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Published byLizeth Killpack Modified over 2 years ago

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Linear Motion Lift Theories

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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

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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.

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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?

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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?

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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

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

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

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

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Starting (Shed) Vortex

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Prandtl’s Experimental Photo of Starting Vortex

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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”.

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Photo of Tip Vortices

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