sail aerodynamics

[ivor Bittle]

I am grateful to Brian Eiland and the forum for drawing my attention to this paper. The author has used CFD to find a flow pattern round a single sail and round a Bermuda rig when close hauled.

I first drew these flow patterns about 15 years ago when I drew them in chalk on the square paving under a bedroom window so that I could rub out the chalk and change the pattern and see what it looked like from overhead. They were not guesses. There are rules for drawing flow patterns. These patterns are shown in the first section of my website at www.ivorbittle.co.uk. This Italian paper is the first time that I have seen anyone else with essentially the same flow pattern and the first time that I have seen anyone accept that sails work when stalled in the aerofoil sense. I think that sailing people are so keen to be able to claim their sails to be efficient that they become blinded to the tractability of real sails that comes
from working in the stalled condition.

The author of this paper is wedded to the idea that the jib is the counterpart of a slat on a wing. In my website I suggest that it is better to treat the jib as operating in the air that has been diverted upwards and over the luff of the mainsail. Then, when close hauled, the jib drives the boat and the main sail makes no contribution. This is why having the main in front of the jib is not successful. The little sail cannot divert enough air to affect the much larger main in front of it. I see that sheeting the main to windward is becoming more popular.

[yipster]

Originally Posted by ivor Bittle

The author of this paper is wedded to the idea that the jib is the counterpart of a slat on a wing.

well wedded i aint but glad you sayd that. in my thinking also a jib works indeed as leading edge extension like on a wing and is the reason the combination preforms better than the sum of the parts
like to design my dreamboat better, note the LEX but installing a wifi connection with two 54 lan sticks should be easy they say, but dont you belive it, not in vista, no free rides nowhere

[RHough]

Originally Posted by ivor Bittle

... This Italian paper is the first time that I have seen anyone else with essentially the same flow pattern and the first time that I have seen anyone accept that sails work when stalled in the aerofoil sense. I think that sailing people are so keen to be able to claim their sails to be efficient that they become blinded to the tractability of real sails that comes from working in the stalled condition.

The author of this paper is wedded to the idea that the jib is the counterpart of a slat on a wing. In my website I suggest that it is better to treat the jib as operating in the air that has been diverted upwards and over the luff of the mainsail. Then, when close hauled, the jib drives the boat and the main sail makes no contribution. This is why having the main in front of the jib is not successful. The little sail cannot divert enough air to affect the much larger main in front of it. I see that sheeting the main to windward is becoming more popular.

Wow ... am I the only one to see the glaring flaw in the diagrams?

Yes, it is possible to trim the sails so the jib has a large separation bubble, and above the head of the jib the main is stalled. That does not make it the optimum trim condition. Note that the AoA of the upper part of the main in the diagram is exactly the same as the AoA of the lower part behind the jib ... twist? Anyone ever hear of twist or wash out in aerodynamic terms?

The trim shown in the diagrams is a near maximum lift condition and not very good trim at that. Drawing the conclusion that good sail trim leaves sails with large separation bubbles and nearly complete flow separation above the jib cannot possibly lead to a conclusion that sails are efficient when stalled.

Two sails are not 'seen' as separate entities by the air. The total force generated is purely a matter of mass of air deflected and how much it is deflected ... F = MA^2

It does not matter one little bit if the area is split into two surfaces or what the distribution of that area is. If you want high lift per unit area, all you have to do is design the foils to produce the flow pattern you need to get it. At high lift per unit area, induced drag is predominate, the shape you use to get the lift is a very small part of it. What keeps the main from stalling is the increased pressure at the trailing edge of the jib.

What does trimming the main boom have to do with anything? At high sailing angles (close to the wind) an easily driven hull does not need much of the force from the sails to have a forward vector. At the point where the boat has constant velocity (drive = drag) Maintaining attached flow on the main may well require the main boom be carried above the centreline. The sail twists away from the boom to the head and the sail does NOT have an average 'to weather' trim and the sail is NOT stalled (when sailing upwind).

