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Equations for divergence of a simple beam Divergence can be understood as a simple property of the differential equation(s) governing the wing deflection. For example, modelling the airplane wing as an isotropic Euler–Bernoulli beam, the uncoupled torsional equation of motion is = ′,
A raised aileron reduces lift on that wing and a lowered one increases lift, so moving the aileron control in this way causes the left wing to drop and the right wing to rise. This causes the aircraft to roll to the left and begin to turn to the left. Centering the control returns the ailerons to the neutral position, maintaining the bank angle ...
Yawing also increases the speed of the outboard wing whilst slowing down the inboard wing, with corresponding changes in drag causing a (small) opposing yaw moment. N r {\displaystyle N_{r}} opposes the inherent directional stiffness which tends to point the aircraft's nose back into the wind and always matches the sign of the yaw rate input.
Deflection of control surfaces modifies the pressure distribution over the vehicle, and these are dealt with by including perturbations in forces and moments due to control deflection. The fin deflection is normally denoted (zeta). Including these terms, the equations of motion become:
Frise ailerons accentuate this profile drag imbalance by protruding beneath the wing of an upward-deflected aileron, most often by being hinged slightly behind the leading edge and near the bottom of the surface, with the lower section of the aileron surface's leading edge protruding slightly below the wing's undersurface when the aileron is ...
Lifting line theory supposes wings that are long and thin with negligible fuselage, akin to a thin bar (the eponymous "lifting line") of span 2s driven through the fluid. . From the Kutta–Joukowski theorem, the lift L(y) on a 2-dimensional segment of the wing at distance y from the fuselage is proportional to the circulation Γ(y) about the bar a
The natural outcome of this requirement is a wing design that is thin and wide, which has a low thickness-to-chord ratio. At lower speeds, undesirable parasitic drag is largely a function of the total surface area, which suggests using a wing with minimum chord, leading to the high aspect ratios seen on light aircraft and regional airliners ...
Structural: A long wing has higher bending stress for a given load than a short one and therefore requires higher structural-design (architectural and/or material) specifications. Also, longer wings may have some torsion for a given load, and in some applications this torsion is undesirable (e.g. if the warped wing interferes with aileron effect).