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Marcus Bole University of Strathclyde Naval Architecture and Small Craft Design
Marcus Bole
Parametric Generation of Yacht Hulls
This project took one year to complete to the current stage. During this time I have received help from and would like to give thanks to; Dr. B. S. Lee, my project advisor who initially posed the subject for the project and passed comment on the project and report during its progress. I would also like to thank Mr. T. B. Davis, who allowed me access to the Internet while working from home, so that current projects in industry could be evaluated. Finally, I would like to thank Mr. A. W. York as through his interest in unorthodox and extreme yacht hull forms tested the hull generation procedure.
® ® ®
University of Strathclyde, 1997
Marcus Bole
Parametric Generation of Yacht Hulls
Acknowledgements Synopsis
1 Introduction 2 Project Aims
3 Critical Review 4 B-Spline Functions 5 Yacht Design 6 Choice of Parameters
7 Method 1 8 Method 2 9 Method 3 10 Further Development
11 Implementation of the method 12 Applications of Hull Generation Procedures 13 Discussion 14 Conclusion
15 References 16 Appendices Appendix 1- TheYD-40 Appendix 2 - Calculation of Area and Centroids of B-spline Functions Appendix 2 - Resistance Optimisation Procedure Appendix 3 - A Desktop Interface - The YachtLINES Project
University of Strathclyde, 1997
Marcus Bole Parametric Generation of Yacht Hulls SUMMARY There are currently no procedures for parametrically generating yacht hull forms. 1997 iii . This project investigates a parametric hull generation technique for yacht hull forms and defines the hull shape with B-spline functions. The development of the yacht design is examined. by looking at the trends in the development of yacht design over the last century. BSplines functions provide the primary technique in most Computer Aided Hull Design packages for modelling the hull shape and they have not been used in a numerical hull generation procedure. and illustrated with the development of a resistance optimisation process and a graphical interface. Finally applications of the hull generation procedure are discussed. Then. the project looks at the techniques that have been developed in the past to generate hull forms and comments on the applicability of these techniques to yacht hulls and B-Spline functions. to review how the process has changed and how numerical factors have become more import. creating a niche for a parametric hull generation procedure. A basic parametric yacht hull generation method is developed which provides the yacht designer with ability to quickly develop a yacht which can be analysed by other processes. Initially. ® ® ® University of Strathclyde. the important parameters involved in the design of yacht hulls are found.
the process of manually fairing the shape has not changed. Despite the development of these techniques. Today the computer is a prerequisite for the naval architect. to perform. With the power of the computer. This allowed the designer to model ships accurately in three dimensions. without the need of the skills required to make a half model and removing the two dimensional failings of the lines plan. performed by the naval architect. now found prominence as the reasonable amount of computation required for these methods was easily performed by the computer. some naval architects thought about the process of design. however. Design remained the same until the computer became a practical possibility. once the ship attained commercial and military viability it was necessary to quantify the design in some manner. A few methods have been developed that generate ships hull from numerical parameters. however. would it not be possible to input the goals and the output to be a hull? Techniques were developed that created ships hulls. provided an efficient method of accurately representing the ship. for centuries. However. It the design and performance of calculations which. But. The Lines Plan and the Half Model. They could see the large amounts of time required for modifying and fairing the shapes of vessels so that predefined goals. Once generation techniques for designing hulls became possible. 1997 1 . Mathematical curve and surface generation techniques developed earlier this century. University of Strathclyde. allowing measurements to be taken for the full size ship and calculations possible. if not days. allowing it to be reproduced in the future. This project investigates the possibility in using a similar system in yacht design. before. the main method of acquiring a fair hull is still by manual modification. For centuries Naval Architecture was an art. the medium in which the hull is designed has changed.Marcus Bole Parametric Generation of Yacht Hulls 1 INTRODUCTION Since the computer became widely available. In naval architecture it can be used to design the shape of the hull. factors of design and coefficient could be met. could have taken hours. it has been used for a variety of engineering purposes. which allowed hulls to be rapidly created and more complex design properties such as resistance and motions could be analysed in a shorter time.
Due to this difficulty there are hardly any hull generating methods which use B-spline functions to define the shape of the hull. The B-spline is a curve generating technique which is used in most hull design packages. so that shapes defined by this process can be transferred to many different applications. Since high profile events such as the America's Cup became big business and where national pride is at stake. The VPP models the interaction of the sails and the hull and computes the effect. It is based on research performed on commonly used sail plans and hull configurations. A velocity prediction program is one of the major parts of the much promoted International Measurement System (IMS) rating system. As B-splines are standard University of Strathclyde. how the yacht will perform. without the need for expensive tank testing. but in yachts. 1997 2 . The result was a very successful vessel with the famous winged keel. One of the most useful tools that came out of this research was the Velocity Prediction Program (VPP). such as forming a curve to bound a certain area. it is more difficult to use B-spline functions to perform any normal numerical task. This technique is very powerful as a wide range of different effects can be modelled. The most noticeable turning point was the event in 1983. A good hull generation system would take account of the processes involved in the VPP and design a hull based on more important performance parameters rather than the basic geometric parameters. a value that can be applied to a yacht's performance in a race. excessively large amounts of money have been poured into the design of these small vessels. Industrial standards have be developed around B-spline functions. allowing it to compete on equal terms with other yachts racing. a greater variety of parameters and goals are required to complete a successful design. Unfortunately. Therefore. Yacht design today owes much to the work that was performed for this one race. B-spline functions do not flow through a set of known points or have an easily modified function.Marcus Bole Parametric Generation of Yacht Hulls The yacht design process is similar to that of ships. A lot of money was spent on tank testing and computer modelling various prospective hulls for the Australian challenger. These programs allow the yacht designer to see. which perform tasks such as hydrostatic calculations or numerically controlled machine cutting. This system calculates the performance of a yacht and finds a handicap.
the yacht hull does not have any straight sections. as the hydrodynamics of the hull are important and yachts do not carry cargo. this is mainly due to economics. as most ships essentially have the same shape. To select of a set of parameters to model a yacht hull is more difficult than for a ship. The hull of the general merchant vessel has many straight regions. ® ® ® University of Strathclyde. 1997 3 . there are also more beneficial uses for this type of procedure. However. A hull generating method developed for the general merchant vessel does not have to be as flexible as one developed for the yacht hull. A set of parameters is required for a parametric hull generation method.Marcus Bole Parametric Generation of Yacht Hulls functions throughout most hull design programs. Alternatively. the yacht is almost exclusively made up of curves and a choice has to be made to how much of the shape is controlled by parameters and how much is controlled by the hull generation method. these parameters hold values of certain properties which the generated hull must have. as a hull with straight sections can be constructed easier and can contain a greater cargo capacity. This investigation looks into some of the uses of the hull generation procedures to show that they can play a large part in the efficient design of marine vessels. A method to numerically generate yacht hulls would reduce design time. The choice of which parameters to use depends on the type of hull shape to be modelled. a hull created in a hull generating procedure using B-splines can be easily transferred to other CAD applications. allowing the hull to be modified further or to allow other design features to be added.
with a view to investigate if there is any method which would be applicable to yacht design.Marcus Bole Parametric Generation of Yacht Hulls 2 PROJECT OBJECTIVES • To perform a critical review of current generation techniques used to create hulls. to be used as a useful tool. ® ® ® University of Strathclyde. • To look at the applications of a parametric yacht hull generation process to justify how these procedures can be used to speed up design and allow other aspects of a yacht to be review in a shorter period. 1997 4 . • To identify the factors and parameters that are important in the design of a yacht and can be used in a parametric hull generation process. • To research what requirements and mechanics a yacht generation method would need to have. • To identify and recommend areas of further study.
But with the advent of powerful microcomputers. when computer time and power was at a premium. Kyan [2]. Jorde [3] and Vacanti [4]. it was thought to include all the major works on the subject directly relevant to the current project. in the time given. less research has be undertaken in the area of parametric hull generation methods. The publications examined here include Reed and Nowacki [1]. The result of this is that software developers have tended to depend on user interaction to create hulls. 1997 5 . software could be developed which allowed more people access to design applications for a cheaper price. but. This could be one of the main reasons that over the last decade. This is by no means and exhaustive review of the subject.Marcus Bole Parametric Generation of Yacht Hulls 3 CRITICAL REVIEW Most of the research into parametric hull generation was performed in the 1970's. There are quite a few methods around for generating hulls. University of Strathclyde.
shape. 1997 6 . centroids and local effects Waterline Curve inputs affecting size. (b) To adapt the lines creation process to the medium of interactive design by computer graphics terminal. Each of the influence function is responsible for representing one of the constraints without affecting any of the others. A break down of the parameters is as follows. Using this technique simplifies calculation of hydrostatic and hydrodynamic properties for the hull. shape. The study itself is dedicated to looking at two areas: (a) The introduction of Conformal Mapping functions to represent the underwater sections.Marcus Bole Parametric Generation of Yacht Hulls 3. draft and section area. By including more parameters in the mapping technique more features of the section shape can be controlled. These techniques are well known. to generate a section shape which can be used to perform many powerful calculations governing ship motions. No of Parameters 6 17 11 What Parameters Affect General Inputs affecting global size and shape Section Area Curve inputs affecting size.1 INTERACTIVE CREATION OF FAIR SHIP LINES Reed and Nowacki [1] is an extension of previous work from many sources mentioned in the paper. These polynomials are computed once only and do not need to be resolved if the design constraints are changed. The conformal University of Strathclyde. It uses only three free parameters. beam. There are many parametric inputs for this method. Underwater sections are created by conformal mapping techniques. centroids and local effects. The basic curve generation process is based on using polynomial influence functions. This is one of the standard tools found in this type of method. This process creates a polynomial curve by the superposition of other polynomial functions called influence functions. sheer line is assumed to be parabolic. Keel inputs by a certain number of polynomial segments. The Lewis Transformation is one of the most well known of these techniques. Deck inputs by offsets and slope.
transom stern. Tuck and von Kerezek [11] demonstrated. By using a light pen and teletype. 1997 7 . an undesirable feature in bow and stern sections. which is based on a quadrant of a circle of unit radius between − π / 2 ≤ θ ≤ 0 . hull forms could also be created with the method. The advantage of this system. the mapping process. Polynomials can be fitted to the section so that the upper sections can be formed. is that the influence functions only have to be solved once.Marcus Bole Parametric Generation of Yacht Hulls mapping procedure used in this particular method extends the Lewis Transform so that it also includes x-moment and y-moment coefficients. This feature must have been one of the most helpful aspects of the method for the computer system available at the time. This method was developed in 1974 when computer technology was still in its infancy. It allows the quick generation of lines with the added advantage that all the information about ship motions is included in the process. The input parameters are varied and include many which describe local effects. To overcome this problem. The solution of the influence functions is achieved by using a Newton-Raphson least squares technique. Fine high speed. But the slope at the waterline created by the conformal mapping is infinite. user interaction was possible on a graphics terminal. The method was developed to work on the University of Michigan's IBM 360 67 computer. as mentioned. The major drawback of using conformal mapping techniques is that the process only models the underwater section of the hull. It is not mentioned how the accuracy of the motion characteristics is effected by sections which do not use the full quadrants in the mapping process. which is one of the methods which has the fastest convergence to a solution.7. This method of creating hull forms seems fairly useful especially from the ship design point of view. close fits could be made of the Series 60 hull form. is changed. University of Strathclyde. The influence functions provide a very useful method for modelling the constraints. The range of shapes that can be created depends on the number of coefficients used in the conformal mapping function. so that the mapping process is carried out to a different value of θ producing a variable slope at the waterline. by using seven coefficients in the mapping and a Block coefficient of 0.
is important in a yacht as the flow of water must be considered in heeled conditions as well. this is not dissimilar to the modern yacht. It is not thought that this method would breakdown if the parallel middle body was removed to model a yacht. given that the influence functions are defined over the whole length of the hull. The appeal of conformal mapping is that the sections produced are circular in nature. This region of the hull. and would have been investigated had not the study been restricted to B-Spline functions only. around the waterline. This means that a fairly detailed study must be made of the profile of the vessel before using this process. 1997 8 . University of Strathclyde.Marcus Bole Parametric Generation of Yacht Hulls It is necessary to input offsets for deck and offsets are also required for the calculation of the keel polynomial. It is not mentioned how underwater part of a section is blended into the upper part of a section. Conformal mapping techniques seem to be good idea. Parallel middle body is one of the parameters required in this method.
Marcus Bole Parametric Generation of Yacht Hulls 3. Parameters are used as an input. Super elliptic curves are also used to define the shape of the bow and stern profiles. 1997 9 . the correct Block coefficient and longitudinal centre of buoyancy. The hull form for this method has been taken from published sources of hull forms. to generate the shape of the hull. but with different varying vertical shapes. As this procedure is based on varying a similar shape it requires a basic hull form to start with and this is used to base the initial functions for volume and moments of volume. for generating ships hulls is similar to most other methods. • Block Coefficient and Longitudinal Centre of Buoyancy • Sectional Area Curve • Midship Section Coefficient • Bow Profile • Stern Profile • Aft Control Section • Shape Coefficient (A coefficient describing how similar the section is to 'U' or 'V' shapes) • Functions of Volume and Volume Moments The main intention of this procedure is to generate hull forms with the same key design parameters. University of Strathclyde. Beam. The sections are defined in super elliptic equations and can be varied so that the desired Shape Coefficient is obtained. The study is primarily concerned with obtaining for a hull form. Draught and Depth.2 DIRECT GENERATION OF FAIR SHIP HULL SURFACE FROM DESIGN PARAMETERS The method used by Kyan [2]. The series 60 hull form is one which was followed closely in this study.Length. The parameters are: • Primary Dimensions .
