Jim Michalak's Site 

has some of the very best information available on  home boat building. He also has a book in the works. I hear it's at the printers - be sure to get your hands on it when it's available.

Here's what Jim has to say on rules of thumb for making darts in polytarp sails.

I have presented in past issues articles on making sails from common polytarp. Sails made from those articles have worked quite well. In general the sails are made with the one piece tarp which is cut to a predetermined shape, shaped with one or two "darts", which are tapered folds sewn in place, and then rimmed with a sewn in hem with stiffening elements like fiberglass tape and then given sewn in patches in places where the sail will be tied to the spars.

Although the method of making the sail is pretty straight forward, the calculation of the predetermined shape is not. In particular, the size of the shaping darts is critical but not easily calculated. I was hoping to come up with some "rules of thumb" to simplify the process.

WHY SHAPING DARTS....

Sails should be three dimensional surfaces which will get the most out of making the wind pull the boat forward. A good sail will have a surface shape like the wing of an airplane (indeed, some boats have wings for sails) with a "camber", which is a smooth outward curve. Aero scientists have argued for 100 years about the best camber shape - the optimum shape varies with the speed of the wind. I'm not getting into that except to say that Marchaj, the sailor's aero scientist, stated somewhere that the optimum camber for almost all sailing is 10%. So a sail with a width of 10' would curve outward by 1'.

But, you say, many homemade sails are made from flat panels simply cut to shape and hemmed, with no 3D shaping. True. I think the reason they have had some success is that homemade sails are often made from stretchy materials that give and bulge out on the leeward side, making a camber of sorts.

All sails made by sailmakers have this shape sewn right in. Those sails will not lie flat on the floor. This is where most of the witchcraft of sailmaking is applied and sailmakers don't talk much about how it is done. Usually the sails are sewn together from 3' wide cloth. By varying the width of the seams and by cutting and adding seams where needed, they can shape their sails in 3D. If you are interested in real sailmaking, you might try getting info from Sail Rite Kits or the book The Sailmaker's Apprentice.

When I made my first polytarp sail, that is how I did it. I cut the big tarp into 3' wide strips and sewed it all back together like I would a Darcron sail. I worked fine but It was clear that the idea of cutting the thing apart and sewing it back together was not efficient.

My second effort was to use the full sheet of polytarp and slit it where the shaping seams would be and then sew it back together with a gusset over the slit. Then one builder had his wife make a polytarp sail to those instructions but she knew a lot more about sewing than I do. She used regular shaping darts, as are common in tailored clothes, to simulate the varying seams of the sailmaker. I tried it and found it superior!

Eventually I found a way to put all the shaping in one or two darts instead of placing a dart every 3' as the sailmaker does with his material. Four sided sails like the lug and gaff sails I often use need two. Triangular sails need only one! Here is an example, my own Piccup Pram, using a triangular sail:

The Piccup sail went very well. You can barely make out the shaping dart in the photo running from the tack to a dark shaded point in the center of the sail.

The full details of making this Piccup sail in polytarp were presented in the 15jul99 issue of this webpage. You can still look at it by going to the past issues links at the bottom of this page and clicking on "the way back issue archives". That takes you to a large site where the old stuff is stored with an index.

To review, the sail is drawn in "3D", with the perimeter as shown on the boat drawing and with a point in the center of the sail bulging outward. Like this for the sail shown on the Piccup:

Next the lengths of all the lines shown above are calculated and then the sail is redrawn as a flat pattern with one edge slit like this:

Then this sail flat pattern is drawn out full sized on the polytarp and cut out (with allowances for hems, etc.). When it is sewn up the gap is sewn shut with a "dart" like this:

So the final sail is not flat but has a 3D shape to the size and draft specified. It really works!

IF YOU DON'T LIKE DOING MATH...

