Optimum sail draft for wind speed

All sail trim books discuss ways to manage the size and position of the draft with the tools at our disposal: luff tension, sheet tension, car positions, rig tension etc,., etc., and then point out how the size and position of the draft is important to handle varying wind speeds, sea states and points of sailing. But none of them explain why.

• Why does a deeper draft produce better performance in light airs?
• Why do we move the draft forward in calm water.
• Why do we ease the sheets and increase the draft when sailing off the wind?

There are scores of principles of trim and rig tuning that experience has shown to the boat go faster! But that's not theory, that's practice!
None of them explain the theory.
Consider this.
All the sailing writers, Jobson, North Sails etc., have learned their theory from the published authors like Marchaj, Gentry, Fossati etc., who themselves have, either consciously or unsconciously, used theories arising from fluid dynamics, like Bernoulli's Theorem, Kelvin's Circulation Theory, Reynolds laminar flow etc., or the classical mechanics of Newton.
None of these writers explain how these theories explain the principles of sail and rig trim.
Why?
Because the theories behind fluid dynamics all use incompressible fluids. Water is an incompressible fluid. Air is a gas. It is compressible. Fluid dynamics doesn't apply to wind over sails.
Newtonian mechanics applies to the motion of objects. Air is not an object - it's a gas!
As you will read in Aerodynamic force on a sail , "the aerodynamic force arises because the sail is compressing the air to windward and decompressing it to leeward."
Maybe some of the mysteries of sail and rig tuning can be explained with Swept Volume Theory, and maybe they may yield an answer to your question.
Certainly, in the past 100+ years, none of the current theories have been of any use.

 

I really like your thinking here. However, the question remains. If I have a sail that's not going to be adjustable in any meaningful way, what draft is best for all around use?

I personally believe that having a sail where you have to worry about "luff tension, sheet tension, car positions, rig tension etc, etc," is foolish. I am going unstayed, constant draft, a modification of the junk rig. And very strongly considering the biplane rig without headsails. Just putting the helm over while tacking seems very appealing to me. Watching people run feverishly around the cockpit while tacking bothers me, I can only imagine the seriousness of having to do that in a "situation".

 

Woohoo, a believer!

Wow! that's a biggie. Every one will be good for one condition and bad for all the others! There are heaps of conditions, of:

• Wind strength
• Sea state
• Wind constancy in speed or direction (gusty, shifty)
• Point of sail

You have to decide what condition you want to optimise for.

 

Draft in a sail is like gears on a car. The question of what is the best draft that will work in all condition, is like asking what is the gear in my car that will work well at low and high speed. The answer is "none".

 

On the other hand, if you only had one gear to start from a dead stop and drive something somewhere, use low gear. High gears tend to stall out when trying to start from a stand still. You may take forever to get down 95, but at least you can get on 95 and keep it going.

If I had a high performance hull, one that planed, or got up on one narrow cat hull, I'd go with flat, forward camber. Tack down wind, sail hard on the wind, or lose performance in low, unsteady winds, but you would still go, until you needed to sail hard to weather or sail down wind faster than the wind, then sail like a banshee and get out of that approaching storm's way fast.

If your hull is a trawler, got with a low aspect ratio and a fuller sail to follow the trades or stick to the coast.

-Will

 

The way I see it is that a sail at whatever draft will produce lift until the flow starts to separate. To me this eliminates high draft sails because I imagine they will stall in high wind. Very slight draft seems like it would be inefficient in light wind. So to me this means somewhere in the middle is what I should aim for. What is the middle? According to Wikipedia "Forces on Sails":

For light air (less than 8 knots), the sail is at its fullest with the depth of draft between 13-16% of the cord and maximum fullness 50% aft from the luff.
For medium air (8-15 knots), the mainsail has minimal twist with a depth of draft set between 11-13% of the cord and maximum fullness 45% aft from the luff.
For heavy (greater than15 knots), the sail is flattened and allowed to twist in a manner that dumps lift with a depth of draft set between 9-12% of cord and maximum fullness 45% aft of the luff.

So 11-13%? According to the graph just below this there isn't a large difference in propulsive and heeling forces between 10 and 14.25% draft, but 5% is significantly less efficient. According to the same article there is little difference between draft positions. Junk rigs with little to no draft seem to do ok. Anyway, I'm thinking in the 10-12% range. What do you think?

In the case of airfoils the answer is not none, unless taken to some extreme. It's more like having an electric motor rather than an internal combustion engine. I leave my mid drive electric bike in the same gear all the time unless I'm going up a steep hill.

 

It will be a very slippery catamaran.

 

The proposal for fixed curvature for battens reminds me of this Bolger sketch:
https://proafile.com/images/article_images/_large/bolgerproa_2.jpg
Of course, tacking something like this is going to be interesting, because you have to swing it around in front of the mast. Then again, in something like the proa shown, this isn't necessary.
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At 20 knots, the compressibility of air is negligible. At that speed, the dynamic pressure is 0.00936 psi, vs. about 14.7 psi ambient pressure. In other words, the dynamic pressure is 0.06 percent of ambient pressure. You could also look at it as Mach 0.03. Compressibility doesn't become important until your Mach number is a significant fraction of 1. Furthermore, fluid mechanics, at this point anyway, can take compressibility into account. But there's no need until we get up into hundreds of knots. If you go fast enough, you have to take compressibility into account in water, too, but the speed of sound in water is much higher. It's not exactly incompressible, though. For instance, if you have a sufficiently rigid container, like maybe a heavy glass pipe, and you ballast it to about the density of water, you can control the depth it floats at by screwing a piston in and out to change the volume, and therefore the density, of the container. It will then drift up or down until it gets to water that's of equal density. Some oceanographic buoys use this principle.
Dynamic Pressure https://www.engineeringtoolbox.com/dynamic-pressure-d_1037.html
Fluid mechanics is basically working out the consequences of Newtonian mechanics as applied to fluids (or gases). F=ma is the name of the game.
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If you think about it the right way, the reason sails need to be flatter in higher winds is easy to understand. Let's say you're sailing upwind with a sail draft of 12 percent, when there's a gust. You ease the sheet, changing the angle of the sail relative to the wind. Now, the wind starts pushing on the back side of the front part of the sail, creating a really awful shape and creating drag. The sail may even start to luff. We've all seen this. If the draft was only 6 percent, the angle of the front of the sail would be different, and the sheet could be eased further without causing problems. With deeper draft, the sail can generate more lift (I don't mean up or down, I mean force perpendicular to the wind). At low speeds, where there isn't any problem with heeling, more force is desired, so more draft is good. At high speeds, the sail can work efficiently with less force if you reduce the draft. One caveat is that, if your sails are really small, and the wind really weak, the effects of viscosity may mean a sail can't actually use that extra draft, but now we're talking about really small RC sailboats. I haven't worked out just how small or how slow, but it's not going to be much of an issue with a sail that's several feet wide.

P.S. I know that more draft in low wind works, because that's what all the dinghy racers who were beating me had in their sails. I saw a lot of transoms with that crowd.