Herein, exact algebraic expressions for the non-circulatory (added-mass) forces on elliptic airfoils are derived for any two-dimensional motion – including simultaneous rectilinear acceleration and rotation – embedded in a steady free-stream flow. Despite the lengthy history of the added-mass concept and its widespread application to cylinders of various cross-sections, such closed-form expressions for elliptic cylinders, in terms of kinematic and geometric parameters alone, have remained absent from the literature until now. Inspection of the derived equations reveals that for pure pitching about a point on the chord-line, increasing thickness always decreases the added-mass force magnitude. For any given motion of the chord-line, the difference in force between thick and thin airfoils is proportional to the square of the thickness, although this difference may be positive or negative for the general three-degree-of-freedom case. In the special case of zero thickness and small pitch angles, Theodorsen's added-mass lift force on rigid thin airfoils is recovered; for large pitch angles, an exact generalization of Theodorsen's expression, applicable to the chord-normal direction, is given.

中文翻译：

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椭圆机翼上的附加质量力

在这里，椭圆机翼上的非循环（附加质量）力的精确代数表达式针对嵌入在稳定自由流中的任何二维运动（包括同时直线加速和旋转）推导出来。尽管附加质量概念的历史悠久，并且广泛应用于各种横截面的圆柱体，但迄今为止，仅就运动学和几何参数而言，椭圆圆柱体的这种封闭形式的表达式仍然没有出现在文献中。对导出方程的检查表明，对于弦线上一个点的纯俯仰，增加厚度总是会降低附加质量力的大小。对于弦线的任何给定运动，厚翼型和薄翼型之间的力差与厚度的平方成正比，尽管对于一般的三自由度情况，这种差异可能是正的或负的。在零厚度和小俯仰角的特殊情况下，恢复了Theodorsen对刚性薄翼型的附加质量升力；对于大的俯仰角，给出了适用于弦法线方向的 Theodorsen 表达式的精确推广。