Explain why the dutch roll mode characteristics are often unacceptable in large civil transport aircraft. (a) The yaw control transfer function for a large civil transport aircraft cruising at 33,000 ft is given by
Evaluate the stability modes characteristics and assess these for Level 1 flying qualities. (b) The aircraft is fitted with a yaw damper to improve the dutch roll characteristics. Draw a root locus plot showing the effect of yaw rate feedback to rudder via gain Kr. Draw mode limit boundaries on the root locus plot corresponding with Level 1 flying qualities and suggest a suitable value for Kr. Evaluate all three modes for the chosen value of feedback gain and comment on the comparison with those of the unaugmented aircraft.
The Correct Answer and Explanation is :
The Dutch roll mode is a coupled oscillatory motion of the aircraft that involves both rolling and yawing. This mode can be highly undesirable for large civil transport aircraft because it leads to discomfort for passengers and can be difficult for the pilot to control. The characteristics of Dutch roll modes in such aircraft are often unacceptable due to their low damping and the fact that they can persist for long periods of time.
(a) Yaw Control Transfer Function and Stability Modes
From the given yaw control transfer function, we can assess the stability modes by evaluating the roots (poles) of the transfer function. In the context of aircraft stability, the modes are classified based on their real and imaginary parts:
- Dutch roll mode: This is typically a lightly damped oscillation with a natural frequency (ω_n) and damping ratio (ζ). For large civil aircraft, a lightly damped Dutch roll can lead to oscillations that persist too long, causing passenger discomfort.
- Spiral mode: This represents the long-term instability of the aircraft in yawing and rolling motions.
- Phugoid mode: Involving pitch dynamics, though not directly relevant to Dutch roll, can affect overall aircraft behavior.
To evaluate for Level 1 flying qualities, the damping ratio of the Dutch roll mode should ideally be greater than 0.1, and the natural frequency should be above 0.2 Hz for smooth and comfortable operation.
(b) Yaw Damper and Root Locus Plot
The yaw damper is a control system designed to provide feedback on the yaw rate to reduce Dutch roll oscillations. By adding yaw rate feedback to the rudder, the system’s poles (stability modes) are shifted, improving the damping of the Dutch roll. A root locus plot for this system shows how the poles change with varying feedback gain ( K_r ).
In a root locus plot:
- As the yaw rate feedback gain increases, the poles of the Dutch roll mode move toward the left half of the complex plane, improving stability (damping). The plot will show how the modes shift from lightly damped (high oscillation) to more stable (damped) as ( K_r ) increases.
- Level 1 flying qualities require the Dutch roll damping ratio to be above 0.1, so the plot should be analyzed for gain values where the damping is sufficient to meet these standards.
Suggested Value for ( K_r ):
A typical value of ( K_r ) would place the Dutch roll damping ratio in the range of 0.1 to 0.2, which would stabilize the mode without introducing excessive control inputs.
Evaluation of Modes with Feedback:
For the chosen ( K_r ), the Dutch roll mode will have higher damping, leading to a smoother flight experience. The spiral mode will likely remain unchanged, as it’s primarily a low-frequency, steady-state stability issue. The phugoid mode will also remain unaffected. Comparing with the unaugmented aircraft, the augmented aircraft with the yaw damper will exhibit a higher damping ratio and reduced oscillatory motion.
In summary, adding the yaw damper improves Dutch roll characteristics, providing better stability and comfort while adhering to Level 1 flying qualities.