where is a degenerated form of the Kochin function. We also have:
θ is the angle between Ox and the direction of propagation of a given wave component and Ko is the longitudinal wave number. The wave elevation ηff(x,y) can also be written as a function of u, F(u) and G(u):
The functions F(u) and G(u) are the coefficients of the far field wave amplitude spectrum which, when integrated, yield the wave resistance:
These coefficients are obtained by a Fourier transform of the wave height measurements along a longitudinal cut which is required to extend to infinity downstream. In practice, the signal is truncated before the reflected waves are present in the signal (figure 1) and the coefficients F(u) and G(u) would tend to 0 for small values of u. The missing part of the signal is treated by introducing a weighted Fourier transform with an analytical asymptotic expression for ηff(x,yc) valid when u → 0:
However, the coefficients c1, c2, and c3 can only be determined based on a regression on the signal before truncation. Hence, the amplitude coefficients of the transverse waves (θ<35°16') are to a great extent determined by the truncation correction. Since, for moderate Froude numbers, the larger part of the wave resistance is generated by transverse waves, the point where the signal is cut, and the accuracy of the correction, play a large part in the accuracy of the computed wave resistance. For higher speed models the contribution of transverse waves to the resistance diminishes as shown in figure 2.
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Accuracy of Wave Pattern Analysis Methods in Towing Tanks ."
Twenty-First Symposium on Naval Hydrodynamics . Washington, DC: The National Academies Press,
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