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Unformatted text preview: Fluids Lecture 7 Notes 1. Elliptical Lift Distribution Reading: Anderson 5.3.1 Elliptical Lift Distribution Definition and lift calculation Consider an elliptical spanwise circulation distribution given by 2 y 2 ( y ) = 0 1 b y b/2 0 b/2 where 0 is the circulation at the wing center at y = 0. The overall lift on the wing is the integral of the corresponding lift/span distribution L ( y ) = V ( y ). b/ 2 b/ 2 2 y 2 L = L ( y ) dy = V 0 1 dy = V b b/ 2 b/ 2 b 4 The integral can be evaluated via integral tables, or by inspection by noting that the area under an ellipse is / 4 times the area of the enclosing rectangle. Downwash calculation Computation of the downwash first requires knowing the trailing vortex sheet strength, which is minus the derivative of the circulation. d 4 y ( y ) = = dy b 2 1 (2 y/b ) 2 The downwash at some location y o is then b/ 2 y 1 b/ 2 ( y ) dy 0 dy w ( y o ) = = 4 b/ 2 y o y b 2 b/ 2 1 (2 y/b ) 2 y o y As in thin airfoil theory, the mathematical problem is considerably simplified by making the trigonometric substitution b y o = cos o 2 b y = cos 2...
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
- Fall '05