The Sailcut CAD Handbook

Robert Lainé

Jeremy Lainé

Sailcut CAD 1.3.1 - 1 October 2007


Table of Contents

1. Introduction
1.1. About Sailcut CAD
1.2. How to obtain Sailcut CAD?
1.3. Technical information on the code
2. Using Sailcut CAD
2.1. Upgrade notes
2.2. User preferences
3. Creating a sail
3.1. Dimensions dialog screen
3.2. Mould dialog screen
3.3. View controls
3.4. Sail panels development
3.5. Loading and saving sails
3.6. Exporting 3D sails
3.7. Printing data and drawings
4. Creating a rig
4.1. Saving and Loading a rig file
4.2. View controls
4.3. Rig dimensions
4.4. Mainsail luff curve
5. Creating a hull
5.1. View controls
5.2. Saving and Loading a hull file
5.3. Hull dimensions
5.4. Planks adjustment
6. Creating a boat
6.1. View controls
6.2. Adding and removing boat elements
6.3. Saving and loading a boat file
6.4. Shifting boat elements
7. Sails surface formulation in Sailcut
7.1. History
7.2. Of the complexity of the definition of the surface of a sail
7.3. Some Maths
7.4. Other aspects of the surface formulation
8. Where can I find more information about Sailcut CAD?
8.1. I think I found a bug, what should I do?
8.2. I would like to help develop Sailcut CAD, what should I do?
9. File formats used by Sailcut CAD
9.1. Text representation of developed sail
9.2. Text representation of 3D sail
9.3. XML representation of a sail
10. Copyright

1.  Introduction

1.1.  About Sailcut CAD

Sailcut is a software for designing boat sails and developing then into flat panels. Sails can be either 4 sided sails like for old timer gaff rig or 3 sided sails like jibs or main sails for Marconi rig.

The first version of Sailcut was developed in 1978 and used by Robert Lainé for making the sails of his IOR 1/4 ton named "Flying Sheep III". Sailcut has been available on the web since 1994 and is used by many professional and amateur sail makers for offshore racing, cruising and recently for model yacht.

Sailcut uses a unique mathematical definition of the surface of the sail which ensure that the sail profile is smooth and aerodynamic.

1.2.  How to obtain Sailcut CAD?

You can download the latest version of Sailcut CAD from the project's home page at http://sailcut.sourceforge.net/. Sailcut CAD is made available both in binary (compiled for you) and in source code form.

1.3.  Technical information on the code

Sailcut CAD is written with portability in mind. As such it is written in C++ and uses the Qt library from Trolltech for the graphical user interface. Sailcut CAD uses OpenGL to display the 3D view of the sail. Sailcut CAD is known to compile and run on GNU/Linux, Microsoft Windows and MacOS/X.

2.  Using Sailcut CAD

2.1.  Upgrade notes

As of release 0.6.5, Sailcut CAD uses different extensions for each file type instead of ending all files with ".xml". If you wish to open sails created with a previous version of Sailcut CAD you should rename your sail definition file so that it ends with ".saildef". When opening the resulting old file, all dimensions data except for the mould will be preserved. Redefine your sail mould, then save the file.

2.2.  User preferences

2.2.1.  Preferences file

Your preferences are stored in a file called .sailcutrc. On UNIX-like platforms, this file is located in your HOME directory. On Windows this file is located in your Documents and Settings\USER directory.

2.2.2.  Internationalisation

As of release 0.5.5, Sailcut CAD has support for internationalisation. Translations of the user interface in various languages are currently provided. On startup, Sailcut selects the language corresponding to your locale. You can use the Language submenu of the View menu to switch to another language.

3.  Creating a sail

When you start Sailcut CAD, you are presented with a default sail. At the top of the window you will find a number of roll down menus. The File menu is used for loading an existing sail, saving the parameters of the sail and Export the developed panels.

You can modify the dimensions of the sail by using the Dimensions entry of the View menu.

You can modify the profile of the sail through the Mould entry of the View menu.

You can display several sails on the same rig through the Rig entry of the View menu.

3.1.  Dimensions dialog screen

You can access the sail dimensions dialog from the Dimensions entry of the View menu.

The program is tailored to design either triangular or quadrangular boat sails. A classical triangular sail is essentially a quadrangular sail with a very small top edge.

The surface of the sail is generated from a single set of equations defining the profile of the sail at all levels. The profiles rest on the edges of the sails which are defined by their length and the amount of round (also called roach) in each side and the twist of the sail. The Definition window is divided into a number of boxes which group the parameters defining the sail.

You can use the Compute button to compute and display ancillary data like IRC width. This can result in some text box color being changed. Red color indicate that the value exceed the upper limit and yellow indicate that it is below the lower limit. The value itself will be changed to the acceptable limit.

When you have finished entering the dimensions, press OK to display the sail in 3D.

3.1.1.  Rig geometry

The first step is to select the type of sail you are going to work on, then enter the data defining the correspônding rig geometry and sail plan such that the sail will have the proper orientation.

