Use of Lagrangian Coordinates for Ship Wave Resistance (First- and Second-Order Thin-Ship Theory)
CALIFORNIA UNIV BERKELEY BERKELEY United States
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The wave motion generated by the steady motion of a ship is formulated exactly in Lagrangian coordinates. An approximation scheme is then developed based upon a method of iteration. The first iteration can be chosen so as to yield the Michell thin-ship theory. The second iteration produces more complicated formulas. However, if the smallness of draftlength is taken into account, the formula for the resistance simplifies to one similar to Michells, but with the integral taken over a modified region and with a modified hull function, plus a line integral over the profile which represents a distribution of dipoles with strength proportional to the waterline slopes.