What is the explanation of the pitch down torque on a stalling aircraft?
Sometimes this is a simple matter of wing design. In setting our aircraft for most efficient flight, through a combination of trim and ballast, we can set the aircraft center of gravity at, or near, the center of lift, so that little trim is needed to maintain level flight. In other words, the center of lift for the full wing is at and through the center of gravity.
Most wings are designed with slight washout, meaning that the outer panel of the wing has been twisted to reduce the angle of attack of the wing in that outer panel region. If we examine lift across the entire wing with the airplane in trim, the center of lift for the wing is through the center of gravity for the plane. And, considering flight speed and wing loading, the center of lift may be very slightly ahead of the center of gravity. Why? One additional factor at play is the pitching moment of the wing. In neutral flight, most wings have a negative pitching moment, meaning the wing has a very slight tendency to pitch downward even when the aircraft is in trim.
As the wing stalls, the stall progression usually begins at the wing root and progresses outward across the inner panel of the wing. The wing tip, however, is unstalled because washout gives that section of the wing a lower angle of attack. Consequently, absent lift from the functional inner panel, the center of lift for the outer panel is slightly behind the center of gravity, thereby causing a slight nose-down moment during the stall. This can be assisted by the very slight downward pitching moment of this unstalled portion of the wing. Hence, the nose pitches down.
You can, I believe, trim a small plane so that it will execute a series of pitch up, stall, pitch down, recover cycles with no input from the pilot.
As we can well imagine, if the airplane is in a near-trim condition, and a stall is incurred, the nose will pitch forward and the aircraft will gain airspeed. As this occurs, the unstalled condition of the wing is restored, and with the center of lift restored, the aircraft will gently pitch nose-up in recovery. If the pilot does not capture this recovery with a slight down elevator trim input, the aircraft will continue on an upward path, losing airspeed, and once again stall. This process may continue ad-infinitum until corrective action is taken.
Some aircraft are designed so that the wing is completely neutral; the center of lift for the wing is always through the center of gravity for the plane. The nose down tendency of the wing is incurred then, only by the pitching moment of the wing. Consequently, the plane must be actively flown to maintain its flight attitude. What planes fly like this? Think pylon racers. Or Mike Patey's Turbulence. (Oh, boy!)