A numerical scheme is developed by using the "tent" function to compute the hull surface area and then the ship frictional resistance in a quadratic form in terms of ship offsets. Combining with the wave resistance, a total ship resistance formula is derived in a standard quadratic form. With a set of linear-inequality constraints, the optimal solution of ship offsets for minimum total resistance can be obtained by applying a quadratic programming method to the problem. Computations have been carried out for three conditions which have exactly the same constraints as those required to obtain the optimal forms for minimum wave resistance shown in an earlier work .3 The optimal forms found for minimum total resistance also have either bow or midship bulbs. The new optimal bulbs have a relatively small size, higher vertical slope to the baseline, and less curvature at the tip of the bulb.
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September 01 1984
Optimal Ship Forms for Minimum Total Resistance
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Hsiung, Chi-Chao, and Dong Shenyan. "Optimal Ship Forms for Minimum Total Resistance." J Ship Res 28 (1984): 163–172. doi: https://doi.org/10.5957/jsr.19188.8.131.52
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