The high lift trim also produces a turning moment, on an airplane it is a pitch moment (nose up/down) on a sailboat it is a a yaw moment (bow up/down or weather/lee moment) Some 'weather helm' is required to force the keel and rudder to both lift to windward. In general increased camber (the same as trimming the main boom to centre or above) increases the moment and any small sacrifice in drive or drag from the sails, is more than made up by the reduced leeway from the water foils.

Once a boat is fully powered up ... when all the available righting moment is used, high lift per unit area is no longer required. Gains upwind are made from drag reduction, not increased force. Now the trim is far from the near stall high lift trim that was needed, the trim goal is to minimize drag ... since drag induced from lift is the major component, *reducing* lift reduces drag. As Angle of Attack is reduced, so is lift. At some point, a profile that gave high lift per unit area (high CL) starts to have profile drag = or greater than induced drag and further gain must come from changing the profile. For soft sails, that means reducing camber and twist and keeping the flow attached.

For an aircraft wing, during take off and landing high CL is required. During cruise, there is no need for high CL, low drag is the design goal. In order to achieve this, the area is split by combinations of leading and trailing flaps/slats or other flow control devices. Moving the leading and trailing edges to increase the effective chord increases the effective area. Lift *always* equals weight in level flight. The requirement for change is to allow slow speed take off and landing while at the same time allowing efficient high speed cruise. For displacement hull boats, once the sails produce enough power to drive the hull to 'hull speed' plus a bit, any extra force just goes to increase heel, the sails get trimmed close to the airplane's cruise profile. For upwind planing boats and multihulls, the trim change comes when sail heeling force equals righting moment, then the sails go from high lift (and high drag) to more moderate lift and drag trim.

Going up wind with the sails stalled is NOT a normal condition. Going downwind with the sails stalled is only acceptable for slow boats. Fast planing boats and multihulls sail downwind with the apparent wind well forward of the beam ... stalled sails downwind don't work well for them either.

Real sails on real boats are not intentionally trimmed to the stalled condition except on slow heavy boats that cannot easily exceed the 1.34 S/L ratio that is their hull speed.

I think that the idea that the jib and main of a sloop act as separate foils is what keeps sailors from understanding sail trim. They are not separate, they are but parts of a single system, that cannot be considered separately to good result. When sailing upwind or with the apparent wind well forward, changing the trim of one sail much be matched with a change in trim of the other, and the effect of the sail trim on the water foils cannot be ignored. It is MUCH more complex than 'the jib drives the boat upwind and the main does nothing'.

[Guest625101138]

There could be confusion here over flow separation and stall.

There is a good discussion here on stall:
http://igitur-archive.library.uu.nl/...1950226/c2.pdf
go to page 27.

Once again I can recommend JavaFoil if you want to do your own quantitative analysis with particular sails. I have attached a sample from JavaFoil similar to that provided in the paper.

Rick W.

[yipster]

Originally Posted by yipster

installing a wifi connection with two 54 lan sticks should be easy they say, but dont you belive it, not in vista, no free rides nowhere

appears a vista error? manual IP adress instead of auto works and working on it..
RHough, thanks for the drag and Rick for the javafoil link, thats next

[brian eiland]

Originally Posted by ivor Bittle

... This Italian paper is the first time that I have seen anyone else with essentially the same flow pattern and the first time that I have seen anyone accept that sails work when stalled in the aerofoil sense. I think that sailing people are so keen to be able to claim their sails to be efficient that they become blinded to the tractability of real sails that comes from working in the stalled condition.

The author of this paper is wedded to the idea that the jib is the counterpart of a slat on a wing. In my website I suggest that it is better to treat the jib as operating in the air that has been diverted upwards and over the luff of the mainsail. Then, when close hauled, the jib drives the boat and the main sail makes no contribution. This is why having the main in front of the jib is not successful. The little sail cannot divert enough air to affect the much larger main in front of it. I see that sheeting the main to windward is becoming more popular.

