I will be talking through a little of what I have discovered over the years about spinnaker design, and will use a common sailmaking design program – SMAR-Azure Project to illustrate some of the concepts. I am not re-writing a software Manual, so these notes are for general interest.
The way computer software deals with spinnakers is, in many ways, pretty easy to understand. It gets a workable spinnaker model up on your screen in a short time. In the end though, spinnakers are not easy to design and although the computer wizards can help, they do not replace the knowledge and expertise required to design a fast and easily flown sail.
So I will go through the basics of getting a good spinnaker design through Azure Project, as an example – other programs exist which deal with the concept in largely similar ways. I am going to design using the “Project” so we can see the boat and rig at all times. My reasons for this will become clear later.
In an attempt to simplify the process as much as possible, most designers have some way to deal with the big issue of Aspect Ratio. This dramatically changes the design of the sail, and is the biggest single reason for a spinnaker being wrong – in some cases really very wrong indeed.
I am going to go through some history and theory first……
2D Spinnaker Design
Traditionally, spinnakers were designed flat on the sail loft floor. The sail was conceived as a triangle with roach for the leeches, and a curve which was the mitre or centre join. This allowed sailmakers to calculate and make the sail the same way as any other sail they made, only in two parts, joined at the mitre. Best think of this as two jibs sewn together down the luff! The first operation was to mark out the basic triangle, of the straight leech, half foot, and mitre length. These edges were marked out with rigging twine laid around the spikes .
The leech curve was often a complex curve, and took some time on each sail for the sailmaker to be happy , since this was critical for the sail to fly well. Much of the art of a senior sailmaker was to oversee the shape of these splines.
This was where decisions on the panel layout were made, and there were many variations. The general principle of keeping the strongest and least stretchy part of the cloth in line with the most load – the leech. For this reason the cloth was laid with the fill threads running parallel to the cut leech. Where cross cut sails are mainly used – One Design – this pattern is the one used.
Variations included – the fill parallel to the straight leech and (especially in the early days of nylon) , the warp parallel to the straight leech.
The broadseams would be marked on using a batten, and again a lot of skill was required here to get the “right” shape. This is where most of the “art” of sailmaking lay, and we will return to this at a later time.
With everything all marked and the edges cut – the excess could be used for patches.
I have missed a few stages of the method of construction in the drawing for clarity. The broadseams were marked on, cut, and the both sides sewn together before the sail was put back on the floor, over its mark triangle and curves and then the edges were trimmed finally.
The main reason for this long explanation is right here – the important aspect to note is that the mitre curve, when seen here, is of course a huge broadseam itself, and is the major shaping in the sail. The “normal” broadseam shapes major function is to change the shape of the section – to take it from a V-shape to a nice arc or elliptical shape.
It was this ability to change the cross sectional shape of the spinnaker very easily that has allowed the cross-cut spinnaker to be such a big force in one-design – and still the case to this day.
In this case, the most powerful influence on the sail shape is the mitre seam “broadseam”.
We apply a % of the mitre as the curve we want the mitre to have, and apply a % for the leech roach as well.
As a spinnaker is made bigger, then the leech and the mitre gets longer too. This means that the mitre curve gets proportionally bigger as well. This would be OK if the width of the sail gets bigger proportionally. The spinnaker would simply scale up nicely.
But lets consider what happens when the width of the sail does not grow proportionately – lets make the leech and mitre longer, but the width stays the same. The mitre curve gets bigger because the mitre does. But the sail is no wider than before, the % applied to the seams is no bigger, and therefore the broadseams are no bigger – the sail will be more V-shaped. That’s not good, but there is much worse.
As we will see later, to have the SAME performance and characteristics, a higher aspect sail should have less shape – not more. Therefore the % curve in the mitre needs to become less as the aspect ratio increases
3D Spinnaker Design
In the 1960s and 70s, a few sailmakers (Bruce Banks, Austin Farrar, John Black and others), with either an engineering, navigational or mathematical background began looking at spinnakers a different way. If the top of the spinnaker was a part of a sphere (ball), then perhaps the panels could be shape as parts of a sphere, and develop a good and repeatable and scalable shape. This could be done with some trigonometry, and some powerful techniques were developed to be able to do this in a production setting. Templates were created and panels could be repeated time after time.
