Swept Volume Theory

No need to apologise, I hope you recover quickly.

 

I agree, unless you are sailing in 500 MPH winds.

 

My apologies for looping back to aircraft. You are correct, they do introduce unnecessary complications.
In my defence, I was only trying to remind us all that ATM is pretty damn big, and it only takes a small %age of it to generate some pretty big forces.

One of the issues I have is that I can't get a bead on the actual size of the aerodynamic force required from the wind/sail interaction to race my boat.
(A Farr 40 has a sail area of about 100 m^2 and will do 7 kts upwind in 12 kts of true wind at a TWA of 40° with a leeway of 4°, which gives an apparent wind of 17 kts at 25°)
And by that, I mean to balance the hydrodynamic force from the hull , keel, and rudder plus aero drag from superstructure and rig.

I think it's somewhere between 2,000 and 5,000 Newtons, but haven't been able to nail it down.
One of the challenges of course is to actually measure it. Towing it with a power boat with a strain gauge in the towline only gives part of the story. The 4° leeway will add a big chunk to the drag, and I can't think of a way of measuring that without an expensive test tank. I have been unable to find any documentation. I suspect it's held as a commercial secret in the safes of naval architects and sailmakers.

Yes, I freely admit that I have yet to quantify my theory. It is entirely qualitative, but it does simply explain the source of the higher pressure to windward and the lower pressure to leeward of a sail. However large or small those pressure differences are, they are the only source of the aerodynamic force that balances the hydro forces.
I'm not sure what point you were making here, why you link the size of the volume change to the lack of quantification of my theory.

 

Would a figure like this one help narrow it down?

 

The solution is to find the CE of the sails. Rigs wires from the mast, boom and bow to make an attachment point at that location and tow the boat from it.

 

Without any context, it's bit hard to tell, but I don't see any reference to leeway - which is my primary concern.

 

If it was that easy, there'd be no problem!
Think about the track the towing boat would have to take to keep the cable taut!
It would have to travel parallel to the yacht whilst applying a big force at a significant angle.
It would have to be on rails (aka a towing tank).

 

In support of this extremely valid objection, can anyone provide an explanation, using classical mechanics (high school physics), for the force that the wind over the sail generates on a yacht working upwind that does not refer to aircraft wings?

 

Quoting from Theory of Wing Sections: "The surfaces that support the aircraft by means of dynamic reaction on the air are called wings."

To comply with your request, I would just change "support the aircraft" to "propel the sailboat" and "wings" to "sails."

Need it be more complicated?

 

You are just messing with me!
The title, revised with your suggestion: "Theory of sail sections" somehow doesn't cut the mustard.


I'm not sure any of this a) can apply to sails or b) is covered in high school physics!
And where, in its 700-odd pages does it explain the source of the force?

You are not helping.

 

The towing boat will keep a constant heading, like the wind does. It should not be parallel. Obviously, the towing vessel can't be a dinghy but has to be of appropriate size and power.

 

I don't really understand the difficulties with the term "wings", it is just another word for a device that creates a force by deflecting a fluid flow. A more general term is "foil", as in hydrofoil or aerofoil; in other languages you associate to "blade" or "shovel" et c.

Could it be that you are confusing the effects of the mean ("spine") line camber and the effects of profile thickness distribution?
A sail is a foil with constant foil thickness, just as the impeller blade of a fan often is stamped out of a plate. Such profiles were investigated by Fritz Weinig (google his name and a number of references will pop up) in the early 1930:ies.

In Europe much of what is written on foils is in German, but if you search on "George F Wislicenus" there should be a bunch of texts in English coming up. Constant thickness foils are very common in turbomachinery design; a sail just has another frame of reference. If you want to see a research report on different sections, this is a classic: https://www3.nd.edu/~ame40462/RiegelsAerofoilSections.pdf. It also gives the theoretical background.

Edit change of phrase "confusing" instead of "mixing" for clarity (?)

 

If the towing boat's heading is constant but not parallel to the yacht's the towing cable will snap!

 

I'm not messing with you.

The source of the force is given in the one sentence that I quoted (and also in the 1st sentence of baeckmo's answer.)

 

And you wonder why I am asking for a simple text about sails???