AERODYNAMIC OPERATORS

An aerodynamic operator relates the aerodynamic force acting on an airfoil and the motion of the airfoil. In aeroelasticity, the drag force and the skin friction being generally neglected, the most important aerody­namic operator is concerned with the aerodynamic lift and moment.

The complexity of the aerodynamic operator is the major difficulty in aeroelasticity. The explicit form of the aerodynamic operator, giving pressure distribution as a function of arbitrary wing deflection, is yet unknown even for such an idealized surface as an infinitely thin rectangular plate of finite span. It is here that a number of simplifying assumptions must be introduced. First, linearization of the hydrodynamic equations is imperative; hence, the theory will be applicable only to thin flat lifting surfaces. Second, it is necessary to tabulate the results numerically; hence, the form of the wing-deflection surface must be specified.

It is therefore evident why the method of generalized coordinates and the method of iteration are particularly suitable for aeroelastic problems. In each step of the iteration, as well as for each degree of freedom in generalized coordinates, the elastic deformation is known. Hence, the aerodynamic problem can be solved beforehand and the results tabulated.

It is also evident why the strip assumption on aerodynamic-force distribution across the span of a finite wing is so often made. When the strip assumption is used, it is necessary to tabulate only the two-dimen­sional flow cases. Without the strip assumption, it would be necessary to tabulate the results for every particular planform and every mode of motion of the wing.

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