The modification process uses many features which are present in a ship hull and these features are not normally found in a yacht hull. The other draws on the use of the parent hull to change the value of the Block coefficient.Marcus Bole Parametric Generation of Yacht Hulls Surface equations based on power series are used to define the surface shape of the hull. The method could probably be implemented easily today in modern spreadsheet computer packages. Today as computer aided design and analysis is becoming more common. The method uses two approaches for varying Block coefficient. the basis hulls are or less importance. In this way resistance and seakeeping behaviour could be known in detail about a certain hull. A naval architect could draw on this information to produce a similar hull which would perform well. 1997 10 . But higher order moment functions are required as part of the process. This method has been specifically developed for the normal merchant ship shape. The higher order functions become increasingly difficult to obtain due to the complexity of ship hull shapes. Given that this method was written at a time when computer systems were not as common as they are today. This method is dependent on having a parent hull form to base initial calculations upon and the for the creation of initial functions. the method draws well on standard functions and equations used to modify hull forms from the basis shape. For example. As computers have only be a fairly recent introduction to the shipping industry as a whole at the time of the work. for ships to be designed around. features such as "Flat of Side" are used to change the shape of the hull through the use of the moment functions of volume. One approach uses the standard system of changing the section area curve by modifying the length of the parallel middle body. as hulls can be developed and analysed much quicker than ever before on computer based systems. The method draws on the large amount of information that has been created over the years on certain hull forms. Volumes and moments of volumes can be calculated from these equations. Recurrence relationships are used to find the higher order functions necessary for the hull modification process. University of Strathclyde. it was necessary to research for hull forms which could be used as a basis.
notably those involved in the America's Cup. be a suitable approach to take for yacht hulls. For this method to be useful though. keeping costs down. This is where this method would come in. the shapes of yachts are varied and the shapes can be based on the current racing trend or a pretty look. Many of the large companies which build yachts for mass production have been previously using development similar to the shipbuilding industry. Recently. 1997 11 . Yacht naval architects generally design new vessels based on the information and the experience from a previous designs successes and/or failures. A ship hull has be developed for reasons different to those of a yacht. As will be discussed later. the information from these projects is generally kept confidential and it takes a long time for this research material to enter the public domain. Although there has been much of research performed on certain hulls. to come up with a hull which performs well. with the theory and testing facilities available at the time. to develop hulls quickly. based on the same basis hull. these companies have started to look at their methods of hull development.a flexibility which this method does not pretend to be capable of. Owners requiring a vessel normally have enough money to spend on a yacht for the designer to use care and attention to detail. A completely new hull design is going to cost a ship owner a lot more money than one that has been developed from a tried and tested family of hulls. as yacht design has become technical and scientific. The direction followed by this method could be used successfully over a short period of time to develop a fleet yachts of different sizes.Marcus Bole Parametric Generation of Yacht Hulls Yacht design has not benefited from the use of standard hulls in the past. it would have to be able to adapt itself to new designs . University of Strathclyde. Such companies have enjoyed good success through the early stages of the growth of this leisure industry. Yacht design would not benefit well from this type of development. The economics is one of the most important factors in ship design. therefore. New companies have started to produce yachts whose performance greatly exceed the old designs and the pioneering companies in this field have had to change their design strategy. It would not. the forefront of yacht design is based around testing new designs and discovering new shapes and techniques.
creation of the sections. Fortunately. waterline. It has been constructed so that it can be programmed into a spreadsheet. The method is fairly simple in that the curves used are cubic polynomials of the form: Y = A + Bx + Cx 2 + Dx 3 This basic function is used to generate every curve used in the process. The parameters for each section are then given to a function which creates the sections. The keel line is formed by inputting the offsets of the keel at various sections. it goes to proving that large computing power is not necessarily required to use a hull generating technique. 1997 12 . p. The section area curve is created using various lengths. q is a constant that controls the order of the function. k is a constant dependent on the rise of floor. i. This recent method by Jorde [3].3 MATHEMATICS OF A BODY PLAN. and an above-water part. The deck line and a knuckle line are created by specifying the distance of these lines above the waterline.0. the section area coefficient is formed for each section. Given that the method has been developed for a standard spreadsheet. The lower part of the sectional shape is created with a polynomial function with constants k. The example given uses Microsoft Excel 5. an underwater part. By setting the slope of these two curves at the bow and the stern and by modifying the lengths. Now with all the longitudinal geometric lines formed. deck line.e. has been developed to demonstrate how body plans should depend on the main design parameters instead of using a parent hull or artificial input. forming of the longitudinal curves. Section area curve is modelled using a cubic curve at the bow and at the stern of the vessel and joining the two curves by a straight line dependent on the parallel middle body. the shape of the section area curve can be changed. a copy of the original calculation as well as the paper was made available to the author. The waterline is created in a similar fashion. The sections are again created in two parts:. while p is a scalar of one University of Strathclyde.Marcus Bole Parametric Generation of Yacht Hulls 3. q. including length of parallel middle body. The method can be looked at in three parts: creation of section area.
The method that is obtained when the formulation process is followed is dependent on the type of hull to be generated. p and q are found through integration of the sectional area. for instance. Also a knuckle line is found below the deck line. There are many parameters which govern local effects and the keel line must be formed by supplying offsets. A method based on one type of hull cannot be used to create another type of hull. This method shows how a hull can be created by using fairly simple mathematical techniques. The spreadsheet is protected so that an University of Strathclyde. The major problem with a system based on using standard polynomial functions of explicit form is that. These functions take the parameters of draught and waterline beam. Above waterline sectional shape is created by attaching a third order polynomial with the same slope as found in the lower part at the waterline. the curve of section area coefficient. Once the sections have been created. although the mathematics involved appear to be simpler. It is thought that the idea behind this project is that a new method should be created for each different hull form. The spreadsheet example is fairly difficult to use as the input parameters are placed well apart around the spreadsheet. the addition of a knuckle line. How these curves are analysed is not mentioned and the p and q lines are not shown in the example spreadsheet. the range of hulls that can be created is smaller than when using parametric polynomials. which would suggest that if larger modifications were required many method would have to be developed. Rise of floor is controlled by having a global value of the slope and applying it to all the sections. This paper has tried more to demonstrate how easy it is to create a preliminary hull design based on mathematical formulation.Marcus Bole Parametric Generation of Yacht Hulls of the components. but the example method was somewhat restrictive in the degree of hull form variation. The spreadsheet example is given and it became clear that a good knowledge of the formulation of the method is required in order to make full use of it. It is fairly difficult to go into the spreadsheet without knowing what all of the parameters are. The method also demonstrates how easy it is to add other effects to the hull. This make the method less versatile than others. p and q are analysed. 1997 13 . This is a fairly appealing concept.
1997 14 . when developing a procedure which creates a function to fulfil a range of criteria. A good amount of preliminary work should be performed on the hull to make sure that it is good and fair. Additional information would be required on how to construct a method to ensure that the formed hull was fair. One of the problems found with explicit polynomial functions is that. Although there is still the problem of a second order discontinuity in the section shape at amidships.Marcus Bole Parametric Generation of Yacht Hulls investigation into the details of this method cannot be made. The paper only shows the basic theory involved in creating a method. To create a yacht with this method would be fairly easy. This is one feature of using parametric B-splines for the yacht project. This method is very effective. This is one of the reasons why the B-spline technique has been chosen for the current study. the curve produced by the function will be completely useless for any hull. where the two section area functions are joined. as they generally keep a good shape even when applied with many boundary conditions. is that the more boundary conditions that are applied to the function. Generally. but should only be used to create a preliminary hull. University of Strathclyde. the less fair the curve produced by the function becomes.
1 currently shows Length overall. so that the coefficients such as block and prismatic coefficient match your goals.4 PROLINES 6. Figure 3. but it seems to bridge the gap between a full parametric design method and the normal interactive B-spline surface design computer application. The application. powered vessel or a cargo ship.2 shows the surface produced by the process. 1997 15 . The hull creation dialogue box. Half Beam and Draft corresponding to the example yacht designed in Larsson and Eliasson [6]. Figure 3.1.Marcus Bole Parametric Generation of Yacht Hulls 3.1. This makes the design process quicker as all one has to do is modify the hull. does not use a true parametric generation process. The figure 3. The powered vessel has three chine variations. Prolines uses a basic generating technique to create the B-spline surface used for design.23 This commercial system [4]. which is of the correct size. University of Strathclyde. on the user selecting "New" displays figure 3. It can be seen that there are three basic types of vessel that can be created: sail.
2. The method that the program uses for designing hull is by having a basis hull and scaling it by the input parameters. The cargo ship in this example has a bulbous bow which would be very difficult to modify and retain a fair hull. However.1 The application produces a B-spline surface of quadratic order with five-by-five control points net. This limitation can be overcome if more longitudinal control vertices are added to the net. but this point was not raised by the authors. ® ® ® University of Strathclyde.Marcus Bole Parametric Generation of Yacht Hulls Figure 3. The initial hull produced by the options set in figure 3. it is really only useful for vessels which do not have hulls with special effects. 1997 16 . This procedure for creating a hull is fairly useful. Then modification is made to get the desired hull by manually moving the control vertices.
However. Alternative methods of curve generation. these techniques are unsuitable for ab initio design.Marcus Bole Parametric Generation of Yacht Hulls 4 B-SPLINE FUNCTIONS Defining a curve in space using standard mathematical functions such as explicit polynomials can be difficult when these curves are to be used for design purposes. However. Figure 4. Figure 4. suitable for ab initio design were developed. such as cars and shoes. design is a spiral process where many iterations may be used to design and evaluate the potential solutions. During the design of a vessel the shape of the ship may change many times. Explicit functions have a limited flexibility rendering them unsuitable for developing ships hull surfaces. This is true for ship design as well. An obvious relationship between the numbers and the shape of the curve produced by these techniques does not always exist. can be used do define the shape of curved objects. Design is a process of looking at an existing problem to obtain a solution. the invention of parametric piecewise functions such as B-Splines. such as Cubic splines.1. A B-spline curve is generated from a defining control polygon. Curve fitting techniques. 1997 17 . B-spline functions University of Strathclyde. Numerical specification of the direction and magnitude of tangents. In modern ship CAD applications the surface of the hull must be defined by some mathematical method. The B-spline basis was first suggested in 1946 by Scoenberg and practical recursive algorithm was developed independently by Cox (1971 and de Boor (1972). used in many of these curve fitting techniques do not provide the intuitive 'feel' required for ab initio design. A B-spline and control polygon. In many cases. has allowed rapid advance in using CAD for ships and other curved objects.1.
without the whole object changing. as it allows small regions of a object to be modified. B-spline functions allow objects and shapes to be shared between CAD applications. of almost any shape. as a relatively small amount of data can be used to store a complex shape. today. there are no techniques for integrating B-spline functions directly and so the current hull generation technique uses Simpson's rule for approximate integration. However. B-splines. would have advantages over techniques using other curve functions. A hull generation procedure. as a B-spline hull definition can be directly exported to other applications. using B-splines. have developed into powerful functions with associated buzzwords. However. Unfortunately. the major advantage that explicit functions over parametric functions such as B-spline functions. many more hull generation techniques may have been developed if this property had not been discovered. the shape of the Bspline curve is only changed over a small area local to the control vertex. 1997 18 . More technical details about B-spline functions can be found in Rogers and Adams [13]. is that explicit functions can easily integrated. ® ® ® University of Strathclyde. When a single vertex of the B-spline control polygon is modified. which is very useful in iterative design. This effect is extremely useful.Marcus Bole Parametric Generation of Yacht Hulls exhibit the property of local modification. NURB function surface is one feature which many modern CAD applications support and can be used to develop objects.
so that design trends and the reasons for the current shape of the yacht hull can be identified. The word 'yacht' is of Dutch origin and is a shortened form of the earlier jacht schip. The first yachts were not the light vessels found today. it is necessary to review the development of the yacht. University of Strathclyde. To understand why the sailing yacht can be seen in such diverse forms today it is necessary to look at the origin of the design of these small vessels. Yacht: Light vessel for racing or pleasure. The original yachts were powered vessels. commerce or pleasure. It was not until the end of the 19th century that the design of the sailing yacht came close to the form it is seen in today.1. A parametric hull generation procedure requires numerical parameters to define the shape of the yacht. The industrial revolution had created many affluent people who had money to spend on their leisure.Marcus Bole Parametric Generation of Yacht Hulls 5 THE DEVELOPMENT OF THE YACHT Figure 5. To make a choice as to which parameters to select. A DutchLatin dictionary published in 1599 described a jacht schip and a jacht (or joghte) as a swift light vessel of war. but the large luxury barges the Emperors of China entertained their guests upon. The yacht has been around for many centuries. 1997 19 . Since then the sailing yacht hull has developed through many shapes. used for special occasions or extra homes. PRB. Yachting was one popular pastime for the wealthy. The Open 60. This concept was developed over the years. mostly by the noble and the rich to be a small private vessel that could be used for pleasure.
A 'J' class racing yacht. resulted in uncomfortable sailing angles of up to 75º. The racing yachts used the fore and aft sailing rig and much testing was required to develop these rigs into efficient propulsion systems.science only played a small part in the design.2. There was the fairly wealthy owner who spent weekends and holidays on his reasonably small vessel of around 6 to 7 metres in length. people like heads of state and large business owners. Initial designs were based on supplying the most amount of sail possible. Working vessels were built on tradition and a "trial and error" basis . two types of yacht owners could be found. The working sailing vessels at this time were either the large square rigged ships or "fore and aft" rigged fishing boats.Marcus Bole Parametric Generation of Yacht Hulls At the start of this century. These vessels would probably have been designed by a naval architect with experience mostly of fishing vessels and their related construction techniques. University of Strathclyde. These vessels were around 30 to 40 metres in size with correspondingly large sail areas. The other yacht owner would be the extremely wealthy type. When the yacht was developed scientifically the initial design of the yachts changed. Examples of these vessels are the J-Class and Pre J-Class racing yachts. 1997 20 . This metamorphosis is demonstrated well in yachts that have raced in the America's Cup competitions. The naval architects who designed these vessels were just starting to appreciate the different factors involved in the design of large sailing vessels. This and the fact that yachts of the time had very large length to beam ratios. These vessels were almost always used for racing and required finances in large scale to fund good performance over a racing season. Figure 5.
reducing the wetted surface area. giving an area which could be changed without affecting the rating of the yacht. Although most of the designs were supposed to be secret. it was found that vessels performed better when wetted surface area was reduced. The sail area was reduced. Reducing keel size was one of the ways the surface area could be minimised and has given rise to the exceptionally small keels found on some racing yachts today. therefore. testing various designs. sometimes in what can be considered a nonsensical manner to leave the rating unchanged. The long deep keel was a feature found on all vessels. The job of the yacht designer is to design a vessel which can beat others while still complying with the rule. Sponsors found originally that by throwing more money into the design than the other competitors. Rating rules have also played a large part in the design of yachts. Research establishments were gladly funded by syndicates. However. As yacht design developed. and would design and test prospective competitors. This type of designing. University of Strathclyde. resulting in the designs found today. As the size of the keel reduced. The rule measured certain dimensions at various point along the vessel. 1997 21 . The weight of the original heavy wooden yachts could be reduced by using modern materials such as glass fibre reinforced plastics. in the case of IOR. It. Either by designing a better vessel on physical principles. The rules restrict the dimensions of a yacht so that it is able to compete on level terms with other yachts in a race.Marcus Bole Parametric Generation of Yacht Hulls The initial design of the hull of large racing yachts was similar to fishing vessels. did not necessarily consider the areas between the measured points. as less power was needed due to the lighter weight. Rating rules were originally designed to measure performance and seaworthiness. The major advances in design can be seen to come from the major racing events such as the America's Cup. the discoveries filtered out to the rest of yacht design. Much study was performed in the test tank and wind tunnel. or by modifying a yacht hull. This 'U' shape was found to have a major advantage as flat sections create a certain amount of hydrodynamic lift raising the vessel out of the water. the shape of the hull became less of a 'V' shape and more of a 'U' shape. The effect of rating rules is to restrict development. called "rule cheating". The now defunct IOR (International Offshore Rule) is one example where rule cheating was common. can be applied in to ways. their yachts would win races.
i. an author who sailed extensively in the South Pacific in his first vessel. a phenomenon where the waves break dangerously over the stern of the vessel. The Fastnet Race disaster in 1979 led to an examination which analyse why so many yachts were disabled or lost. 1997 22 . The vessel is gaff rigged with a "Swedish Pole Mast". The IMS (International Measurement System) rule. Colin Archer was a Norwegian naval architect of Scottish origin. Mr Tambs refused to reduce sail and the 14 meter vessel pitch-poled (a longitudinal capsize) in the middle of the Atlantic twice. They are called "Double Enders" as they have a sharp stern similar to the bow. Rule cheating could be used here as well by analysing the formulae used in the VPP. Sandefiord. These lifeboats were heavily constructed in wood to deal with the weather conditions common to the North Sea. the Colin Archer designed pilot vessel Teddy. It was found that the restrictions of the IOR rule produced inherently unsafe vessels. they generally behave well when sailed in bad conditions with a crew who sail the vessel very hard. These types of vessels have been known to sail all over the world and are very forgiving. which was developed to supersede the IOR rule. It would be very difficult to find a modern light vessel that would be able to undertake this amount of punishment at sea and be able to continue sailing. uses full analysis of a yacht's performance to judge it with other vessels. After wrecking the Teddy off the north coast of New Zealand he took the Redningskiote or Lifeboat. the heavy construction of the vessel allowed it to sail on to its destination.e. reducing "pooping". A sharp stern has found to be very effective in following seas. However.Marcus Bole Parametric Generation of Yacht Hulls yachts became less seaworthy. which was basically a very large diameter mast that allowed the rigging to be smaller. They have long deep keels. across the Atlantic from Norway to America. The IMS rule uses a velocity prediction program (VPP) to analyse performance and this uses many empirical formulae. The "Colin Archer" type vessel is regarded as one the most seaworthy small vessels. In a storm. Besides racing. University of Strathclyde. removing the mizzen mast and a crew member was lost. One example of this is a voyage made by Earling Tambs [12]. He designed the polar ice ship Fram and also developed sailing vessels for the Norwegian life boat service. designs based around operability have also been developed.
weekend sail boats. had developed techniques for controlling the shape or lines of a vessel. In summary the design of a yacht is based on many factors. long distance cruising yachts. 1997 23 . It simply stated that the section area should vary at the same rate that the volume of water is removed from the path of a vessel. However. offshore racing. designer of the Great Eastern. It does show. If these were categorised then the design of a yacht could be based on the following. they have both been discredited modern naval architects. ® ® ® University of Strathclyde. • The age of the vessel. • The style preference of the owner/designer. There was great discussion over which of these methods was better or true. Based on observations. which linked the variation of section area over the length of a vessel to the wave making characteristics of a hull. • Developments due to coastal layout and. that even one hundred years ago hull generation techniques were being developed. While a yacht used for long distance cruising would be best with a long deep keel and modest to high displacement. for example. or local weather conditions. A light hull of round bilge with 'U' shaped sections would have been developed from a racing background. nevertheless. • Function of the vessel. Colin Archer constructed a simple formulation based on a circle. A quick glance at a yacht will show the basis that the vessel was designed around. local racing round the buoys.Marcus Bole Parametric Generation of Yacht Hulls It is interesting to note that even in the late 19th century Colin Archer and another naval architect John Scott Russell. John Scott Russell developed a similar method at the same time but this was based on the shape of the waterlines.
