Linear Motion
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Transcript of Linear Motion
Linear MotionLift Theories
Requirements for a Valid Theory
1) A valid theory is a rational explanation of observed phenomenon
2) A valid theory can be used to predict future observations
3) 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 Lift
For 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 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.
Generation of Lift
Why 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 Lift
Why 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 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
Lift is Generated
Uniform Flow + Doublet + Vortex
Euler Equation Solution
Lift
The Kutta Condition
No Lift
Mapped Uniform Flow + Doublet Mapped Uniform Flow + Doublet+ Bound Vortex
Bound Vortex Theory
Lift = L = V
Uniform + Doublet + Bound VortexBound Vortex Theory
Kutta-Joukowsky Theory
Free stream velocity = V
Vortex strength =
Air density =
Lift Coefficient
Angle of Attack
Theory correctly predictsslope of curve = 2 for thin airfoils
V
Starting (Shed) Vortex
Prandtl’s Experimental Photo of Starting Vortex
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”.
Photo of Tip Vortices