What is the trajectory of the aircraft propeller points relative to the ground?

If an airplane with a running engine is standing before acceleration, then the point on the propeller blade moves in a circle at some distance from the r-axis, returning through each revolution to the starting point. When the plane is flying, forward motion is superimposed on the circular motion. This leads to the fact that, having made a revolution around the axis, the point does not fall into the initial position, but is shifted by some step d. It turns out a turn of a helix. In the future, the cycle is repeated and it turns out that the point moves along a cylindrical helical line.

The point located on the axis of the screw moves in a straight line with respect to the ground.

Answer: The trajectories of the aircraft propeller points in relation to the ground are cylindrical helical lines.