Dynamics

Question 1

What do lateral equations of motion consist of

Answer 1

• side force
• rolling moments
• yawing moments

Question 2

For spiral mode what is ignored in lateral equations

Answer 2

side force

Question 3

For dutch roll mode what is ignored in lateral equations

Answer 3

neglect control and roll moments

Question 4

What is inertial cross coupling

Answer 4

idea that rotational motion about one axis can cause (unwanted) rotational motion about another

Question 5

What are the 2 possible stability characteristics aircraft require for high rates of roll

Answer 5

1) small longitudinal and large directional static stability
(slender supersonic aircraft at subsonic speed)
- roll-pitch coupling

2) small directional and large longitudinal static stability
(slender supersonic aircraft at supersonic speed)
- roll-yaw coupling

Question 6

Define dynamic stability

Answer 6

how fast an aircraft returns to trim conditions after a disturbance

Question 7

Define 3 possible cases when solving 2nd order ODEs

Answer 7

• 2 real roots (over damped)
• 2 complex roots (damped sinusoid)
• 1 double root (critically damped)

Question 8

What can be derived from long period (phugoid) approximation about stabilising it

Answer 8

• stability decreases as L/D improves

- therefore only option is automatic stabilising to prevent phugoid oscillation

Question 9

describe importance of short period mode

Answer 9

• if this mode has high frequency and heavily damped, the aircraft will respond quickly to an elevator input
• if low frequency and lightly damped, aircraft will be difficult and dangerous to control

Question 10

Give state space equation

Answer 10

x(dot) = Ax + Bu^c

Question 11

Describe method to find if system controllable

Answer 11

F - 2X2, G - 2X1

Qc = ( G, FG ) - 2X2

det(Qc) = 0 (not controllable)

det(Qc) doesn’t = 0 (controllable)

Question 12

Describe method to find if system obserable

Answer 12

F - 2X2, G - 2X1, H - 1x2

Qo = ( H1, H2 ) - 2X2
HF1, HF2

det(Qo) = 0 (not observable)

det(Qo) doesn’t = 0 (observable)

Question 13

How to find eigenvalues

Answer 13

Qc (2x2)

use quadratic equation

comment on roots

lambda*I - Qc | = 0

Question 14

Describe physical limitations of designing feedback system

Answer 14

• large gains can cause actuator saturation (physical limitations to how far actuators can move)
• large gains need more powerful actuator (more power means more weight and volume)
• need to avoid exciting unmodelled structural dynamics
• large gains amplify noise in system (this can mess with controls/readings)

Question 15

What are stability augmentation systems (SAS)

Answer 15

used to improve stability characteristics of aircraft with poor flying qualities

method:

• find eigenvalues
• compare these to desired flying qualities
• state feedback used to design controller to provide the desired flying qualities