Sail Twist: The Math

[konajoe]

Wind speed increases the further one moves from the surface due to drag at the water surface. To keep the sail tuned correctly at all heights, sail makers build twist into the sails. This is to account for different apparent wind angles at different heights.

For a given wind speed and given rig, will the sail need more or less twist as it's speed increase? The answer may surprise you.

Pick a constant wind speed for the lower portion of the sail. Pick a higher constant wind speed for the upper portion of the sail. Move at a 90 deg angle to the true wind. Now compare the difference in apparent wind angles at different speeds.

Who wants to do the math?

[dmitrynizh]

In Excel, one might express it as

angle_diff =(DEGREES(ATAN(board_speed/bottom_tws)) - DEGREES(ATAN(board_speed/top_tws))

here DEGREES(ATAN(board_speed/tws)) is how many degrees AW deviates from tws at given board_speed. it is 45 when board_speed = tws.

My calculations show that typically, max difference is at board speeds comparable with true wind speed, less so at significantly higher or lower board speed to TWS ratios.... Often, such angle difference is around 13-15 degrees assuming typical wind-height distribution.

Assuming idealized wind-height distribution, we can have 30 kts at the mast tip and about 18kts at the lowest sail section. Max difference in the apparent wind angles is about 15 degrees at board speed ~ 24kts. For TWS range of 18 to 10 kts alone the mast, about the same angle is at 14kts of board speed. When board goes 22kts, it drops to about 13 degrees.

With more radical TWS reduction at the level of sail foot, say, down to 30% of mast-tip speed, the max angle difference goes up and will be at the level of 30 degrees, but at lower board speeds (about 60 or so % of wind speed) and will be around 20-25 degrees at more typical sailing speeds.

With wave/chop impact, 30% reduction or TWS alone the sail height, and maybe even more, is likely common, hence 25 degrees of AW twist is likely a realistic typical wave/chop sailing number.

If you take it to the extreme and place the sail foot at water level where in theory TWS approaches zero, the max angle diff approaches 90 degrees at board speeds approaching zero. It is 45 degrees at boards speed equal to mast tip TWS and less of that at higher board speeds.

[konajoe]

So, in simple terms, the maximum required sail twist is near at or near the point where the board speed is the same as the wind speed near the top of the sail. Required twist reduces as board speed gets slower or faster than that wind speed. Correct?

[boardsurfr]

The biggest actual twists seem to be in slalom sails, though. Slalom sailors often go faster than the wind speed - 2x as fast is pretty common for big sails. Since the induced wind should be height-independent, slalom sails should indeed require less twist than freeride sails.

I suspect that other factors are just as important as wind speed differences, and perhaps even more so. Things like control are hard to quantify, though. I'd love to see force curves for different sails - I'd think that sails with more twist have a broader curve, making them more controllable in gusty conditions (e.g. around buoys or when sailing in a pack). Another interesting question is how the force curves differ for top sections of the sail, which have little profile, to the bottom sections, which have deep profiles.

[scottybda]

[Sailboarder]

The bible of French yachting (Le guide des Glénans) debunks the idea that the twist is required in yacht sails because of differences in windspeeds. Using a yacht motor to travel at sailing speeds in wind, strings attached to a mast don't show rotation from top to bottom. They theorize it may be because the hull will accelerate the slowest wind at the bottom since it raises it from sea level.

Anyway, twisted sails are faster for yachts too. One reason is the fact that a jib deflects air and the main sail is more efficient if twisted to align with the air flow. Second reason they give is that even if it's less aerodynamically efficient, it's better to have the top more open to increase stability. More open leads to a bit less forward force, and a lot less sideways force. The top part has a big leverage and would shake the boat more, slowing it in the end.

[bred2shred]

Bill Hansen (original owner & sailmaker for Windwing sails) used to have some very detailed information on his website regarding this subject. The information included apparent wind calculations and polar diagrams for various windspeeds/headings. Frank Bethwaite's bood High Performance Sailing also has some very in depth discussion into the effect of and need for twist in sails.

Twist does several things in addition to aligning the sail surface more closely with the apparent wind direction. It also provides a more forgiving sail plan (the sail can open/close to self-regulate power). This is essential to windsurfers because we are strapped directly to the airfoil. Non-twisted sails provide a very "twichy" ride where the power from the rig is either on or off. The twist also allows the very top of the sail to act as an "end plate". The top one or two panels are basically aligned directly into the apparent wind and make virtually no lift. The power in the sail reduces to zero as you go up and this reduces induced drag (tip vortex) that occurs with a non-twisted sail.

sm

[Sailboarder]

[konajoe]

I think people confuse twist with what is observed with a floppy leach. Twist is something that is done to compensate for changes in apparent wind direction in different portions of the sail. As mentioned earlier in this thread, that floppy portion of the sail doesn't have any draft, and aligns itself like a weather vane. It can't generate lift, so it doesn't really count as twist. Try to rig a windsurfing sail with no twist. I don't think it can be done on any windsurfing sail produced in the last 20 years.

Excessively twisted sails would luff at the top. That flat floppy section can't luff or stall.

I know that lots of folks think that you would want more twist in light wind, but not so.

Less twist is also required for high performance stuff that goes much faster than the true wind speed. So, any excessive twist is a compromise needed to dump power. If you put telltales at a point high in the sail, but in an area that still has draft, it will probably be luffing.

[whitevan01]

Sailboarder, if you want to know the truth about the aerodynamics of sailing you need to read books by C.A. Marchaj.

Sailing Theory and Practice
The Aero-Hydrodynamics of Sailing

I raced boats from Lasers, Blue Jays to Sonars, J-24s, MORC boats (long defunct), modern sportboats, ILC 40s, up to 55 footers (Cannonball - it's in the opening sequences of the movie " Masquerade") for 40+ years. In fact, I studied physics because I thought that would be the way to learn how to make sailboats go faster.

You always start to induce twist in sails to retain control in windy conditions.

I don't have time to go into it all because I am on my way to go windsurfing but you should take a look at those books when you have time.