# AEM5333HW4-1x

Πολεοδομικά Έργα

16 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

233 εμφανίσεις

Stephanie Carlson

David Dickie

Mark Weimer

Dario Canelon

I.

Modal Analysis

The longitudinal modes are the short period mode, the “fast” mode, and the phugoid
mode, slow and lightly damped mode. These can be seen on the figure above. The
lateral
-
directional modes are the roll mode, spiral mode, and dutch
-
roll mode. The
roll mode i
s the amount of damping of a rolling motion because there is no restoring
moment, also known as the “fast” mode. The spiral mode is a combination of the roll
and yaw stability, also known as the “slow” mode. The dutch
-
roll mode is the
oscillatory combined
roll and yaw motion. These can be seen in the figure below.

II.

Simulation of the AC Response

The primary input for longitudinal dynamics is the elevator deflection and the
output is the pitch

rate
. The primary in
put

for lateral dynamics is

ru
dder deflectio
n
and the output is

yaw

rate
.

Phugoid mode response:



p

16
.
324



p

0
.
833

Short period mode response:



s

0
.
513



s

0
.
385

Spiral and Roll

mode

Response
s
:

0.055

12.34

Dutch Roll mode
Response:

0.7941

III.

Transfer Function and Frequency Response

Transfer functions:


N

long

s
4

27
.
6
s
3

419
s
2

1653
.
9
s

651
.
7
(
s
2

27
.
196
s

266
.
47
)(
s
2

0
.
395
s

0
.
263
)


N

lat

16
.
5598
s
3

269
.
3779
s
2

328
.
9021
s

224
.
989
(
s

12
.
34
)(
s

0
.
055
)(
s
2

9
.
38
s

34
.
88
)

Characteristic equations
:



lon

(
s
2

27
.
196
s

266
.
47
)(
s
2

0
.
395
s

0
.
263
)



lat

(
s

12
.
34
)(
s

0
.
055
)(
s
2

9
.
35
s

34
.
88
)

Roots of longitudinal
characteristic equation:



13
.
5925

9
.
0398
i



0
.
1975

0
.
4735
i

Roots of the lateral characteristic equation:

0.055

12.34

-
4.6750

3.6089
i

IV.

Ultrastick Nonlinear Simulation