Prandtl Lifting-Line Theory

Ludwig Prandtl is considered by some to be the greatest aerodynamicist of all time. He was responsible for solving several of the most important theoretical problems in aeronautics, including the correct manner for treating viscous effects by means of boundary-layer theory and the fluid dynamics of finite wings by introduction of the elegant yet simple idea of the bound vortex.

Two important vortex theorems attributed to Helmholtz must be reviewed before the analysis may begin. These theorems state that:

(a) The strength of any vortex filament must be constant along the length of the filament.

(b) A vortex filament cannot end in the fluid; it must close on itself or end at a boundary in the fluid.

These ideas provide a useful visualization of the problem and motivate many of the mathematical steps in developing the theory for lift generation on a finite-wing surface.

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