By Hermann T. Schlichting, Erich A. Truckenbrodt (transl. by Heinrich J. Ramm)
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Extra info for Aerodynamics of the Airplane
By taking a suitable streamline as a solid wall, the other streamlines then form the flow field above this wall. The velocity components in the x and y directions, that is, u and v, are given by AIRFOIL OF INFINITE SPAN IN INCOMPRESSIBLE FLOW (PROFILE THEORY) 37 u a0 d IF c9x 7y V c70 0'l-1 Jy Jx The function F(z) is called a complex stream function. From this function, the velocity field is obtained immediately by differentiation in the complex plane, where dF dz = it - i V = w(z) (2-17) Here, w = u - iv is the conjugate complex number to w = u + iv, which is obtained by reflection of w on the real axis.
Er-o a b Figure 2-7 Development of circulation during set- ting in motion of a wing. (a) Wing in stagnant fluid. (b) Wing shortly after beginning of motion; for the liquid line chosen in (a), the circulation 0; because of flow around the trailing edge, a vortex forms at this station. (c) This vortex formed by flow around the trailing edge is the so-called 1' starting vortex -r; a circulation +1' consequently around the wing. develops 36 AERODYNAMICS OF THE WING 2-2-3 Methods of Profile Theory Since the Kutta-Joukowsky equation (Eq.
Forces and moments in rotary motion An airplane in rotary motion about the axes x, y, z, as specified by the modes of motion of Sec. 1-3-3, is subject to additional velocity components that are produced, for example, locally on the wing and that change linearly with distance from the axis of rotation. The aerodynamic forces and moments that are the result of the angular velocities wX, wy, wZ will now be discussed briefly. During rotary motion of the airplane about the longitudinal axis (roll) with INTRODUCTION 19 angular velocity co, the lift distribution on the wing, for instance, becomes antisymmetric along the wing span.