Mechanics/statics facts:
Fact 1:
Universal joint cant transfer moments,only forces.
What does it mean in windsurfing?
That mean that sail cant transfer moment to the board and vice versa.It can only transfer forces,for example "mast foot pressure" is vertical force.
Fact 2:
Steady state:
-Sum of all horizontal forces must be zero
-Sum of all vertical forces must be zero
-Sum of all moments must be zero.
What does it mean in windsurfing?
That mean that board is sailing with constant speed,not accelerate or decelerate.Also that all parts in system are not rotate in any direction. (A moment causes a rotation about a point or axis.)
What is rotation in our case?
Rotation are all situation where moments are not zero,catapult is rotation where moment from sail is greater than moment from sailor,lifting windward rail up is also rotation where moment from fin is greater than moment from sailor feet weight over rail etc etc...
Assumption 1
I will consider that sailor use arms only for control sail,so 100% his pull is made through harness line.That will simplify calculation.
Assumption 2
Sailor ankle when stay in footstrap can make additional moment(lift toes/push heel) against fin moment.I will not take this in calculation in board balance(step 5 and 6) because of two reasons:
1)It will simplify calculation.
2)It is very hard to determine how much moment ankle can produce ,depend on muscles/tendons..
Task
Calculation:
So if you want ride board flat you can put smaller fin(solution above-step 5 ) or you can ride board with windward rail up(solution below-step 6)
Lets see if fin will be too big and rollover board or board will be in balance even in railing mode...Note when windward rail lift up,force Fhydrolift will shift to the right because left part of board is not in contact with water any more...
For this example board is in balance in railing mode too ,super we dont need change fin if we want railing!
You can see from calculations that force Fsail depend on ;sailor weight,sailor lean out angle,distance (L),harness line T1 angle,COE height etc..
You can play with geometric(angles and distances) or sailor weight and see how Fsail ,feet vertical force,MFP and other forces changing.
This is all well and good.. kinda cool actually... My only question is; What is the point? ... When i go sailing I'm not exactly thinking about what angle my feet are touching the board at for optimum balance.... Anyway, cool stuff 
Looks like somebody is trying to build a windsurfing robot. Even our fun is going to be automated out of existence
Good job. No wonder fins bend. I would have estimated the sailor in the photos C of G makes an angle of 30 degrees with the vertical from where his feet contact the deck. Are you sure that isn't -10.4 kg for the mast's horizontal component in fig 4 ?
Reading these posts is giving me a crazy idea about a radio control mini windsurfer. I can see that being a blast to mess around with!
Select to expand quoteMagicRide said..
Reading these posts is giving me a crazy idea about a radio control mini windsurfer. I can see that being a blast to mess around with!
Good luck with that! Would be easy with no uni joint, but balancing all those forces, will need good sensors and fast responses with electric motors or solinoids. So fun with a raspberry pie or arduino perhaps. but then it's got to be water proof. That's just to go on one tack, now add a gybe or tack into the equation. It's starting to look very close to impossible to me. Unless you're good at waterproof robotics.
The fin would serve as 2 purposes, a rudder/fin combination. The board would be about 3 feet long, with a planing hull design with a top speed of 15 mph would be good. The mast would fit into a sealed rubber boot and snap into place on the deck of the board with the sail attached, but the sail would have a windsurf sail shape to it. All the electronics for the mast adjustment would be in the sealed rubber boot and adjusted as desired on the water with The hand held remote control. The mast would have a wireless adjustment on the hand held remote control to shift the angle of the mast forward, aft, windward and leeward like we do in windsurfing. Didn't even think to scour the net to see if this even exists. This would be a fun project!! If I only had the time to persue it. Will put it on the bucket list of things to accomplish!
ie. I'm thinking, still using using your calculations and trigonometry, that when looking at lateral forces acting on the board, ( there's only four of them : two feet, mast base and fin ). That the fin side force = Ffin = 47.7 - 10.4 = 37.3 kg.
That just means that the mast base and the feet act in opposite directions, ie. to compress the board, and that if the mast base breaks it will flick up and hit you in the knees.
(unless of course your sail plan is symmetric about the boom, like that of a wind wing which doesn't need a mast base at all!)
Select to expand quoteMadge said..
Just forget all the numbers and go and have some fun.......
What does it say when comments like that get all the green thumbs?
(You wouldn't be having half as much fun if it wasn't for Jim Drake. Even if he did do all his calculations in lbs?)
joewindsurfer.blogspot.com/2008/04/jim-drakes-windsurf-physics.html
Select to expand quoteIan K said..
>>>
What does it say when comments like that get all the green thumbs?
It says, people just want to have fun and forget about science. Without realising, that without the science they wouldn't be having any fun.
If you are actually interested in going faster, or higher, or longer, this stuff can give you some very interesting clues. 
Select to expand quoteIan K said..Madge said..
Just forget all the numbers and go and have some fun.......
What does it say when comments like that get all the green thumbs?
(You wouldn't be having half as much fun if it wasn't for Jim Drake. Even if he did do all his calculations in lbs?)
joewindsurfer.blogspot.com/2008/04/jim-drakes-windsurf-physics.html
I'd say that as a sail maker who has worked for some of the biggest brands in a time of innovation and change that theres soo much crap put out there with numbers and figures that its simply taking away the pleasure of the actual sport itself and theres soo many variables within our sport that with todays sails and boards and materials used that we shouldn't be looking at a list of numbers and just enjoying ourselves.
