sail aerodynamics

[Paul Scott]

If you split a cat rig of AR 4 in two, turning it into a split rig of the same sail area that occupies the same 2 dimensional space as the cat rig (that is, the system planform is the same heighth, and the system chord is the same width as the single sail), is the whole sail/wing system AR still 4? If you then split the same (cat) rig again in two, but use an overlap of the 2 resulting wings/sails to put the same sail area into a 2 dimensional space that has the same (system) span, but is smaller in effective (system) chord, is the whole rig's AR higher? Does this result in better performance than the split, non overlapping, lower AR 4 system, everything else being equal?

The reason I ask is that Marchaj, in Sail Power, seems to indicate that separating the two elements would give more power. Which would seem, I think, to lower effective system AR. (This is apart from stagger, that is, moving the jib to leeward, at least upwind.) I don't think Frank Bethwaite would concur. So is overlap beneficial when it is counted as Sail Area? Any threads on this?

Or is this merely Gedanken Experiment?

Paul

[gggGuest]

Originally Posted by Paul Scott

If you split a cat rig of AR 4 into a split rig that occupies the same 2 dimensional space, is the whole sail/wing system AR is still 4?

As I understand it the drag that aspect ratio relates to is induced drag. which is simply proportional to the span of the foil - ie length parallel to the airflow. So if you have two 10m3 sails, each of width 2m you end up with the same induced drag as one 20m3 sq ft sail width 4m. But if you have two 10m3 sails of width 4m you have double the induced drag,and if you have a 20m3 sail of width 2m you havw half the induced drag. Of course the lower rigs have less heeling mment, but no-one said this was easy.

[brian eiland]

Aspect Ratio (AR) of rigs on cruising vessels

I was looking back thru “Principles of Yacht Design” by Larsson and Eliasson this morning and noted some of their observations on the subject of Aspect Ratio (I’ve underlined some portions where I sought to emphasize that passage):

Originally Posted by book

At the top of the sail and at the boom the lift force goes to zero and vortices are shed, giving rise to an induced resistance. The larger the height of the sail, the smaller the effect of the vortices. As for the keel, the most important efficiency parameter for the sail is the aspect ratio. We define it here as the luff length (P or I) divided by half the foot length (E or J in the IOR notation) so neglecting the roach it corresponds to the definition of the previous chapter. It should be mentioned that in some sailing literature the foot length is not divided by two in the definition, so the aspect ratio is half as large.

Very interesting studies of different planforms have been carried out computationally by Professor J H Milgram at Massachusetts Institute of Technology (MIT). For a masthead rig he varied systematically the aspect ratios of the main and fore triangles by changing the foot lengths. The calculations were for the upwind condition, and the computed force was resolved into its driving component R and side force S. These forces are given in coefficient form: Cr and Cs respectively, in Figs 7.3 and 7.4 (attached) Note that the coefficients are obtained by dividing by a sail area, which is either the real one (thick line) or the measured one according to the IOR (thin line).

Although this rule is not much used today, it is interesting to see how the penalties imposed affect the efficiency. The coefficients may thus be considered representative of the force for a given area, either real or measured. The graphs for the mainsail have been obtained keeping the fore triangle aspect ratio constant (AR 6) and vice versa. In Fig 7.3 (attached)it can be seen that the driving force increases considerably with increasing AR. To a certain extent the advantage is offset by the penalties of the rule, but for the fore triangle there is still a great advantage in a high aspect ratio. The side forces of Fig 7.4 (attached)decrease greatly with aspect ratio if the IOR area is kept constant. This is because the real area is reduced due to the penalties. If the real area is used as a reference, the side force is relatively constant.

What I found rather interesting here is something I’ve commented on before, the influence of ‘rating rules’ on designing boats and interpreting sailing science, ie; “interesting to see how the penalties imposed, affect the efficiency.” We need to keep this in mind as we refer to observations (usually our reinforcing ones) based upon particular classes of racing sailboats.
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Originally Posted by book

In another interesting series of calculations Professor Milligram varied the point of attachment of the forestay to the mast. Four rigs were computed, where the attachment point was at 3/4, 7/8, 15/16 and 1/1 of the full mast height, respectively. The results may be seen in Fig 7.5 (attached) There is a significant gain in driving force for the real sail, when the fore triangle height is increased, while the side force is almost constant. For the IOR sail the gain in driving force is not so large, but the side force is reduced

I found this observation interesting in several ways. I have been a proponent of the ‘masthead rig’ for a long time, and this work indicates a “significant gain in driving force for the real sail when the fore-triangle height is increased.”

