ORIGINAL: khodges
Most of the higher math is way over my head, and this is a fascinating subject for me. My train of thought may be way off, but it seems to me that the forward motion of the aircraft introduces an inertial force that whatever combination of gyroscopic precession and P-factor are less able to overcome as the airspeed increases, which would be a reason (among others) that the effects are more apparent during take-off, or at other times when the aircraft is at high-power / low airsped conditions. Anything to that?
No! As airspeed increases, P factor isn't present. Think of it as a boat on the water. As you add throttle, the nose comes way up, the prop isn't striking the water the same on both sides, one side has a higher pitch to it. As the boat speeds up, the nose lowers, it gets on the step and the prop is getting the same bite per say on both sides because it is more like 90 degrees to the water going through it. Not an exact way to explain it, but you get the point. The plane does the same thing, as it speeds up, it doesn't move through the air as nose high and the prop blades both bite the same instead of one biting more than the other.