Select the type of sail by pressing the corresponding Radio Button:

  • Jib for any sail which will be set on a stay,

  • Mainsail for any sail set on a mast,

  • Wing for any type of kite symetrical about the foot.

The rig data are used for displaying the sails in their proper relative position with the rig.

Figure 1. Sailcut plan definition

Sailcut plan definition


3.1.2.  Sail identifier

You enter there a text describing the sail you are working on (maximum 40 characters spaces included).

3.1.3.  Sail dimensions

This is where the dimensions of the sail are entered.

On a main sail the minimum value for the gaff length (headboard) is constrained to 5 mm. Value smaller than that will default back to 5 mm. The gaff angle is constrained to 90 degrees maximum between the gaff and the luff.

Positive round (roach) of the luff, foot, leech and gaff extend the sail outside of the straight edge line.

Negative round is equivalent to hollowing that edge of the sail.

The position of the round or roach is expressed in percentage of the side length starting from the lower or most leftward end of that edge.

Figure 2. Sailcut edges definition

Sailcut edges definition


Dimensions and angles defining the sail plan are expressed in millimetre and degrees.

Length of the sail sides and diagonal are the 3D straight line distance between the corners of the sail.

The actual length on the finished sail lais on the floor can be slightly longer depending on the shape of the sail. For example, the foot length entered in the screen below is 3600 mm. If the foot camber is null then that will be the actual distance between clew and tack (straight foot) of the finished sail. If a 10% camber is entered for the foot depth, then the actual foot will be the length of the arc which has 10% camber, that is 2.7% longer than the straight line foot length.

Having entered the sail main dimensions you can press on the Compute button to obtain additional informations on the sail, like the X-Y coordinates of the corners of the sail, the perpendicular length LP measured from the clew to the luff as well as IRC racing rules width.

The X-Y coordinates of the sail corners are usefull to quickly adjust the data entered. For example if you find that the clew height (Y) is way below or above the height of the tack when you would like it to be leveled, then you can substract or add the difference to the leech length.

3.1.4.  Layout

Click on the radio button corresponding to the desired layout of the sail. The layout of the panels does not affect the shape of the sail which is defined by its dimensions and its mould.

Except for the Radial cut layout, the number of panels is determined by the cloth width and seam width entered in the Cloth box.

  • The most commonly used layout is the Crosscut. The panels are laid perpendicular to the straight line joining the peak to the clew of the sail.

  • The Twist foot layout is similar to the cross cut except that the lower panels are rotated such that they do not intersect the foot of the sail.

  • The Horizontal cut layout lay the seams in the horizontal plane. This option can be used to visualise the profile of the sail at various levels and to output files with the 3D coordinates of the sails for use by CFD tools.

  • The Vertical cut layout places the panels parrallel to the straight line joining the peak to the clew of the sail. This is the favorite layout for the old timer's main sail.

  • The Mitre cut layout is the favorite for the old timer's genoa. The sail is divided in two parts by a line joining the clew to the mid point on the luff and the panels organised to be perpendicular to the foot in the lower part of the sail and perpendicular to the leech in its upper part.

  • The Radial cut is used mostly for competition as the cloth is mostly aligned with the directions of maximum strain. When using the Radial cut option it is important to understand the definition of the number of sections, number of radial gores and number of luff gores (see Figure 3, “Radial cut gores definition ”).

Figure 3. Radial cut gores definition

Radial cut gores definition


3.1.5.  Sail shape

You enter there the depth of the sail at 3 levels, near the foot, in the middle of the sail(the exact position being defined in the mould screen) and near the top of the sail.

The twist angle is the angle expressed in degrees by which the top of the sail is rotated with respect to the foot. The twist is globally determined by the amount by which the apparent wind at the top of the mast is rotated with respect to the apparent wind at deck level. For a jib the twist is sometime driven by the need to have the upper part of the leech sufficiently open to clear the spreaders. For a mainsail the twist is also driven by the ability of the rig to carry the tension in the leech, in particular a gaff rig will have more twist in its main sail than a Bermuda rig. It is important that the twist angle entered in Sailcut reflects the reality of the shape of the leech when sailing in an average wind.

The sheeting angle value is the actual sheeting angle measured from the boat centerline when the sail is set on the boat. For a jib the minimum value is 5 degrees. The value is of importance to ensure that the sail is properly positioned when displayed in the rig viewer. You can then visualise for example the slot between a jib and the main sail as set on the boat.

3.1.6.  Cloth

Enter there the width of cloth used, the width of the seams between adjacent panels, the width of material to be added to the leech to make the leech hem and the width of material for the other edges hems.

Figure 4, “Sailcut seams and hems definition ” describes the location of the various hems and seam width. Sailcut will compute the panels such that they fit within the declared cloth width including the seam and hems width as appropriate, except for a radial cut sail for which the width of each panels is computed from the number of radial panels entered.

