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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 ...
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 ...
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]
The Spitfire wing may be classified as: "a conventional low-wing cantilever monoplane with unswept elliptical wings of moderate aspect ratio and slight dihedral".. The wing configuration or planform of a fixed-wing aircraft (including both gliders and powered aeroplanes) is its arrangement of lifting and related surfaces.
In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint distribution forms an ellipse and an ellipsoid , respectively, in iso-density plots.