This report is concerned with the theoretical wave resistance of an air-cushion vehicle (ACV) traveling over water of uniform finite or infinite depth, in steady or unsteady motion Referring first to steady motion, it is shown that the unrealistic oscillations in the wave resistance curve at low Froude numbers found by previous workers can be eliminated by using a smoothed out pressure distribution rather than one with sharp edges studied exclusively in the past.The main result of unsteady motion calculations is that the peak wave resistance in shallow water, ever in moderately accelerated motion, is appreciably less than the corresponding steadystate value. In fact, cases have been found where an ACV starting from rest under the action of a constant thrust would seem to be unable to cross the critical depth Froude number on the basis of quasi-steady estimates of wave resistance, while the more elaborate unsteady calculations show that it has sufficient power to reach its final supercritical cruising speed. An interesting feature of unsteady motion is that besides wave resistance there is another mechanism transferring energy to the free surface which is here called the dynamic sustention power. Contrary to intuition, the wave resistance in unsteady motion over finite depth sometimes becomes negative at supercritical Froude numbers before finally approaching zero at infinite speed.ii ACKNOWLEDGMENTS

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This paper covers an extension of the study of Doctors et al. (J Ship Res 52(4):263-273, 2008) on oscillations in wave resistance during the constant-velocity phase of a towing-tank resistance test on a ship model to the case of relatively shallow water. We demonstrate here that the unsteady effects are very prominent and that it is essentially impossible to achieve a steady-state resistance curve in a towing tank of typical proportions for a water-depth-tomodel-length ratio of 0.25. This statement is particularly true in the speed region near a depth Froude number of unity. However, on the positive side, we show here that an application of unsteady linearized wave-resistance theory provides an excellent prediction of the measured total resistance, when one accounts for the form factor in the usual manner. Finally, a simple application of the results to the planning and analysis of towing-tank tests is presented

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The wave resistance of a two-dimensional pressure distribution which moves steadily over water of finite depth is computed with the aid of four approximate methods: (i) consistent small-amplitude perturbation expansion up to third order; (ii) continuous mapping by Guilloton's displacements; (iii) small-Froude-number Baba & Takekuma's approximation; and (iv) Ursell's theory of wave propagation as applied by Inui & Kajitani (1977). The results are compared, for three fixed Froude numbers, with the numerical computations of von Kerczek & Salvesen for a given smooth pressure patch. Nonlinear effects are quite large and it is found that (i) yields accurate results, that (ii) acts in the right direction, but quantitatively is not entirely satisfactory, that (iii) yields poor results and (iv) is quite accurate. The wave resistance is subsequently computed by (i)-(iv) for a broad range of Froude numbers. The perturbation theory is shown to break down at low Froude numbers for a blunter pressure profile. The Inui-Kajitani method is shown to be equivalent to a continuous mapping with a horizontal displacement roughly twice Guilloton's. The free-surface nonlinear effect results in an apparent shift of the first-order resistance curve, i.e. in a systematic change of the effective Froude number.