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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 ...
The morphism h is a lift of f (commutative diagram). In category theory, a branch of mathematics, given a morphism f: X → Y and a morphism g: Z → Y, a lift or lifting of f to Z is a morphism h: X → Z such that f = g ∘ h.
The aerodynamic center is the point at which the pitching moment coefficient for the airfoil does not vary with lift coefficient (i.e. angle of attack), making analysis simpler. [ 1 ] d C m d C L = 0 {\displaystyle {dC_{m} \over dC_{L}}=0} where C L {\displaystyle C_{L}} is the aircraft lift coefficient .
A beam supported at its Airy points has parallel ends. Vertical and angular deflection of a beam supported at its Airy points. Supporting a uniform beam at the Airy points produces zero angular deflection of the ends. [2] [3] The Airy points are symmetrically arranged around the centre of the length standard and are separated by a distance equal to
Garrett demonstrates how those diagrams translate into lift and drag, for a given sail, on different points of sail, in diagrams similar to these: [33] Polar diagrams, showing lift ( L ), drag ( D ), total aerodynamic force ( F T ), forward driving force ( F R ), and lateral force ( F LAT ) for upwind points of sail
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The tangent gives the maximum L/D point. The accompanying diagram shows C L against C D for a typical light aircraft. The minimum C D point is at the left-most point on the plot. One component of drag is induced drag (an inevitable side-effect of producing lift, which can be reduced by increasing the indicated airspeed). This is proportional to ...
For example, a covering map has a property of unique local lifting of paths to a given sheet; the uniqueness is because the fibers of a covering map are discrete spaces. The homotopy lifting property will hold in many situations, such as the projection in a vector bundle, fiber bundle or fibration, where there need be no unique way of lifting.