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An elliptical spanwise lift distribution cannot be achieved by an untwisted wing with an elliptical planform because there is a logarithmic term in the lift distribution that becomes important near the wing tips. [4] Elliptical wing planforms are more difficult to manufacture. [5]
The Lanchester-Prandtl lifting-line theory [1] is a mathematical model in aerodynamics that predicts lift distribution over a three-dimensional wing from the wing's geometry. [2] The theory was expressed independently [3] by Frederick W. Lanchester in 1907, [4] and by Ludwig Prandtl in 1918–1919 [5] after working with Albert Betz and Max Munk ...
English: Non-uniform lift distribution Realistic lift distribution. A uniform lift distribution over the wing of an aircraft would cause the shedding of two wingtip trailing vortices and a (stationary) starting vortex. Note that in reality, lift distribution cannot be uniform, and that viscosity causes decay of the trailed and starting vortices.
English: Realistic lift distribution. A hypothetical, non-uniform lift distribution over the wing of an aircraft. Any spanwise change in lift would cause the shedding of a trailing vortex, not necessarily at the tip. In practice, the lift varies continuously over the surface of the wing and a sheet of
Washout is a characteristic of aircraft wing design which deliberately changes the lift distribution across the span of an aircraft’s wing. The wing is designed so that the angle of incidence is greater at the wing roots and decreases across the span, becoming lowest at the wing tip.
For a given wing span and surface, minimal induced drag is obtained with an elliptical lift distribution. For a given lift distribution and wing planform area, induced drag is reduced with increasing aspect ratio. As a consequence, aircraft for which a high lift-to-drag ratio is desirable, such as gliders or long-range airliners, typically have ...
Typically, the elliptical spanwise distribution of lift produces the minimum induced drag [15] for a planar wing of a given span. A small number of aircraft have a planform approaching the elliptical — the most famous examples being the World War II Spitfire [ 13 ] and Thunderbolt .
Given the distribution of bound vorticity and the vorticity in the wake, the Biot–Savart law (a vector-calculus relation) can be used to calculate the velocity perturbation anywhere in the field, caused by the lift on the wing. Approximate theories for the lift distribution and lift-induced drag of three-dimensional wings are based on such ...