decrepit said..
I've always thought it would be better to attach harness lines as high as possible, that's why I was perplexed by advice to lower the boom when overpowered.
So we'd need sails with a cut out about 2.5m up for the attachments??? I've some old sails, I could experiment. But I can foresee loose ropes whipping around being a problem, and securing them before a gybe tricky. Maybe they clip into normal lines, then you can transfer from one to the other as needed?
Is this worth pursuing?

It's going to alter sail dynamics of course, mast bend will be altered significantly, may not get maximum benefit unless a sail maker is also involved.

Yes, and what USA46 has brought to our attention is how the height of the connection can change the moment that a sailor at a given orientation hiking out board can generate! I suppose we were locked into the thinking behind dinghies with rigid stayed masts where the method of supporting the hiking sailor doesn't matter. It's all the same whether supported by a trapeze wire or a hiking plank. That's because it's a rigid triangulation and a small change in mast lean results in the exact same small angle of ballast movement.

Trouble with windsurfers is that the mast, boom, mast foot , sailor and harness lines form a pentagon with only one angle, boom to mast fixed. A small movement in theta in the diagram causes a small movement in phi behind the sailors feet. But the ratio of the angular movements is not constant, it depends on the height of the harness hook. Unlike a triangle that whole pentagon distorts, and the sides are all different lengths.

This is where I thought it easier to look at it from an energy conservation aspect rather than try and analyse the forces. Force times distance against the wind = force times distance lost to gravity. But the trigonometry is still horrendous. But I'm pretty convinced, just looking at the diagram, that there will be an optimum hook height given that the boom height is constrained by being at a comfortable height for the sailor to do the fine control but leaving the bulk of the righting component to the harness lines. Maybe we'd get used to chest harnesses again if we could show they had advantages if we tolerated the discomfort?

Maybe USA46 can do the trigonometry for us and use a bit of differentiation to find the optimum?

Way beyond my abilities, I'm a suck it an see man. Intuition guided trial and error. Can be slow and painful, but also fun if you learn something. Even better if it's something useful

Of course, I just realised that this morning! How could we miss such a basic point? It's all to do with 2d diagrams leading us astray I think.

Not sure what I mean by optimal? Still thinking about it. But thanks US46, your diagram with the exaggerated low hook shows that as you go lower the leverage on the sail increases. (67 vs 62). Not by all that much though. So I suppose if you get lifted by the sail while the board remains flat you could lower the hook. If the board lifts on the leeward rail and you maintain position raise the hook for more comfort. Is the sweet spot where both happen at once?

Sorry USA46. I read your post too quickly. Jim Drake's method is not incorrect. He is analysing forces on the system as a whole.

Jim states this " A useful method for the analysis of forces on a body (in this case the body is the combination of board, rig and sailor)"

It doesn't matter whether the internal forces are rigid or articulated the analysis is valid.

Jim Drakes's method is all you need if you just want to analyse the external forces, the fin, the sail. He just estimated the sailor's C of G relative to the board, the height of the sail's centre of lift and away he went.

If you need to wonder about the forces on the universal, the harnesses you use your method.

Another advantage of your method is that by starting with the requirement that the sailor can balance the rig you can then consider what is needed to balance the system with the sail force already independently calculated.

As well as considering the length of the fin you can also determine where the centre of hydrodynamic lift is under the hull. Jim has assumed it is on the centreline of the hull. But that was in the days of narrow boards not so much of an issue. With wide boards the centre of hydrodynamic lift can move off centre towards the leeward rail to make sure the system is balanced. We all know this, you can sheet in more on a wide board if you get the windward rail up a bit. (red arrow, first post figure 6)

(Anyway trigonometric wiz that you undoubtedly are if you apply your method and Jim's method to your scenario and don't come up with the exact same answer, you've made a minor slip up somewhere. Though you did use your hydrodynamic lift centre, when you checked using Jim's method? Jim assumed it on the centreline. That's not incorrect he makes it clear,that he's done it. It's an approximation. Both methods have plenty of approximations )

25 kg. Assuming hydrodynamic lift from the hull is on the centreline and vertical.

( How the fellow can stand vertically while holding the boom is a problem internal to the system. Maybe he's made of titanium and his feet are welded to the deck. Not something we are asked to solve)

USA46 said..

Ian K said..
25 kg. Assuming hydrodynamic lift from the hull is on the centreline and vertical.

( How the fellow can stand vertically while holding the boom is a problem internal to the system. Maybe he's made of titanium and his feet are welded to the deck. Not something we are asked to solve)

wrong answer..

Sailor stand 100% vertical his- pull is zero,so Fsail= 0, system is not in balance,sailor will sink windward rail..
(we know that sailor dont have titanium feet,we also know that feet are not welded to board and we also know that sailor can not transfer moment to sail via board)

(if mast is conected to board with rigid conection,than Fsail=25kg ,system is in balance)

"wrong answer.."
"we know that sailor dont have titanium feet,"

We also know you'll never be able to find a photo like that to base your calculations on, But if you did find such a photo you would have to assume something like that is going on.. Shrouds made of invisible dark matter maybe?

As far as sailing goes, angle "C" does have an effect. It changes the direction of F so the component of vertical lift changes. This will affect board trim.

Not sure about that, yes less forward thrust, but the sail is taking some of the vertical lift off the hull, this may help to get a more ideal hull trim. And reduce hull drag
I thought that was why that very fast foil boat (sorry ancient brain forgets names) had the sail heavily canted to windward.

USA46 said..
Yes you are right, but I think for windsurifng at +50knots so small area of board is in water,that we dont need so much lift from sail.

That's OK, I haven't managed 40kts yet, but would like to optimise trim, to give me a chance of getting there.