True Round

Metal Boat


Bezier Chine Design

D. L. Schaffer

The Design procedures detailed in this book reflect the authors’ own experience and research.  The authors takes no responsibility for the use or misuse of the information contained herein.







  Copyright   2021  

D. L. Schaffer









No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the written permission of the publisher.



 Introduction:                                      Page  6

 Surface Design Concepts:                         Page  7

 The Model File:                                   Page 13

 Profiling Transverse Frames:                      Page 27

 Defining Transverse Frames:                      Page 34

 Creating Longitudinal Frames:                     Page 38

 Defining Longitudinal Frames:                      Page 45

 Plating Developable (Flat) Surfaces:               Page 49

 Defining True Round Shell Plating:                 Page       57

 Plating & Longitudinal Crossings:                   Page 67

 Alternate Longitudinal Placement:                 Page 73

 Redesigning The Bezier 12.5:                     Page 77



 Master Curves Dimensions:                       Page 82

 Entity Descriptions:                              Page 89

 Bezier 12.5 Photo's:                             Page 91



My first book 'True Round Metal Book Building - Bezier Chine Design' is 'Bezier Chine' - 101'.  That book defined the theory of 'Bezier Chine Design' and the methods of fabrication and construction.  It is a must read before continuing on to 'True Round Metal Boat Design - Bezier Chine Design' or 'Bezier Chine' - 102'. 

'Bezier Chine Design and Construction' is a completely pre-engineered design and building process.  This book is not intended to instruct anyone on the intricacies of Yacht Design, but to introduce Designers working in steel and aluminum construction how to apply  'Approximate' Sheetmetal pattern development to the complex True Round surfaces encompassing the hull, deck, and house shell plating.

The book covers the idiosyncrasies specifically related to metal boat design and construction, such as: The limitations of Developable surfaces, the 'Natural Lay' of Sheetmetal, 'Floating the Longitudinals', Working with Developable and Ruled surfaces, Theoretical chines, and more. 






Design Concepts













Book Conventions:   

The two principle programs for the purposes of this book are:

·         A 3D dimensional Surface marine design program, where the entire boat structure can be defined.

·         A 2D dimensional Cad drawing program, where Architectural drawings, Full size pattern, and CNC cutting files can be defined, from geometry exported from the 3D dimensional Surface hull design program.  

·         The 3D marine Surface design software, I use, needs a little describing.  In this software there is a 'Hierarchy of Entities' where complex surface designs are built up from 'Points', to 'Curves', to 'Beads', to 'surfaces', to 'Snakes', to' Ring' Objects, in the form of 'Parent-Child' relationships.  This relationship will unfold in [Figure I], [Figure II], and [Figure III].

In this Surface design program each and every Object created is given a specific name.  Each and every Object has it own specific set of parameters.  See Addendum Two for a description of Entities that create the Objects used in this book. 

·         The Entity that creates an Object is presented in Bold text enclosed by  parenthesis.   For example:  (Entity).

·         The name of the Objects created by an Entity will be in Bold and Italic text and have No Capitol Letters.  For Example:   object name.

·         When referring to an Entity group it will be enclosed in Single Quotes.  for Example:   'points'.

·         Figures are in Bold and Italic text with Brackets.  If the Figure is a Prospective View a 'P' will follow, if the Figure is in Plan, Profile, or Section view an 'XYZ' will follow.  For Example:  [Figure ???-XYZ].


Defining Points - Curves - Beads:

In this example [Figure I-P] I have created four (4) (Absolute Point) objects named Control pt #1, control pt #2, control pt #3, and control pt #4.   These points will be used to define a (B-Spline Curve) named base curve.  The 'points' are the parents of the 'curve'. 

With 'Parent'-Child' relationships you cannot delete any of the 'points' that define the 'curve', without deleting the 'curve' first.  The 'curve' base curve is the 'Child' of the 'Parent' 'points':  

Control pt1, control pt #2, control pt #3, and control pt #4 However, you can move a point to another location and the curve base curve will instantly update to reflect that change.

To locate a position on a 'Curve,' an (Absolute Bead) would need to be created.  The 'bead' would be constraint to lay on the chosen 'curve'.  Its position would be determined by a parameter know as know as 't'.  The start of a 'curve' has a 't' location of '0' and the end of a 'curve' has a 't' location of '1'.  A location beyond the start and end of the 'curve' will follow the nature extension of the 'curve'. 

