Lecture 16 - Tutorial Sheet 3

Question 1

What is the roll-to-yaw ratio? What value deems a system stable?

Answer 1

Ratio of peak roll to peak yaw in dutch roll mode.

Less than 1 means stable

Question 2

What can make a spiral mode hard to notice?

Answer 2

Adverse weather

Question 3

What 2 characteristics of longitudinal stability does a well-designed a/c have? How are these characterised?

Answer 3

2 symmetric phugoid modes

2 symmetric short period modes

Characterised by complex roots

Question 4

What 3 lateral/directional stability characteristics does a well-designed a/c have?

Answer 4

1 spiral mode (non-oscillatory)

1 roll damping mode (non-oscillatory)

2 dutch roll modes (oscillatory; 2 complex roots)

Question 5

To what extent can spiral instability be tolerated?

Answer 5

As long as the time to double the amplitude is gradual (>4s).

Question 6

What are the 3 lateral directional motion variables?

Answer 6

Yaw angle; roll angle; sideslip angle

Question 7

How do you find the damping ratio, natural frequency, and time period when given a transfer function? What is the fraction on the LHS of the transfer function equation?

Answer 7

Firstly, only interested in denominator.

2nd order equation is for the dutch roll and is equivalent to the general characterstic equation, so can solve for damping ratio and frequency.

1st order equations are equivalent to “s+1/tc”, so can solve from this.

Question 8

Equation for damped frequency?

Answer 8

wn * sqrt(1-DR^2)