Parametric Hull Design with Rational Bézier Curves and Estimation of Performances

Tommaso Ingrassia,Davide Tumino,Vincenzo Nigrelli,Antonio Saporito,Antonio Mancuso

doi:10.3390/jmse9040360

Abstract

In this paper, a tool able to support the sailing yacht designer during the early stage of the design process has been developed. Cubic Rational Bézier curves have been selected to describe the main curves defining the hull of a sailing yacht. The adopted approach is based upon the definition of a set of parameters, say the length of waterline, the beam of the waterline, canoe body draft and some dimensionless coefficients according to the traditional way of the yacht designer. Some geometrical constraints imposed on the curves (e.g., continuity, endpoint angles, curvature) have been conceived aimed to avoid unreasonable shapes. These curves can be imported into any commercial Computer Aided Design (CAD) software and used as a frame to fit with a surface. The resistance of the hull can be calculated and plotted in order to have a real time estimation of the performances. The algorithm and the related Graphical User Interface (GUI) have been written in Visual Basic for Excel. To test the usability and the precision of the tool, two existing sailboats with different characteristics have been successfully replicated and a new design, taking advantages of both the hulls, has been developed. The new design shows good performances in terms of resistance values in a wide range of Froude numbers with respect to the original hulls.

Highlights

In the work of an engineer, the design is often the central and more important part of the entire process
An intensive effort in this sense, nowadays is not possible to describe the hull with one equation because the geometry of a hull depends on several parameters and most of them are related one each other [5]
Other authors were more focused on the optimization phase as in [10] where a novel simultaneous engineering design approach has been proposed or in [2] where an interactive design approach for hull forms optimization is developed

Summary

Introduction

In the work of an engineer, the design is often the central and more important part of the entire process. One of the most popular methods used to define a VPP is presented in [11] and an updated version in [12] Both are based on the experimental campaign conducted at the Delft Ship Hydromechanics Laboratory of the Delft University of Technology; in these formulations the resistance of the hull is linked to its coefficients and parameters such as the prismatic coefficient, the length of the waterline, the beam of the waterline, the displacement and so on. In [11] the allowable range in terms of Froude number to estimate the value of the resistance of a sailboat is between 0.10 and 0.60; while in the updated version [12] the Froude number ranges between 0.15 and 0.75 Another popular approach is presented in [13], the focus of the authors in this study is related to the evaluation of the resistance for planing hulls in smooth and rough water.

Rational Bézier Curves

Estimation of Resistance for a Sailboat

Design Approach

Design of a New Sailboat

Findings

Conclusions