Note that when using the radial layout, the seam width between horizontal sections will be twice the width of the seams between adjacent panels of the same section.

Figure 4. Sailcut seams and hems definition

Sailcut seams and hems definition


3.2.  Mould dialog screen

You can access the mould dialog from the Mould entry of the View menu.

The depth and the shape of the sail can be entered at three levels located at the bottom (foot) the middle (sail's maximum depth height can be adjusted) and at the top of the sail.

The position of the point of maximum depth of a profile is shown under the depth value. This position which depend of the luff and leech shape factors is expressed in relation to the cord of the profile. For exemple: 0.34 means that the point of maximum depth is at 34% of the local cord counting from the luff end of the profile.

The luff shape and the leech shape can be adjusted for the Top profile and Middle profile only. The foot profile is always an arc of circle.

Under the luff shape factor, the corresponding value of the angle of entry of the profile is provided in degree. The angle under the leech shape factor is the exit angle of the profile. These angles are refered to the local cord and if you want to know for exemple the real entry angle of a profile with respect to the axis of the boat you have to add to the entry angle the twist at the level of the profile plus the sheeting angle.

The vertical position of the sail's maximum depth profile is controled by the vertical slide bar to the right of the left vertical frame.

In order to avoid that the leech makes a hook in the upper part of the sail when the wind increases, it is recommended that the Top profile luff shape value be higher than that of the middle profile and that the leech shape value at the top be lower than the middle value.

3.3.  View controls

It is possible to zoom, pan and rotate the sail in the view window:

  • Rotation : you can control the rotation that is applied to the sail by using the elevation and azimuth sliders located at the edges of the graphic pane.

  • Pan : click on a point with the left mouse to center the view on that point.

  • Zoom : to zoom in press CTRL + and to zoom out press CTRL -. You can also use the zoom buttons in the view controls or your mouse wheel to zoom in and out.

3.4.  Sail panels development

The developed sail is display by clicking on the Development tab from Sailcut CAD's main window. This presents you with a view of the developed (flat) panels of the sail. The view controls are the same as those of the main window. The blue line represents the edge of the finished panel (draw line) and the red line represents the outer edge taking into account the seam and hems width allowance (cut line).

You can export the points which define the edges of the developed panels with the draw line and the cut line to the following file formats from the Export development submenu of the File menu:

3.5.  Loading and saving sails

Once you have customised your sail, you can save it to a file by using the Save or Save As entries in the File. You can reload it by using the Open entry of the File next time you want to work on it.

Both the sail's dimensions and the parameters of the mould are saved simultanously. This feature allows you to reload a sail and reuse its mould even if you change the dimensions of the sail to fit a new rig.

Sailcut CAD uses XML files to store the sail data. These files are plain text so they can easily be viewed using your favourite text editor.

3.6.  Exporting 3D sails

In addition to Sailcut CAD's native file format, it is possible to export all the 3D points located on the edges and seams of the panels that make up a sail. You can export the three dimensional sail to the following file formats from the Export 3D sail submenu of the File menu:

3.7.  Printing data and drawings

The Print submenu of the File menu offers various printout possibilities:

  • The data menu entry will print the data of the sail,

  • The drawing menu entry will print a drawing of the complete sail,

  • The develop menu entry will print all the developed panels with key points coordinates (1 panel per page). The definition of the developed panel key points coordinates is given in Figure 5, “ Developed panels drawing ”. The X,Y coordinates are absolute coordinates referenced to the lower left corner of the box enveloping the contour of the CUT line of the panel (edge of cloth). The dX,dY coordinates are relative to the straight line joining the end of the corresponding edge and it should be remembered that the origin of dX is at the left end of the edge and positive value of dY indicate that the point is left of the straight line joining the origin to the end points of the edge.

The printout scaling is such that the sail drawing and the largest developed panel automatically fit in one page. For printing panels to a precise scale it is preferable to export the developed sail in a DXF file and use a CAD package to print the panels.

Figure 5.  Developed panels drawing

Developed panels drawing


4.  Creating a rig

This module allow the design of a mast with up to 3 levels of spreaders. It is accessed via the Rig entry of the main screen's File New menu.

The Dimensions entry of the View menu will display the screen from which you can enter and modify the dimensions of the rig.

The definition of the various dimensions is given in Figure 6, “ Sailcut Rig definition ”. Please note that, in order to allow the design of sails independently from the design of the rig, the definition of the mast rake and mast curve are refered to the full mast length which are different from that of the sail luff rake and curve of the sail design module which are refered to the sail luff length. This rig module provides the data to be used when designing the mainsail which fit on the rig.

Figure 6.  Sailcut Rig definition

Sailcut Rig definition


4.1.  Saving and Loading a rig file

The Save entry of the File menu is used to save a rig.

Any Rig which has been saved can be later opened as an entity with the Open entry of the File menu and can be used as an element to constitute a boat.

