Solutions for Home Work 2
Problem 3
Consider a wing-body model with Cmac,wb 0.022 ,
h 0.33 , hac,wb 0.22 ,
awb 0.08 . The area and chord of the wing are 0.1 m 2 and 0.1 m, respectively. Now assume that
a horizontal tail is added to this model. We have the

Homework #2
Due: 5pm, Sep. 28, 2015
1. Problems 2.1 (10pints)
2. Problems 2.3(15pints)
3. Consider a wing-body model with Cmac,wb 0.022 , h 0.33 , hac,wb 0.22 ,
awb 0.08 . The area and chord of the wing are 0.1 m 2 and 0.1 m, respectively. Now
assume that

5.2 GRAM-SCHMIDT PROCESS AND QR
FACTORIZATION
How can we construct an orthonormal basis?
Say, from any basis v1, v2, . . . , vm of a subspace
V?
If V is a line with basis v1:
1
w1 =
v1
v1
When V is a plane with basis v1, v2, we rst
get w1 as above.
Next n

Quiz #4
Due 7am Dec. 14 ( a box outside of B222)
Name_
(Print Your Name)
I certify that I have neither given help to, nor received help from, any individual in
matters relating to this examination.
_
Signature
NOTE:
1) Include your code in the submission

Quiz #3
Due in class 5pm Nov. 9 (submit paper)
Name_
(Print Your Name)
I certify that I have neither given help to, nor received help from, any individual in
matters relating to this examination.
_
Signature
NOTE:
1) Please write down your steps clearly.

Aircraft Flight Dynamics
Lecture 5
XIAOLI BAI
SEP.21, 2015
Xiaoli Bai
Notice
Please leave ASAP after the lecture. We have a few students
take a quiz. Thanks for your corporation!
Differences between the slides and the book: some are from
the recommended

Quiz #5
Due 7am Dec. 14 ( a box outside of B222)
Name_
(Print Your Name)
I certify that I have neither given help to, nor received help from, any individual in
matters relating to this examination.
_
Signature
NOTE:
1) Include your code in the submission

Homework #2
Due: 5pm, Sep. 26, 2015
1. Problems 2.1 (10pints)
2. Problems 2.3(15pints)
3. Consider a wing-body model with Cmac,wb 0.022 , h 0.33 , hac,wb 0.22 ,
awb 0.08 . The area and chord of the wing are 0.1 m 2 and 0.1 m, respectively. Now
assume that

Aircraft Flight Dynamics
Lecture 19
XIAOLI BAI
NOV 16, 2015
FOR EDUCATION PURPOSE ONLY
Notes
HW 9: posted
Final Proposal:
start
Estimation: will guide you next class
Return those either disqualified or I have concerns
Others, feel free to discuss if y

Particle Kinematics: x-y Coordinates
Current unit: Particle Kinematics
Last class: Curvilinear, Circular, Projectile Motion
Today:
(a) Math Preliminaries: Dot notation, chain rule
(b) Path Known x-y Problem
(c) Parametric Equations x-y Problem
Math Prelim

Aircraft Flight Dynamics
Lecture 21
XIAOLI BAI
NOV 23, 2015
FOR EDUCATION PURPOSE ONLY
A few schedules
HW 10 assigned, due Dec. 7 ( 2 weeks, so make plans)
Final presentation: Dec. 7 (5-6:30pm)
Flight Day:
Dec. 21, 4pm - 7pm
tentatively, will check w

Aircraft Flight Dynamics
Lecture 20
XIAOLI BAI
NOV 18, 2015
FOR EDUCATION PURPOSE ONLY
Notes
Extra lecture: Nov. 23
2 responses
Then I will have this in my office.
Revised Proposals: ASAP, so you can start.
Sample Final Project: next slide
FOR EDUCA

Aircraft Flight Dynamics
Lecture 17
XIAOLI BAI
NOV 9, 2015
FOR EDUCATION PURPOSE ONLY
HW8: assigned
4.6
4.7
4.9
4.10
4.11
FOR EDUCATION PURPOSE ONLY
2
Todays class:
FOR EDUCATION PURPOSE ONLY
3
FOR EDUCATION PURPOSE ONLY
Read/Study page 57 of Nelson.
4
Re

