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High speed theory for the planing of a flat plate at high Froude number

机译：高速理论在高Froude数下对平板进行刨削

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摘要

A flat plate is planing at a very high speed U in which the angle of attack varies with speed. A harmonic function K is introduced. The harmonic function is the Green function only in the limiting case when Froude number goes to infinity. The Green's theorem together with K yields the solution of the first order potential. Then we obtain the angle of attack as α～(W/(ρL_WB))~(1/2) 1/U, where L_W, B, W are the wetted length, breadth and weight of the plate. The hydrodynamic pressure is zero at the leading edge and increases toward the trailing edge where the pressure is infinitely large due to a logarithmic singularity. The lift L is a monotone function of Froude number and approaches W as Froude number goes to infinity whereas the drag D decreases paradoxically to zero in the limiting case.
机译：平板以非常高的速度U滑行，其中迎角随速度变化。引入谐波函数K。仅在弗劳德数变为无穷大的极限情况下，谐波函数才是绿色函数。格林定理与K一起得出一阶电势的解。然后我们得到的迎角为α〜（W /（ρL_WB））〜（1/2）1 / U，其中L_W，B，W是板的湿润长度，宽度和重量。流体动力学压力在前缘处为零，并向后缘增加，在后缘处由于对数奇异性，压力无限大。升程L是Froude数的单调函数，并且随着Froude数变为无穷大而接近W，而阻力D在极限情况下自相矛盾地减小为零。

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