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In other words, there is no component of flow normal to the surface. Mathematically, this is described by1 S-7 VF = 0 (75) This equation can be linearized about any reference shape. We have linearized the potential equation (33) about an undisturbed uniform flow as described by equation (39). Thus, the boundary condition will be linearized in kind, about an undisturbed and uniform flow. As mentioned earlier, this is a severe restriction. Basically, this limits us to modelling flow disturbances over slender bodies and thin wings.
The velocity vector is not allowed to deflect as the flow passes over the trailing edge. If it does deflect, the velocity becomes locally infinite. This trailing edge condition and wake are completely characterized for incompressible flow . Linearized steady compressible flow over planar wings can be transformed to the incompresible case (using the Prandtl-Glauert transformation) and therefore the trailing edge condition is well understood. For linearized unsteady compressible flow, the trailing edge condition is not as clearly characterized.
The undeformed midplane is conveniently designated as the z = 0 plane. Kimlohei, PP 191 30 (76) = U U2, the aerodynamic (77) Linearized Boundary Conditions from First Principles For the remainder of this text, we redefine u, v, and w differently than in equation (7) to represent the small disturbance from the uniform free stream. We substitute equations (76) and (77) into equation (75) and denote h = hm ± ht* (U +U) A Ah VAh W= 0 (78) We desire a linear relation between the velocity components at the surface of the wing and the function h (x, y, t).