4.2.  View controls

The controls of the viewer are identical to those of the sail viewer. You can rotate the rig with the sliders located around the graphic display, zoom with the mouse's wheel, pan with the mouse left click, view in wireframe or shaded surface modes.

4.3.  Rig dimensions

The Dimensions entry of the View menu display the rig dimension screen which is divided in boxes corresponding to the entities listed below.

Note that angles are expressed in degrees and linear dimensions in millimetres.

4.3.1.  Rig ID

A free text identifying or describing the rig can be entered in this box. The number of characteres is limited to 40.

4.3.2.  Fore triangle

The height = I and base = J of the fore triangle are entered in the corresponding fields. Note that the dimensions are measured in the vertical and horizontal directions. In particular be carefull when measuring the J dimension when the mast is inclined.

4.3.3.  Mast

The mast is assumed to have a constant section from foot to tip. The heights are refered to the stem fitting horizontal plane.

Mast height = MH is the straight line height of the mast top above the stem. It shall be greater than J.

Mast round = MRnd is the maximum deviation from the straight line.

Mast round position = MRndPos spin box is used to enter the relative height of the point at which the mast round is measured. It is expressed in percentage of the mast height.

Mast rake = MRkM is the horizontal distance between the tip of the mast and its foot. Sailcut CAD will compute and display the corresponding mast rake angle = MRkD.

Mast cord = MC is the fore-aft width of the mast section.

Mast width = MW is the transverse width of the mast section.

4.3.4.  Mainsail

See below the chapter about mainsail luff curve.

4.3.5.  Shrouds

Cap shrouds height = CSH is the height of the point of attachment of the outer shroud to the mast.

Cap shrouds base width = CSB is the base width of the outer shroud measured from the central line.

Lower shrouds base width = LSB is the base width of the lower (inner) shroud which shall be smaller or equal to the cap shroud base width.

4.3.6.  Spreaders

Number of spreaders = SPNB can be from 0 (none) to maximum 3. If only no spreader is present, the outer shroud will be identical to the lower shroud.

Spreaders height SPH are entered in ascending order with 1 being the lowest.

Spreaders length SPW are measured from the ecentral line.

4.3.7.  Checking and validating data

Use the Check button any time after entering new data to perform a verification that the data entered are consistant with a reasonable rig design and the ancillary data are computed. In case of inconsistancy between data, the color of the fonts will tell you which data is suspicious. Red indicate a too high value, purple a too low value and blue signals which related parameter is to be checked.

Once you have entered all necessary data, click on the OK button to close the rig dimensions window and display it. If there is an incompatibility in the data, the dimensions window will not close until it is corrected.

4.4.  Mainsail luff curve

In most case users have designed sails independently from the design of a rig. However the user may wish to design a sail compatible with a rig. In the rig dimensions screen, the box labeled Mainsail is used to compute the mainsail tack position and luff curve which will fit the rig. These data can be used for creating the corresponding mainsail or to verify that a mainsail luff curve will fit the rig.

The only data to be entered are the mainsail tack height = BAD and head height = HAD. Sailcut CAD will compute the other data.

5.  Creating a hull

Please note that this module is not yet fully operational, for the time being a single chine hull ouline will appear whatever the number of chine is entered.

This module allow the design of a hard chines hull. It is accessed via the Hull entry of the main screen's File New menu.

5.1.  View controls

The controls of the viewer are identical to those of the sail viewer. You can rotate the hull with the sliders located around the graphic display, zoom with the mouse's wheel, pan with the mouse left click, view in wireframe or shaded surface modes.

5.2.  Saving and Loading a hull file

The Save entry of the File menu is used to save a hull.

Any hull which has been saved can be later opened as an entity with the Open entry of the File menu and can be used as an element to constitute a boat.

5.3.  Hull dimensions

You can modify the dimensions of the hull by using tab Deck and bottom of the screen Dimensions entry of the View menu.

The deck and bottom screen is divided in boxes in which the various dimensions of the hull are entered.

The hull is constructed upward from the bottom planks. The most important line is the chine which defines the outer edge of the bottom planks. The height are refered to any arbitrary horizontal datum plane located conveniently near the bottom of the hull. Angles are measured in degrees from the same horizontal datum plane.

5.3.1.  Hull ID

A free text identifying or describing the hull being designed can be entered in this box.

5.3.2.  Deck

Forward height

Aft height

5.3.3.  Bottom

Length

Stem angle

Transom angle

Forward height

Chine angle

Aft height

Max width

Max width position

Aft width

Forward shape

Aft shape

Dead rise angle

Bottom sweep angle

5.3.4.  Planking

Number of planks

Automatic planking

Top plank angle

lower plank angle

5.3.5.  Checking and validating data

Use the Check button any time after entering new data to perform a verification that the data entered are consistant with a reasonable hull design and the ancillary data are computed. In case of inconsistancy between data, the color of the fonts will tell you which data is suspicious. Red indicate a too high value, purple a too low value and blue signals which related parameter is to be checked.

