Prandtl Lifting Line Theory Lifting Line Theory

In Lifting Line theory, explain the origin of downwash.

In terms of drag, what is the difference between downwash and upwash?

Is there a net drag benefit to design a wing with upwash? Design of a Wing

The circulation distribution is represented by the Fourier series

Г[y(t)] = 2U&£~1 An sin nt

Подпись: y(t) = —b cost, 0 < t < nb

Design the simplest wing (meaning the wing with the least number of non-zero Fourier coefficients) with zero strength tip vortices, in order to minimize risks for airplanes caught in the wake of the wing. To achieve this goal, combine modes 1 and 3 in such a way that

Подпись:at y = ±­7 2

Note: you can impose

d Г [y(t)] n _ n л = 0, at t = 0 and n dt

Подпись: d Г( y) dy Подпись:

Prandtl Lifting Line Theory

to find a relation between A1 and A3(verify your result as the rest depends on it), then verify that

Use the following identity: cos 3t = cos t (4 cos21 — 3).

Sketch the circulation distribution Г[y(t)] in terms of y or t. Use the following identity: sin3t = sin t (4 cos21 — 1).

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