WHAT is this

Originally Posted by RHough

Wow ... am I the only one to see the glaring flaw in the diagrams?

Yes, it is possible to trim the sails so the jib has a large separation bubble, and above the head of the jib the main is stalled. That does not make it the optimum trim condition. Note that the AoA of the upper part of the main in the diagram is exactly the same as the AoA of the lower part behind the jib ... twist? Anyone ever hear of twist or wash out in aerodynamic terms?

Yes, I agree.

The trim shown in the diagrams is a near maximum lift condition and not very good trim at that. Drawing the conclusion that good sail trim leaves sails with large separation bubbles and nearly complete flow separation above the jib cannot possibly lead to a conclusion that sails are efficient when stalled.

Yes, I agree.

Two sails are not 'seen' as separate entities by the air. The total force generated is purely a matter of mass of air deflected and how much it is deflected ... F = MA^2

It does not matter one little bit if the area is split into two surfaces or what the distribution of that area is. If you want high lift per unit area, all you
have to do is design the foils to produce the flow pattern you need to get it.

Well here I disagree. Probably the two sails are not 'seen' as separate entities, but rather as a 'multi-element airfoil'. There is a distinction, as pointed out by AMO Smith's paper posted here:
http://boatdesign.net/forums/showpos...&postcount=313
We'll disect this later.

Once a boat is fully powered up ... when all the available righting moment is used, high lift per unit area is no longer required. Gains upwind are made from drag reduction, not increased force. Now the trim is far from the near stall high lift trim that was needed, the trim goal is to minimize drag ... since drag induced from lift is the major component, *reducing* lift reduces drag. As Angle of Attack is reduced, so is lift. At some point, a profile that gave high lift per unit area (high CL) starts to have profile drag = or greater than induced drag and further gain must come from changing the profile. For soft sails, that means reducing camber and twist and keeping the flow attached.

Yes, I agree.

Going up wind with the sails stalled is NOT a normal condition. Going downwind with the sails stalled is only acceptable for slow boats. Fast planing boats and multihulls sail downwind with the apparent wind well forward of the beam ... stalled sails downwind don't work well for them either.

Yes, I agree.

I think that the idea that the jib and main of a sloop act as separate foils is what keeps sailors from understanding sail trim. They are not separate, they are but parts of a single system, that cannot be considered separately to good result.

We think differently here.

And I believe a few other folks see this differently also, including Avery Gentry, AMO Smith, and Tom Speer

I'll bring this subject up in a new posting.

[brian eiland]

Originally Posted by brian eiland

I haven't had time to review this paper...just ran across it while looking for something else. But it sure looked like a paper that belonged in this subject thread:

AERODYNAMIC SIMULATION OF UPWIND AND DOWNWIND SAILS
http://www.nautica.it/superyacht/517/tecnica/sail.htm

Upon reflection, I'm sorry I posted this paper. I really don't see it as useful information. It seems to rely on a lot CFD study.

I might refer you back to my posting #44 in this subject thread;

What I am finding in my review of some of this computational methods of investigating sail forces and flow analysis (CFA, CFD, vortex lattice models, etc) is that generally there are so many assumptions made upfront in order to simplify the equations so the computer can solve them, that the results get skewed quite a bit from reality:

.....ie, a quote from one of the annalist;
"CFD = Computer Fluid Dynamics. CFD is a great tool for visualizing and explaining flow phenomena. While the latest flow software is very powerful and capable of calculating amazing things at astonishing accuracy, the old saying "garbage in, garbage out" is more true than ever. Besides of presenting the problem in a meaningful way, one needs lots of knowledge and experience to interpret the results correctly. Simulation through CFD is especially useful at giving qualitative information - when it comes to quantitative results or hard numbers, you have to be even more cautious when drawing conclusions about the merits of one design over another. Wind tunnel tests are needed to calibrate and validate the CFD code before reliable results are obtained."