I also believe this indicates a need to consider the AR’s of the individual sails separately rather than as one ‘combination of jib and main’.

Originally Posted by CT 249

Which leads me to ask - when we look at aspect ratio, is the important factor the AR of the individual sails, or the whole rig?????

Originally Posted by tspeer

The whole rig. The best indicator of lift/drag ratio is the wetted aspect ratio - the span-squared divided by the total wetted area

I believe the key word here is indicator. Sure the overall AR of the rig as a unit is an INDICATOR of the lift/drag aspects, but it does not explain the difference between a mastheaded sloop and a fractional sloop of the same height and AR.

Originally Posted by CT 249

I have a yacht with a low-aspect genoa and high-aspect main. I can see intuitively that this may mean that the low-aspect genoa "wants" to operate at a different angle of attack to the mainsail, but is this correct?

It not only wants to do so as a result of the aspect ratio, but also as a result of the difference in sweep angles for the two sails, and more importantly the upwash/downwash situations created by the interplay between the two sails
From Paul Bogotaj’s “How Do Sails Work",
Flow Angles. Reviewing all of the affects so far reveals that both sails experience increasing flow angle with height. The foresail operates in the twisted flow of the apparent wind, with upwash induced by itself due to taper and sweep, and in the upwash field of the mainsail. The mainsail is operating in the same twisted apparent wind, with additional upwash caused by its taper, but somewhat lessened by its forward sweep. It is. also flying in the downwash field of the foresail, which is probably twisted because the foresail flies in a twisted fashion. This is particularly exaggerated with a fractional rig.
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Originally Posted by book

The results of the previous figures seem to indicate clearly that the aspect ratio of the sails should be as large as possible. This is not true under all circumstances, however. Considerations, which have to be made in a real case, include:
1) points of sailing other than upwind
2) the effect of the mast on the mainsail flow
3) the increase in heeling moment with aspect ratio.

The latter disadvantage is fairly obvious and its importance depends on the wind strength and the stability of the boat. We will not discuss this any further, but consider the other two points in some more detail.
C A Marchaj has reported wind-tunnel tests for sails of varying aspect ratios. All points of sailing were considered. Fig 7.6 shows the driving force and Fig 7.7 the side force for three aspect ratios: 6, 3, and 1. The latter is an almost square gaff sail. It can be seen that for small apparent wind angles, ie upwind, Milgram’s conclusions are confirmed. Around 30° the high aspect ratio sail develops more than twice the driving force of the square sail. However, at large wind angles the situation is different. Around 120° the square sail is superior, and develops 50% more thrust than the narrow sail. At 70° the thrusts are almost equal. The side force of Fig 7.7 increases somewhat with aspect ratio at 30°, but the opposite is true above 45°. The general conclusion is that the positive effect of high aspect ratio is reduced if all points of sailing are of interest.

In general we have three basic sailing directions we need to consider, upwind, reach, downwind. And for the cruising sailor the upwind 1/3 of the total is not even an equal partner (as many cruisers often chose not to fight upwind work). As Marchaj and many others have reported, high aspect ratio is principle beneficial for upwind work.
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Originally Posted by book

A disadvantage of the masthead rig which is often referred to for smaller boats, is the difficulty in trimming the mast properly

Or in other words, on many boats the capability to utilize the bendy characteristics of the mast to reshape the mainsail for a variety of conditions does not lend itself to the masthead configuration. Many racing classes depend upon this mast shaping feature and thus utilize fractional rigs. Or in the case of multihulls with rotating mast, the fractional jib is practically a necessity. But this should not be taken as an endoresment of the fractional rig nor a condemnation of the masthead rig from a purely aerodynamic standpoint. For a fixed-rig cruising vessel, I submit again that the masthead rig is likely superior.

