Velocity in the lift equation 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?
 A: 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.
A: It's not the speed you run, it's the speed of the plane relative to the air.

As shown above, the red arrow is the direction of air movement at the top of the wing. This direction is not perpendicular to the normal line at the top of the wing and is greater than 90 degrees. Therefore, the air tends to leave the wing along the normal line, so the air pressure at the top of the wing decreases.
As shown above, the blue arrow is the movement direction of the air at the bottom of the wing, which is not perpendicular to the normal at the bottom of the wing and is less than 90 degrees. Therefore, the air tends to approach the wing along the normal, so the air pressure at the bottom of the wing increases.
The air pressure at the top of the wing decreases, and the air pressure at the bottom of the wing increases. There is a pressure difference, which leads to the generation of lift.
It can be seen from the cause of lift that the relative velocity of wing and air is necessary.