The 't' location of the 'bead', named, bead on curve is located at a 't' of 0.85.  The 'x', 'y', and 'z' location of any 'bead' can be found by selecting and viewing the 'beads'  properties.

Defining  Surfaces - Magnets:

For clarity, the parent 'points' that define the (3) three (B-Spline Curves) in [Figure II-P] named curve one, curve two, and curve three have been hidden.

These three 'curves' support a (C-Lofted Surface) named compound surface.   The three support curves are the parents of the (C-Lofted Surface). 

To locate a position on a 'Surface' a 'magnet' is created.  A 'magnet' is constraint to lay on a 'surface'.  Its position would be determined, again, by a parameter know as 't'.    There a two (2) values for 't' for a 'surface' entity.  They are 'u' and 'v'.  In this case 'u' runs longitudinally and 'v' runs vertically.  The four (4) corners would determine the values of 't' at each corner of the 'surface'.  

The 't' location of the 'magnet' named position has a 't' of 0.625,0.625.  The 'x', 'y', and 'z' locations of any 'magnet' can be found by selecting and viewing its properties.

Defining  Snakes - Rings:

Snake one [Figure III-P] is a (C-Spline Snake) located on compound surface.  It is defined by four (4) 'magnets':  mag one, mag two, mag three, and mag four which are restraint to lie on compound surface.  Snake one is the child of the four 'magnets'.

(Absolute Ring), named ring one, will be the 'child' of snake one.  As with 'Curves' the value of 'T' is used to define location of a  'rings'.

The Parent-Child relationship goes on and on.  If the Designer decided to delete snake one for example, he could not be able to do so without deleting the 'ring' named ring one  first. 

Illustration Conventions:

A soft border Image like this is a Photo or Sketch.

A narrow bold border such as this indicates that the drawing was created using the 3D Surface Marine Design Program.

A wide bold border such as this indicates that the drawing was exported into a 2D drafting Program.


                                       Model File

Beginning a Bezier Design:

The starting point is a blank computer screen and an initial hand sketch [Figure IV-XYZ] along with a great deal of assumptions, target design coefficient's, basic structural calculation, displacement guestimates.  You name it.

This book is not about any of your design objectives, except one, incorporating those objectives into a True Round Metal hull design where every part of the hull, deck, and superstructure can be pre-engineered.

This book  centers around the 'Prototype' and 'Proof of Concept' build for 'Bezier Chine Design and Construction'.  The Bezier 12.5 is a type two  hull design where the True Round Surface runs from the Sheerline around the turn of the Chine to a flat developable surface at the bottom of the hull.

Master Curves are the framework [Figure V-P] that support the surfaces that define the hull.  There are seven Master-Curves use to define both the True Round and Developable portions of the Bezier 12.5.

I have decided for the purposes of this book to divide the Master-Curves into three groups:  The Bow definition is Master-Curve One, the Transom definition is Master-Curve Seven. The Master-Curves between the aforementioned are Master-Curves Two through Six.

While not actual Master-Curves there are four (4) longitudinal 'curves' which connect the transverse Master-Curves:  sheer long, fairing long, chine long, and Fairbody long.  They define the prominent visual hull lines of the design and 'Fair' the transverse Master-Curves.   Chine long and Fairbody long are also used to create the flat bottom surface of the hull.

Before actually beginning  I would like to acknowledge that I am aware of the Design Cycle [Figure VI], however do to necessity the process is presented in a very linier fashion.

With my hand sketches and assumptions at hand I usually start a new design with an (AbsPoint) located at 'x' = 0.000, 'y' = 0.000 and 'z' = 0.000.  This location represents the location of the 'Design Waterline' at the centerline of the hull and the foremost point on the hull.  I usually name it base pt.

The very next point I establish is the Fore Point of the hull.   Its position in 3D space is: 'x' =  0.000" 'y' =  0.000 'z' = 27.444".  This location represents the foremost point of the sheer line on the centerline of the hull, and the distance above the 'Design Waterline.  I name this point mc-1-pt-1.   With these two single points established, believe it our not, the model takes form within my mind.  I instinctively see the master curves to be created to define the Bezier 12.5.  Well I do have all my Sketch's and Calculation to guide me.