I have worked within the F1 industry too and believe me they sometimes just bend something by hand and the car feels ten times better then they measure it.
In a time where we can look at the figures more than ever it still won't get me to plane quicker than my mate, who always out planes me, because I like to drink more beer than him and eat more pies........
And the bloke who actually invented our sport was from Hayling island and was a school boy......Also your telling me that all those figures were worked out on the original windsurfer, a board where the mast foot popped out on a regular basis and gave your plums a good whack.
Exactly !
Numbers are great for engineering, but windsurfing, and every other sport, relies on the human equation.
In my many years involved in this sport and many others at a high level, I have made a sad observation.
Some of those who cant follow the math, numbers and technicalities, sometimes try to belittle and dismiss those who can or want to, because it makes them feel better about themselves. Anti-science, anti-intellectuallism and 'Tall Poppy' syndrome at it's worst!
Just like some of those who can't do the numbers in competitions dismiss it as 'just numbers' and say they are not important, just go out and "have fun".
If you are not intereseted in the physics and 'engineering' of windsurfing, good for you. You can have as much fun as anyone else. But please spare us this pointless whinging about how it is irrelevant to "fun" and putting down of those who do have an interest.
And you are right that it's the human element and the interface of almost all sports that most make it interesting and fun, but we all benefit from the discoveries and developments of those who look into the system more deeply, and who find a great deal of enjoyment (fun?) in the challenge of technical analysis and finding ways to improve the system, or their own 'numbers'. We all benefit from what people like that learn, so why put them down?
If you are most interested in getting out there and doing it just for fun, no one should put you down for that at all, and I think it is mark of a true sportsman that they understand and embrace all ways of approaching a sport.
Have fun and stay safe! 
Select to expand quoteLeeD said..
And that's why we don't have engineers as leaders of people.
But you do have an engineer that was the president of the USA. Don't forget 8 of the richest people in the world are engineers!
Engineering is cool, math is cool, windsurfing is cool, windfoiling is cool.
When it's windy, go sailing or foiling and learn by feel, when it's calm (or dark), seek to understand sailing, foiling and people.
Aren't we all privileged.
Select to expand quotesailquik said..
In my many years involved in this sport and many others at a high level, I have made a sad observation.
Some of those who cant follow the math, numbers and technicalities, sometimes try to belittle and dismiss those who can or want to, because it makes them feel better about themselves. Anti-science, anti-intellectuallism and 'Tall Poppy' syndrome at it's worst!
Just like some of those who can't do the numbers in competitions dismiss it as 'just numbers' and say they are not important, just go out and "have fun".
If you are not intereseted in the physics and 'engineering' of windsurfing, good for you. You can have as much fun as anyone else. But please spare us this pointless whinging about how it is irrelevant to "fun" and putting down of those who do have an interest.
And you are right that it's the human element and the interface of almost all sports that most make it interesting and fun, but we all benefit from the discoveries and developments of those who look into the system more deeply, and who find a great deal of enjoyment (fun?) in the challenge of technical analysis and finding ways to improve the system, or their own 'numbers'. We all benefit from what people like that learn, so why put them down?
If you are most interested in getting out there and doing it just for fun, no one should put you down for that at all, and I think it is mark of a true sportsman that they understand and embrace all ways of approaching a sport.
Have fun and stay safe!
Very true statement, and with respect to how many operate and view life on a daily basis. Unfortunately not everyone sees it through your eyes. But I 100 percent agree with you.
I want to share my philosophy, because I have been told it's more on the unique side of things. In my life, I have always looked for the best in people. I don't believe in dismissing a person for one or more things, when I can find something else that I like about that person. My friends, aquintences are so night and day from each other because of many characteristics each one of them has, that the other doesn't have. Now if I got all those people together, it would end up in arguments. So I chose to get together with each person individually. Some people you just can't shake, and I leave it that. Deep down, we are all so different in our own way.
Windsurfing is an awesome sport and it can be so much fun. And yes I appreciate that without Jim Drake the sport as we know it wouldn't exist (even if his calculations are imperial - I'm not going there).
USA46 has done an awesome job to start the thread complete with assumptions and calculations.
Forums allow for different opinions as we are individuals not being normal but a bit of good crazy
I did Physics, Applied maths, maths in seventh form nz school (year 13). This year my year 11 daughter is learning to windsurf and studying Physics, taking an interest in her home work has reignited my interest in Forces.
I spent 5 years building epoxy/polystyrene sandwich boards and later worked with sail maker so had awesome board/sail combinations and discussed pros and cons of different designs with some field testing but never used figures or a calculator.
Engineers rock !
Even though an engineer can't make a radio controlled foiling windsurfer yet , we are close . We've made a Segway. I've ridden one , they are amazing , almost foolproof .
The amount of maths involved in what's going on in windsurfing is huge . I suppose it can be calculated , and we do it , it's called balance . It's a big thing.
what our inner ear and imagination does is truly amazing.
Select to expand quotejn1 said..
Could somebody explain the difference between a force and a moment ?
Force/"moment"of force
Because I have no interest in the subject doesn't mean I don't understand it, I understand root canal perfect.
OP USA 46 , has been mute. I detect that he is in The San Francisco/ Berkeley area. Might clear things up.
California is in lock down.
ps I have owned a Mikes Lab, hardy a distinction, unless it's in Maine .