Computers were only their infancy, and 3D programs were not yet known, and when later they became available, many considered them so poor as to be unusable. I used Excel and Autocad (2D) as my main spinnaker design and cutting tool for many years, even after having used some good 3D programs for fore & aft sails– why?
Well I knew what I wanted, and nothing was hidden! One of the early problems with the software was that computers were not as powerful as today, so to keep the software running acceptably quickly, some assumptions were made to keep the maths easy. But some of these assumptions were not that good, especially for more complex sails, and I and others preferred to use our maths skills to create 3D shapes which was true. Particularly, as will be discussed later, the understanding of geodesics was not well sorted in these first programs – and therefore frequent re-cuts after the first race. Some of the biggest sailmaking names erected masts on their loft grounds to enable them to check this problem, and recut before delivery to the customer.
We all had good reasons initially to distrust some of the answers given in the early days – on the water, where it counted. Using maths in this way I never had to re-cut a spinnaker.
We were using spherical maths to calculate a 2D shape from a 3D concept, to then make a 2D panels into a 3D result – developing or lofting a shape. We had no “model” to see, just the outcome out on the water. How this was done is described below, and we will go through the mathematical 3D principles used.
If we want the sphere to come down to the mid-girth, the “equator” of our ball will lie at the mid-girth.
This means that the “North Pole” to the “equator” (90 degrees from the pole to the equator) at half of the leech length equals 10m.
the line of the shortest distance between two points on a sphere.
The girth is 10m also, so that is 90 degrees from one line of longitude to the other –
this is the position for the other upper leech of the sail.
This is important, and you can prove it to yourself by taking a piece of string along a part of a line of latitude, then pulling the string tight – it will move to the geodesic – the “Great Circle” in oceanic navigation.
This concept can be thought of as cutting an orange into a quarter – the head of 2:1 spinnaker.
Of course this only gives one half of the sail – we now need to consider the bottom half!
The Bottom Half.
The diameter of the sphere we used for the top has to be the same otherwise the two sections will not join up properly in a smooth way. So we stretch the sphere out until it is long enough to have the correct foot width at the correct half leech length.
The resultant “Prolate Spheroid” or ellipsoid is a much more complex mathematical structure, but the more complex maths can be used to develop panels in the same way.
It also has geodesics, with the same rules as before.
These geodesics will be seen in Azure, and refer directly to these concepts.
So we now have the upper and lower halves of our simple spherical design.
The early radial head sails were (when designed like this) very good, and a huge step forward from the previous sails. However. some of these sails were unexpectedly poor! – when designers tried to design this look of sail without understanding how it was thought through.
At this stage it was very hard to design a radial sail that was constrained by too many rules – it was at its best when under IOR/IMS/IRC rules where only one girth was measured.
To get a flatter sail, the head angle is reduced, therefore making the equator of the sphere get closer and closer to the foot of the sail
If we allow the head to be 90 degrees, then the whole leech length must be equal to the girth – the FOOT is at the equator.
This then is a reacher shape, and may be too flat to be a fast sail in average conditions. Look at the photo opposite, where the Aspect Ratio is almost 1:1, and the look at the leeches are still curving outwards almost to the foot.
One Design is also a group of sails which may get a 1:1 ratio, and are commonly held by their rules to a shape some way between these two extremes. If there were no rules, then 180degress head angle would be useable – see below……
If there were no rules, then head angles getting close to 180degrees would be useable – and were on some metre boats. 12 metres under performance pressure of the Americas Cup, saw the most development of the widest head angles.
One Design is the group of sails which most closely gets to 1:1, and are commonly held by their rules to a shape some way between these two extremes.
So as aspect ratio reduces the head angle should go up to have the same Vertical Mitre Curve.
Computer 3D modelling
All this basic theory – why do we need to know this today. Surely the computer makes it easy?
Well, yes and no! Most modern programs make it look initially straightforward to get a nice sail that performs well. But since all of them set out to design using essentially the older sailmaking concepts of luff curves, girths and cambers, then we must be careful to ensure we know the effects of our design actions.
All modern spinnaker design programs use 3D shaping – they start the design from what it will look like on the boat. So, they use edge size, edge shaping, girth and camber as a starting point – in the way a headsail is designed – and this is where some complications start to show up.
