A sail block
Dan Sherman has helped correct my earlier analysis and triggered this re-think. I've prepared a new spreadsheet (17 kb) which carries out the calculations discussed below.
The spreadsheet starts by asking for the characteristics of your block. In the example shown, the block is a lump that is 300 mm long, its "hump" rises 30 mm above the chord, and it has a 6 degree bevel angle. It then reports some information about your block geometry, the most interesting being the block curvature or radius, shown as around 390 mm here.
How do you get draft into a sail?
Much of the necessary draft to a sail is given by simply moving the outhaul forward. This gives you the draft you would find in an ordinary single-panel sail. The Outhaul effect page shows an unshaped sail of four panels, but its seams have no draft sewn in at all. It seems that the outhaul influence is around 55% at the bottom seam (one quarter the way up the sail), around 25% at the middle seam (half-way up the sail), and 0% at the top seam. You want to sew in extra draft in a seam for two main reasons.
One is to make adjustments to how the draft is distributed from head to foot. Opinion differs, but most professional sails do not have the same draft at each position up the sail. Some have reducing draft, but most have increasing draft sewn in.
The other is to introduce draft that the outhaul, leech tension, or wind pressure does not. For example, you might want to add around 2% draft to the lower seam, 3% to the middle seam, and 5% at the top seam. (The actual numbers are dependent upon what you think is sensible. I'm not a sail maker, and don't know!)
If you set the outhaul to, say, "10%" draft in the foot, and you have sewn in 2% at the bottom seam, 3% at the middle, and 5% at the top seam, you might then obtain actual flying drafts of around 8%, 7%, and 6% respectively. The important thing is to note that you are not sewing 7% or 6% draft into a seam!
What is the "bevel angle" all about?
Imagine the block has zero bevel angle. That is, the two surfaces are perfectly continuous. Even though these surfaces have a radius of curvature, when you join two panels on a block with zero bevel angle, you put no draft into the sail seam at all. Then, imagine a "block" with 90 degree bevel angle. Such a block would effectively be a thin flat piece of wood in the profile shape of an aerofoil section, each side being one of the "surfaces". When you join two panels on such a block, it would be impossible to lay out the resulting sail, it would have such a pronounced draft hump. In this case, you have put all of the block curvature into the seam.
The bevel angle therefore regulates the amount of block curvature that actually gets put into the sail seam to give you the "sewn-in" sail draft. The bevel angle mechanically translates the block curvature so that it can be reliably and repeatably sewn in.
The key effect of the bevel is to increase the length of the sail material over the block's "hump". We imagine that, when you first lay your sail panels over your block, they drape an amount of material (called the girth, "s") over the block. Let us imagine you want to sew a seam that will be 200 mm. When draped over the block and not laid over the bevelled surface just yet, they will have some nominal draft (called height, "h"). This is shown as 12.75 mm in the example, due to the block curvature.
When you now lie the panels over the bevel surfaces, the bevel increases the amount of material (s' in the diagram below) the goes into the seam. Because the chord (c in the diagram) stays constant, the result is an increase in the draft of the sail (h'). When you take the seam off the block, you have now shaped the seam because you have put some draft into it, h', across a chord which is now s.
It turns out that a rather small increase in the girth (s') of the sail causes quite a dramatic increase in the draft (h'). In the example, the girth increase is 0.57 mm, and this results in a draft of 6.54 mm being sewn into the seam (3.27% as a percentage camber). The approximate formula for how much the draft (h') increases when you increase the girth (s') but keep the chord (c) constant is shown above. It is an approximate version of Pythagoras' theorem, adjusted for the fact that the one side is curved, not straight.
The bevel, according to my current thinking, does two things, and here are a couple of photographs to help visualise what goes on.
The two "panels" in the photos are pieces of card, and they are not even curved, they are simply creased to make the mechanism as obvious as possible. You probably will want to get some card yourself and try this if three-dimensional trigonometry isn't your strong point. I've overlaid an imaginary block on the left-hand photo in red, and show its bevel in yellow.