Aircraft Flight Dynamics
Lecture 18
XIAOLI BAI
NOV 11, 2015
FOR EDUCATION PURPOSE ONLY
.
Review: For a linear 2nd order system:
.
x + 2zwn x + wn2 x = 0
l2 + 2zwn l + wn2 = 0
Characteristic Eqn
l1,2 = -zwn +/- i wn 1- z2
Eigenvalues
wn
Natural Frequency
z

Aircraft Flight Dynamics
Lecture 16
XIAOLI BAI
NOV 2, 2015
FOR EDUCATION PURPOSE ONLY
Quiz 3
Take-home exam with a survey
Assigned on Nov. 3 evening
No class on Nov. 4
Submit on Nov. 9
Cheating: give help or received help from any other individual
FOR ED

Aircraft Flight Dynamics
Lecture 13
XIAOLI BAI
OCT 21, 2015
FOR EDUCATION PURPOSE ONLY
NOTE
HW # 5 due Monday (Oct. 26). 5pm.
By Nov 9, a proposal about the problem you want to undertake for
your final shall be submitted to the instructor. The instructo

Homework 2 Solutions
Problem 1
Solution:
1) Determine the trim lift coefficient
= @
+ = @
=0
+
=0
pitch moment at zero lift is equal to 0.08 @
the slope of the Cm versus CL curve is 0.15
airplane is flying at the trim point = 0
=0
= 0.15
therefore 0

ATTITUDE REPRESENTATION
Attitude cannot be represented by vector in 3-dimensional space, like
position or angular velocity, even though attitude is a 3-dimensional
quantity.
Attitude is always specified as a rotation relative to a base, or reference
frame

Aircraft Flight Dynamics
Lecture 19
XIAOLI BAI
NOV 30, 2016
FOR EDUCATION PURPOSE ONLY
Note
Two lectures left: Nov. 28 and Nov. 30
Presentation due: 11:59pm Dec. 4.
Your 3 min talk: the part you are mostly proud of your project.
Label your presentatio

Homework 10 Solutions
Problem 1
Solution:
For this problem we must first develop the equation of motion
=
From Figure P5.3 we can easily see that the model spins down from
10.5 rad/s to zero roll rate when the motor drive is disengaged. This
implies tha

Aircraft Flight Dynamics
Lecture 16
XIAOLI BAI
NOV 16, 2016
FOR EDUCATION PURPOSE ONLY
NOTE
We will have a 30min lecture, and then you will take a 30min quiz.
If we have time, I will briefly talk about the derivations of the rotational kinematics, and t

Aircraft Flight Dynamics
Lecture 15
XIAOLI BAI
NOV 14, 2016
FOR EDUCATION PURPOSE ONLY
Note
A short quiz on Wed. Nov. 16. After 30min of lecture.
Focus on:
State space
Solutions of ODEs we have talked in the class
Perturbation concept
Difficult leve

Let the vectcr w dene the instantaneous rctatinnal velcrcitjvr cf the 5 frame
relative tn the N frame. Te avcid having tn integrate the directinn cnsine matrix
directlv given an a: time histnrjv, the Euler angle kinematic differential equatinns
are needed

Homework 6 Solutions
Problem 1
Solution:
a)
Reason#1
Inertia matrix will be time invariant since the mass distribution is not changing in
time relative to the body-fixed reference, also the controls and the measurements
are often defined in this frame.
Re

Quiz 4 Solutions
Problem 1
Solution:
a) Choose and
as our state variables and let 1 = and 2 =
1
S = [ ]
2
2
1 = =
; 2 = 2 = 3
2 + 4 = 32 21 + 4
-10points
Thus, the state space form can be written as:
S = +
1
0
[ ] = [
2
2
1 1
0
] [ ] + [ ] 1
3 2
4
0
1

Homework #6
Due: 5pm, Nov. 7, 2016
Problem 1:
(a) Provide two reasons of why equations of motion in airplane flight dynamics are always
expressed in a body-fixed reference and not in an inertial reference.
(5 points) Reason #1:
(5 points) Reason #2:
(b) (