The key to 'Bezier Chine Design and Construction' for type One and Two configurations is based in the tangency between the  surface types.  This tangency point-curve is represented by Theoretical Chines between  two

surface types.  To the Builder it may not look like a Chine - To the Designer it is a Chine.  The Theoretical Chine point between surface types is most visibly seen in a section view of a Transverse master-curves.   Master-Curve Three(3) is used to illustrate.  [Figure VII-XYZ].

Master Curve - Three:

·         To create Master-Curve Three:  Create four (4) (Absolute Points) by entering their 'x' 'y' and 'z' locations for the following Control points:   mc-3--pt-1, mc-3--pt-2 ,mc-3--pt-3, and mc-3--pt-4.  The position of these points can be found in Addendum One.

·         A Type Two (B-Spline Curve) can now be created to define the True Round upper curve named mc-3-bezier by choosing pointsmc-3--pt-1,  mc-3-pt-2 , mc-3--pt-3. 

·         The (Line) Entity is used to create mc-3-line to define the flat portion of the hull by choosing points:  mc-3--pt-3, and mc-3--pt-4.  It should be apparent that the 'Point of Tangency' is at mc-3--pt-3.

While this configuration of (Absolute Points) to define Master-Curve Three is accurate in all ways including the 'Point of Tangency' between the two surfaces, there is however somewhat of a caveat.  It we were to move any of the support points, the 'Point of Tangency' would be lost.  In other words the two surfaces would no longer flow smoothly into each other.  There would no longer be a Tangency between surfaces at mc 3 pt 3.

To solve the 'Point of Tangency' problem, mc 3 pt 2 is going to be replaced by an (Absolute Bead) created to lie on mc 3 line.  I will name this new (Absolute Bead) , mc 3 bead 2.

To define the 't' location of mc 3 bead 2 we will drag it to a position where it directly over mc 3 pt 2 or as close as possible.  To substitute one point for the other delete curve mc 3 bezier and point mc 3 pt 2.

Than, create a new Type Two (B-Spline Curve), keeping the original name, mc 3 bezier and chose the new control points:  mc 3 pt 1,  mc 3 bead 2 , mc 3 pt 3. 

This arrangement will allow any of the (Absolute Points) and (Absolute Bead) to be moved while keeping the 'Tangency' between surfaces.  If the control point is an (Absolute Point) it can be moved anywhere in three dimensional space.  It the control point is a (Absolute Bead) it can only be moved along the line it is constraint to lie on, that is mc 3 line  

Master-Curve Three was the example.  Using the same line of thought  create  Master-Curve Two, Master-Curve Four, Master-Curve Five, and Master-Curve Six.  When this is done your  computer model of the Bezier 12.5 should look like <Figure VIII-P>.

Bow Master Curve:

Master-Curve One is longitudinal in direction and defines the bow curve of the hull, [Figure IX-XYZ]Before we can define Master-Curve One, we must first create an (Absolute Point) mc 1 pt2 somewhere between the previously created (Absolute Point) mc 1 pt1 and mc 2 pt4.  This new (Absolute Point) mc 1 pt2 is needed to establish the desired bow curvature

To create Master-Curve One a type three (C-spline Curve) named fairbody needs to be created first.  The control points to define fairbody are: mc_1_pt1, mc-1-pt2, mc-2-pt4, mc-3-pt4, mc-4-pt4, mc-5-pt4, and mc-6-pt4.

Master-Curve One is a (SubCurve) of fairbody.  To place a (SubCurves) on the existing curve Fairbody three (3) (Absolute Beads) need to be created.   Bead 1 is placed at a 't' of  0.0  on fairbody.  Bead 2 is placed at a 't' of 1.0 on fairbody.   Bead-1-divide-pt marks the point of division between the True Round portion of the hull and the developable portion of the hull.  See Addendum One for this positions.

 Figure IX-XYZ
To created 'Master-Curve One' mc 1, which will be a (SubCurves) on fairbody choose bead-1 and bead-1-divide-pt as 'parents'Next create (SubCurve) named lower fairbody choosing  bead-1-divide-pt and mc-6-pt4.

