Requirements for a Valid TheoryA 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
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.Generation of
LiftFor a lifting airfoil, the surface static pressure varies from
top to bottom and from 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 Bernoullis
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.Generation of
LiftWhy does the surface static pressure 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?Generation of LiftWhy does the surface velocity vary top
to bottom and front to back?
What determines the values for the local surface velocity, and
therefore the local surface pressure, and ultimately the amount of
the lift?Generation of LiftThe flow around the airfoil must satisfy
the conservation laws:
Conservation of mass (continuity)Conservation of momentum (2 or
3 components) Conservation of energy
Lift = L = V Uniform + Doublet + Bound VortexBound Vortex
TheoryKutta-Joukowsky Theory GFree stream velocity = V rVortex
strength = Air density = rGLift Coefficient Angle of Attack Theory
correctly predictsslope of curve = 2 for thin airfoilspGrV
Starting (Shed) Vortex
Prandtls Experimental Photo of Starting Vortex
Prandtl Lifting Line TheoryBound VortexTip VortexThree
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.