The shape of yacht hulls are so various that a method developed to model all types of hulls would find it difficult to complete the task well. then it is likely that there would be some parameters that are used on certain types of hulls and for others. Figure 6. If it were possible to develop a method that could create any hull. Yacht Profiles By necessity parametric hull generation system will be mostly based on numbers. In Figure 6. as the waterplane shape has hardly changed.Marcus Bole Parametric Generation of Yacht Hulls 6 6. It is the profile of the yacht that has changed the most and it is this shape that presents the most difficult problem in modelling all yacht hulls. An effective parametric hull generation method should be able to deals with these shapes. new parameters may have to be included in the University of Strathclyde. It goes without saying that the success of such a method depends on its ability to model the hull.1 a selection of photographs show how variable the shape profile can be.1 CHOICE OF PARAMETERS HULL TYPES Yacht hulls come in many shapes. 1997 24 .1. forms and flavours. If a new type of hull were developed.
Marcus Bole Parametric Generation of Yacht Hulls method for the system to accommodate the new hull. performance and rating under a rule. The keel is normally part of the hull and is faired into the hull. This approach is not necessarily good. it is necessary then to look at which types of hull could benefit from the parametric design. In this type of design today. a good understanding of how hull factors can affect performance is necessary. Such a universal system would be difficult to develop as it would have to allow for the use of dynamic parameters. as it can take many hours to design the correct shape. The traditional hulls have much more variation in the different shapes that can be found. 1997 25 . The designer must be able to analyse the results to see how the hull can be optimised. changed or removed from the method. This type of hull. The best that this method can cope with is a number of offsets to implement the shape and these will not capture the true shape.e. would benefit the most from a hull generation method as a computer is much faster at making modifications. whereas on a modern yacht the keel is basically an appendage which is bolted on to the bottom of the vessel. The most efficient way a tradition profile could be modelled is by having one input to the program similar to the approach taken by Jorde [3]. These may include size. The racing hull from the beginning is involved with numbers. A yacht generation method should to the same and allow it to specialise and model that type of hull well. i. therefore. The key problem encountered in modelling a traditional style yacht is the variation of the profile. as the design of light cruiser/racer yachts developed over the past decade has reached a stage where all yachts look very similar. the Velocity Prediction Program (VPP) is becoming the designer's most important tool. There has been some resurgence in traditional style yachts. This utility analyses the performance of a yacht and returns the results as numbers. Naval architecture in this respect has lost its art to science. To be a good racing yacht designer. Numerically. A University of Strathclyde. those parameters which could be added. The integral keel of traditional yachts gives rise to 'Y' shape sections. The hull of a traditional yacht is very different to the modern shape. To select a yacht type to model. Traditional yacht design is still an art. Most generation methods concentrate on one type of hull. the best type of hulls that would benefit from the use of a parametric generation method is those involved in racing. introducing high curvature.
Hulls of the modern yacht are mostly similar and have become easy to design.2. Computers are used to design the hull. This said. new yacht designs such as the Truly Classic range designed by André Hoek have traditional styling above the waterline.Marcus Bole Parametric Generation of Yacht Hulls computerised generation method would find it difficult to deal with these types of hulls and is more likely to produce many unsuitable hulls. It would be of more benefit to "Yacht Design". so that these yachts can win races. modern theories are used to produce yachts that not only look impressive but have respectable performance too. The modern fast cruiser/racing hull has benefited the most from computer technology. designing traditional yachts is much harder as in the past the curves have been judged by eye instead of numerical analysis. assess sailing performance and evaluate structural aspects. while. A parametric hull generation would be unable design the traditional hull form as it would be unable to compete and should not be allowed to compete with the skills of the traditional yacht naval architect. 6. below. if methods used for designing modern yachts are evaluated rather than to develop a method that was able to generate a yacht with traditional styling. Figure 6.2 CHOOSING THE PARAMETERS University of Strathclyde. There are no areas where tight curvature is found. 1997 26 . Moreover. Truly Classic 75 by André Hoek.
(a) Overall Dimensions To start with . the lengths in x. y and z. Some yachts do not have a stern post so these parameters would be useless to use on a yacht of such type. There are the global parameters which can be used to define any marine vessel. In the other set there are the other parameters which are defined as local. and these include parameters such as waterline length (LWL) and block coefficient (CB).the basic dimensions of the vessel should be selected. • Maximum beam (BMAX). These affect the shape over small areas and are normally a function of the type of yacht being designed. An example of this would be any parameters defining the shape of the stern post.Marcus Bole Parametric Generation of Yacht Hulls The parameters used to define the shape of the hull can be divided into two sets. (b) Form Coefficients University of Strathclyde. • Draught (TC). • Waterline length (LWL or DWL). The basic dimensions include: • Length overall (LOA). 1997 27 . i. • Freeboard. at different points. • Waterline beam (BWL). To any vessel there is more that one of these length dimension in any of the three axes.e. • Depth (D).
Under a scaling transformation these parameters would have to be changed pro rata to stop the centroid from moving relative to the shape of the hull. The centroids of these areas and volumes need to be specified because the correct balance of the yacht depends on it. • Waterplane coefficient (CWP). The form coefficients are important and also play an important role in calculating resistance through the Delft Yacht Series [5]. as a percentage of LWL. (c) Centroids The hull has many area and volumes. The centroids available are: • Longitudinal centre of buoyancy (LCB). 1997 28 . The quantities are normally linear dimensions measured from a reference point to the centroid. when the vessel is scaled. If the positions of the centroids were specified in a non-dimensional forms then under a scaling transformation the position of the centroid relative to the hull would not change. University of Strathclyde. • Midship section coefficient (CM). The basic form coefficients which are available are: • Block coefficient (CB).Marcus Bole Parametric Generation of Yacht Hulls Once the basic size of the yacht hull has been selected. • Vertical prismatic coefficient (CVP) . These non-dimensional coefficients are very useful. the coefficients do not change. as. A coefficient should have a value which lies between 1 and 0. keeping the volume and areas scaled in with the size of the vessel. One way of achieving this is to specify the positions of the centroids as percentages of the given waterline length. • Prismatic coefficient (CP). coefficients need to be selected which describe the effectiveness of the hull.
3 REQUIREMENTS FOR MORE DETAILED ANALYSIS University of Strathclyde. • Bow profile .angle at deck.tangent above WL. 1997 29 . the number of bow profile parameters was reduced to two.angle at WL. These are: • Bow profile .Marcus Bole Parametric Generation of Yacht Hulls • Longitudinal centre of flotation or longitudinal centroid of the waterplane (LCF). (adjusts forefoot depth). as a percentage of LWL. • Transom angle. To create these curves it is necessary to use parameters to specify local effects. • Bow profile .deck tangent. • Vertical centre of buoyancy (VCB). • Aft Extreme . In later methods. as a percentage of LWL.tangent below WL. as they are required to set up the algorithm which creates these curves. waterline and sheerline. one varies the curvature in the bow by adjusting the angle of the tangents. It was felt that there were too many parameters defining the shape of the bow profile. 6. • Bow profile . The other parameter was the original bow profile . • Centre of Lateral Resistance (CLR). as a percentage of the hull draught TC.tangent below WL. (d) Local Parameters The generation method will create the shape of the profile. These parameters will be mentioned in more detain in Chapter 8. • Bow profile .above WL.
• Position of rudder on yacht. • Taper ratio. 1997 30 . • Sail area and factors corresponding to sail size. Beside needing information about the hull. • Taper ratio. • Depth of keel (TK). Rudder: • Aspect ratio. University of Strathclyde. • Position of keel of the keel on the yacht.Marcus Bole Parametric Generation of Yacht Hulls The Velocity Prediction Program has been mentioned previously as a tool that can analyse a yachts performance. If the parametric hull generation process was taken a step further so that it was included as part of a VPP then the following parameters could be used to describe the other appendages found on a yacht. this program requires information about the devices attached to the hull. Keel: • Aspect ratio. • Depth of rudder. • Centres of effort (CE) and Area. • Position of mast on yacht. Sail Plan: • Mast height. • Sweep angle.
These parameters would give all the information that the VPP needs to know about the yacht. • Wave frequency (also affecting resistance in waves). as percentage of LWL). As the VPP attempts to model the performance of the yacht at sea. it also requires parameters to describe the operational environment. • Wave height (affecting resistance in waves). ® ® ® University of Strathclyde. These would be: • Wind speed (affecting power generated by sails). 1997 31 .Marcus Bole Parametric Generation of Yacht Hulls • The "Lead" (the distance between CE and CLR.
Most curves of form will be produced. where permitted. The deck and sheerline are essentially the same space curve. The draught at any point along the hull can be found by inspecting the draught form curve. The basic approach of this system is to create the vessel by considering the various beams. University of Strathclyde. Initially. • Waterline. draughts. it is one of the major curves which effect the look of a yacht. to the approach taken by Jorde [3]. • Section area curve. By varying the curves of form. The curves of form used in this method are: • Deck and Sheerline profile. • Profile. the method was developed similarly. 7.Marcus Bole Parametric Generation of Yacht Hulls 7 7. the correct goals and targets specified by the parameters can be met. The curve is not coplanar and it is. such as the draught. therefore. depths and areas of sections along the length of the vessel. by using the curves of form.2 CURVES OF FORM The curves of form model the shape of certain properties of the hull. Once the curves of form are created. (a) The Deck and Sheerline This curve is the most complex shape to produce. with cubic or fourth order B-spline functions. Each of the curves of form have to be defined fully before they can be used. more difficult to control its formation.1 METHOD 1 INTRODUCTION It was now necessary to put all the concepts together to develop the hull generation technique. the hull sections can be generated to give a full hull definition. 1997 32 .
• Straight sheer. there are a variety of sheerline shapes. • A cubic spline.1.Marcus Bole Parametric Generation of Yacht Hulls however. the shape formed may not be pleasing to the eye. A method must be selected that allows all these types of sheer to be produce so that whatever shape is in fashion can be modelled. On yachts today. Techniques generating the deck and the sheerline were considered . the basic shapes are straight sheer.separately. The following curve techniques were considered. Figure 7. There are a variety of methods that can be used to produce the sheerline. Types of Sheer. if the curve was developed with only one curve technique. if technique generating the sheerline produce an unsuitable curve it could easily be replaced. • A B-spline Fit. normal sheer and inverse sheer as shown in Figure 7. • Circular sheer. • Standard Sheer.1. in the event that. 1997 33 . University of Strathclyde.
3. The B-spline control polygon producing the deckline is shown in Figure 7.Marcus Bole Parametric Generation of Yacht Hulls These techniques were tried and the differences between each technique were not large enough to be illustrated within a diagram. The freeboard can be specified at the bow. The deckline is the sheerline curve. but was unable to produce straight sheer. The circular technique produced a good sheerline shape. stern and amidships as in Figure 7. The cubic spline and the B-spline fit techniques seem to produce the best shaped curves. Figure 7. Standard Sheer is used mostly in ship design. because B-spline functions are used exclusively throughout the rest of the method and the specification of a minimum freeboard height was not considered a limitation. Parameters affecting the shape of the Sheerline. The control point at mid length is varied by an iterative University of Strathclyde. but viewed in plan. A quadratic B-spline function is used to create this curve. The point of maximum beam along the length is free. as to the number of vertices in the control polygon is only 3. However. This curve is formed with a normal B-Spline. The shape of circular sheer is fixed and more "interesting" sheer profiles cannot be produced with this technique. there are some functions which are better than others for describing the Sheerline. The maximum beam (BMAX) and the beam at the transom (BTRANSOM) are parameters used specified to the shape of the curve. 1997 34 . but minimum freeboard or the lowest point of the sheerline cannot be directly specified with the B-spline fit technique. it cannot form a straight line and the sheer that is produced by this method is not classed as suitable for a yacht.2. The B-spline fit was chosen to create the sheer profile.2 and a good shape is produced.
9 1. Advice is given in [7] about what the waterplane entrance angle should be.0 Entrance Angle Degrees 30 26 22 18 14 10 10 Table 8. The entrance angle of the waterplane can have an important role in the resistance of the yacht. 1997 35 . is specified with the longitudinal centre of flotation (LCF).8 0. based on the speed to length Ratio. The maximum point of width on the waterline is controlled by the waterline beam (BWL). The Deck Line and B-Spline control polygon. Figure 7.6 0.7 0. until maximum point of the curve is equal to the maximum beam specified.Marcus Bole Parametric Generation of Yacht Hulls process.0 2.5 0.3. It is a key factor which influences the resistance of the vessel. The area is specified with the waterplane area coefficient CWP and the centre of area. It is possible to specify the area and centre of area of the waterplane shape.4. that a good waterline shape is vital in most ships. Table 8. To define the curve with a maximum beam as specified.4. The point of maximum beam along the length of the hull is free and a more natural shape is produced as a result . a process similar to that used to create deck line was employed. Entrance angle based on Speed-Length ratio. a quantity important in longitudinal stability. V / √L 0. The parameters used to specify the shape of the waterplane are shown in Figure 7. (b) The Waterplane The waterplane is an important shape in any marine vessel.5 University of Strathclyde.