Your Computer Model of the Bezier 12.5 should look like [Figure X-P].

Longitudinal Master Curves:

The three (3) Longitudinal Master Curves [Figure XI-P] are created next.  The are:  Sheer long, fairing long, and chine long.  These Longitudinals fair the lull along its length by manipulating the points that define the transverse Master-Curves.  Note, that the fairbody longitudinal previously created  is divided into two distinct curves - mc-1 and lower-fairbody.

Points that define sheer Long are:  mc 1 pt 1, mc 2 pt 1, mc3 pt 1,   mc 4 pt 1, mc 5 pt 1, and mc 6 pt 1.

Points that define fairing Long are:   m 2 pt 2, mc 3 pt 2, mc 4 pt 2, mc 5 pt 2, and mc 6 pt 2.

Points that define chine Long are:   bead 1 divide p -2, mc 2 pt 3, mc 3 pt 3, mc 4 pt 3, mc 5 pt 3, & mc 6 pt 3.

Points that define Fairbody, previously defined are:  mc 1 pt 1, mc 1 pt 2, mc 2 pt 4, mc 3 pt 4, mc 4 pt 4, mc 5 pt 4, & mc 6 pt 4.

Lower fairbody and mc 1 are (SubCurves) of fairbody.

Transom Master Curve:

The Bezier 12.5 has a flat transom, angled to the degree of the keel  and sports a little tumblehome. [Figure XII-XYZ] and [Figure XIII-P].


 Create four (4) (Absolute Beads), one each anywhere on sheer-Long, fairing-Long, chine-Long and fairbody-long.   Name these  (Absolute Beads):  sheer bead aft, fairing bead aft, chine bead aft and Fairbody bead aft. 

In profile move, sheer bead aft and Fairbody bead aft past the endpoint of their 'parent' curves to a position that meets your expectations of the transom angle and the desired aft Points of the sheerline and Fairbody line.  See Addendum One for these locations.

Create an 'y' Offset (Plane), named hull cl plane, on the centerline of the hull.

Create a (Projected Point) onto (hull cl plane), named transom cl pt using sheer bead aft as the 'Parent'.

Create a three point (3-Point Plane), transom-plane,  using fairbody bead aft,  sheer bead aft and transom cl pt as parents.

Move, in profile fairing bead aft and chine bead aft until they coincide with the (3-Point Plane), named transom plane.

Create a type two (B-Spline Curve) mc-7-bezier by choosing sheerline bead aft, fairing bead aft, and chine bead aft as parents.

Create a (Line) named mc-7-line by choosing chine bead aft and Fairbody bead aft as 'parents'

Add sheer bead aft, fairing bead aft, chine bead aft and fairing bead aft to the list of 'Parent' to their respective Longitudinal curves sheer-Long, fairing-Long, chine-Long and or Fairbody-long.

Your Model File should now look something like this rear prospective. [Figure XIV-P]

Creating the Surfaces:

Bezier True Round Surface:

  The true round portion of the hull [Figure XV-P] is a type three (C-Lofted Surface) surface named Bezier Surf.  The transverse master curves that 'Paren' Bezier-Surf are:  Bezier at bow, mc 2 bezier, mc 3 bezier,  mc 4 bezier, mc 5 bezier,  mc 6 bezier and mc transom bezier. 

Bottom Flat Surface:

Choosing a surface type for the flat bottom surface [Figure XVI-XYZ]  of the Bezier 12.5 is not a straight forward choice.

One would naturally assume that a (Developable Surface) would be the natural choice.   However, I am going to use a  (Ruled Surface) for the Flat Bottom shell plate named bot surf ruled.  The parents are chine long and lower Fairbody long.


Transverse Master-Curve locations are determined, by the Designer, at locations that best define the ultimate hull form.

Longitudinal Master curves are 'Fairing' curves.  Fairing the hull is an interactive procedure.  Changing one location of any points affects every other aspect of hull shape.

All the 'Points' are at their final location.  The hull was faired using the tools within the 3D marine design Program.

You can find a list of the points that define the 'Model File' in Addendum One.

This concludes creating the 'Modell File'.  In the next Chapter the Transverse frame will be Profiled.

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