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Old 07-15-2011, 08:58 AM
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cactusflyer
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Default RE: Does gyro on rudder work against aileron?

ORIGINAL: HarryC

ORIGINAL: cactusflyer
Ok Harry, I have a couple vodkas onboard, I will bite on this one! if there is ALWAYS yaw in a turn. Can you explain the yaw relationships in a coordinated turn, side slip and a skid?......Assuming it's an airplane turning and not a Mini Cooper or boat.
A level turn is a combination of rotation about pitch and yaw axes. Imagine looking at your model from behind while it is banked over some amount and turning. There is no axis of rotation pointing vertically up at some angle through the model while it is banked, yet the turn is a rotation about that non-existent axis. If the turn was purely yaw around the yaw axis, you would see the nose go down due to the angle of bank. If the turn was purely pitch around the pitch axis, you would see the nose go up. So somewhere in between those is the turn, it is a combination of yaw and pitch rotations. In a very shallow bank it is almost purely rotation around the yaw axis. In a very steeply banked turn it is almost purely rotation about the pitch axis. If you want to picture it more precisely, the yaw fraction is the cosine of the angle of bank and the pitch fraction is the sine of the angle of bank. So as bank angle increases, the yaw fraction starts high and falls towards zero, the pitch fraction starts at zero and heads towards 1.

At 90 degrees angle of bank, the yaw fraction is zero and the pitch fraction is 1. But a level balanced turn at 90 degrees angle of bank is impossible, in reality it is impossible beyond some number quite well below that, so the cosine of the angle of bank, which is the yaw element, never reaches zero in a balanced level turn. However beyond 60 degrees angle of bank the yaw fraction is becoming small and falling rapidly. A yaw gyro will sense only the rate of the yaw fraction of the turn, not the entire rate of turn. So a very rapid turn can be a high rate of turn but if it is very steeply banked the yaw gyro will see very little to counteract. For example, suppose a little park flyer and a fast model jet are flying together and both make a rapid turn at the same rate around the same 360 degrees. The circles will be very different sizes due to the speeds but the yaw gyro does not sense that, only the yaw rate. Suppose both models are flown to turn the circle in the same time, so the park flyer is a shallow bank and the fast jet is banked very steeply. Now, both have the same rate of rotation around the circle. But the yaw gyro in the jet will record a low rate of rotation whereas the yaw gyro in the park flyer will record a very large rate of rotation. Both are rotating in the circle at the same rate, but the yaw gyro sees the rate multiplied by the cosine of the angle of bank. Therefore the gyro in the park flyer will kick far more against the turn than the one in the more steeply banked jet, despite both turns being the same rate.

PS. Frank, that is a super model.

H.
OK So how come my coffee stays steady in the cup and there is no perception of a turn in a coordinated turn, but in a slip or skid the brew sloshes around to one side of the cup or the other and I can feel the yaw rate? I no nothing of the "non-existent" axis...............Fifth Dimension maybe?

I think you are confused about what the yaw axis is and you are using it to describe the rate of turn. The yaw axis is perpendicular to the pitch axis and therefore varies with bank. The airplane can be in a turn with no yaw rate sensed in the cockpit and hence sensed by the gyro.

Tailwinds,

John