Once you have entered all necessary data, click on the OK button to close the hull dimensions window and display it. If there is an incompatibility in the data, the dimensions window will not close until it is corrected.

5.4.  Planks adjustment

Individual side planks can be ajusted by using the tab Planks of the screen Dimensions entry of the View menu.

The planks screen is divided in boxes in which the various dimensions of the hull are entered.

5.4.1.  Forward height

5.4.2.  Aft height

5.4.3.  Plank angle

5.4.4.  Sweep angle

5.4.5.  Chine angle

5.4.6.  Checking and validating data

Use the Check button any time after entering new data to perform a verification that the data entered are consistant with a reasonable hull design and the ancillary data are computed. In case of inconsistancy between data, the color of the fonts will tell you which data is suspicious. Red indicate a too high value, purple a too low value and blue signals which related parameter is to be checked.

Once you have entered all necessary data, click on the OK button to close the hull dimensions window and display it. If there is an incompatibility in the data, the dimensions window will not close until it is corrected.

6.  Creating a boat

This boat design module allows you to assemble hull, rig and sails files created earlier and make a virtual boat. It is accessed via the Boat entry of the main screen's File New menu.

6.1.  View controls

The controls of the viewer are identical to those of the sail viewer. You can rotate the hull with the sliders located around the graphic display, zoom with the mouse's wheel, pan with the mouse left click, view in wireframe or shaded surface modes.

6.2.  Adding and removing boat elements

The boat viewer is initially showing a black screen and files are added via the Add entry of the main screen's File menu. A new tab will appear with the details of the file selected and the element identification which was given at the time of creating the element (sail ID, Rig ID, Hull ID).

A boat element can be removed by selecting the corresponding tab and then clicking on the Remove button.

6.3.  Saving and loading a boat file

The Save entry of the File menu is used to save the file of a boat with any combination of hull rig and sails.

The file of a boat can be opened as an entity with the Open entry of the File menu.

6.4.  Shifting boat elements

All boat elements will be displayed in the position entered at the time the element was created. Please remember that the point of coordinate X=0, Y=0, Z=0 is located at the forward end of the deck of the hull (stem).

The boat elements can be individually shifted in X, Y or Z direction by adjusting the corresponding offset in the element spinbox, then clicking on the Update button.

At any time, clicking on the Reload button will restore the corresponding element to its initial position.

7.  Sails surface formulation in Sailcut

This section is a translation of the paper presented by Robert Lainé to the second Workshop Science Voile IRENAV in Brest, France, on 21 May 2004.

7.1.  History

Sailcut software was initially written in 1978 in Basic language on a computer with 1.6 KB of memory, one line text screen and a small 32 columns text printer. Hence the necessity to keep the surface formulation simple for designing the sails which I built and used on my IOR ¼ton.

This short cycle: "design => manufacturing => utilisation => modification", without commercial constraints linked to sailmakers work habits has allowed me to converge quickly on a compact and robust way of describing the sail surface. The method is valid for classical triangular sails and also for quadrangular sails used on old timers and modern rigs with very large headboard. Later on, the use of Sailcut by professional sailmakers has necessitated the addition of graphic interface to the kernel of Sailcut, but that is an other story... Since 1993 the Microsoft Visual Basic version of Sailcut is available at http://www.sailcut.com/ and since 2003, the source code of Sailcut re-written in C++ is available at http://sailcut.sourceforge.net/. For protection of the intellectual rights, the name Sailcut is a registered trademark, but the author maintains free and unrestricted access to Sailcut.

7.2.  Of the complexity of the definition of the surface of a sail

A sail is a complex surface which sailmakers have historically defined by notions like depth at various height and position of the point of maximum depth along the local cord of the profile. This method of defining the surface of the sail by control points allows for an easy comparison of the shape between the intended design and reality. Unfortunately a large number of different surfaces can pass through these few control points. Then notions like the slope at the leading edge and trailing edge of the profiles were introduced to help sailmaker get a better control of the shape of the sail profile. Using interpolation between basic control points, with or without constraints on the tangents at the extremities of the profiles, to determine the depth of the sail in all points were too demanding for old days personal computer processing capability.

From the beginning of my racing activities, I was interested in the aerodynamic of sails. The books Theory of wings sections by Ira H. Abbott and Albert E. von Doenhoff, and Sailing Theory and Practice by C.A. Marchaj convinced me that the distribution of camber along the profile was the determining factor in the quality of a sail profile. I was very sceptical about the definition of a profile by its depth, the position of its maximum depth along the cord and segments of cubic or quadratic curves on either side. Rather than trying to reproduce existing sail shape based on depth measurements, I looked for a law of distribution of its camber giving a reasonably aerodynamic profile on the complete sail surface. The first attempt was to model directly the distribution of camber, however that required to process simultaneously the first and second derivative of the surface many points of the sail surface, far too much work for my small computer. At the time I was racing on the North Sea often in relatively heavy weather for my ¼ ton and I wanted sail profiles with a high peak of pressure very far forward to fight against the tendency of the depth to move backward as the cloth stretched in increasing winds. I finally selected a simple equation defining only the second derivative of the profile and giving a monotonic decrease of its value along the cord of the profile. Experience showed that with the then available cloth, the leech was sometime falling to leeward in the upper part of the sail. I then introduced a second term in the equation to be able to control the minimum value of the second derivative at the leech. This equation is therefore controlled by only two parameters.

