What exactly is the nature of the velocity in the lift equation? I have read that it is the velocity of the aircraft, and I think I have read that it is the relative velocity of the air to the wing/airfoil. If I were holding a wing over my head and running at 5 mph into a breeze of 5 mph, would the velocity for the lift equation in this instance be 10 mph?
The velocity is the free-stream velocity which is the velocity the body sees in a body-fixed coordinate system.
So, if you are moving forward at 5mph and there is a 5mph wind in your face, then in the body-fixed coordinate system, the velocity is 10mph and this is the free-stream velocity.