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Ian, is that diagram correct for his planing speeds in strong winds as a speed to true wind ratio of 1.2:1?
The course theorem makes the assumption that the lift to drag ratio of the aerodynamics (includes sail plus all windage on hull and rider) remains constant for all wind strengths. At different angles in a constant true wind though the apparent wind will be of different strength. Your sail with your weight may have best lift to drag at say 20 knots of apparent wind but it drops off in efficiency at 25 knots apparent wind . If the "90 degrees" coincides with the 25 knots apparent wind you may not get your best speed there. Same assumption for the hydrodynamic lift drag of the hull/fin combination.
So maybe your best bet, if you have the luxury of sailing fast in any direction on a flat course (Primbee, L George), is to see if you're sailing broad or tight to the theoretical 90 degrees when you've determined your best angle by feel or beeping GPS. If you're going broad of 90 degrees try and tune up with a smaller sail and run tighter. If you're tight of the 90 degree optimum tune up the next larger sail and run broader. You'll need pencil, paper, calculator all the anemometers etc.
But there's no assumption in the theorem on overall efficiency, works in no particular order for ice boats, AC72s, kitefoilers , moths, windfoilers and slappers .
Thanks Ian.
There is something about this that does not ring true to me. I cant get my head around it but it is a feeling that as efficiency increases and speed to true wind increases, one should than be able to sail a broader course to true wind as apparent wind will comes around further towards your course. (more from ahead of the boat).
But MI was doing 50 knots in barely more than 25 knots of wind, and at what appeared to me to be a lesser angle off the true wind than what us windsurfers did. I seem to remember them throwing around the 118-120 degrees number.
Clearly, they were able to sail much more efficiently at a close angle to the wind.
We windsurfers need significantly stronger wind (30kts) to go 40 knots, and we seem to be at a significantly broader angle to true wind (130-135 degrees)
In my mind, that means the Beta angle will be larger. If I understand it correctly (A big IF! 
) that means the apparent wind would be closer to 90 degrees from our actual course than 45 degrees on the nose.???
And doesnt the article linked above say as much??
) that means the apparent wind would be closer to 90 degrees from our actual course than 45 degrees on the nose.???
The apparent wind angle (beta) is typically 18 degrees off the nose for the standup boards with a windsurfer rig and between 11 and 14 degrees off the nose for my quad miniyacht with a cantilevered mast. The sensitivity of the impellers have a cosine response (relative unit response along the axis of rotation and zero at right angles to the rotating shaft). The rotating shafts are orientated +/- 45 degrees relative to the board or yacht centreline.
I forgot to mention that the board is positioned such that the wind is blowing parallel to the starboard impeller shaft in the above photo. The impeller is rotating at its max (rpm/knot) sensitivity. The port impeller is not rotating.
The board is not moving so that apparent wind is equal to the true wind.
Sailquik said:
"Or you hit a drag speed limit because of body form drag on the stand up, of which you have far less in the presumably 'body position reclined' land yacht."
It has nothing to do with whether you are standing up or not although the drag limit is more severe on my standup board.
The drag limit for my quad mini is shown above by the locus of the plus signs. The solid blue lines are the stability limits imposed by capsize. You cannot go faster than the blue lines on any heading without turning over - and must ease the sheet to prevent it.
Some other young brave loonies went very fast though! 
I would not do it now without full body protective gear and a good helmet! 
What does my head in are the creases, I get that twist works, even if (and this thread backs it up) no one is EXACTLY sure why, but from my dingy sailing days creases are air flow killers, and even the fastest guys at Luderitz have sails with massive creases. Im no expert but in a game that is now getting down to hundredths of a second surely this is an issue? How could it be improved? Does it need to be? Am I just a neat freak?
Barney said:
stability limits for Sailrocket?
I guess that you have never seen the photo of Sailrocket a hundred feet in the air - inverted!
That was the original Sailrocket which had several design flaws one of which was to link the angled wing to the forward planning hull thereby increasing the AoA of the wing (hence the lift) when the forward hull got lifted by the wing. Ergo, backflip at speed.
Needless to say, they they went back to the drawing board, built a new boat called Vestas Sailrocket, eliminating those flaws and linked the wing to the rear hull so any lifting depowered the wing. This is the boat that smashed the record and generally is regarded as "the" sailrocket by the sailing community and is the one Andrew refers to not the one you noted was good for backflips and other problems.
Exactly as pacey and YOYO said.
And I was referring to heeling stability. Sailrocket2 is the only succesful craft I know of which has no heeling stability issue.
Barney. Have another look at your plot. If you go broader, you could have gone faster and had more stability. By going broader you decrease your apparent wind slightly, and therefore your heeling moment, and increase the forward vector thrust. Methinks you are too blinded by your sums.
Stability limits for windsurfers are not as you imagine it. It is extremely rare to see a windsurfer on a speed course simply get catapulted by being overpowered. I dont think I have ever seen it. It may be because they sheet out a little, but that most likely increases thrust in a vector closer their course, increasing speed. On a free course, we simply go broader, and faster. The only times I can remember running out of stability were on the tight run up where I have had to feather the sail to stay on the water until I can get broad enough to fully sheet in. One memorable occasion was around 2007-2008 when I was physically lifted off the water at over 30 knots on the square run in by a huge gust, and flew for 15meters under the sail like a hanglider. It fair knocked the wind out of me when I finally landed on my back. . That just isn't going to happen on the best speed angle, or at least it is very hard for me to imagine it, and I have never experienced or seen anything close to it.
On a fixed angle course where the wind is too tight, there are issues with being lifted off the water, but speeds will be lower anyhow..
Nobody here has claimed that windsurfers 'invented' sail twist, that would be ridiculous. But I dont think any windsurfers consiously 'copied' dingy sailors either. It just evolved in windsurfing to counter particular issues related to that platform. And of course there is always crossover of ideas between all the forms of sailing.
Some other young brave loonies went very fast though! I would not do it now without full body protective gear and a good helmet!
That looks like a constant entry angle all the way up the mast. I'm thinking now this is a big factor.
At a guess Charles pic, wind 12kts board 15-18kts. Check how it is planing nose up n in straps.
2nd pic id think board is doing 20-23kts. Wind 15-18kts.
Is there a purpose or a point to this guessing? 
It's very hard to estimate wind strength from photos as I have said.
Estimating wind strength when standing in it and watching the signs live is very different. 
But to humor you : Sails from that era and that size had a very small wind range. I would guess they were out of their controlable range at around 15 knots of wind, so probably less than that. The appearence of the water is not much help as it could be behind a sand bar. There are no signs of cresting wavelets. If not behind a sand bar, it is very light wind. The board is on a broad reach from the look of the wavelets, and there is a bit of spray off the rails, so my guess is 'maybe' up to 20 knots of speed, but most likely high teens.
Here is a good example of what I mean:
Check how flat the water is! Not many clues there. But looks quite fast eh? When you have had a guess at the sail size, wind strength and board speed, I am sure Dezza can fill us in on the exact numbers.