"With the power of modern CFD at the desktop, it is too easy to produce beautiful pictures with little connection to reality. Often these pictures are produced by flow experts with little sail-specific knowledge, and then interpreted by sail designers without sufficient understanding of the CFD tool, and as a result you get just that - pretty pictures."

[RHough]

Originally Posted by brian eiland

We think differently here.

And I believe a few other folks see this differently also, including Avery Gentry, AMO Smith, and Tom Speer

I'll bring this subject up in a new posting.

I've not seen anything from any of those gentlemen that says that two or more elements don't produce a single flow pattern. A single circulation pattern. Changing the trim of any element effects the whole system.

The argument for multi-element systems is that they provide a solution to flow separation at high AoA (High CL). Maximum CL is only needed on a sailing boat when the area is too small to provide the force needed at moderate CL.

I the real word, that means in the windspeed range of 0-10 knts or so ... under canvased boats might need maximum CL from 0-14 ...

The fact is that even heavy boats in the 300 D/L area ... (very heavy by modern standards) the sails are only trimmed to maximum CL when reaching, going upwind they are *not* at maximum CL.

I happen to have the polars for my heavy old boat ... I wanted to know what the difference was between a 13.2 LP Jib (100%) and a 19.8 LP Genoa (150%).

In true wind speeds up to 12-14 knots the 100% jib/main has a maximum CL=1.83, however the best upwind performance is not at max CL.
Best upwind:
6 knts CL=1.64
8 knts CL=1.66
10 knts CL=1.66
12 knts CL=1.57
16 knts CL=1.19

Below 12 knts true wind, the sails are trimmed to full chamber, above 12 knots they are flattened to reduce camber and reduce drag.

The 150% Genoa/main has a maximum CL=2.346 (this shows the benefit of overlap). Again, best performance upwind is *not* at maximum CL.
Best upwind:
6 knts CL=2.07
8 knts CL=2.12
10 knts CL=1.87
12 knts CL=1.61
16 knts CL=1.21

With the greater area, the sails start getting flattened at 10 knots compared to the 12 knots of the smaller sails.

The point of this is, that even heavy old boats don't sail to weather at the sailplan's maximum CL. As the SA-D goes up, the requirement for high CL sailplans goes down.

It makes more sense to add area than to add elements. Other constraints like RM, rating rules, construction difficulty, and ease of sail handling place effective limits on area. If the hull is a brick, the extra power from high CL multiple element sailplans can be the best solution.

A wing sail with great area that would drive the boat at low CL would be a much better solution if you could reduce the area and lower the height of the CE when the RM limits are reached.

There is no magic to multiple elements, they are a soft foil solution to a design requirement for high CL where flow separation is a problem. If you could build a boat with high RM, high SA/D and low D/L ... like a fast catamaran, there is no need for CL over 1 or so. CL=1 does not require high AoA and multiple elements.

[tspeer]

Originally Posted by brian eiland

We think differently here.

And I believe a few other folks see this differently also, including Avery Gentry, AMO Smith, and Tom Speer

Excuse me, please do not put words in my mouth. Nor should you speak for Arvel Gentry or A.M.O. Smith.

I agree with RHough. The main and jib do have to be considered together, rather than as separate entities. I do not subscribe to the notion that the main is but an inefficient appendage to the jib.

[brian eiland]

Dear Randy and Tom,
I will be answering both of your recent postings very soon here, however I wish to try and clear up a misconception I seem to detect that you may have about my concept to legitimize the jib/mainsail configuration.

It appears to me that you think I believe the two sail (jib/mainsail) system should be considered two sail entities unto themselves, and that the jib-genoa is the more powerful of the two, thus deserving a more prominent position in any sail rig design, and particularly in my aftmast concept. Or that I would even consider that headsails are so superior that they can act on their own.