7.3.  Some Maths

The coordinate system used is such that the plane X-Y contains the tack, the clew and the head of the luff. The X axis is horizontal and orientated positively from tack toward clew. The Y axis is vertical orientated upward and the Z axis (depth) is perpendicular to the X-Y plane. Profiles are defined by the intersection of the surface of the sail with an horizontal plane parallel to Z-X plane. The depth Z of any point of a given profile is a function of the local X ordinate normalised to the profile local cord as shown in Figure 7, “ Sailcut coordinate system ”.

Figure 7.  Sailcut coordinate system

Sailcut coordinate system


The following equation is used to describe the second derivative of the profile function of X:

Z''= K*[-A*(1-X)^AV - AR*X]

After a first integration it gives the slope of the profile:

Z'= K*[A*(1 - X)^(AV + 1) / (AV+1) - AR/2*X^2 + C]

Finally after a second integration the equation giving the depth at any point is:

Z = K*[-A*(1-X)^(AV+2) / (( AV+2)*(AV+1)) - AR/6*X^3 + C*X + B]

To meet the profile end conditions (X=0, Z=0) and (X=1, Z=0) the constants B and C are:

B = A / ((AV + 2) * (AV + 1))
C = AR / 6 - B

The maximum depth is obtained when the slope Z' is equal to zero, this allow to calculate K such that the depth at that point is the one desired.

The factors AV and AR give a measure of the camber at the leading edge (AV) and trailing edge (AR). Together with the maximum depth value these factors are sufficient to describe the profile of the sail at any height.

The factor A defines different families of profiles with a different distribution of fullness fore/aft. In practice A = 1 give good profiles for sails used in light conditions. I prefer to use sail profiles with more fullness forward and a flatter leech as obtained with the factor A = 1 + AV / 4. This is the factor used in Sailcut and it give a good range of utilisation of the sails.

The following table give an example of profile data obtained with the above equations.

AV = 5.00
AR = 0.02
K = 2.94
A = 2.250
B = 0.054
C =-0.050
curvature = z" / (1+ z'*z')^3/2 

x

z"

z'

z

curvature

0.0

-6.615

0.955

0.00

-2.503

0.1

-3.912

0.438

0.0674

-3.007

0.2

-2.179

0.140

0.0949

-2.117

0.3

-1.129

-0.021

0.1000

-1.129

0.4

-0.538

-0.101

0.0934

-0.530

0.5

-0.236

-0.138

0.0812

-0.230

0.6

-0.103

-0.154

0.0665

-0.099

0.7

-0.057

-0.161

0.0507

-0.055

0.8

-0.049

-0.166

0.0343

-0.047

0.9

-0.053

-0.172

0.0174

-0.051

1.0

-0.059

-0.177

0.00

-0.056

Having defined a single equation for all profiles it is a matter of varying the maximum depth and the factors AV and AR as function of the height of the profile to generate the complete surface of the sail. The profile at foot level being always an arc of circle, the factors AV and AR are equal to zero and only the depth of the foot is entered by the user. A profile called "mid profile" is located around the middle of the height and the factors AV and AR are set such that the profile has the required shape. A third control profile defined as for the "mid profile" is located at the top of the sail. For all other profiles the depth value is interpolated by a quadratic equation and the factors AV and AR are interpolated linearly between between the foot, the middle and top values.

In total 3 values of depth, 2 pairs of factor (AV, AR) and the vertical position of the "mid profile" are used to define the basic mould of the sail.

Note that in Sailcut software the value displayed for the luff factor is equal to the AV ceofficient while the leech factor displayed is 50 time the AR coefficient used in the above equations such that the users can use more friendly range of data than second and third decimal figures.

7.4.  Other aspects of the surface formulation

The above basic mould is not sufficient to define a real sail. Indeed the luff, gaff, leech and foot of the sail are never straight and further more the sail profiles are always twisted from the foot to the top of the sail. I use the distance from the point of maximum round to the straight line and two arcs of parabola rejoining the adjacent corners to define the real edges of the sail. The profiles defined by the sail mould described above are resting on the real edges of the sail. The twist of the sail is finally obtained by applying to each profile a rotation around the leading edge end point.

It is to be noted that this method of modelling the surface of sails gives shapes without bumps or hollows and guarantees that there is no inversion of camber in the profiles. The method is applicable to triangular and quadrangular sails and Sailcut is commonly used for designing old timers gaff sails.

