Starting from the assumption that certain time and length scales for the vessel and its wave pattern are short compared with the time and length scales of the wave motion, the theory models the vessel as a point mass constrained to move on a surface governed by the hydrodynamic equations of wave motion. Normal and tangential equations of motion are derived, and their solutions investigated, for the general case of an arbitrary two-dimensional wave motion, then specialized to periodic progressive waves. The relevant resistance characteristics of the vessel are identified, and a new type of towing-test series using a single model ballasted to several different displacements is proposed to predict surfing performance. Numerical solutions are presented for the case of sinusoidal progressive waves, using an assumed resistance function and coefficients representing a "Cal-40" class sailing yacht.

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