6. The control polygon of cubic B-spline function chosen to create the waterplane shape is shown in Figure 7. Figure 7. The Waterplane B-Spline control polygon. University of Strathclyde.6. (c) The Profile The shape of the profile is one that defines the style of the yacht. each adjustments are made to the control polygon by iterative processes. 1997 36 . Parameters affecting the shape of the waterplane.Marcus Bole Parametric Generation of Yacht Hulls Figure 7. The profile with the shape of the sheerline can make the yacht look fast or slow. The main difficulty is producing the correct shape.7 shows the basic parameters required to create the profile.5. Figure 7. With all these parameters. The profile has the most number of parameters defining the shape. the shape of the waterline curve can be produced.
7. because this made specification of the profile easier to understand. the angle of the curvature in bow profile and forefoot depth.8 shows the control polygon of the 4th order B-spline curve used to define the profile shape. Figure 7.8. The number parameters controlling the bow was reduced to two. This shape does not use any iterative processes. F igure 7. The profile requires many local parameters to produce the shape. Profile Parameters. Later. where the profile joins at the deck and at the where the profile intersects with the waterline. 1997 37 . The depth of the forefoot needs to be controlled. The B-Spline control polygon defining the profile shape. as well as aspects of the transom. as all of the parameters directly modify parts of the control polygon.Marcus Bole Parametric Generation of Yacht Hulls Figure 7. These parameters are used to define the angle of the bow and if there is any curvature in the bow. the definition of the bow profile was made with five parameters. University of Strathclyde. To begin with. each controlling the various features.
A quadratic B-spline function was chosen to model the shape of the section area curve.9. making it easier to solve. 1997 38 . However. Parameter affecting the shape of the Section Area Curve. parallel middle body is undesirable for yachts and the section area curve normally does not contain a straight line segment. but without a parallel section. The section area curve is one of the forms that are used is most hull generation techniques. Most techniques used in other hull generating procedures require a parallel section. Figure 7. as a result. however. Figure 7. if the length of parallel section was set to zero. This can be helpful as it allows the curvature between the bow and stern area to be separated and the section area curve can be solved in two parts. It was found that at least a fifth order polynomial function was required to produce a section area curve which featured no discontinuities.9 shows the main parameters which are used to define the shape of this curve. a discontinuity would be created in the section area curve.10 shows the University of Strathclyde. A direct mathematical section area curve was investigated for the current study to see if it would have any advantages over a B-spline method. because it breaks up the solution of the section area curve. these techniques cannot be used for yacht hulls as a continuous section area curve is required. In these techniques. Most section area curves defined for generation methods incorporate a section of parallel middle body. as the curve produced by a third order B-spline function was closer to the shape of a yacht section area curve than a fourth order B-spline curve. The shape produced by the derived function.Marcus Bole Parametric Generation of Yacht Hulls (d) The Section Area Curve Figure 7. The curve was developed in a similar way to the section area curve developed by Jorde [3]. is utterly useless for a section area curve as it apt to oscillate between positive and negative.
The modification is made by moving control points A and B. Modification • is used to make the maximum point of the curve coincide with maximum sectional area defined by the input parameters.10. These modifications. University of Strathclyde. The modification is made by moving control points A and B. Modification " was originally set by parameters. But in later methods ( as can be seen later ) these end tangent vectors are used to correct the shape of the sectional area coefficient curve. modification of the B-spline curve could be performed to achieve the specified goals. closer together or farther apart. both forward or both aft.Marcus Bole Parametric Generation of Yacht Hulls control polygon adopted in this study to define the sectional area curve.' and ƒ. •. The modification is made by moving control points. By using iterative processes. are made by the computer program to reach the specified goals. Modification ƒ is used to modify the longitudinal centre of buoyancy. A and B. vertically together. 1997 39 . Modification ' is used to change the immersed volume. Figure 7. The B-Spline control polygon defining the shape of the Section Area Curve. together. horizontally.
This effect is undesirable in a hull generation technique. as a yacht heels when it is sailed. Figure 7. it is up to the designer.11 shows the layout of the diagonals. destroying the integrity and flow of the iteration procedure. created by planar cuts though the hull. the angles chosen for the diagonals. The diagonals are primarily used to fit new sections into the hull. so that heeled waterplanes remain fair. this phenomenon is called the property of local modification. Diagonals are normally shown on lines plans. Diagonals are. This can be difficult to ensure. Relying on transverse sections only. An iterative hull generation procedure would find it difficult to maintain diagonals normal to the surface of the hull. transverse sections will be used instead of a full surface. which are either close to being normal with the hull at amidships or for ease of draughting. but there does seem to be any standard location for diagonals on a hull. can result in the longitudinal curvature effects being ignored. as the angle between a plane through the hull and the hull surface will change along the length of the vessel. But when the control points of B-Spline surface are modified. used to judge the fairness of the hull. 1997 40 . For the best results. In more detail: University of Strathclyde. The diagonals secondary function is to keep the longitudinal shape of the hull under control. diagonals should be drawn so that intersection with the hull takes place. Diagonals are curves. Diagonals can be used to represent the shape of the waterplane in heeled conditions. To keep longitudinal curvature under control.Marcus Bole Parametric Generation of Yacht Hulls 7. In design. similar to waterlines.3 THE SECTIONS AND DIAGONALS The shape of a hull can be modelled with a B-Spline surface. Normally. generally. a naval architect will generally select angles for diagonals. are set so that the diagonals are close to being normal to the hull and also easily defined.. In the current study. diagonals are employed. These lines become more important for a yacht hull. an area local to the control point is also changed. For this hull generation method. but diagonals are not generally horizontal or vertical cuts. angles which are found on a set of triangles or set-squares. as a shape controlled by one process can be modified by another unconnected local process. as the angle of the diagonals would have to change every time the hull was modified.
the correct section area coefficient and waterline University of Strathclyde. • Diagonal (2) is an intermediate between diagonals (1) and (3). for example. Section shape is modelled with a cubic B-Spline curve. The angle of Diagonal (4) is set to 10º so that it has a greater weighting at sections found amidships and a much smaller weighting effect at sections found towards the ends of the hull.11. The layout of the diagonals. section beam at the deck and section draught.2º. • Diagonal (3) is set. i. This seem to be the only diagonal which has a standard angle and intersection point throughout yacht design. Figure 7. is used to specify the properties of a certain section. This data provides parameters to section generation procedure. The end vertices of the B-Spline section control polygon can be placed easily. allowing half sections to be generated instead of full sections.4º. This diagonal has a angle of 63. the draught dimension of a section. Generally. It also intersects with the maximum waterline beam on the waterplane. It intersects the centre plane at an eighth of the waterline beam above the waterplane and it has an angle which is the average of the angle of diagonals (1) and (3). so that it intersects the hull centre plane at a point a quarter of the maximum waterline beam above the waterplane. B-Splines do not travel through known points. 54. using the given parameters which describe section freeboard.Marcus Bole Parametric Generation of Yacht Hulls • Diagonal (1) has an angle of 45º and it intersects with the centreline of the waterplane. Therefore. Data taken from points on the various curves of form.e. unless some procedure has been used to fit a curve or if there are discontinuities present. 1997 41 . • Diagonal (4) is used to stop a Cusp forming at the keel.
Figure 7. The position of the control vertex on diagonal (4) is controlled by University of Strathclyde. which are used specify the shape of the curve between the edge of the deck and the keel. It can be seen in Figure 7. Figure 7. It is necessary to use a iterative process to vary points on the section control polygon until the specified goals for section area and waterline beam are reached. The position of the diagonals allow a simple mechanism to be developed. which controls the shape of sections.12.13. 1997 42 . that D3 can be used to control the waterline beam of a section. Figure 7. The vertices on a section control polygon can be modified more efficiently. Figure 7. The mechanism controlling section shape.13 shows the mechanism and control polygon that is used to control the shape of sections.13. Complications occur because there are only two parameters. section area and waterline beam. Sections can be then be modified by "sliding" vertices along the diagonals. Parameters controlling section shape.Marcus Bole Parametric Generation of Yacht Hulls beam cannot be simply formed by placing vertices.12 shows the parameters that are passed to the process generating section shape. when attached to diagonals.
to develop the diagonals. Figure 7.0 will create a rectangular section etc.14 shows how the diagonals are fitted through the section control polygons. Using co-ordinate geometry. However. processing is reduced.Marcus Bole Parametric Generation of Yacht Hulls the draught of the section. The initial arrangement of the diagonals. Assuming that a section area coefficient of 0. by making assumptions about the shape of the section. as the process does not have to consider the actual section shape. and vice versa. Attaching the section control polygon to the diagonals makes the longitudinal fairing shape easier.. 1997 43 . Figure 7. the angle of the control polygon segment.5 will create a approximately triangular shaped section and a section area coefficient of 1. University of Strathclyde. Leaving D1 and D2 to control the amount of section area and the overall shape of the section. between diagonals (1) and (2) can be predicted. to allow D1 to be found from D2 using the angle of the control polygon segment between D1 and D2.14. a function can be designed to link D1 and D2 together. functions can be developed. the longitudinal shape of the hull is kept fair. based on the value of section area coefficient. By using diagonals fitted through the vertices of each section control polygon.
it is not desirable to create each section from the basic parameters supplied by the curves of form only. When further sections are created. the initial shape of the control polygon can be obtained from the location of the diagonals at that length of the hull. Figure 7. has only to be modified by small amount.15.15. Figure 7. from the initial shape. as a "family" of sections will not be created.Marcus Bole Parametric Generation of Yacht Hulls During the process of generating the hull. Three initial stations can be created. The section now. from basic parameters. to allow diagonals to be fitted to the section control polygons. The insertion of a new section University of Strathclyde. 1997 44 . to reach the goals specified in the section parameters.
An interesting problem now arises. between the true CX curve formed from the Curves of Form at all stations and a CX curve constructed from a B-Spline function fitted through the values of CX at stations 1. What is the correct shape for these form curves to take? This problem is not mentioned in any of the other methods looked at in the review. 10.16. By considering the difference. The profile is set by the values of the parameters. and 19. By taking this criterion and using it for the current method. University of Strathclyde. the correct the shape of the Section Area curve can be obtained. analysis can be made on how to change the bow and stern tangents of the section area curve so that two CX curves can match up. To acquire the correct shape. 1997 45 . the data has to be connected together to enable a hull to be generated. the section area curve is a shape which although easily defined. However. measured by ∆CX(BOW) and ∆CX(STERN) in Figure 7. the Section Area curve is created by maintaining a fair Cross Section Area Coefficient (CX) Curve.17. The waterline is set by the parameters and should be roughly symmetrical about the midsection. The waterline and profile shapes are fairly standard shapes. the vertices of the control polygon must be placed in the correct place. The difficulty is to find the correct shape that the section area curve should be.2) can now be used to modify the section area curve to obtain the correct shape. can be wrong.Marcus Bole Parametric Generation of Yacht Hulls 7.4 Method 1 Now the basic form definition curves have been defined. Method 1. Figure 7. The tangents at the bow and stern of this curve (See (d) of Section 8. In the method developed by Jorde [3].
To analyse in more detail. A completely fair CX curve cannot always be produced by this process.17. Actual and Fitted CX curves.3. The aft perpendicular is created by analysing the conditions at this station. The midship section is created using the parameters CM and BWL and the method as detailed in 8. a more comprehensive analysis is unlikely to increase the fairness of the hull. The stations are created from initial values taken from the diagonals. The next stage in the method is to create the stations. The control vertex of diagonal (2) is set to lie on the waterline so that the curvature is maintained across the station centreline.Marcus Bole Parametric Generation of Yacht Hulls Figure 7. The control vertex of diagonal (3) is set to lie directly below the deckline so that this segment of the control polygon University of Strathclyde. The first step is to set the initial shape of the diagonals. at least three known points are required. Diagonals (1) and (4) are zero as they lie on the waterline which has no beam at this point. The diagonals at the bow are attached to the stem profile by setting the values of the diagonals to zero when they reach the stem. The stations are numbered from 0 to 20 with Station 0 forming the Forward Perpendicular (FP). points on the midship section (Station 10) and point on the aft perpendicular (Station 20). For this. 1997 46 . the differences between these two curves would require more processing time. However. Twenty one stations are used because at the bow and stern more stations better define the shape and it is easier to work with stations of uniform spacing. as the differences between the actual CX curve and fitted CX curve are only measured at stations 5 and 15. The diagonals are fitted through point on the bow profile.
There are now three known points for each diagonal. directly. 7. so the hulls produced must be analysed over a range of different parameter specification. An extra parameter could be used to modify the position of the control vertex on diagonal (3). The Delft Series is a set of functions based on a fit of data from test experiments. A quadratic B-Spline function can now be fitted through these points to give the other stations information about what shape to take. but it is thought that the current arrangement of the control polygon at station shall not affect the overall results of the method. Resistance is important and the Delft Series [5] supplies a method for calculating the value of these factors. cannot be relied upon to produce a real hull. A matched set of parameters would allow a real hull to be analysed.5 TESTING The process detailed here was constructed into a program and the following five figures show the results of this process. the Curves of Form curves and the diagonals.14. CP and longitudinal centre of buoyancy. The body plan of the hull can now be created using. The most important variables in these functions are block coefficient. These quantities seem to affect resistance the most. LCB. A quadratic least squares fit is now made through these points to remove some of the effects of having fixed the shape of the curve. A range of hulls must be created by the method. Parameters chosen arbitrarily. This creates a sectional shape which is fixed throughout all hulls. 7.Marcus Bole Parametric Generation of Yacht Hulls is parallel to the section centreline. It was necessary to choose a set of parameters which were close to a designed yacht. 1997 47 . 13 and 17 are modified after using the same process and 5 and 15. Next stations 3. A fourth order B-Spline function is now fitted though five points. Stations 5 and 15 are modified from their basic shape defined by the diagonals. full analysis of these parameters with respect to resistance performance is given University of Strathclyde. Then the diagonals are fitted to the three original points and new points found on station 5 and 15. Now each diagonal is defined by nine points. These functions use many of the parameters used for the current method as an input. The result produced is shown in Figure 7.
6 55% Table 8.18 University of Strathclyde. The resistance functions of the Delft Series are only valid for a certain range of CP and LCB. 1997 48 . Table 8. The method will be tested at the limits of this range to see if hulls can be produced.Marcus Bole Parametric Generation of Yacht Hulls in Larson and Eliasson [6].18 shows the valid range of the Delft Series with respect to CP and LCB is: Low 0.52 50% Parameter CP LCB (% of LWL from Bow) High 0. This range corresponds to the region in which most popular sizes of hulls exist.
Marcus Bole Parametric Generation of Yacht Hulls 7.57.19. LCB = 53% University of Strathclyde.RESULTS Figure 7.CP = 0. 1997 49 . Method 1 .6 METHOD 1 .
LCB = 50.57.CP = 0.5% University of Strathclyde. 1997 50 .20.Marcus Bole Parametric Generation of Yacht Hulls Figure 7. Method 1.
CP = 0. 1997 51 . Method 1 .Marcus Bole Parametric Generation of Yacht Hulls Figure 7.57.21. LCB = 54%. University of Strathclyde.
1997 52 .CP = 0.Marcus Bole Parametric Generation of Yacht Hulls Figure 7.52. University of Strathclyde.22. LCB = 53%. Method 1 .
53%.CP = 0.60. LCB = 0. Method 1 . 1997 53 .Marcus Bole Parametric Generation of Yacht Hulls Figure 7.23. University of Strathclyde.