8.  Where can I find more information about Sailcut CAD?

The Sailcut CAD project lives at http://sailcut.sourceforge.net/. This is where you will find links to all matters related to Sailcut CAD!

8.1. I think I found a bug, what should I do?

Sailcut CAD is constantly under development and feedback from users is very welcome! If you think you found bug, visit Sailcut's homepage , you will find instructions in the "Reporting a Bug" section.

8.2.  I would like to help develop Sailcut CAD, what should I do?

You can help us improve Sailcut even if you are not a programmer! Simply using Sailcut and reporting any bugs you might find is of considerable help to us. We are also looking for people to help keep translations up to date and to produce new translations. If you are interested in translating Sailcut into your native language, visit the Sailcut CAD homepage and send an email to the development mailing list!

If you have some knowledge of C++ and are interested in making Sailcut CAD a better program, visit the Sailcut CAD homepage where you will find both snapshots of the Sailcut CAD code and how to access to the CVS repository. Once you have had a chance to familiarise yourself with the code, contact us via the forums or our mailing lists!

9.  File formats used by Sailcut CAD

9.1.  Text representation of developed sail

This section describes the structure of the file generated by Sailcut CAD using the to TXT sail entry of the Export development submenu of the File menu. The extension of a text sail file is ".txt".

A sail is made of a number of panels, each panel has 4 basic sides : left, top, right, bottom which are joined by a drawing line. The origin is at the bottom left corner of a rectangle surrounding the panel. These four basic sides define the net area of the panel after assembly in the sail.

Around the basic panel there is provision for stiching the panels and sail edge hems, the outer side of the panel is defined by four sides named cutLeft, cutTop, cutRight, cutBottom and the material is cut along these sides.

Depending on whether or not you have added material for hems around the sail some of these sides may be identical to the basic sides of the panel.

Test main sail cross cut (flat)   // name of the sail
===== CPanel : 0 ====           // begining of panel 0
== CPanelLabel : name ==        // marker for panel label name
0
== CPanelLabel : height ==      // marker for label height
5
== CPanelLabel : color ==       // marker for label color
1
== CPanelLabel : origin ==      // marker for label origin coordinates
427.717 764.064 0               // X Y Z coordinates (Z is always =0)
== CPanelLabel : direction ==   // marker for label orientation
168.204 -57.8975        0
== CSide : left ==              // begin left side of panel
#0      92.5718 886.006 0       // X Y Z coordinates of point 0
#1      92.5718 886.006 0       // X Y Z coordinates of point 1
...
== CSide : top ==               // begin top side
#0      92.5718 886.006 0       // X Y Z coordinates of point 0
#1      262.77  886.006 0
...
== CSide : right ==             // begin right side
#0      3533.09 25.5986 0
#1      3526.2  169.113 0
...
== CSide : bottom ==            // begin bottom side
#0      92.5718 886.006 0
#1      259.921 823.943 0
...
== CSide : cutLeft ==           // begin left cut line
#0      0       899.006 0       // X Y Z coordinates of point 0
    of left cut line 
#1      0       899.006 0
...
== CSide : cutTop ==            // begin top cut line
#0      1150.25 899.006 0
#1      262.77  899.006 0
...
== CSide : cutRight ==          // begin right cut line
#0      3574.36 0       0
#1      3566.15 171.031 0
...
== CSide : cutBottom ==         // begin bottom cut line
#0      0       899.006 0
#1      252.966 805.191 0
...
===== CPanel : 1 ====           // beginning of panel 1
== CPanelLabel : name ==        // marker for panel label name
1
== CPanelLabel : height ==
5
== CPanelLabel : color ==
1
== CPanelLabel : origin ==
889.341 2.64113 0
== CPanelLabel : direction ==
170.396 0.562482        0
== CSide : left ==
#0      548.746 0.388633        0
#1      367.439 68.706  0
...
== CSide : top ==
#0      203.679 871.331 0
#1      393.052 872.078 0
...

9.2.  Text representation of 3D sail

This section describes the structure of the file generated by Sailcut CAD using the menu to TXT sail entry of the Export 3D sail submenu of the File menu. The extension of a text sail file is ".txt".

A 3D sail is made of a number of panels, each panel has 4 basic sides : left, top, right, bottom which are joined by a drawing line.