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Originally Posted by book

The mast reduces the positive effect of a high aspect ratio mainsail even further. For a given sail area, the higher the aspect ratio the thicker the mast required, and the smaller the average chord length of the mainsail. Both effects tend to increase the proportion of the sail, which is ineffective due to the mast disturbance. Marchaj found in wind-tunnel measurements that a 6.0 aspect ratio sail was less effective, even upwind, than a 4.6 aspect ratio sail, and this was attributed to the mast disturbance. In these tests the mast diameter was 8% of the average chord length of the high aspect ratio sail. This seems to be a bit more than is used today, so the effect was probably somewhat exaggerated, but it shows that there is a limit for the positive effect of the aspect ratio of the mainsail.
Experiments at Southampton University with a mast/sail combination indicated large effects of mast disturbance. Thus, when a circular mast with a diameter of 7.5% of the sail chord was put in front of the sail the driving force upwind was reduced by about 20% compared to the case without a mast. A thicker mast of 12.5% was also tested and the driving force was almost halved. It was however, possible to regain almost half of the loss by turning the mast in such a way that the leeward side of the mast/sail junction became smooth….There is no doubt however that the top part of the sail will be significantly disturbed.

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Pitch & Heave

Here is another item that might be kept in mind when considering tall high aspect ratio rigs; their contribution to pitch and heave motions. When a vessel moves in a seaway, the waves impose motions of all kinds on the hull(s). The most important ones, from a resistance point of view, are the heave and pitch motions, which are usually strongly coupled. When the hull heaves and pitches it generates its’ own wave system, which carries energy away in much the same way as the still water wave pattern, thereby creating a resistance force. The pitch and heave motion will be affected by the mass moment of inertia of the yacht and the encountered wave frequencies.

Every object on the vessel contributes to its mass moment of inertia not only by its mass, but also by the distance to the center of gravity squared. Objects positioned far away will have a large influence. It turns out that the rig itself is a very large contributor. In some cases it’s twice as important as the hull, and four to five times as important as the keel for the moments of inertia. Multihull vessels can be particularly affected as their overall lightness makes them more sensitive to pitching and heaving, as well as their long thin hull forms that are less adept to dampen out the those motions so readily. These motions can very quickly kill all drive from the sails regardless of AR or all other factors.

[Paul Scott]

ggGuest & Brian

So, what do you think: assuming the same overall sail area & mast section & mast heighth & Mainsail area, in a rule free environment, does exploiting higher AR with an overlapping jib v. non overlapping jib (and let's say a masthead jib with a rigid mast, upwind, for grins) lead to performance gains?

Brian- as long as you mentioned IOR practice, any idea what the AR for mains was when the point of diminishing returns was reached in the IOR? Seems to me it was around 4ish, but that's a guess based on memory.

Paul

[CT 249]

Brian, re "Or in the case of multihulls with rotating mast, the fractional jib is practically a necessity."

In that case why do A Class and C Class not use jibs?

The funny thing about the common complaint about rating rules is that they get blamed for so many things. For example I have many articles from the early days of the IOR which blame the IOR for encouraging massive genoas and tiny mains. The rule was NOT changed and yet a few years later, there was a swing to tiny genoas and massive mainsails.

For example, the IOR rule didn't rate overlap. Therefore, a large genoa had a lot more un-rated area than a small genoa.

[gggGuest]

Originally Posted by Paul Scott

So, what do you think...lead to performance gains?

I think anyone who gives any answer other than "it depends" is hopelessly over simplifying things.

[Paul Scott]

ggGuest-

So this inquiring mind has GOT to know! "it depends on....?"

Just for arguements sake, lets say a light planing dinghy, non bendy wingmast, masthead rig, 30% main, 70% jib (assume that the jib furls as wind increases), say 10 sq m of sail, AR 4.

Paul

[gggGuest]

Originally Posted by Paul Scott

ggGuest-
lets say a light planing dinghy...

It depends...

There are still too many variables to call, not least being the average wind conditions where the craft in question sails. All you can do is take a look at what development boats there are out there that don't have rig height limits and see what they use.

