
– (Differential masses)...
... sin
γ
!
"
#
#
#
$
%
&
&
&
Relationship of Inertial Axes
to Velocity Axes"
Aircraft Equations of Motion - 2
Robert Stengel, Aircraft Flight Dynamics, MAE 331,
2012
"
ã Rotating frames of reference"
ã ... center
of mass"
Alternative Frames of Reference"
ã Orthonormal transformations connect all reference frames"
Next Time:
Linearization and Modes of
Motion
Reading
Flight Dynamics, ...
v
B
=
1
m
F
B
+ H
I
B
g
I
B
v
B
B
= I
B
1
M
B
B
I
B
B
( )
ã Rate of change of
Translational Position "
ã Rate of change of
Rotation Matrix "
ã Rate of change of
Translational...
...
"
#
$
$
$
$
$
$
$
%
&
'
'
'
'
'
'
'
ã Four (6 x 6) blocks distinguish longitudinal and lateral-directional effects "
F =
F
Lon
F
Lat−Dir
Lon
F
Lon
Lat−Dir
F
Lat−Dir
"
#
$
$
%
&
'
'
Effects of longitudinal ... Numerically"
First differences in f( x,u,w)"
ã Analytically"
Symbolic evaluation of analytical
models of F, G, and L"
F( t ) =
∂
f
∂
x
x =x
N
(t )
u = u
N
(t )
w = w
N
(t )
G(t ) =
∂
f
∂
u
x ... matrix"
L(t) =
f
w
x =x
N
(t )
u =u
N
(t )
w =w
N
(t )
=
∂
f
1
∂
w
1
∂
f
1
∂
w
2
∂
f
1
∂
w
s
∂
f
2
∂
w
1
∂
f
2
∂
w
2
∂
f
2
∂
w
s
∂
f
n
∂
w
1
∂
f
n
∂
w
2
∂
f
n
∂
w
s
"
#
$
$
$
$
$
$
$
$
%
&
'
'
'
'
'
'
'
'
x...
... ) + L
Lon
Δw
Lon
(t )
F =
∂
f
1
∂
V
∂
f
1
∂γ
∂
f
1
∂
q
∂
f
1
∂α
∂
f
2
∂
V
∂
f
2
∂γ
∂
f
2
∂
q
∂
f
2
∂α
∂
f
3
∂
V
∂
f
3
∂γ
∂
f
3
∂
q
∂
f
3
∂α
∂
f
4
∂
V
∂
f
4
∂γ
∂
f
4
∂
q
∂
f
4
∂α
$
%
&
&
&
&
&
&
&
&
&
&
&
'
(
)
)
)
)
)
)
)
)
)
)
)
G ... =
∂
f
1
∂
V
∂
f
1
∂γ
∂
f
1
∂
q
∂
f
1
∂α
∂
f
2
∂
V
∂
f
2
∂γ
∂
f
2
∂
q
∂
f
2
∂α
∂
f
3
∂
V
∂
f
3
∂γ
∂
f
3
∂
q
∂
f
3
∂α
∂
f
4
∂
V
∂
f
4
∂γ
∂
f
4
∂
q
∂
f
4
∂α
$
%
&
&
&
&
&
&
&
&
&
&
&
'
(
)
)
)
)
)
)
)
)
)
)
)
G =
∂
f
1
∂δ
E
∂
f
1
∂δ
T
∂
f
1
∂δ
F
∂
f
2
∂δ
E
∂
f
2
∂δ
T
∂
f
2
∂δ
F
∂
f
3
∂δ
E
∂
f
3
∂δ
T
∂
f
3
∂δ
F
∂
f
4
∂δ
E
∂
f
4
∂δ
T
∂
f
4
∂δ
F
#
$
%
%
%
%
%
%
%
%
%
%
&
'
(
(
(
(
(
(
(
(
(
(
L ... Dynamics"
∂
f
3
∂δ
E
=
1
I
yy
C
m
δ
E
ρ
V
N
2
2
Sc
$
%
&
'
(
)
∂
f
3
∂δ
T
=
1
I
yy
C
m
δ
T
ρ
V
N
2
2
Sc
$
%
&
'
(
)
∂
f
3
∂δ
F
=
1
I
yy
C
m
δ
F
ρ
V
N
2
2
Sc
$
%
&
'
(
)
∂
f
3
∂
V
wind
= −
∂
f
3
∂
V
∂
f
3
∂α
wind
= −
∂
f
3
∂α
∂
f
4
∂δ
E
= −
∂
f
2
∂δ
E
∂
f
4
∂δ
T
= −
∂
f
2
∂δ
T
∂
f
4
∂δ
F
= −
∂
f
2
∂δ
F
∂
f
4
∂
V
wind
=
∂
f
2
∂
V
∂
f
3
∂α
wind
=
∂
f
2
∂α
...
... Stability-and-Control
Derivatives"
∂
f
1
∂
v
∂
f
1
∂
p
∂
f
1
∂
r
∂
f
1
∂φ
∂
f
2
∂
v
∂
f
2
∂
p
∂
f
2
∂
r
∂
f
2
∂φ
∂
f
3
∂
v
∂
f
3
∂
p
∂
f
3
∂
r
∂
f
3
∂φ
∂
f
4
∂
v
∂
f
4
∂
p
∂
f
4
∂
r
∂
f
4
∂φ
#
$
%
%
%
%
%
&
'
(
(
(
(
(
Stability ... top!
Dutch Roll, front!
Why Modify the Equations?"
F
LD
=
F
DR
F
RS
DR
F
DR
RS
F
RS
!
"
#
#
$
%
&
&
=
F
DR
small
small F
RS
!
"
#
#
$
%
&
&
≈
F
DR
0
0 F
RS
!
"
#
#
$
%
&
&
Effects ...
Δ
v(t)
Δ
p(t)
Δ
r(t)
Δ
φ
(t)
#
$
%
%
%
%
%
&
'
(
(
(
(
(
=
∂
f
1
∂
v
∂
f
1
∂
p
∂
f
1
∂
r
∂
f
1
∂φ
∂
f
2
∂
v
∂
f
2
∂
p
∂
f
2
∂
r
∂
f
2
∂φ
∂
f
3
∂
v
∂
f
3
∂
p
∂
f
3
∂
r
∂
f
3
∂φ
∂
f
4
∂
v
∂
f
4
∂
p
∂
f
4
∂
r
∂
f
4
∂φ
#
$
%
%
%
%
%
%
%
%
%
%
%
&
'
(
(
(
(
(
(
(
(
(
(
(
Δv(t)
Δp(t)
Δr(t)
Δ
φ
(t)
#
$
%
%
%
%
%
&
'
(
(
(
(
(
+...