Test main sail cross cut (3D)   // name of the sail
===== CPanel : 0 ====           // begining of panel 0
== CPanelLabel : name ==        // marker for panel label name
0
== CPanelLabel : height ==      // marker for label height
5
== CPanelLabel : color ==       // marker for label color
1
== CPanelLabel : origin ==      // marker for label origin coordinates
427.717 764.064 0               // X Y Z coordinates (Z is always =0)
== CPanelLabel : direction ==   // marker for label orientation
168.204 -57.8975        0
== CSide : left ==              // begin left side of panel
#0      92.5718 886.006 0       // X Y Z coordinates of point 0
#1      92.5718 886.006 0       // X Y Z coordinates of point 1
...
== CSide : top ==               // begin top side
#0      92.5718 886.006 0       // X Y Z coordinates of point 0
#1      262.77  886.006 0
...
== CSide : right ==             // begin right side
#0      3533.09 25.5986 0
#1      3526.2  169.113 0
...
== CSide : bottom ==            // begin bottom side
#0      92.5718 886.006 0
#1      259.921 823.943 0
...
===== CPanel : 1 ====           // beginning of panel 1
== CPanelLabel : name ==        // marker for panel label name
1
== CPanelLabel : height ==
5
== CPanelLabel : color ==
1
== CPanelLabel : origin ==
889.341 2.64113 0
== CPanelLabel : direction ==
170.396 0.562482        0
== CSide : left ==
#0      548.746 0.388633        0
#1      367.439 68.706  0
...
== CSide : top ==
#0      203.679 871.331 0
#1      393.052 872.078 0
...

9.3.  XML representation of a sail

This describe the structure of the file generated by Sailcut using the menu to XML sail entry of the Export development or Export 3D sail submenus of the File menu. The extension of an XML sail file is ".sail3d".

A sail is made of a number of panels Each panel has 4 basic sides : left, top, right, bottom which are joined by a drawing line. The origin is at the bottom left corner of a rectangle surrounding the panel. These four basic sides define the net area of the panel after assembly in the sail. Around the basic panel there is provision for stiching the panels and sail edge hems, the outer side of the panel is defined by four sides named cutLeft, cutTop, cutRight, cutBottom and the material is cut along these sides. Depending on whether or not you have added material for hems around the sail some of these sides may be identical to the basic sides of the panel.

<!DOCTYPE Sailcut >
<CSailDoc>                          // header begin file
<CSail name="sail" >                // begin sail + name of sail
<vector size="10" name="panel" >    // indicate that the sail is made
                                       of 10 panels
<CPanel name="0" >                  // begin panel 0
<CSide name="left" >                // begin of left side of the panel
<vector size="7" name="point" >     // number of points on left side is 7
<CPoint3d name="0" >                // first point = 0
<real value="92.5718" name="x" />   // first point coordinate X
<real value="886.006" name="y" />   // first point coordinate Y
<real value="0" name="z" />         // coordinate Z is always 0 
        // for a developped panel
</CPoint3d>                         // end of first point
<CPoint3d name="1" >                // second point = 1                             
<real value="92.5718" name="x" />                
<real value="886.006" name="y" />
<real value="0" name="z" />
</CPoint3d>                         // end of second point 
 ...
</vector>                           // end of list of left side points
</CSide>                            // end of left side 
<CSide name="top" >                 // begin top side
<vector size="21" name="point" >    // number of points on top side is 21
<CPoint3d name="0" >                // first point = 0
<real value="92.5718" name="x" />
<real value="886.006" name="y" />
<real value="0" name="z" />
</CPoint3d>
<CPoint3d name="1" >                // second point = 1
<real value="262.77" name="x" />
<real value="886.006" name="y" />
<real value="0" name="z" />
</CPoint3d>
 ...
</vector>                           // end list of points of top side
</CSide>                            // end top side
<CSide name="right" >               // begin right side
 ...
</CSide>                            // end right side
 
<CSide name="bottom" >              // begin bottom side
 ...
</CSide>                            // end bottom side

<int value="1" name="hasHems" />    // header indicating that the panel 
                                       has hems cloth around the edges
<CSide name="cutLeft" >             // begin left side cut line
<vector size="7" name="point" >     // left side has 7 points 
<CPoint3d name="0" >                // first point = 0
<real value="0" name="x" />
<real value="899.006" name="y" />
<real value="0" name="z" />
</CPoint3d>                         // end first point
 ...
</vector>                           // end list of left side points
</CSide>                            // end left side cut line
<CSide name="cutTop" >              // begin top cut line
 ...
</CSide>                            // end top cut line
<CSide name="cutRight" >            // begin right cut line
 ...
</CSide>                            // end right cut line
<CSide name="cutBottom" >           // begin bottom cut line
 ...
</CSide>                            // end bottom cut line
</CPanel>                           // end of first panel
<CPanel name="1" >                  // begin second panel = 1
<CSide name="left" >                // begin left side
<vector size="7" name="point" >
<CPoint3d name="0" >
<real value="548.746" name="x" />
<real value="0.388633" name="y" />
<real value="0" name="z" />
</CPoint3d>
 ...
</vector>
</CSide>                            // end left side
 ...
 ...
</CSail>                            // end sail
</CSailDoc>                         // end file

10.  Copyright

Copyright (C) 1993-2007 Robert & Jeremy Lainé.

Sailcut is a Registered Trademark of Robert Lainé.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. See http://www.fsf.org/ for the licence terms and details.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

The authors would appreciate that publications on sails designed with Sailcut include some acknowledgement of their work.