Why is yaw damper inop limited to a maximum altitude?

[Flash131]

A non-mathematical explanation as to why yaw damping decreases with altitude:

Imagine sitting, facing forward, on the tail of an aircraft that is yawing (i.e. the yaw angle is increasing steadily) to the right. If the aircraft is otherwise stationary on a still day, you will feel a faint wind on your left cheek. This wind will appear to come directly from your left. Now imagine that, at the instant we are considering, there is also a light wind blowing from straight ahead. There will now also be a component of wind from straight ahead and you will feel the resultant wind to originate from somewhere forward and left. The fin will experience this same wind and generate a side-force that acts to oppose the yaw rate.

If we now progressively increase the headwind, the resultant wind will appear to come more and more from ahead. So the apparent wind angle seen by the fin decreases with forward speed. The important aspect, as far as yaw damping is concerned, is that the relevant forward speed is the true rather than the indicated air speed.

Note that I am ignoring any apparent wind angle due to the actual yaw angle. The argument applies only to the angle induced by the rate of yaw.

Now imagine two identical aircraft, one at sea level and one up in the flight levels. If both are flying at the same equivalent airspeed and yawing at the same rate, the fins of both will see the same equivalent wind speed. But the fin of the higher aircraft will see the wind as coming nearer from straight ahead, due to its higher true airspeed. Its fin therefore generates less side-force to oppose the yaw rate.

So, the higher you fly, the lower the yaw damping.