Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Study on principal factors of the hull form
in relation to the propulsive performance
Takehiro Ikeda and Munehiko Minoura
Department of Naval Architecture and Ocean Engineering, Osaka University, Suita, JapanABSTRACT

estimate the resistance characteristics of a high-speed planing hull in theinitial planning, using the required speciﬁcations such as speed and displacement as inputs. Kanai et al. (2010) proposed an estimation methodthat can take into account more detailed hull characteristics by handlingfeatures of the bow and stern shape as hull form parameters in addition
to hull principal dimensions.

A method to express the hull form by applying the Fourier series expansion to the cross section of the hull is proposed. By this method, the hullshape can be expressed with accuracy while reducing the order of parameters. In addition, the correlation between each coeﬃcient of Fourier
series expansion and propulsive performance is discussed considering
the hull form. This method more quantitatively gives us the tendency ofcorrelation between viscous resistance / self-propulsive factors and theshape of the stern frame line. Furthermore, an estimation method of the
propulsive performance utilizing the neural network constructed with thetraining data including a set of the coeﬃcient of Fourier series expansion
and corresponding propulsive performance is presented.

Once the hull principal dimensions are determined, the development of
the hull form, which involves the modiﬁcation of the shape, moves to thenext stage. In this stage, not only hull principal dimensions but also thehull shape itself is designed. Traditionally, hull forms have been represented by lines, and therefore, a lot of technical knowledge has been accumulated in relation to lines. When focusing on the viscous resistanceand the self-propulsive factors, the stern shape, especially the tendencyof the stern frame line, has a dominant inﬂuence on both of them. Therefore the optimization in the frame line of the stern part is often carriedout in the process of hull form development. However, the frame line
is a collection of many oﬀset data, and if we try to optimize the frameline directly as these oﬀset data, the number of parameters will be toolarge, which is not easy to handle mainly due to the limitation of computational power. Arai et al. (1999) proposed a mathematical expression
method using the Fourier descriptor method to represent the frame line.
In the above method, the frame line is regarded as a curve in the complex
plane, and the Fourier series expansion is performed simultaneously inthe width and depth directions. However, this method has a problem thatthe accuracy of the approximation decreases near the draft waterline andthe bottom of the ship.

KEY WORDS: hull form expression; hull design; Fourier series expansion; propulsive performance; neural network.

INTRODUCTION
It is essential to ﬁnd the relationship between the hull body shape and the
propulsive performance in the development of the hull form. In most of
the research on hull form optimization using mathematical expressions,the design parameters are deﬁned as the variation of the change in itsshape. In other words, the original hull form from which the optimization starts ﬁrst exists. In the design of hull form, how to select suchoriginal hull form can be an important factor for achieving the target performance. Usually, the hull form is expressed with oﬀset tables or lines.
If the oﬀset which consists of a large number of point data is employed
as the means of expressing the hull form, the number of design parameters to be optimized becomes enormous so that it is diﬃcult to handle.
Therefore, in order to construct a hull form optimization method with design parameters including the selection of the original hull form, whichhas been mainly left to the experience and knowledge of the designer, amethod to directly express the hull form numerically in this paper.

In this paper, the width and draft directions are treated separately, andthe Fourier series expansion method is applied using the girth length as aparameter variable. The ﬁnal schematic of the design system is shown inFig. 1. In order to estimate the performance of a ship, it is necessary toconstruct an estimator (neural network) by training, and it is important torepresent the hull shape as an input eﬀectively. However, it is importantto represent the hull shape as an input eﬀectively, i.e., the parameterization of the shape is important, and the mathematical expression methodof the hull shape in this report corresponds to it.
The structure of this paper is as follows. First, a method of mathematicalrepresentation of lins is introduced. Second, the relationship between theIn the early stage of hull development, only a part of the hull principal
dimensions are known, and the designer needs to ﬁnd the optimal values
for the remaining unknown hull principal dimensions. There have been
many studies on the application of neural networks to this optimization
problem. For example, Matsumura et al. (2004) proposed a system to3762