1. Lift Theories
Linear Motion

7. Requirements for a Valid Theory
A valid theory is a rational explanation of observed phenomenon
A valid theory can be used to predict future observations
A valid theory produces numerical results

12. Generation of Lift
For a lifting airfoil, the surface static pressure varies from top to bottom and from front to back.
For a lifting airfoil, the average pressure on the upper surface is lower than the average pressure on lower surface.
The difference in pressure produces the lift.

13. Generation of Lift
Why does the surface static pressure vary top to bottom and front to back?
The ideal surface velocity varies from top to bottom and front to back. The surface of the foil is a streamline, so Bernoulli’s equation relates the surface velocity to surface pressure.
When we include viscosity, the surface velocity is zero, but the local velocity varies at the boundary layer edge.

14. Generation of Lift
Why does the surface velocity vary top to bottom and front to back?
The flow must follow the surface contour (or the edge of the boundary layer). Flow can not pass through the airfoil.
What determines the values for the local surface velocity, and therefore the local surface pressure, and ultimately the amount of the lift?

15. Generation of Lift
What determines the values for the local surface velocity, and therefore the local surface pressure, and ultimately the amount of the lift?
The flow around the airfoil must satisfy the conservation laws:
Conservation of mass
(continuity)
Conservation of momentum
(2 or 3 components)
Conservation of energy

17. Euler Equation Solution
Uniform Flow + Doublet + Vortex
Lift is Generated

18. Bound Vortex Theory Lift No Lift The Kutta Condition
Mapped Uniform Flow + Doublet
Mapped Uniform Flow + Doublet
+ Bound Vortex
Lift
No Lift

19. Bound Vortex Theory Uniform + Doublet + Bound Vortex Vortex strength =
Free stream velocity = V r
Air density = V G
Kutta-Joukowsky Theory
Lift = L = V r G
Lift Coefficient
Theory correctly predicts
slope of curve = 2
for thin airfoils p
Angle of Attack

20. Starting (Shed) Vortex

21. Prandtl’s Experimental Photo
of Starting Vortex

22. Prandtl Lifting Line Theory
Bound Vortex
Tip Vortex
Three dimensional version of Bound Vortex Theory
A continuous line of bound vortices terminating at the wing tips with “tip vortices” that continue downstream to the “starting vortex”.

23. Photo of Tip Vortices