23 and 7. The procedure developed to produce the section area may not create a curve in many cases. Low values of section area have been supplied to sections and the waterline beam goals have also be met.21. The section area curve procedure can produce more extreme examples of this effect. As the iteration process has no knowledge of the limits for the length of these segments. The iteration process analysing the shape of the CX curve is the only process that adjusts the segments of the control polygon defining the section area curve. the hulls produced can not be used as yacht hulls. In this situation the program with either produce an mathematical error or the procedure will produce an infinite loop. it can specify unsuitable values.22. 1997 54 . The result is that the section area curve can The method produces sections at the bow with very University of Strathclyde. however. The result is that sections are often assigned areas which result in section areas coefficients greater than 1.0. The reason why stations are produced with this shape is through the use of the section area curve. the section shape produced is wrong. This phenomenon is illustrated in Figures 7. however. final process constructing the sections is unable to finish the task due to the extreme section shapes involved.7 DISCUSSION OF RESULTS The first method has many problems. Figure 7. at the bow of the yacht has a very steep gradient. large hollows. this shows that the method for producing stations with assistance from the diagonals works. The stations produced follow a "family" of curves. The opposite situation can presented in Figure 7.22 gives good example of this failing. the curvature in the lower bilge area of the sections present some interesting results.Marcus Bole Parametric Generation of Yacht Hulls 7. These situations cannot be predicted or be recovered from. The process developing the Section Area curve has no feedback from the stations about the shape responds to area assigned area. all does is produce a B-spline curve which has represents the correct volume and LCB. The section area curve produced. The procedure that develops the section area curve is a blind process. However. The unsuitability of the section area curve is exhibited in all of the five examples produced by this method. The most noticeable feature in these results is the shape of the stations produced. It is able to produce a hull.
The arrangement developed so that the diagonals are able to modify section shape is not efficient at producing sections that are position well away from amidships. at the bow the height of this diagonal above the waterline is about half the freeboard. the waterline beam becomes much less that maximum waterline beam. ® ® ® University of Strathclyde. It can be seen from Figure 7. as a result of evaluation at every possible point. At the bow. The shortcomings of this method were analysed to produce method 2.22 that the functions adjusting section shape. based on these parameters only. 1997 55 . do not have enough information to produce suitable sections. is in the wrong position. The stations produced. At amidships diagonal (3) is close to the waterline. Modifying the shape of every section may not be the best way of producing a hull. Fairer hull may be produced if less sections were used during generation process. however. The remaining sections could be produced from the diagonals at the end of the process. the result of this is that diagonal (3). The vertex on diagonal(3) is too far away from the waterline to adjust the waterline beam of a section correctly. have a very fixed shape. which is used to change the waterline beam.Marcus Bole Parametric Generation of Yacht Hulls sometimes have end segments of negative length resulting in a curve longer than the waterline or the section area curve can acquire "loops" if the end segments are too long. It is necessary to consider the effects of curvature to stop unsuitable hull being produced.
had to take a step back and examine the method of generation the section area coefficient curve. the exact curve is required.5. Moving towards the bow end. the CX curve goes through a point defined by the midship section coefficient CM. resulting in more triangular sections. as beam and draught at these sections are zero. by modifying the section area curve. by some procedure. therefore. Various methods for producing a section area curve were examined.1 METHOD 2 INTRODUCTION It was necessary to analyse the shortcomings of Method 1 to rectify the process which caused the problems outlined at the end of the last chapter. then the condition where large section areas were produced would not occur. The CX of these section should be close to 0. it is possible to assign a dummy a value for CX at these points. to identify key characteristics. the ends of the CX curve become undefined. 8. By making assumptions. these refused to produce the required results. University of Strathclyde. a close examination of the CX curve is necessary. The underwater sections near the bow of a modern yacht can generally be said to be "V" shaped. with two relatively flat sides. To do this. the CX curve. The section area curve appears to have a simple shape. converge to a point at the lowest point. the magnitude of the section area curve cannot be limited to stop the area of a certain section becoming too large. 1997 56 . In method 1. Unfortunately. such as direct mathematical approaches. To solve this problem it was necessary to find a new way to produce the section area curve. however. it can be seen that the primary goal was to fair the curve of section area coefficients. the sides of these sections become flatter. If the CX curve could be specified. It is known that at the midship section.Marcus Bole Parametric Generation of Yacht Hulls 8 8. The study.1 The Process Considering method 1. correctly. however.
for example. The shape of the section at the bottom is flat and almost horizontal. Using this procedure.1. however.Marcus Bole Parametric Generation of Yacht Hulls Figure 8. To limit the CX curve to CM or less. The value for CX found at these sections will again be close to 0. Next. Figure 8.2.5. These points are move to the correct values for Volume and LCB to be obtained. points placed on the curve at stations 5 and 15 meet this modification well. At the stern. it is necessary to have one of the other form curves as a variable. Triangular sections at the bow. The underwater shape of the sections close to the Aft perpendicular will be approximately triangular. Moving towards the aft end of the yacht hull. Approximately triangular sections at the stern. it is still possible to for the CX curve to produce section area coefficients of greater than 1. the bilge shape of sections becomes flatter. the sections are generally referred to as being "U" shaped. The profile was selected to be the variable curve. To stop this occurring the value of midship section coefficient (CM) was selected to be the maximum magnitude the CX curve. points are required to vary the shape of the CX curve. 1997 57 . as it is not as important University of Strathclyde.
Marcus Bole Parametric Generation of Yacht Hulls as the waterline from the resistance point of view. Method 1 could produce sections where the lowest point did not coincide with the centreline. it was possible for the lowest point of a section to not coincide with the centreline.3. however. is the shape of the sections. A more direct approach to the problem was necessary. By analysing the curvature of the sections. it was thought that an effective technique would be produced by inspecting the second derivative of the B-spline function. a technique could be developed to allow the shape of section to controlled further. Figure 8. Another consideration examined by method 2. By inspecting the layout of the section control polygon. points at stations 5 and 15 on the profile curve allowed the rocker shape of the hull to be varied. this did not always produce the required result and increased the time required. 1997 58 . Various techniques for analysing the section shape were investigated. so that the method can make a correction to the CX curve. University of Strathclyde. to generate a hull.3. More specifically. Initial. In method 1. significantly. Figure 8. this feature can be detected.
4. Figure 8.5. By inspecting this value at stations 5 and 15. 1997 59 . University of Strathclyde. the process can adjust the shape of the CX curve to reduce any unwanted effects. Figure 8. The mechanism used to generate the CX curve. could be used.Marcus Bole Parametric Generation of Yacht Hulls Figure 8. The height of the triangle formed by control vertices on diagonals (1). as measure of the current bilge shape of a section.4. (2) and (4). The distance used to detect unsuitable sections.
with the possibility that the curve produced may have values of CX which are higher than one. the curvature of stations 5 and 15 is analysed again to see if it is suitable. By modifying the profile shape.5 shows the control polygon used to define the CX curve. Figure 8. The procedure analysing curvature detects the effects of this process as a change in the gradient of line APBP. A target angle for line APBP is set by the curvature analysis procedure. The result of this is that the line APBP will generally go through the point CM. aft sections that have a high amount of curvature.6 University of Strathclyde. generally produce bow sections with low amounts of curvature. Figure 7. It the curvature is not suitable then the target angle is adjusted by interpolation. When the angle of APBP reaches the Target Angle. The iteration process can position these points anywhere. it was necessary to use some process. 1997 60 . the aft sections of the profile have an increased draught and bow section have a reduced draught. Points AF and BF are used to change the volume and LCB of the hull.Marcus Bole Parametric Generation of Yacht Hulls To implement the analysis of the CX curve.23. As can be seen from Method 1. producing bulbous effects. The analysis procedure changes the shape of the profile curve so that line APBP has an average height of CM. A flow chart for Method 2 is shown in Figure 8. the curvature of the sections will be changed.
A flow chart of method 2. 7. 1997 61 .Marcus Bole Parametric Generation of Yacht Hulls Start Initialise Diagonals Create Sheerline Create Waterline Create Profile Create Cx Curve Check magnitude of Cx Values Values of Cx above Cm Values of Cx Below Cm Generate Stations 5 and 15 Generate Diagonals Generate Stations 3.6. 13 and 17 Check Curvature at stations 5 and 15 Suitable Curvature End Unsuitable Curvature Figure 8. University of Strathclyde.
57. Method 2 . 1997 62 .3 RESULTS Figure 8.7. LCB = 53%. University of Strathclyde.CP = 0.Marcus Bole Parametric Generation of Yacht Hulls 8.
LCB = 50% University of Strathclyde.8.CP = 0.Marcus Bole Parametric Generation of Yacht Hulls Figure 8. 1997 63 .57. Method 2 .
CP = 0.9.Marcus Bole Parametric Generation of Yacht Hulls Figure 8. University of Strathclyde. Method 2 . LCB = 55%. 1997 64 .57.
LCB = 53%.CP = 0.54. Method 2 .10. University of Strathclyde.Marcus Bole Parametric Generation of Yacht Hulls Figure 8. 1997 65 .
Marcus Bole
Parametric Generation of Yacht Hulls
Figure 8.11, Method 2 - CP = 0.60, LCB = 53%.
University of Strathclyde, 1997
Marcus Bole
Parametric Generation of Yacht Hulls
Method 2 produces section with better shape that method 1. An interesting factor to note is that since the method now analyses the shape of certain stations, the shape of the stations almost stays the same throughout the range of values investigated. The side effect of this methods ability to evaluate section shape, is that the Rocker profile is modified to correct section shape. In cases where unreasonable sets of parameters have been specified, the maximum draught of the hull is ignored, producing a profile shape which is unsuitable for a yacht, illustrated in Figures 8.8 and 8.10. In these figures the LCB was specified at the limits values for the Delft series, 50% and 55% of LWL. The method is increased the draught of the profile to allow this
parametric goal to be met. The method finds difficulty in obtaining hulls with prismatic coefficients of below 0.56, for the YD-40 basis hull. If the specified prismatic coefficient is less than 0.56 the method goes into an infinite loop and fails to produce any hull. Further analysis of the sections produced by this method shows that, at the bow, the waterline beam is larger than what should be expected on a yacht hull. The waterline curve suffers from similar problems as the section area curve, i.e. it is difficult to obtain the correct shape. Different ways of producing a better waterline curves were considered. Unfortunately, none of the techniques tested produced a waterline shape that was more suitable than the one currently being used. The amount of time taken to produce a hull greatly increased, due to the increased number of iterative procedures. The time required to produce a hull is on average around ten to fifteen minutes. This may be much longer than a professional designer would take to produce a fair hull in a modern computer package. A more appropriate technique for changing the shape of the CX curve was, later, brought to the attention of the author. By using a quadratic B-spline function to define CX, An iterative procedure would not be required to place the CX through CM, as the point CM would always lie on APBP. The use of this technique would have greatly reduced the amount of time that was required to run the process.
University of Strathclyde, 1997
Marcus Bole
Parametric Generation of Yacht Hulls
9 9.1
The increased complexity and the analysis of curvature in method 2, did not produce hulls with a suitable enough range of parameters. These methods were developed in a similar way to the approach taken by Jorde [3]. The approach take by Jorde to produce a hull generation technique does not work well with B-Spline functions or yacht hulls. B-Spline functions generate unsuitable shapes as more shape constraints and/or goals are applied. The system of connected sections and diagonals, developed for the current hull generation procedure, could restrict the ability of method 1 and 2 to produce a hull. The connected sections and diagonals form a structure which is similar to a surface. Therefore, section area and waterline curve are already produced, by the surface. Previous methods may have failed, because the section area and waterline curves produced by the surface, cannot take the same shape as produced by the curves of form. By modifying the surface, defined by the diagonals and sections, the section area and waterline curves would always produce the correct shape.
9. 2
Method 3 was developed to use the surface defined by the sections and diagonals. However, the curves of form are still required. The profile and sheerline are necessary to define the edges of surface. It is also, still necessary to use a generated waterline curve, although only in the initial stages of the method. This allows the waterline beam at amidships, Station 10, to be found, as this is rarely the maximum waterline beam. To create the initial shape of the diagonals, the Bow Profile, Station 10 and the aft perpendicular are used, allowing all sections along the hull to be generated. The section area coefficient (CX) for each section can be calculated to allow the volume and longitudinal centre of buoyancy to be found. An iterative process now begins. This adjusts the section area coefficient for stations 5 and 15, until the goals specified for volume and longitudinal centre of buoyancy. All
University of Strathclyde, 1997
In Method 2 the shape of stations was analysed. Analysing the shape at this University of Strathclyde.Marcus Bole Parametric Generation of Yacht Hulls the sections in the hull are linked to stations 5 and 15. The goals affecting the shape of the waterline are only used to create the initial shape of this curve. The flow of Method 3. 5 and 15 Fix Diagonal (1) Fit Diagonals Generate All Stations Cx Achieved? No Yes End Analyse Volume and LCB Ok Generate All Stations Not Ok End Figure 9.e. the diagonals and all the sections have to be reproduced to allow the volume and longitudinal centre of buoyancy to be calculated. the analysis of the section shape take place as they are created. As method in previous methods. Start Initialise Diagonals Create SheerLine Start Create Waterline (used initially only) Assume a Station Based on the current state of theDiagonals Create Profile Adust Diagonal vertices to achieve Cx Goal Create Cx for Sta. to allow a hull to be produced with a reasonably suitable shape.1. Every time stations 5 and 15 are modified.1. 1997 69 . after all the other goals were satisfied. This may have been one of the factors that increased the amount of time that was required to produce a hull. i. The complete process is outlined in Figure 9. in the last process. This reduced the complexity of the method. 5 and 10 Cx Achieved? No Yes Curvature Ok? Not Ok Ok Adust Diagonals to achieve Cx Goal Generate Sta. In the new development of the method. through the diagonal. the shape of the sections is important.
Once a section has been created with this method.2. the control polygon further reviewed.Marcus Bole Parametric Generation of Yacht Hulls level allows the global iteration process concerning the hull to be unaffected by the process looking at individual sections. The process of governing the area of the section is restarted and the area is corrected with the position of the vertex on diagonal (1) fixed. so the vertex lies fixed. This modification and the modification performed to generate the correct section area. The process inspects the position of the control vertex on diagonal (1). If the vertex is found to be in a position below the maximum draught of the section. produces sections with a distributed shape. the effects produced by methods 1 and 2 are greatly reduced by distributing the shape more efficiently. however. The angles used to detect the shape of the section. An iterative process changes the angle of the segment between diagonals (1) and (2) until the difference between a and b is within a defined tolerance.2. 1997 70 . it is modified. analyses the shape of a section by inspecting the control polygon at angles a and b. 9. on the maximum draught. Figure 9.3 RESULTS University of Strathclyde. Inspecting the shape of a section in this manner does not always make the lowest point coincide with the centreline. shown in Figure 9. The process used to generate sections.
3. Method 3 . University of Strathclyde.CP = 0.Marcus Bole Parametric Generation of Yacht Hulls Figure 9. LCB = 53%.57. 1997 71 .
Method 3 .57.CP = 0.Marcus Bole Parametric Generation of Yacht Hulls Figure 9. 1997 72 . University of Strathclyde.4. LCB = 50%.
University of Strathclyde.Marcus Bole Parametric Generation of Yacht Hulls Figure 9.57. Method 3 .5. LCB = 55%. 1997 73 .CP = 0.
University of Strathclyde.6.Marcus Bole Parametric Generation of Yacht Hulls Figure 9.CP = 0. 1997 74 . LCB = 53%.52. Method 3 .