And maybe a portion of this misconception results from the fact that I emphasize that my aftmast rig is 'mainless' (no mainsail), or that I appear to have only two headsails. This might infer that I do not see the necessity for a mainsail (like that quote above by Ivor, "Then, when close hauled, the jib drives the boat and the main sail makes no contribution).

Absolutely, I do NOT believe this to be the case. I have long recognized and expressed in numerous postings that it requires a trailing sail to generously impart to the leading sail (two elements) the special gifts of extra power and better pointing capabilities.
I've just chosen a 'different configuration' for my trailing sail. I call it a mainstaysail rather than what normally would be the traditional mainsail.

Regardless of what you think about the rest of my aftmast rig concept as far as practicality, engineering, extra drag, etc, I think it might be said 'that from a purely aerodynamic viewpoint my mainstaysail foil, in the two-element foil system, is more favorably disposed to help the headsail foil than is the traditional mainsail foil.'

[brian eiland]

Originally Posted by tspeer

Excuse me, please do not put words in my mouth. Nor should you speak for Arvel Gentry or A.M.O. Smith.

I agree with RHough. The main and jib do have to be considered together, rather than as separate entities. I do not subscribe to the notion that the main is but an inefficient appendage to the jib.

Hello Tom,
First let me say that I very highly respect your opinion, and I have learned a lot from you...so don't give up on a total conversion of me yet.

I was not trying to 'put words in your mouth'. I will quote some of your previous postings that led me to believe, that like myself, you see the interaction of the two-element sail system to be advantagous to the headsail.

Originally Posted by tspeer

It doesn't appear that the forward quarter of the mainsail is directly contributing a great deal, but you can get a sense of how the jib benefits from the presence of the main, making the combination more powerful. http://www.boatdesign.net/forums/sho...09&postcount=8

Originally Posted by tspeer

In upwind sailing, if the maximum aerodynamic L/D is below stall, it may pay to trim the rig for maximum lift instead of maximum L/D, even though the aerodynamic drag angle will increase. The added lift can improve the hull's L/D and reduce the hydrodynamic drag angle more than the loss in the aerodynamic drag angle, and improve performance.

In general, for the kinds of boats we're talking about, the windage is so high that the rig will stall before it reaches maximum L/D. So there's benefit in improving the maximum lift as well as the L/D of the rig alone. But the really big gain may come from reducing windage.
http://www.boatdesign.net/forums/showpost.php?p=111366&postcount=94

Originally Posted by tspeer

The theoretical effectiveness of the headsail is not due to its cleaner leading edge. It's due to its interaction with the mainsail. The mainsail gives a boost to the head sail, and the headsail reduces the lift of the mainsail. It's exactly the same as lee-bowing your competitor - the jib gets a lift from the main, and the main gets a header from the jib. But the effectiveness of the whole combination is increased, so there's a net gain.
http://www.boatdesign.net/forums/sho...&postcount=152

Originally Posted by posting #115

…. Most boats have so much windage that the maximum L/D occurs above stall onset. So that's a big reason why you want to raise the maximum lift as high as possible.

Originally Posted by posting#109

… Multiple surfaces properly shaped and arranged can produce a higher maximum lift than any single surface of the same chord. For a more in-depth discussion, search this forum for A.M.O Smith's "High Lift Aerodynamics".

Originally Posted by posting#92

… I think you ought to consider the planform area of the main and jib together when talking about aspect ratio. They really act more like one multi-element airfoil than separate foils.

Brian added: key word…multi-element airfoil, not just single airfoil

Originally Posted by posting#64

.. Exactly. The main does indeed make the jib act like it's got a flap deflected. This is why people find that jibs are more powerful than mainsails of the same area.

Originally Posted by posting#60

… The main really does transfer lift to the jib. The combination of the two is more effective than the same area allocated to either one separately. This is true even if both of the elements are good performers in their own right.

