Optimal Ship Forms for Minimum Wave Resistance

Abstract

By introducing a set of "tent" functions to approximate the ship hull function, the Michell integral for wave resistance is reduced to a standard quadratic form in terms of ship offsets. With linear-inequality constraints of the type 0 ≤ H(x, z) ≤ B;C ≤ Hx(x,z) ≤ D(where H(x,z) is the hull function and B, C, D are constants), we are able to find various optimal ship forms of minimum wave resistance by applying quadratic programming techniques to the problem. Three optimal forms have been chosen among a number of computed results for tests in the ship-model towing tank. All three models have afterbodies identical with that of Series 60, Block 60, a standard merchant ship hull of good quality. Although the experimentally determined residuary resistance is in no better agreement with the theoretically predicted results than is usual in such comparisons, the order of "goodness" of the hull-forms as predicted and as measured was the same for Fn ≥ 0.36 and also for 0.20 ≤ Fn ≤ 0.26.

Continuity with respect to the speed for optimal ship forms based on Michell's formula

“…We think that this "sinking" phenomenon can be related to the midship bulbs obtained by some authors such as Hsiung [30,31] and Gotman [24]. They used a similar model based on Michell's wave resistance in the case of a fixed domain.…”

“…This "sinking" process can be related to the non-existence of a minimizer in the case where no bounding box is added to the formulation of the problem. It gives a new interpretation to the midship bulbs obtained by some authors in the case of a fixed domain [24,30,31].…”

“…) in order to compare the infimum of J 0 over the set (30) with the infimum of J 0 over the set (27). The assumption that the x-axis does not belong to R × R plays an essential role here.…”

“…The numerical simulations in [18,31,35] showed that the famous bulbous bow [20,26] can be very efficient in minimizing the total resistance, for some values of the parameters. In some cases, a midship bulb was also found to be interesting [15,23,30,31].…”

Thin or bulky: Optimal aspect ratios for ship hulls

“…Quite surprisingly some of them only consider wave drag in the optimisation setup (see e.g. [15][16][17]). Others consider both the skin drag and the wave drag [14,18,19].…”