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Unformatted text preview: Fluids Lecture 9 Notes 1. General Wings Reading: Anderson 5.3.2, 5.3.3 General Wings General circulation distribution and downwash The assumption of elliptic loading is too restrictive for the design of practical wings. A more general circulation distribution can be conveniently described by a Fourier sine series , in terms of the angle coordinate defined earlier. N ( ) = 2 bV A n sin n n =1 This is a superposition of individual weighted component shapes sin n , shown in the fig- ure plotted versus the physical coordinate y . The induced angle for this distribution is sin A 2 sin 2 A 3 sin 3 A 1 2 bV y y y ... y evaluated by first noting that N d d dy = d = 2 bV nA n cos n d dy d n =1 which is then substituted into the induced angle integral. N 1 b/ 2 d dy 1 cos n i = = nA n d 4 V b/ 2 dy y o y 0 cos cos o n =1 This integral was evaluated earlier, which gives the final result. N sin n o i ( o ) = nA n sin o n =1 Each component of ( ) has a corresponding component of i ( ). The leading n = 1 term 1 sin 2 A 2 sin 3 i A 1 A sin 3 sin ... y y y y is the same as the elliptic loading case, with the expected uniform induced angle. The remaining terms deviate the loading away from the elliptic distribution, and deviate the downwash away from the uniform distribution....
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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