University of Strathclyde.7. Method 3 .Marcus Bole Parametric Generation of Yacht Hulls Figure 9.60. 1997 75 . LCB = 53%.CP = 0.
4 the stations at the bow quarter. due to position of the diagonals. In Figures 9.4. This effect is not so pronounced on hulls produced with values of CP and LCB close to the optimum values associated with the YD-40 hull. This method produced hulls to a suitable standard within the region that the Delft Series is valid. This method is also able to produce a solution hull. quite a fair hull has been produced. In Figure 9. at around mid draught. Figure 9. The aft sections have specified with section coefficients which are too high. The previous five figures show the various hulls that have been generated by this process.4 DISCUSSION OF RESULTS The results of Method 3 proved to be very good and is the quickest of the three developed so far.5 and 9. with parameters set at values which not be found for a yacht hull. The bow sections produced are suitable to be used on a yacht hull. producing an unsuitable profile shape. The shape of the section area coefficient curve in all figures is good and there are no abrupt changes in the shape to suggest inconsistencies in the sectional area curve. 1997 76 .7 the parameters are set to the limits of the Delft Series and unsuitable hulls are produced. In Figure 9.6.3 shows a hull generated with the prismatic coefficient and longitudinal centre of buoyancy similar to the YD-40. this modification attempt failed. stations produced by the method at the bow can have small fluctuations in shape. This effect shows up well on the CX curve. to allow the profile shape to specified at stations 5 and 15 by parameters. producing a shape which go below the maximum draught of the section. Considering the previous figures. This figure demonstrates that. it is conceivable that the major dimensions would hull would have to be modified. although most of the stations have a fair shape. where the section of the curve at the bow has a definite change in gradient. 9.Marcus Bole Parametric Generation of Yacht Hulls 9. The previous method tried to eliminate the effect of high values of CX by modifying the shape of the Rocker profile. University of Strathclyde. However. To produce more suitable hulls with the values of prismatic coefficient and longitudinal centre of buoyancy used in the figure. A better approach may be. have bunched close together.
® ® ® University of Strathclyde. This method produces a hull which can be used in preliminary design and will be developed further so that the complete hull is produced. especially values of CP and LCB within the range associated with the Delft series. 1997 77 .Marcus Bole Parametric Generation of Yacht Hulls This method has demonstrated that a fair hull can be produced quickly. It can produce hulls over a reasonable range of parameters.
given a suitable set of parameters and the shape of the waterplane is indirectly controlled by parameters such as longitudinal centre of buoyancy and some hull dimensions. 10. Further testing was necessary. had a low beam to length ratio and high draught to waterline beam ratio. so the procedure develops something which can be used for design purposes. producing a slender hull. Two hull forms were considered.1. There does not seem to be any disadvantage to losing the ability to create the correct waterplane. It would also increase the time required to produce a hull by three or four times.Marcus Bole Parametric Generation of Yacht Hulls 10 FURTHER DEVELOPMENT Now that a process has been developed. further. 10. the hull would become less fair. which can produce a hull quickly and efficiently. The method can now be developed further. to see if a range hulls could be generated with different main dimensions. University of Strathclyde. the first. which would be commonly found on the current Open 50 and Open 60 class racing yachts.2 FURTHER TESTING Testing. This testing demonstrated the ability of the method to develop hulls with different geometric ratios. as long as an efficient waterplane is produced. had a high beam to length ratio.1 WATERPLANE SHAPE Method 3 does not obtain the goals used to specify the shape of the waterplane. 1997 78 . has been concerned with making sure that the method can produce a yacht hull over a predefined range of prismatic coefficient and longitudinal centre of buoyancy. corresponding to the Delft series. The process generates a good hull. so that the waterplane shape was restricted with parameters. so far. The second hull form. The second hull form is one which has ratios. It is thought that if the method 3 was developed. Figure 5.
The iteration procedure was unable to cope with the rapid change in the sign of the angle and a section of unsuitable shape was produced. As the iteration process varied the shape of the section. very wall sided. an inverse tangent function was developed. The slender hulls tested were. This range of angle only takes account of the gradient of the segment and not the direction. In the previous methods. Figure 10. Generally. to a point on the bottom of the transom. Various transoms produced with the original profile mechanism. the direction certain polygon segments became close to vertical (90º). the inverse tangent function has a range of -90º to 90º. generally. the angle of segment can be found. as a result. The angle of each polygon segment is obtained by considering the gradient of the segment.Marcus Bole Parametric Generation of Yacht Hulls First the slender hull was tested. The curvature in a section is analysed by considering the layout of the B-Spline control polygon. the aft perpendicular is the transom.1. a problem which existed in both hull of both form was discovered. The current process used to define the profile does not allow these types of hulls to be formed well. In this situation. the aft profile is constructed by allowing the curve to go through a specified point on the waterline. Both hull types tend to have very small and in most cases no stern overhang. the inverse tangent function converts the gradient on segment into a negative angle. Angles between certain segments of the polygon are evaluated. the angle of these segments would increase beyond the vertical. By using an inverse tangent function. at the aft perpendicular. During the testing of the second hull form. to produce a range of -180º to 180º. 1997 79 . This initial caused some problems to the procedure analysing section curvature. to obtain angles of more than 90º. During the construction of a hull with wall sided sections. some distance above the waterline. using method 3. to review the uniformity of the curvature in the section. To overcome this problem. In a yacht with no transom University of Strathclyde.
The Open 50 and 60 class yachts are designed. for downwind sailing. A large transom beam created problems. Figure 10. when the overhang of the same yacht is reduced to zero. with the size dependant on the order of the B-Spline function producing the curve. a yacht with no stern overhang could be produced and second. This solved two problems. the position of the extreme end of the transom. Optimising the hull for this sailing direction produces very flat. first. The flat sections are used over most of the stern of the yacht and the beam at the transom is almost the same as the maximum beam. A loop is produced. was allowed to be found by the profile generating process. The main hull University of Strathclyde. To remove this unwanted feature. The fixed section shape of Station 20. the aft profile or "Run" of the yacht was now more hydrodynamically sympathetic. until the profile intersects with the waterline at the aft perpendicular. which allow the yacht to plane at speed. beamy.2. above the waterline. causing a reduction in resistance. Figure 10. deep. Figure 10.Marcus Bole Parametric Generation of Yacht Hulls is possible to create a bad profile shape. at the aft perpendicular. primarily.2. aft sections. created an initial hull with large. aft sections. An Open 60 with the wide stern characteristics. 1997 80 .1 shows the transom of the YD-40 hull and the transom produced. An iterative procedure was developed to vary the position of the this point on the transom.
Marcus Bole Parametric Generation of Yacht Hulls generation procedure attempted to obtain the correct prismatic coefficient and longitudinal centre of buoyancy for the hull. The shape of the diagonals can then be projected to the aft. By using a least squares regression technique. as the B-Spline fit procedure does not allow these curves to be extrapolated. The diagonals are currently. is below the transom. Figure 10.3 Figure 10. when the intersection of diagonal (2) with the transom plane. In this University of Strathclyde. the intersection points between the extrapolated projected diagonals and the transom can be found. to be generated.3 . only defined between the bow profile and Station 20. The fixed nature of Station 20 was changed so that the angle of flare. to the region of the transom. The points can then be used to form the vertices of the control polygon. By using this assumption. The shape of the transom is similar to the sections. 1997 81 . the transom can be formed in a similar fashion to the sections. to diagonals between Station 10 and 20. diagonal (2) will not be able to form part of the transom. with shallower draught. by using the diagonals to specify the vertices of the transom control polygon. the profile contains a segment which specifies angle of the transom. at the deck edge. could be modified to reflect the real shape of hull and to allow sections. however. producing aft sections with section area coefficients higher that one. Assuming that the transom is a plane. a curve of quadratic order can be fitted. 10.Intersection of Diagonals with Transom In some cases.3 THE TRANSOM None of the methods so far have generated the full shape of the transom.
uses matrices to construct the control polygon from the specified fit vertices. similar to the technique employed in B-Spline surface. the standard procedure used to numerically invert matrices is unable to handle the size and amount of numbers that can be involved during the fitting process for a surface definition.Marcus Bole Parametric Generation of Yacht Hulls situation. it is likely that the transom has been projected from a hull that was specified with unsuitable parameters. The first method attempted was similar to the B-Spline fit process used for curve fitting. B-Spline sections are formed from B-Spline diagonals. 1997 82 . If the hull was defined with a surface it could transported to many other ship design applications to allow further modification.4 OUTPUT The hull generation procedure must produce an output for it to be deemed useful. as in these conditions. A second procedure was investigated. Unfortunately. the process detects this condition and places the vertex controlled by diagonal (2) at the bottom of the transom. 10. This used the concept that the system used to create the yacht hull is almost a surface. If a B-Spline surface was used to define the hull. A investigation was made into turning the sections created by method 3. There are a wide variety of methods and formats that this output could take. The most useful format would a surface. into a surface. This is also the position that the vertices of diagonals (1) and (3) are placed. one after the other. The positions of the vertices in the diagonal control polygons must be close to the vertices of the control polygon net for the B-Spline University of Strathclyde. to allow surfaces to be fitted to a set of points. other CAD applications could have access the surface. two B-Spline processes. The procedure was extended. Under the specification of certain parameters it is possible to get unusually shaped transoms. This should not be regarded as a failure. The B-Spline fit process used for curves. There are a variety of ways that a B-Spline surface can be formed from the generated sections.
This develops ship body plans into a B-Spline surfaces by using B-splines fitted through sections and B-splines fitted through waterlines. was discovered. In further development. Figure 10. As this successful procedure followed a similar process to the sections and diagonals of the current hull generating method. the hull generation method may be developed to be surface based procedure or using Jensen and Baatrup [10]. produced a B-Spline surface. into a hull pre-processor for a main stream CAD package such as AutoSHIP or as part of an in-house CAD package. this process failed. the yacht sections may be transformed into a B-Spline surface. are the remaining points for the surface control net. once clear. as yet. University of Strathclyde. 1997 83 . the surface procedure was debugged. the method can be developed further. a similar procedure developed by Jensen and Baatrup [10]. Initially. to see if the result produced is accurate to the original sections and profile. The surface.4. the points that define the sheerline and the profile. However.Marcus Bole Parametric Generation of Yacht Hulls surface. as it was found to contain many errors and. has not been analysed. Once the surface is found to be accurate. All that has to be found.
Marcus Bole Parametric Generation of Yacht Hulls Figure 10. A surface produced during the last development of the method. 1997 84 .4. University of Strathclyde.
where an object forms one of these pieces. compiling. edited and run all within the same application. Programming languages and systems have progressed to the extents that complex programs can be written in very short amounts of time. with is compatible with Turbo Pascal. University of Strathclyde.0 with Objects. An object groups all the information and code relating to a problem or item together so that the situation can be solved in easier stages. There are now a bewildering variety of programming tools some of which provide an integrated development environment in which writing. Turbo Pascal also uses one of the fastest compilers that can be found in compilable high end languages with the possible exception of C. An object oriented programming approach allows a problem to be broken up into smaller pieces. such as B-spline techniques it is essential to use a computer. At the initial stage of this project. Using more complex operating systems such as Microsoft Windows™ could add problems which would not be connected with the hull generation method itself. Programming at the low DOS level means that a system can be simpler. the programs were written using Turbo Pascal 7. 1997 85 . All the main program has to do is interact or "talk" to the object. a "user friendly" interface can be made to this complex process. the program will be ported to a Microsoft Windows based system. editing.Marcus Bole Parametric Generation of Yacht Hulls 11 IMPLEMENTATION 11. Turbo Pascal also supports object-oriented programming. Later in the study. This is an MS-DOS™ based programming environment where a program can be written.1 PROGRAMMING LANGUAGES AND STYLES To be able to use a numerical method. debugging and execution can all be performed at the touch of a few buttons. Using Borland Delphi. OOP. Today. Borland Turbo Pascal has good mathematical functions and the graphics library supplied with this language also allows the display of curves and geometry on the screen so that the results of a calculation can be quickly analysed.
or call other modules. Then a calculation procedure is called to find the value corresponding to the eventual goal to return as Y. but it is much more University of Strathclyde. As mentioned in section 7.1. The function takes the form of Y=F(X). The value of X. The main procedure of a module initialises iteration information. iteration information and a modification function to the iteration process. A differential function for a B-Spline function can be obtained.Marcus Bole Parametric Generation of Yacht Hulls 11. Turbo Pascal 7. Previous hull generation systems have used the Newton-Raphson technique to obtain solutions. such as data storage and retrieval.0 supports OOP. The modular approach also gives flexibility so that various operations can be changed. which for the majority of the hull generation procedure this type of programming is not necessary. The main procedure passes the initial start values. 1997 86 . The modification procedure uses the value of X to modify the shape of the hull.3 THE ITERATION PROCEDURE The design of the process of attaining the goals is very important. which means that the system is made up of separate modules or parts. Each module performs it's own iteration operation on the hull. The modification function resides within the module. numerically. Each module follows a similar format. Each module can control up to two effects. as part of the process. a solution to a function. This allows every module to have a similar format or layout to achieve the iteration goal. but it can be used for the many ancillary systems necessary in any program. generally a volume or area and the centroid of that volume or area. and the program can be debugged and modified in an easier manner during the development process. such as the intended goal to be reached and the accuracy or tolerance at which the goal should be reached. The modules can be called by. is the initial start value of the iteration process and the X value is modified by the iteration procedure until the goal is obtained.2 THE APPROACH A modular approach to programming has been followed. removed or added as necessary. The Newton-Raphson is considered one of the most efficient techniques for obtaining. 11. To use the Newton-Raphson technique with any success one requires a mathematical function which can be differentiated.
Y1) and (X2. then the required CP has be found and the value X3 can be used to create the hull. The iteration process calls the modification function with X1 as a parameter. The structure used in linear interpolation. Next. in this case will be the returned value of CP. to attain goals in the current hull generation method an engineering approach was taken. The line can be extended so that the required prismatic coefficient. University of Strathclyde. the value of X1 is sent to the iteration procedure when it is initially called. Now a line can be placed through the points P1 and P2 with co-ordinates (X1. The result of the modification function. 1997 87 .Marcus Bole Parametric Generation of Yacht Hulls complex to calculate than the original B-spline function. If Y3 is close enough to YGOAL.1. then a line is drawn though P2 and P3 and the process is repeated. however. by using simple standard linear interpolation. the prismatic coefficient CP. it thought that most of the curves iterated in the hull generation procedure are fairly simple.1. YGOAL. If the value of Y3 is not close enough to YGOAL. The linear interpolation technique may fail if applied to a curve with complex shape. for example. X1 is a variable which can be used to vary. as part of the initialisation process. So. the iteration procedure increases X1 by 5% to obtain a value X2. X2 is passed to the modification function which returns a CP in Y2. Y1. Considering Figure 11. can be used to find the value X3. X3 is now passed to the modification function. The modification function takes the form of Yn=F(Xn). Y2). Figure 11. iteration technique.