Any study of rig effectivness points out that on a per-area basis, jibs are more effective than mainsails. That leads to the conclusion that rigs would better if they were all jib - hence the mast aft rig. What these studies often fail to point out is the effectiveness of the jib comes from its interaction with the main. On its own, it doesn't perform as well. And theoretically the main suffers in the exchange, making it look worse. But the combination is more than either sail acting in isolation.

...and finally excerpted from aerodynamicist and North Sails consultant Paul Bogataj’s paper, “How Sails Work” http://www.northsailsod.com/articles/article6-1.html
‘Sails in Combination’, “Each sail by itself is much simpler than the combination of a foresail and mainsail as in the sloop rig. The sails are operating so close to each other that they both have significant interaction with the other. The most interesting feature of this is that the two sails together produce more force to pull the boat than the sum of their forces if they were each alone.
The foresail of a sloop rig operates in the upwash of the mainsail. The wind as far upstream as the luff of a genoa is influenced by the upwash created by the mainsail. Hence, a jib or genoa in front of a mainsail has a higher flow angle than it otherwise would have by itself, causing an increase in the amount of force that the forward sail produces. So, while the mainsail is experiencing detrimental interference from the foresail, the foresail benefits from the interference of the mainsail. Notice that more air is directed around the curved leeward side of the foresail. This causes higher velocity (lower pressure) and more force. The net result is that the total force of the two-sail system is increased, with the foresail gaining more than the mainsail loses”

[Paul Scott]

Brian, this is not on the particular point above, but ever since I've been reading about your mast aft concept, I've wondered- Why not configure your aft mast to be a largish rotating wingmast (4 or 5 ft chord on a 60 ft mast, for example), and at least get some of the benefits of a trailing airfoil out of the mast?

If you have objections to this approach, are they practical? Structural?

Paul

[brian eiland]

Originally Posted by Paul Scott

Brian, this is not on the particular point above, but ever since I've been reading about your mast aft concept, I've wondered- Why not configure your aft mast to be a largish rotating wingmast (4 or 5 ft chord on a 60 ft mast, for example), and at least get some of the benefits of a trailing airfoil out of the mast?

If you have objections to this approach, are they practical? Structural?

Paul

I'd have to give that idea more thought, but two items pop into my mind at the moment.
1) A largish rotating wingmast would likely close off the slot between the headsail and mast mounted mainsail to such a degree that it would present problems.
2) An aft mounted largish wingmast could present real steering problems downwind.

But how about a little less rake forward, and mount the mizzen sail to the mast that is stayed somewhat akin to a B&R

[RHough]

Originally Posted by brian eiland

Hello Tom,
First let me say that I very highly respect your opinion, and I have learned a lot from you...so don't give up on a total conversion of me yet.

I was not trying to 'put words in your mouth'. I will quote some of your previous postings that led me to believe, that like myself, you see the interaction of the two-element sail system to be advantagous to the headsail.

Brian,

None of the quotes support the advantageous to the headsail idea.

The total projected lateral area of a sail plan is the effective area. Overlap does NOT increase projected area.

The total lift of the projected area falls at about the 1/4 chord point of the total area. That happens to be forward of the mast for many boats and leads one to conclude the headsail is doing all the work. Ain't so.

A wing, a single element, can generate a Cl of 1.6 or so with the corresponding high induced drag. If some performance goal requires higher lift force (not higher Cl) and for some reason area cannot be added, then the design must produce the lift force by operating at a Cl higher than 1.6.