I thought there might be a way to simplify things a lot by coming up with some rule of thumb for the size of the gap at the tack shown above. When I made the sail shown in the photo I didn't really measure out all the triangular elements. Instead I figured with math that the gap at the tack would be 4.4" and then I drew the pattern of the sail on the tarp with allowance for a 2.2" "dart" at the tack. (A 2.2" dart would remove 4.4" of material from the surface of the tarp which is what is desired.)

But after making a few of these it was clear that the size of the dart is the main thing you needed to know and that the size of that dart was determined, in a triangular sail, mostly by the size of the foot and by the amount of camber. Since I use Marchaj's advice to stick with 10% camber, it all comes down to the length of the foot. Or so I guessed. If true then the instructions for making this sail in polytarp might be simply to "lay it out on the polytarp and sew in a 2" dart at the tack".

I figured a bunch of examples with math to see if my guess was pretty close.

THE FIRST EXAMPLE...

The model I used in the calculations looks like this:

Then I varied the height h and the width b and calculated the flat pattern that would result in the desired sail shape. Then I calculated the the gap at A. Hopefully a pattern would result such that the gap would be more easily calculated.

I ran through several combinations and here is a table of the results:

Let's first look at sail 1. It has a luff of 12' and a foot of 8' and a draft of 10% of the foot dimension for 9.6". The flat pattern gap at A needed would be 4.6".

Sail 2 is the same except now it has a foot of 12' instead of 8'. The draft stays at 10% of the foot for 14.4". The gap at A required to build this sail figures to be 9.0". That is an increase of 96% when the foot has been increased by 50%. So it is not in proportion to the foot alone.

Sail 3 is the same as sail 2 except the luff has increased from 12' to 16'. The gap required at A figures to be 8.2", only slightly down from sail2's 9.0".

Sail4 is the same as sail2 except the luff is all the way to 20'. The gap required at A figures to be 7.6". So the length of the luff does not have a huge effect - and increase of 100% in the luff reduces the figured gap from 9" to 7.6", about 15%.

After looking at the effect of the luff dimension on the gap at A, I tried one more in sail5. Sail 5 is the same as sail1 except luff is increased from 12' to 16'. The gap needed at A figures to be 4.1" to give a draft of 10% of the foot, down from 5.2" of sail1.

CONCLUSIONS???

If you were building a normally proportioned sail with an 8' width or foot, I would say the gap at point A would need to be "about 5 inches". A taller sail needs a bit less gap and the lower sail needs a bit more.

If you were building a normally proportioned sail with a 12' width or foot, I would say the gap at A would need to be "about 8 inches". A taller sail needs less and a lower sail needs more.

What if your sail is in between? I cranked through a few more examples to get a feel for it. Sail1 was the basic pattern with a luff of 150% times the foot and a draft of 10% of the foot. Here us what came up:

I would use this chart for triangular sails of normal proportions. It starts with a 48 sq foot sail which is about the smallest sail useful. And progresses to a 147 square foot sail, which is about the largest sail I would try with normal polytarp technology. Somewhere in between should be the A gap you are looking for.

I guess the way I would use make a sail this way would be to lay out the sail according to the basic dimensions shown in the plans, and then draw a line from the tack upward where I want the dart to run, about 1/3 to the top of the sail and 1/3 back from luff. Then at the tack I would draw the "gap" that is predicted by the chart and sew in a dart that would remove that amount of material. The resulting sail will be a few inches smaller than the blueprint sail but that should be of no consequence.

Here is how it might look for the sail I used on the Piccup Pram. The width of the sail is almost 9' and the chart predicts a gap at A of 5.8". I would draw it out like this, fold it on the black line going from the tack to the center of the sail, and then sew in a dart more or less on the red lines shown.

Sail Shaping 2

Remember in the last issue I tried to come up with some "rules of thumb" for the darts used to shape the draft in a three sided sail. Here is the resulting chart:

I would use this chart for triangular sails of normal proportions. It starts with a 48 sq foot sail which is about the smallest sail useful. And progresses to a 147 square foot sail, which is about the largest sail I would try with normal polytarp technology. Somewhere in between should be the "gap" you are looking for. The "gap" refers to the amount of material to be removed from the sail's tack to give it the proper shape. In a polytarp sail that might be removed with a shaping dart that is half the size of the calculated gap.