One of the reason for the popularity of UNIX is the fact that it supports that management required for a large number of computer terminals and files.. This means that a program or calculation procedure will be started by typing the command into the operating system. is text based. Thus. it does not support have any graphics system of its own. The iteration procedure. but the University of Strathclyde. The UNIX system. The operating system will load the program. 11.. perform the calculation and return its output in another file. One of the essential ingredients of implementing the hull generation technique is the use of graphics. a command line is used to run and perform operations. 1997 88 .2. Figure 11. however.2.4 USING THE PROGRAM It is historically common for many calculation programs to use "command line" operation because of the wide use of the UNIX operating system.Marcus Bole Parametric Generation of Yacht Hulls The iteration procedure is illustrated in Figure 11. 'Start' Value Iteration Information Modification Function Start Has Iteration Process been Initialised? No Create P1 Yes Increase 'Start' by 5% Create P2 Y=F(X) Y=F(X) Any divide by zero possibilites No Perform Linear Interpolation Yes Fix Start Value Evaluate next point Pn Y=F(X) No Has the goal been reached? Yes Continue. Using graphics not only allows the curves to be displayed. the program will open it's input file.
Modern day computer users are thoroughly spoilt with fancy displays and fast execution to the extent that is essential for the system to be interactive.Marcus Bole Parametric Generation of Yacht Hulls progress of the iteration can be displayed to show the evolution of hulls. the use of graphics enables the system to be interactive. with an attractive easy to use and powerful user interface. to a full graphical user interface as more functions were added. The application was initially developed from simple showing curves on the screen.8 show views of the application that was used to develop the hull generation technique.3. 1997 89 . The application. The Figures 11.3 to 11. Above all else. showing the page used to specify parameters University of Strathclyde. It is useful. Figure 11. in the cases where the iterations do not produce simple-value convergence. The figures show a hull developed with Method 2. for example.
1997 90 . The application showing the progress of a calculation Figure 11.4.5. The display of the stations produced by the application. University of Strathclyde.Marcus Bole Parametric Generation of Yacht Hulls Figure 11.
Marcus Bole Parametric Generation of Yacht Hulls Figure 11.6. The application displaying the profile of the hull Figure 11. 1997 91 .7. University of Strathclyde. The plan view of the hull displayed by the application.
Marcus Bole
Parametric Generation of Yacht Hulls
Figure 11.8, The section area and CX curves produced by the application.
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University of Strathclyde, 1997
Marcus Bole
Parametric Generation of Yacht Hulls
A powerful system has been developed, which creates yacht hulls. The uses of such a system should now be considered. As mentioned in section 10.3, it possible to develop the method further, so that a hull can be modified further, by another program to add other features, such as superstructure, different transoms or detailed interior plans. It also allows the hull definition to be used for construction purposes by using Computer Aided Manufacturing and this technology has become standard throughout the marine industry. However, by developed the method further, analysis can performed on important aspects of the hull, increasing the sophistication of the generation process.
The method generates a hull rapidly, which opens up opportunities for it to be part of a much larger process. There are already systems being developed, which can change a hulls shape, to optimise or analyse more important characteristics than the general hull specification parameters. An American company, New Wave Systems [8][9], is
developing a commercial ship design software suite, the Nautilus System, which contains hull variation and evaluation procedures. The hull variation process used in the Nautilus System appears to be a general system, which can change the shape of any existing hull form to achieve goals similar to those used in the current study. The evaluation process developed by Hollister [9], for the Nautilus system, is a Geosim Coefficient Resistance Evaluation process. However, the resistance evaluation system is dependent on access to a resistance database to analyses certain types of hull form. Other more interesting evaluation techniques are being investigated by New Wave Systems. Five types of evaluation routines are current being developed. 1. Geosim Coefficient Resistance Evaluation - These techniques break the overall resistance of the vessel into their component parts, such as viscous resistance (CV), residual resistance (CR), and appendage resistance. Residual resistances are often determined from a regression analysis of tank test data.
University of Strathclyde, 1997
Marcus Bole
Parametric Generation of Yacht Hulls
2. Planing Hull Resistance Evaluation - This type of resistance evaluation uses the same force breakdown techniques as the Geosim approach, but adds moments of forces about the centre of gravity of the boat. This defines a steady state free body diagram of the boat that can be solved for the resistance and trim of the boat. 3. Sailboat Velocity Prediction (VPP) -This type of resistance prediction is also based on a Geosim approach, but adds sail and hull lift and drag forces. A search technique is used to determine the velocity and heel angle of the boat for each wind speed and wind angle. Note that for certain racing sailboats, the hull variation process is further complicated by the need to meet the shape constraints of any applicable rule, such as the America's Cup rule. 4. Computational Fluid Dynamics Methods (CFD) - These techniques typically use a polyhedron mesh generated from the shape of the hull to perform a full 3D analysis of the resistance of the hull. 5. Finite Analysis Methods (FEM) - These techniques use a polyhedron mesh generated from the shape of the hull to perform a 3D structural finite element analysis of the hull shell. The evaluation processes are being developed around very import fields in marine design and it shows how a hull variation procedure can be used as part of a much complex numerical analysis system using CFD or FEM. Topics, such as CFD and FEM, are too complex to discuss at this level and as this project follows a yachting theme, velocity prediction will be discussed further.
University of Strathclyde, 1997
1. when generating hull in conjunction with a VPP. Even the recently developed IMS rating system uses a VPP to evaluate a yachts performance. heel and leeway angle. It is also common for large. follows a fairly simple process.Specify rudder and trim tab angles. 1997 95 .Marcus Bole Parametric Generation of Yacht Hulls 12. The process is iterative and is similar to the hull University of Strathclyde. Figure 12. boat speed. The yacht hull generation procedure. End Figure 12. A VPP.The Basic VPP procedure. Start Input detailed geometry of canoe body. successful yacht designers to develop their own VPP analysis software. transverse sail force and heeling moment Calculate heel angle from heeling moment and stability characteristics Change heel angle No Is heel angle equal to that assumed? Yes Calculate boat speed from sail driving force and resistance characteristics Change boat speed No Is boat speed equal to that initially assumed? Yes Calculate leeway angle from transversesail force and side force characteristics Calculate for another set of conditions Change leeway angle No Is leeway angle equal to that assumed ? Yes Print the wind speed and direction. heel angle and leeway angle Specify true wind speed and direction relative to yacht heading Calculate sail driving force. would greatly reduce the time required to develop a hull with optimised performance.1 . balancing the forces and moment affecting a yacht. keel. Assume Initial values for boat speed.rudder and sailplan. when under sail.2 VELOCITY PREDICTION AND HULL VARIATION The Velocity Prediction Program (VPP) is becoming one of the most important tools in yacht design. etc.
are used so that the results of tests can be interpolated to other hull and sail configurations. Velocity prediction programs use theories from three areas of study. based on experimental results. A good velocity prediction program will consider all the systems found of a yacht. developed through the regression analysis of experimental data. The functions found in VPPs are. Functions. In this process. 1997 96 . Effects are generated by: 1. the goal is to minimise the difference between assumed and calculated angles. Trim Tabs 6. Propeller Operational environmental factors are considered and these are: • Wind Speed • Wind Direction • Wave Frequency • Wave Direction • Wave Length To analyse all these systems. generally. Keel(s) 3. to determine the performance. This is common practice and it is easy to forget that the data will only be truly valid over the range experiments.Marcus Bole Parametric Generation of Yacht Hulls generation system. The theory used for foil hydrodynamics is studied in University of Strathclyde. a complex set of functions required. Aerodynamics and Foil hydrodynamics. Resistance. Rudder(s) 4. The Hull 2. A VPP has to consider effects generated by the hull and appendages. Sails 5.
as much experimentation has be made on families of foil shapes. The VPP cannot control all features on a yacht. A study of a simple VPP was considered to extend University of Strathclyde. the validity of the analysis functions used in the VPP may be compromised as the hull is changed. Aerodynamics in a VPP are calculated through a similar procedure as resistance. The VPP is highly dependent on experimental data. step would have to be take to stop a hull moving outside of the valid range of the resistance data. A better VPP could be developed in the future. the forces developed by the sails can be estimated. otherwise. 1997 97 . Today. can be analysed. to allow VPPs to have more accurate methods of prediction hull resistance. the resistance of hulls that are not important enough to be tank tested. induced resistance and heeled resistance. for use within the Delft VPP. to construct resistance extrapolators for residuary resistance. including interaction effects between sails. The resistance of the yacht hull has been investigated. A hull generation method can be easily adapted to become part of a VPP. L. Most techniques are recent work. This is likely to make the VPP more accurate and allow valid calculations to be made on hulls of all shapes. This resistance method uses data calculated from 39 test hulls. Computational Fluid Dynamics procedures could be used instead of regression functions based on experimental data. Poor in 1986. If a VPP was used in conjunction with a hull optimisation technique. any hulls that are not within certain boundaries and similar to the original test hull may not give reliable results. the hull produced would not be correctly optimised. Therefore. Using the various lift and drag coefficients developed for the IMS system by C. if a hull generation procedure was used as part of a VPP optimisation process. The main difficulty is to decide which hull features the VPP should control. The sail functions take account of many complex effects. The procedures used to calculate resistance and aerodynamic effects are not as well known. as the system would be to complex and would always produce the same yacht solution. such as the NACA series. Calculation of frictional resistance is made by using Froude's method. The Delft Series has limitations.Marcus Bole Parametric Generation of Yacht Hulls fairly standard and well known. more recently. The University of Delft has developed the Delft Series [5]. through the use of regression functions.
Marcus Bole Parametric Generation of Yacht Hulls this hull generation study. It can now take a matter of seconds to develop a hull. so a smaller study of a resistance optimising procedure is explained in appendix 16. 1997 98 . less design skill is required to produce a hull. Using a hull generation procedure. by considering aerodynamic effects and wind tunnel testing vehicles. 12. generally. a look at the car industry show similar cars have become. A full study of VPPs in relation to hull generation and optimisation would require an investigation greater that the current study. they will all look the same. This trend in design has been recognised and now some manufactures are starting to design cars with "character". The operator of such system does not need to know how to produce a hull or even what is involved in producing a hull. which before may have taken hours. But it is important that the operator should have studied the theory to allow the result from the computer to be checked. This means that. The introduction of a system which can produce hulls quickly has a impact on the types of people using a design system. to develop a system which could vary more than the hull would require a detailed study of sail characteristics. were analysed to see if the performance of the hull could be optimised at a lower level.3 THE IMPACT OF HULL GENERATION PROCEDURES The hull generation procedure developed has shown how easy it is to develop a computer based procedure to rapidly produce hulls.3. A design trend similar to the car industry has been followed in yachts. resulting in mass production yachts with standard "Off the University of Strathclyde. Much design today is already at this stage. Unfortunately. the result produced is less variety in the style of cars available today. The functions used in a VPP governing the hull. however. Although the hull produced cannot always be used directly. The hull only has control over resistance characteristics. This is probably the result of making a car more economical. it shows how the computer can greatly reduce the amount of time required to produce a hull. The hulls produced by this method will be part of the same family.
Generally. even if it performs well. Designers and owners search for even the smallest amounts of extra performance and a hull generation technique assist in the process. ® ® ® University of Strathclyde. 1997 99 . here economy is a priority. The hull generation procedure would be only be effective in optimising the design of racing yachts. an owner will not purchase a yacht unless the look of the yacht is pleasing. which would reduce the variety in yacht hulls. however. A parametric hull generation procedure will produce "Off the shelf" styling. there may not be as much scope for a generation system to be used in yacht design. Hull generation procedures have been successfully developed for ship design.Marcus Bole Parametric Generation of Yacht Hulls shelf" styling.
It is difficult to test these hypotheses with the current method. An interesting application of a hull generative method would be teach prospective naval architects about the numerical values that are used in the design and shape of marine vessels. To develop a good hull. Under most circumstances a shape is produced. 1997 100 .1 REVIEW OF THE FINAL METHOD It has been demonstrated that a good hull can be produced with a parametric hull generation technique using B-Spline functions. in many of the results. The hulls produced by the method are. It was predicted that. skill is required to select parameter. however. University of Strathclyde. There does not seem to be a clear reason for this. fair. However. This function is a very small part of the method. However. generally. However. as in yacht design. A yacht hull can be created with the method in a matter of a minutes. The hull generation technique is heavily reliant on the function linking the control vertices of a section together. possible reasons for these effects could be either (a). the procedure will only produce a fair hull. it can be shown that it becomes difficult to generate good hull without a real grasp of the effects of each numeric parameter. there is a range of numeric parameters. good hulls are not always produced. it would be straight forward and fairly easy to develop a hull with a parametric process. as they are common throughout the design of all marine vessels.Marcus Bole Parametric Generation of Yacht Hulls 13 DISCUSSION 13. in most cases. most hulls will require further by using another program or by "tweaking" some of the numeric parameters. yet. there is a range of numeric parameters for which fair yachts hulls fall within or (b). it is the only part of the keeping sections "yacht" shaped. that by modifying parameters. which generate a good hull and it can be seen. to control the shape of a section. these problems do not transpire and the current procedure has not been tested enough to disprove (b). Most naval architects will be aware of the parameters that are used in the method. however. within which. knowledge about how the different parameters affect a hull is required. a good hull will be only produced if sensible sets of parameters are used.
The quality of the function controlling the section shape has a major influence on whether a good hull is produced. to find out if further development would produce a method. good hulls can be produced and in most cases the hull can be developed further. By improving this function the hull generation method may become a more powerful design tool. with the current method. can be removed.Marcus Bole Parametric Generation of Yacht Hulls The effects of this function should be investigated in greater detail. 1997 101 . which would allow a greater flexibility in the type of yacht hulls produced and to see if the imperfections in the hull produced. into a yacht. ® ® ® University of Strathclyde. to produced an application which provides more functionality that the system developed to date. The generation technique produced in this study will be developed further. Despite these small shortcomings.
Characteristics that are required for a hull generation technique. ® ® ® University of Strathclyde. • Computer based generation procedures do not always provide enough flexibility in the amount of the shape of a hull can be varied • B-Splines do not provide the best method for producing curve which have flow through points and bound areas. which can be used directly or developed further to the taste of the designer. • There seem to be many more applications for hull generation techniques than originally predicted.Marcus Bole Parametric Generation of Yacht Hulls 14 CONCLUSION The final development of the hull generation technique provides a quick and efficient way of designing a yacht hull. • A compromise has to be found to the number of parameters to optimise. The following conclusions can be drawn about a computer method designed to generate yacht hulls with B-Splines: • It is possible to develop a method that generate yacht hulls with B-Splines. 1997 102 . to ensure a hull with the correct proportions is generated and to ensure that hull is suitable to be used as a safe marine vehicle. many of these applications are not considered to be as important in yacht design as they are in commercial ship design. • B-Splines do provide the best method for transporting the hull definition to other applications and programs. however.
"Interactive Creation of Fair Ship Lines". No 4. Glasgow. "Design Your Own Yacht" New Wave Systems. Rogers and J. Hollister. "The Cruise of the Teddy". Alan Adams. "Sailing Yacht Performance in Calm Water and in Waves (The Delft Series)" Delft University of Technology. Vol.newavesys. David Vacanti.serv. Danish Centre for applied mathematics and mechanics. [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] University of Strathclyde. Journal of Ship Research.Marcus Bole Parametric Generation of Yacht Hulls 15 REFERENCES AND BIBLIOGRAPHY 15.newavesys. SNAME. J. "The Representation of Ship Hulls by Conformal Mapping". "Mathematics of a Body Plan". Bergen College. New Wave Systems. A. Kyan..Demonstration Version". Keuning and A. Http://www.Demonstration Version". Eliasson. Inc. "Mathematical Elements of Computer Aided Design". Vol. Reed and Horst Nowacki. Http://www.net/vyd. David F. Norway. Jens-Herman Jorde.1 . Inc. "ProSurf 2. Http://www. "Principles of Yacht Design" Ben Smith. The Technical University of Denmark. Lars Larsson & Rolf E. Jensen and J. Gerritsma. Journal of Ship Research. "Prolines 6. "Transformation of Ship Body Plans into a BSpline surface". 11th Chesapeake Sailing Yacht Symposium. Earling Tambs. Baatrup. 13.23 .1 REFERENCES [1] Arthur M. 1928. Strathclyde University. J.com/hullvary/hullvary. Vacanti Yacht Design. "Direct Generation of Fair Ship Hull Surface from Design Parameters".htm J.. 18. "Automatic Hull Variation and Optimisation". J. Von Kerezek. Versluis. No 2. 1997 103 . McGraw-Hill. 1990. Mr A.com Stephen M.