The way to do this is to use a multi-element configuration to control separation and prevent stall. Cl of over 2.0 can be reached, it might seem reasonable to think that two foils acting together should be able to reach Cl = 3.6 (twice 1.6), but I have not seen a multi-element foil reach that number:

Multiple Element Airfoils Optimized for Maximum Lift Coefficient
ALLEN I. ORMSBEE* AND ALLEN W. CHEN|
University of Illinois at Urbana-Champaign, Urbana, III.
Optimum airfoils in the sense of maximum lift coefficient are obtained for incompressible fluid flow at large Reynolds number. The maximum lift coefficient is achieved by requiring that the turbulent skin friction be zero in the pressure rise region on the airfoil upper surface. Under this constraint, the pressure distribution is optimized. The optimum pressure distribution is a function of Reynolds number and the trailing edge velocity. Geometries of those airfoils which will generate these optimum pressure distributions are obtained using a direct-iterative method which is developed in this study. This method can be used to design airfoils consisting of any number of elements. Numerical examples of one-and two-element airfoils are given. The CLmax values obtained range from 2 to 2.5.

Now, the 2D lift line slope is very close to .1 Cl per degree of Angle.
Cl = 1 is a 10 deg AoA
Cl = 1.6 is 16 deg
Cl = 2.5 is 25 deg

It is NOT possible for the high lift foil to operate a low AoA. A Cl = 1.0 foil will "point" 15 deg higher than the multiple element Cl = 2.5 foil.

Multiple element foils do not point higher than single element foils.

Tom makes a point that I have not fully researched, that increased drive and thus increased speed can allow the hydro forces to compensate for the increased angle and drag of a high Cl multiple element foil, the result might be a course closer to the wind ... "pointing higher" ... I don't know that I'm ready to agree or not.

If you set the drive requirement to equal the drag at a target speed, you obtain that force with a combination of area and Cl. Increasing area reduces the Cl required, increasing Cl reduces the area required.

With greater area and lower Cl the induced drag is lower ... boat 'points' higher. With greater Cl (multiple element foil) and lower area the induced drag is higher ... boat 'points' lower.

If there is a limit to area, the only way to increase drive is to increase lift by using higher Cl. What is the limiting factor for area on a sailboat?

Area is limited by the boat's resistance to heel. In an extreme case you could have a 100 sqft foil with a 100 ft span and a 1 ft chord or the same area in a foil with a 10 ft span and a 10 ft chord.

For simplicity assume the lift acts at the geometric center of each foil. If the drive force is x, the 100 ft foil has a 50x heeling moment and the 10ft foil has a 5x heeling moment. If the boat has a righting moment of 10x, it cannot use the drive of the 100 ft span, the maximum heeling moment the boat can use is 10x.

If the righting moment limits the area so high Cl is required, and the required Cl is greater than 1.6 or so, only then does a multiple element foil become an optimum solution.

On your cruising cat, what is the RM? How tall would a single foil have to be to drive it at a target cruise speed? What Cl is needed produce the required force? Does longitudinal stability limit the height of the rig? Why are you convinced you need a multiple element sail plan?

If it turns out that some factor like bridge clearance or stabilty limits rig height, factors other than simple aerodynamics have to be considered.

From a purely theoretical point of view, the case that multiple element foils are superior (high L/D) cannot be made. It cannot be done, other limits must be applied to justify their use.

[markdrela]

Originally Posted by RHough

Multiple element foils do not point higher than single element foils.

The "pointing angle" of a sail airfoil is mostly irrelevant. All that matters is its Cl and Cd. The AoA can always be set to reach whatever Cl is needed, short of stall.

With greater area and lower Cl the induced drag is lower ... boat 'points' higher. With greater Cl (multiple element foil) and lower area the induced drag is higher ... boat 'points' lower.

Not so. If you double the CL and halve the chord, the lift and the induced drag are not affected, even though the AR has been doubled.
CL' = 2 CL
c' = 0.5 c
S' = 0.5 S
AR' = 2 AR
CDi' = 2 CDi
L' = q S' CL' = q S CL = L
Di' = q S' CDi' = q S CDi = Di


As I've said before, the slot between the jib and mainsail is purely a boundary layer control device. It does not significantly affect the sail's overall potential-flow characteristics:
* it has little or no effect on the sail's CL(alpha) curve
* it has little or no effect on the induced drag at a given speed and lift

Any improvement of L/D caused by the slot will likely be due to a reduction of the mast drag.