The first complication is that any photo taken of a spinnaker has a lot to do with the crew’s setting of it. If that is wrong, then the data is wrong. So you can only use a boat known to you that is well sailed. Even then getting the right photo at the right angle with no waves moving it around is more art than science.
The complications of getting photos to analyse is even more difficult when we look at cambers.
Its very difficult (impossible?) to get any photo from the deck, and aerial photos, which are very good, are difficult to get (very expensive) – and the crew’s setting of it is still very important.
The only real method to get this data is to do a lot of Wind Tunnel Testing – and you still need good sail trimmers to get it right.
Much easier, as this is normally a rule enforced number.
With all this in mind, lets go back to Azure and try to design a spinnaker.
The first and important input (after the sizes) is the Luff Offset.
This defines the initial curvature of the spinnaker.
It is applied equally to both edges, and is like pushing down on the edges of a piece of paper.
What’s the right number?
As discussed photos can help get you started, but there is one other indicator – if the sail is not in the right place on the mast, if it looks like this, it will be pulled out of shape to get to the masthead – and that cannot be right.
Since this is so important, its one of the main reasons why I like to design a 3D model on the rig, and why Project is so necessary.
Check the pole height, the leech lengths, and then the Luff Offset – in that order!
I would start with an Luff Offset of about 12%, and just a simple arc –
8.5% @ 25%
12% @ 50%
8.5% @ 75%
This gives a pretty realistic curve, commonly seen when sailing.
And then you must check the position of the head on the rig again!!!
Like all other sails, a spinnaker has sectional camber, which is best put in correctly now.
I use 40% in the bottom, 35% @ 25%, 30% @ 50%, 24% @75% and 17% at the head.
This gives a sail that has proved fast and stable both on the water and in the Wind Tunnel.
Luff Offset AND Camber combine to give the Mitre Curve, which is not used in Azure, but may be seen in other programs.
It is important however to understand that relationship.
Increasing the camber also shortens the straight line leech length – to check the head position again.
This “iterative loop” of Luff Offset, Leech length and Camber must be understood and repeated until you are happy that all is well.
Girth and Luff Curve (or Luff Roach in some programs)
Other program give you the choice, but you never use both at the same time!
They are effectively, but not exactly, the same thing, and change the shape viewed from ahead or behind the spinnaker
I use girths of:
100% at the foot
65% @ 75%.
This can be altered to fit, of course, but it give a nice sail from which to finesse as you wish.
You use the girths to meet the rule requirements, which may alter things a lot.
We looked at this in the theory part of this article, and now we are going to look at this important issue again.
Azure gives you the tools to check the Geodesics and gives you both the whole leech geodesic AND the half leech geodesic.
For spinnakers it’s the upper one which is normally the important one –the full length one is very important in asymmetrics.
If we take the upper girth to 76% instead of 66%, then this is the result.
The geodesics are showing that the leech is way outside what can be supported by the shape you have made – not a “Great Circle”. We must either reduce the girth, OR increase the camber (a more spherical shape) to support this girth.
An increase of camber will change the Mitre Curve (the profile) of the sail, so that will need to be checked again.
Azure does not show the geodesic outside the sail, so you have no idea if you have overly reduced the girth –you have to move the girth in and out watching for the geodesic just “kissing” the leech.
In Azure, only use the Port edge of the sail, (the one attached to the pole) for judging the geodesic – the other is NOT accurate.
This shows us the results of our 3D work, now expressed as a 2D shape lying flat on the floor.
I would expect to see about 4-5% max on the leech and 9-10% on the mitre in a AP IMS/IRC type spinnaker.
The mitre should be pretty evenly balanced ( the max around the middle, and around 7% at both 25% and 75%.
The Leech curve should have its max at around 60% up.
Also check the <Corner> tab, and see what your head angle is? 85 to 90 degrees is good for a AP spinnaker with a 1.8 – 2:1 aspect ratio.
Spinnaker 3-D design is a cyclic process, going through each parameter and checking, over and again until the sail is right in all regards.
Once you have a library of good designs for all Aspect ratios then you can simply choose the correct one and have very little to do other than checking girths.
One of the major benefits of 3D designing is – if it looks wrong, it probably is!