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On planes, wingtips vortices engender a loss in terms of lift, and an incresed of the drag, so an energy loss. Is there any possibilty to find a mathematical model relating both ? Thanks for the help.

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Lifting-line theory provides a theoretical means of predicting the induced drag due to finite aspect ratio wings for large Reynolds number incompressible flows.

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Although this theory does not predict the non-zero axial velocity of the vortex cores that results from the streamwise favorable pressure gradient. So, there may be some minor differences in to total kinetic energy of the trailing vortices... –  Bryson S. Jul 14 at 0:49

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