Laws

The aerodynamic forces on a body moving at constant velocity are the drag force D opposing the motion and the lift force L in the direction normal to the motion.

For unseparated incompressible potential flow past a two-dimensional body around which there is a circulation :

D'Alembert's Paradox:

According to D'Alembert, no energy is needed to overcome drag!

Kutta-Joukowski:

According to this, we can get nonzero lift without doing any work.

Proof of the laws: we saw before that at large distances, the velocity potential induced by the body approaches a vortex flow. So for large z:

Doing Blasius' integral along a very large circle around the body,

Note that the circulation must be clockwise (increase the velocity above the airfoil) to produce upward lift.

03/22/00 0:27:35