The gap shown in the chart was calculated assuming a 10% draft, which is sometimes thought to be the optimum. I ran some numbers to figure the effect of draft on the gap. The example used in the numbers had a foot of 10' and a luff of 15'. The chart shows a sail with a 10' foot would need a gap of about 6.4". The same sail with a 5% draft would need a gap of just 1.5" and with a 7.5% draft would need a 3.7" gap. So there is a large effect. Showing that as a chart in percentage, it would look like this:

For example, if you had a sail with a 12' foot and wanted a 7% draft, what would the size of the gap at the tack? The first chart shows the gap needed for 10% draft to be 7.6" for the 12' foot. The second chart shows that for 7% draft the gap would be 50% of that, for a tack gap of 3.8" which would mean a shaping dart 1.9" wide.

NEXT...

You may remember that when I did the calculations for the first chart that I put the point of maximum draft 1/3rd of the way aft from the luff and 1/3rd of the way up from the foot. What if the point of maximum draft were lower? I ran an example using the 10' x 15' triangular sail where I lowered the point of maximum draft from 60" up from the foot to just 20". The effect was to increase the tack gap size a tiny amount from 6.4" to 6.8". So I don't think that is really a factor.

FOUR SIDED SAILS...

Next I looked at the darts needed to shape a four sided sail like a lug sail or a gaff sail. I have been using two darts in these sails, one radiating out from the tack and another from the throat. Here is a photo of Jeff Blunk's prototype Frolic2, now owned by Richard Harris in Illinois. The photo was taken at Rend Lake a few weeks ago and you can clearly see the two shaping darts.

From figuring the shape of lug sails in the past I had the opinion that the peaking of the yard has the effect of reducing the size of the dart needed at the throat. In fact I suppose the extreme case would be a Solent lug where the yard is peaked all the way up as an extension of the mast - a triangular sail needing only one shaping dart. I looked at four sided sails that look like this:

So the overall size was the same as the triangular sails, 120" foot and 180" height.

All of these sails needed a gap at the tack of about 5.5" compared to about 6.5" for the triangular sail, 85% of the triangular sail. So the peak angle really has no affect on the tack dart.

The throat dart changes with the angle of the peak. Sail A needs 5.5" gap at the peak dart. Sail B needs 5" gap at the peak dart. Sail C needs 2.6" gap at the peak dart, and sail D needs 3.4" gap at the peak dart.

Plotting it out looks like this:

I expected a smooth curve! But no, there is a bump. I double checked my numbers and it was still there. If there is an error in there I think it is in the 50 degree example. I would expect that sail would need a gap of about 2" instead of 3.4".

Let's think of a real life example. Let's try the large Piccup pram sail which has a foot of 105", and a peak angle of about 45 degrees. Let's assume 10% draft.

Let's figure the tack gap first. If you look at the triangular sail data for 8.75 ft foot, the gap for the triangular sail would be about 5.7". If we use an 85% factor to adjust that to a four sided sail then I would expect the tack gap for the large Piccup sail to be about 4.8".

Now for the throat gap. Looking at the above chart I would expect it to be about 50% of the tack gap, or 2.4".

Back in the 15oct98 issue I figured the large Piccup sail out the long way. The results then were a tack gap of 5.2" and a throat gap of 1". So the tack gap using the above system compares quite well with the complex calculations I did back then. The throat gap is off by a ways, isn't it? I noticed on the Piccup article that I used a flatter draft in the top of the sail then which might account for some of it. I can't explain the rest other than to say the gross approximations I used above give reasonable answers and will give very reasonable sails.

Here is a photo of Rob Rhode-Szudy's Piccup at the Rend Lake messabout with his Piccup with a large polytarp sail made with the twin dart method. It sailed quite well indeed!

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