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The almost uniform lift distribution of a constant-aerofoil section elliptical wing can cause the entire span of the wing to stall simultaneously, potentially causing loss of control with little warning. To improve the stalling characteristics and give the pilot some warning, designers use a non-uniform aerofoil.
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 ...
The Oswald efficiency, similar to the span efficiency, is a correction factor that represents the change in drag with lift of a three-dimensional wing or airplane, as compared with an ideal wing having the same aspect ratio and an elliptical lift distribution. [1]
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 .
The ideal lift distribution across a wing is elliptical, and extending partial-span flaps causes a significant departure from the elliptical. This increases lift-induced drag which can be beneficial during approach and landing because it allows the aircraft to descend at a steeper angle. Extending the wing flaps increases the camber or ...
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 ...
A horseshoe vortex caused by a (purely theoretical) uniform lift distribution over an aircraft’s wing. The starting vortex is also shown. Any spanwise change in lift distribution sheds a trailing vortex, according to the lifting-line theory. The starting vortex is also shown.
The section lift coefficient is based on two-dimensional flow over a wing of infinite span and non-varying cross-section so the lift is independent of spanwise effects and is defined in terms of ′, the lift force per unit span of the wing. The definition becomes
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