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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:
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.
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 = ′,
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 .
Aircraft flight mechanics are relevant to fixed wing (gliders, aeroplanes) and rotary wing (helicopters) aircraft. An aeroplane ( airplane in US usage), is defined in ICAO Document 9110 as, "a power-driven heavier than air aircraft, deriving its lift chiefly from aerodynamic reactions on surface which remain fixed under given conditions of flight".
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 down moving aileron also adds energy to the boundary layer. The edge of the aileron directs air flow from the underside of the wing to the upper surface of the aileron, thus creating a lifting force added to the lift of the wing. This reduces the needed deflection of the aileron.