1988. . 101. 1989. 1979.2 BIBLIOGRAPHY NAVAL ARCHITECTURE AND YACHT DESIGN Preliminary Design of Boats and Ships Cyrus Hamlin. 1993 Yachting World. 1981. Marchaj. 1990. COMPUTERS AND PROGRAMMING The Way of Delphi Gary Entminger. Kinney. 1996. C. Sailing Theory and Practice. Steven Harrington. SNAME vol.Marcus Bole Parametric Generation of Yacht Hulls 15.(VPP Development) Peter van Oossanen Van Oossanen & Associates. 1974. 1983. Computer Graphics: A Programming Approach. The Complete Offshore Yacht Yachting Monthly. A. Aero-Hydrodynamics of Sailing C. The History of Yachting Douglas Phillips-Brit. Colin Archer and the Seaworthy Double Ender John Leather. 1997 104 . University of Strathclyde. Marchaj. Skene's Elements of Yacht Design Francis S. Predicting the Speed of Sailing Yachts. A.
Marcus Bole Parametric Generation of Yacht Hulls 16 APPENDICES PARTICULARS OF THE YD-40. 1997 105 . APPENDIX 1 University of Strathclyde.
Method using this characteristic can find the shape of the curve by a reverse process of analysis. then. Thus area under the basis functions can be found. a direct procedure for finding the shape of the B-spline curves. it is not directly clear what "area" is found by this procedure.Marcus Bole Parametric Generation of Yacht Hulls APPENDIX 2 CALCULATION OF AREA AND CENTROIDS OF B-SPLINE CURVES. It may be possible to use a set of similar piecewise equations on most of the Basis functions to find the area of each. the use of explicit mathematical functions allows areas and centroids to be found easily through the use of integration. the area of a section below University of Strathclyde. the Basis Functions and the control polygon. because the Basis functions are piecewise. B-Spline functions are constructed from two parts. The control polygon imparts a weighting factor on the B-Spline function. However. the basis functions are mostly similar and are only non-zero for four sections of the control polygon of a cubic B-Spline. 1997 106 . due to the complexity of the function. A large number of piecewise functions is required for a B-Spline defined with many more points. In other methods. The numerical procedure for creating a B-Spline curve can be analysed so that Basis functions can be obtained. for the general case would be intensive as it would have to put many small equations together to find the area of each Basis Function. A procedure for finding the area of a B-Spline curve. The parametric nature of the B-Spline function makes it more difficult include boundary features when calculating. These functions are simple and can be easily integrated. for example. It was suggested that. The Basis functions are normally found by the numerical analysis of the knot vector set. A number of equations are required to produce each Basic function. However. This can reduce the size of a method and in most situations a mathematically "elegant" process is developed. There are some interesting problems associated with this procedure. an area can be found for the B-Spline curve by multiplying the area found from the basis functions by the control polygon co-ordinates. Finding the curve properties for B-Splines is more difficult. as the function is parametric and it may not be a quantity that is of any use. if a process could be found for directly integrating B-Spline functions. similar to the other methods could be used.
Finally. 1997 107 . such as used in other methods.Marcus Bole Parametric Generation of Yacht Hulls the waterline. would require more information to place correctly. ® ® ® University of Strathclyde. the vertices of the control polygon. A well defined B-Spline curve has control polygon with many vertices. This complexity may make a mathematical procedure for finding the area of B-Spline curve practically impossible. by the analysis of the area and moments. for example. This procedure would have to result to an iterative process to find the position of these points and no advantage gained over a hull generation method using Simpson's rule to find the area of B-spline curves. An attempt to find the shape of a station.
There are many components which contribute to the resistance of a yacht and the Delft series [5] is one technique which can be used to calculate these components. Functions developed to analyse resistance. Therefore. generally. the energy loss in wave generation and from viscous pressures. the energy lost due to the friction generated between the water and the hull surface can be calculated. there is no control over availability. The Froude extrapolator is also used to calculate frictional resistance caused by the appendages such as the keel and rudder. currently. Although the wind is a free power source.By using Froude's extrapolator. The Velocity Prediction Program is a tool which assists in this optimisation process. unable to change the shape of the hull to optimise the performance.This is a function which Delft series uses to model. journey times can greatly increase. As parametric hull generation methods can produce hulls quickly.This function is used in the Delft series to model. with the addition of a parametric hull generation procedure. Without this. Resistance is important in all vessels. The Delft series is one such procedure and can be used to find many components of resistance for a modern type of yacht hull. which is generated by the hull and appendage foils. The VPP is. there is scope for these types of procedure to include resistance optimisation.Marcus Bole Parametric Generation of Yacht Hulls APPENDIX 3 A RESISTANCE OPTIMISATION PROCESS In most mobile marine vessels resistance is an important factor. however. the sails and the hull have to be designed and constructed in a fashion to reduce the amount of energy lost. this may be possible. through the use of experimental data. however. depend on experimental resistance data. 1997 108 . University of Strathclyde. the energy loss due to the induced drag associated with lift. The functions used to calculate the resistance components of a yacht are: • Frictional resistance . through the use of experimental data. • Residuary Resistance . in a yacht it has a higher priority. • Induced Resistance .
Marcus Bole
Parametric Generation of Yacht Hulls
• Heeled Resistance - This function is used in the Delft series to model, through the use of experimental data, the energy lost when the yacht is heeled. • Wave Resistance - This function models how the resistance is affected when the yacht travels in waves. These components all act to slow the yacht. By minimising the effect of each the hull can be made more efficient. To optimise all these resistance components a Velocity Prediction Program would have to be constructed, as the effects of the sails have to be considered. A simpler resistance optimisation procedure can be developed if only the upright resistance is considered. Upright resistance is the largest resistance component, resulting in
approximately 60% to 80% of the total resistance. Upright resistance is found from frictional and residuary resistance function. A large section of the Hull Design chapter in Larsson and Eliasson [6] details which effects must be considered, when minimising resistance. For a hull of fixed geometric dimensions the resistance is governed by three key factors. 1) Optimum Prismatic Coefficient. 2) Optimum Longitudinal Centre of Buoyancy. 3) Optimum Gyradius. Gyradius is a measure of the rotational inertia of a body and is controlled by the distribution of weight. Gyradius controls how well a yacht performs in waves,
influencing average velocity. In a yacht, gyradius is controlled by the position of ballast, masts, auxiliary engine and outfit. The gyradius cannot be adjusted by a parametric hull generation system. Optimum values of Prismatic Coefficient and
Longitudinal centre of Buoyancy can be adjusted by a parameter hull generation system, as these are some of the main parameters. Graphs of optimum values of these parameters are obtained from [6] and are shown in figure 16.2 and 16.3
University of Strathclyde, 1997
Marcus Bole
Parametric Generation of Yacht Hulls
Optimum Prismatic Coefficient
Prismatic Coefficient (CP)
0.5 0.3 0.35 Froude Number (Fn) 0.4 0.45
Figure 16.2, Optimum Prismatic Coefficient.
Optimum Location of Longitudinal Centre of Buoyancy
Longitudinal Centre of Buoyancy (LCB) % of Lwl from F.P.
50.00% 0.3 0.35 Froude Number (Fn) 0.4 0.45
Figure 16.3, Optimum Position of LCB.
University of Strathclyde, 1997
Marcus Bole
Parametric Generation of Yacht Hulls
Both Figures 16.2 and 16.3 plot optimum values against Froude number. A decision must be made to which speed the yacht will have optimum performance. Larsson and Eliasson state that, normally, hulls are designed to have optimum performance for upwind sailing. The losses involved in upwind sailing are high as the yacht system has do travel against the flow of water, wind and waves. For upwind sailing, Larsson and Eliasson suggest that, the Froude number should be around 0.35. To develop a resistance optimisation procedure it is necessary to include a database of information to allow the resistance to be optimised. Functions can developed from Figures 16.2 and 16.3 could be used to optimise the resistance, however, these may not contain enough information about the range of hulls and sailing velocities that could be considered. An example of the other affects that may be studied can be found the in yachts which competed in the last round the world Vendee Globe yacht race. The race is sailed mostly downwind, as the race is run from west to east. The Open 50 and 60 class yachts sailing in the race, were developed to have optimal performance downwind. To study these vessels the selected Froude number would not be that same as for upwind sailing. A better method to optimise a hulls resistance characteristics can be develop by considering the upright resistance functions from the Delft series. By varying the values of prismatic coefficient CP and longitudinal centre of buoyancy LCB, and calculating the resultant resistance, optimum values for CP and LCB can be found. It is necessary to vary these factors by keeping other parameters constant. For this
optimisation procedure, the displacement was kept constant by allowing the midship section coefficient CM to vary.
University of Strathclyde, 1997
The resistance optimisation procedure was developed further to be part of the desktop interface. The optimum values of prismatic coefficient and longitudinal centre of buoyancy can be found by using multivariable regression.35) and Displacement 1300 1250 1200 Resistance (N) 1150 1100 1050 1000 0.000% 1250-1300 1200-1250 1150-1200 1100-1150 1050-1100 1000-1050 0.4.520 55. YachtLINES. 1997 112 .308% Longitudinal Centre of Buoyancy (%) Figure 16. How resistance varies with CP and LCB for a YD-40 (Fn=0.35). Figure 16. a single variable regression technique could be used. The quadratic regression functions can be easily differentiated to find the minimum point corresponding to optimum values of CP and LCB.615% 0.Marcus Bole Parametric Generation of Yacht Hulls Resistance for YD-40 For constant Froude No (0.077% 52.545 Prismatic Coefficient 53.35. over the data points found from the resistance calculations. The point of optimum resistance can be found from the However. It can be seen that at this Froude number there is a minimum value of resistance. By assuming that the effects of prismatic coefficient and longitudinal centre of buoyancy are independent. which would take time and finding the minimum point would be more difficult. Results from the process agreed well with the optimum values of CP and LCB developed for the YD-40 in [6].769% 50.4 shows the variation in resistance of the YD-40 hull with respect to CP and LCB at a Froude number of 0. which was developed to demonstrate a graphical user to the University of Strathclyde.532 54.569 0.582 0.846% 0. Two quadratic least squares fit were constructed through resistance data points dependent on prismatic coefficient and longitudinal centre of buoyancy. resulting surface.557 0. this method would require the calculation of many resistance data points. An easier method was chosen.594 51.385% 53.538% 50.
Resistance Optimisation Interface to YachtLINES This interface creates an easy method to changes the velocity at which the hull is optimised. Figure 16.5. is displayed.5. It also allows the user to specify which parameters are optimised and shows the progress of the procedure. University of Strathclyde. Finally. about resistance. all the information obtained from the hull. The interface to the resistance optimisation process is shown in Figure 16.Marcus Bole Parametric Generation of Yacht Hulls hull generation method. 1997 113 .
This allows the parametric hull generation system to brought directly from DOS to Windows. • Loading and saving files. Creating a user friendly interface within Windows allows the following functions to be performed easier. application programming for Window. has been implemented from within the basic DOS operating system. with these compilers. The Microsoft Windows operation system removes these headaches from the program. is very simple and allows the programmer to concentrate on giving the application a fully functional user friendly interface. three dimensionally. as there are so many manufactures making equipment. Borland Delphi is a programming language that has been developed especially for the Microsoft Windows operating system and it is fully compatible with Borland Pascal. The parametric hull generation method developed. University of Strathclyde. The operating system has support for most computers and supplies an interface to a program so that it can access all hardware functions. As a result. The compiler does all of the work connecting the program to all different systems within the Windows operating. It does not supply full support for devices such as mice neither does it support high graphical screen resolutions. • Editing of Parameters. so far. To supply device drivers for every computer system is difficult.Marcus Bole Parametric Generation of Yacht Hulls APPENDIX 4 YachtLINES: A DESKTOP INTERFACE. This type of operating system has given rise to visual program compilers such as Visual Basic and Borland Delphi. • Viewing the hull. such as mouse operations. These shortcomings mean that a program has to supply its own software device drivers for every computer hardware system. • Easy addition of extra functions. 1997 114 . to allow t every computer user to use the application in the same way. The method has previously been programmed in Borland Pascal. such as a resistance optimisation process. This operating system was developed to be simple. These systems allow a programmer to draw an application on the screen.
This contains all the parameters allowing them to be edited easily. It also provides feedback from the hull generation procedure about the state of the generation procedure and if any warning or errors have occurred. it was decided to make a less ambitious program. resistance information and hydrostatics.5 to 16.Marcus Bole Parametric Generation of Yacht Hulls The interface was developed initially to support a Velocity Prediction Program with a full hull optimisation process. each is contained in a separate window: • Generator . as time taken to create a hull would have caused an inconvenient pause within program. to allow the parameters to easily edited and to allow the resulting hull to be viewed directly. A system such as this would re-generate the hull every time a parameter was changed. After the hull generation procedure has been run the stations and hull outlines curves are displayed. However.This is a text viewer in which a document can be created containing information such as input parameters. in use. hydrostatic calculations and a file export function to allow the hull to be used in other programs. 1997 115 . It is a view port which displays three the standard views of the hull in a layout similar to a lines plant. when the theory regarding the velocity prediction system was found to be fairly complex and based fully on experimental data. The following figures 16.This provides the primary means of viewing the hull. When parameters are edited. • Yacht Lines .8 show the full application. However. this feature would have slowed down the hull generation process. YachtLINES. This would give the user more information about how the parameters affect a hull. construction lines depicting the boundaries of the hull are displayed within the view port. • 3D Viewer . University of Strathclyde. Besides the parts necessary for parametrically generating the hull other functions included: a resistance optimisation procedure. • Report . The interface consists of four primary parts. It was possible to develop a system which would have allowed the parameters to be edited interactively. The primary aims of the program were to provide a graphical interface.This displays only one hull containing the same lines as displayed in Yacht Lines and it allows the hull to be rotated around in three dimensions.
The display shows the construction lines which outline the region within which the hull exists. The display after the YD-40 parameters have been entered.5.Marcus Bole Parametric Generation of Yacht Hulls Figure 16. 1997 116 . The hull generation procedure can now be started. University of Strathclyde.
1997 117 . The display after the hull generation procedure has been run. The stations and hull outlines are shown in the Yacht Lines view port. University of Strathclyde. Bottom right is the feedback given from the hull generation procedure.6.Marcus Bole Parametric Generation of Yacht Hulls Figure 16.
7.Marcus Bole Parametric Generation of Yacht Hulls Figure 16. The 3D Viewer shows the hull in three dimension allowing the user to gain a better idea of the shape of the yacht hull. 1997 118 . University of Strathclyde.
8.Marcus Bole Parametric Generation of Yacht Hulls Figure 16. containing information such as input parameters. The Report window allows a record of the hull to be kept. resistance information and hydrostatics University of Strathclyde. 1997 119 .
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