What happens when you play with the card (lay your sail panels on your block) is that the middle of the sail seam is lifted up, and the two ends of the seam are overlapped by more than they would normally be if you just overlapped them on some flat (or even curved) surface. This is the key -- the two ends are "twisted" inwards because of the bevel, such that they add a little extra material into the seam. When you then glue your seam -- pinch and hold the cards together -- it has a sewn-in hump, just like the block hump, and this sewn-in hump is remarkably sturdy and fixed in character.
The more the two ends of the panels "twist" inwards, the greater the hump that is produced, and the job of the bevel is to regulate this twisting. By trigonometry, I believe the twist, and hence the increase in material laid over the seam, is proportional (1) to the secant of the bevel angle and (2) to the block curvature. (The secant is the reciprocal of the cosine).
The sketches show the "twisted" or skewed material in red. The length of this material that is forced into the seam is approximately the hypotenuse of each thin triangle.
What is the "radius of curvature" all about?
The radius of curvature represents the draft you want in your sail while it is flying. The smaller the radius, the larger the draft. However, the draft you actually want to sew into your seam is a different amount, some fraction of this.
You want to size your block so that you can sew in the amount of draft you want. The example numbers shown in the spreadsheet screen shot illustrate a block with 6 degrees of bevel and nominal 10% draft. When a seam of 200 mm or so is sewn, only part of the block is used, that part which has a draft "in use" of around 6.45%, and the result is a sewn-in sail draft of 3.27%. You can use the spreadsheet "backwards" to figure out the block you might want for sewing, say, 2% draft into a 300 mm seam. (Did you get a block with a radius of around 1565 mm? That'll do it.)
Yes, but what about the seam "shape"?
Ah. The above sail shape was a circular arc to make the maths easier. Real sails aren't circular arcs. No one knows what they actually are, and in fact the whole joy of making your own sails is that you get to say what you want this shape to be. Here is a picture from the sail shape page, comparing circular, bi-circular, and parabolic shapes, with the addition of a catenary shape. There are other shapes you might like, maybe one of the NACA curves.
Now here is the science bit. You do not necessarily want your sail block to have one of these shapes. Remember what we are doing -- the sail block allows you to sew in some draft in a seam which is additional to the draft, and the shape, given by the major control, the setting of the outhaul, and the other contributors, significantly wind pressure and leech tension. So the shape of the sail block should, ideally, result from two things: the amount of the additional draft you want to sew in, after you have "removed" the default shape given to you by the outhaul and the other factors.
Let's consider a single-panel sail, bent to the mast and boom. What shape does it take up when flying normally? We might imagine it takes up the shape of a catenary, a shape which is "usual" for a length of material under constant force tethered at its ends. Now, what shape do you want in your sail? Well, you might decide you want a parabola. In this case, the shape of your sail block needs to be the difference between a catenary curve and a parabolic curve, in order that your seam pulls the sail into the shape you want instead of leaving it in the shape dictated by "normal" forces. That's the theory, anyway...
The analysis and spreadsheet is for circular arc blocks, and is only roughly correct for other block shapes. As you can see, other block shapes are not really grossly different from circular arcs, and so I think the basic ideas are OK. Also, notice that I've only got to this analysis after thinking something quite different for some time! Who knows how wrong it still is?!?
While much of the necessary draft to a sail is given by the outhaul, this is really only in the lower 1/3 to 1/2 of the sail. Above that, you can pull the outhaul out till there is no camber at all at the bottom and the camber of the top of the sail won't change appreciably. So there are two main reasons to sew in draft in a seam. One is to make adjustments to how the draft is distributed from head to foot, but the other is to put camber in the top half of the sail.
You need to be aware that, in addition to seam draft being a function of bevel angle and radius, the resulting sail camber is also influenced by adjacent seams. And, on a practical note, bevel angles above 8 degrees don't work well, it is too difficult to get the seam wrinkle-free.
The amount of draft put into a seam by the sail block depends both upon the block radius of curvature and upon its bevel angle. That is, a block with a radius of, say, 1000 mm and a bevel angle of 3 degrees will insert pretty much the same amount of draft as a block with a radius of 2000 mm and a bevel angle of 6 degrees.
©2011 Lester Gilbert