Historical Background
Bart Rademaker provides a background history of the VLM in the NASA Langley workshop documentation SP-405.
The VLM is the extension of Prandtl lifting line theory, where the wing of an aircraft is modeled as an infinite number of Horseshoe vortices. The name was coined by V.M. Falkner in his Aeronautical Research Council paper of 1946. The method has since then been developed and refined further by W.P. Jones, H. Schlichting, G.N. Ward and others.
Although the computations needed can be carried out by hand, the VLM benefited from the advent of computers for the large amounts of computations that are required.
Instead of only one horseshoe vortex per wing, as in the lifting line theory, the VLM utilizes a lattice of horseshoe vortices, as described by Falkner in his first paper on this subject in 1943. The number of vortices used vary with the required pressure distribution resolution, and with required accuracy in the computed aerodynamic coefficients. A typical number of vortices would be around 100 for an entire aircraft wing; an Aeronautical Research Council report by Falkner published in 1949 mentions the use of an "84-vortex lattice before the standardisation of the 126-lattice" (p. 4).
The method is comprehensibly described in all major aerodynamic textbooks, such as Katz & Plotkin, Anderson, Bertin & Smith or Houghton & Carpenter
Read more about this topic: Vortex Lattice Method
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