The Analysis of Ship-Side Wave Profiles and Its Application to Hull Form Design

Abstract

In order that the wave-making theory should be applied successfully to the hull form design, it is of primary importance that the theory can reproduce the actual wave-making phenomena of ships as exactly as possible.
Here an attempt is made to obtain the effective wave-making source of a ship from the measurement of hull-side wave profiles rather than from that of the free wave patterns in the rear of a ship.
The integral equation of the source distribution function is simplified and solved numerically under the specific limitation, (a) rectangular, vertical central source distribution plane, and (b) draughtwise uniform.
Two Inuid models M 20 (B/L=0.0746) and M 21 (B/L=0.1184), whose hull-generating sources are optimized to give the minimum wave resistance at K₀L=12 (Fn=0.2887), are wave-analyzed.
The obtained source distribution shows a clear discrepancy from the hull-generating source.
Then the correction function α (ξ) is introduced in a form of the ratio of wave-analyzed source to hull-generating source. The general tendency of the correction function α (ξ) of the wider model M 21 is found as quite similar to the previously proposed μ-correction.
By adopting α (ξ), the calculation shows remarkable agreement with experiment in (a) wave profiles, (b) wave patterns, and (c) wave-making resistance.
As an example of practical application, an asymmetry Inuid model M 21-M is designed so as to minimize the wave resistance under the same restraint conditions as M 21 except that α (ξ) of M 21 is taken into account in the design procedure of M 21-M. From the tank test of M 21-M, it is clarified that almost 40 percent of the wave resistance is reduced, which may suggests that such design procedure is significant.
To investigate the theoretical basis of the correction function α (ξ), the second order contributions are calculated approximately with respect to the two boundary conditions, namely (a) hull-surface condition, and (b) free-surface condition. It is found, however, that the second order terms do not give sufficiently the theoretical basis for the correction function α (ξ), which may suggests the importance of the hull's sheltering effect.