"p (momentum) = m (mass of the aircraft) x v (speed of wing through the air)." represents the momentum of the AIRCRAFT.
It is the change in momentum of the AIR you should examine. Assuming still air, it was sitting quietly minding its own business when along came this a/c and deflected it downwards, thereby changing its momentum from ZERO to something finite.
The change in 'p' depends on how quickly this deflection takes place (ie aircraft speed) and on how big a downward deflection there is eg angle of attack and effective camber.