Originally Posted by Dutch M
An experiment might be to circle around and measure the pitch angle and rudder usage during the circles. I would expect a somewhat sinus shaped change in rudder/pitch position.
You'd be disappointed. The point is - if the wind speed is horizontal and constant in magnitude and direction, there is absolutely no effect on the airplane, except that the center of the circles moves over the earth surface at the speed of the wind. Except for that, the airplane flies perfect circles at constant airspeed, bank angle, pitch angle, angle of attack, and control surface positions.
Another matter entirely is a vertical wind component, or changes of wind speed or direction, but let's keep that for next year ...