To give an example of what does get used here are measurements for the last rig I had built for such a boat was a 12ft lightweight two hander being sailed at coastal events in the UK with max sail area of 12.5m2. Crew weight around 90kg on trapeze, Helm around 65kg sitting out, beam about 1.9m. This is a boat with a 15m2 asymettric kite to get it downhill. The same dimensions probably wouldn't be optimal for a boat without a kite. The key dimensions were as follows and I don't think I'd vary them if I were getting another rig for the same boat today. That doesn't mean I'm right: its awfully difficult to distinguish between two boats with equal racing results, one of which has a great rig and a mediocre crew, and the other a good crew and a lousy rig, but for whatever my opinion is worth I felt this rig was pretty good. The jib was fractional of course and almost completely non overlapping - (maybe just a bit of roach in the middle of the leech overlapping the main. I would never consider a masthead rig on a planing dinghy. The dynamics are all wrong. This rig would be regarded as being high aspect ratio by most folk and certainly has a higher AR than the vast majority of dinghies.

Mainsail
Luff Length 5.97
Foot Length 1.78
Leech Length 5.95
Total Mainsail Area 8.60

Jib
Luff Length 4.38
Foot Length 1.69
Leech Length 3.78
Total Jib Area 3.90

(all measurements in metres)


I reckon that's a 4.1 AR on the main, 3.7 on the jib and around 3 if you look at it as a whole (jib comes down lower than main).

[Paul Scott]

gg

I have to admit here that what you've posited for your skiff is pretty much a smaller version of the rig on my 40' cruising sled (DL 96), which I based mostly on Redwing of Bembridge practice, although I have a tonne of Roach. And my mast setup, with 22 1/2 degree sweep of spreaders, and LOTS of prebend does not give. At ALL. I presume your rig is fairly bendy? I ask because I had three Bruders for my Finn (way back when), and the really really Stiff Mast was the fastest by far, although not comfortable or friendly in any way. Ditto for Windsurfer rigs-RAF's-, which is what got me thinking about a stiff masthead wing rig on a skiffish dinghy, (e.g. Brian's remarks, kind of). Which I realize violates modern practice in extremis, but hey- we're only abusing 1's and 0's here, no? If you can control the power???? And if there is more power??? (Big if.) It seems to me that sportsboat rigs are pretty stiff, and sportsboats are getting smaller and smaller. Crossover? Bongo?

Paul

[brian eiland]

This aero discussion is sure getting lively. I'll try to catch up, but I'm not able to spend a lot of time at the computer at this time.

Originally Posted by CT249

Brian, while I understand the theoretical efficiency of the headsail due to its cleaner leading edge, I'm still puzzled.....if mainsails are so slow, then why do the most efficient boats of all (speed windsurfers, YPE, foiling Moths, C and A Class cats) all use cat rigs?

Why do fractional rigs generally go faster than masthead rigs when they have been tried together on the same hull (apart from perhaps in light wind areas when the fractional carries a fractional kite?).

First I respectively ask for a little clarification of some of our terminology so we are on the same page as we discuss speed and efficiency.
Speed:
When we talk of speed, are we talking of ‘around the race course’ speed, or straight-line, head-to-head speed? From a purely aerodynamic point of view, I would prefer to compare the vessels with different sailing rigs on a head-to-head basis in each of the 3 primary sailing directions. Around the course speed includes so many other factors that might distort the purely aerodynamic factors. Admittedly around the course speed should also be considered in the equations for the ‘fastest boats’ on a race course, but lets look at those additional factors separately and distinctly.
Efficiency:
In a similar manner I believe we have to consider two forms of efficiency; 1)that efficiency from a purely aerodynamic point of view, ie, that forward drive we are seeking from the least amount of sail area, and 2)the overall efficiency of the boat itself to include the rig, and the hull, and the entirety of the boat.

So hopefully you can see where I have some problems with your statements such as “the most efficient boats of all use cat rigs”, and “fractional rigs generally go faster than masthead rigs”. If you are talking ‘around the race course’ your statements could well be considered correct in many cases, but on a head-to-head basis they might not hold up so well.
Even you’ve written:

Originally Posted by CT249

…but the lobe for an AR of 1 at 35-45 apparent is incredibly distinct (in Marchaj) and it could perhaps account for a lot of the way that assys light up at certain angles.
Is Marchaj correct re AR and angle of incidence? Much of his info seems correct to my gut feeling; I know high-aspect rigs (F16 cats, Canoes) really light up at tight angles and get quite ordinary at broad angles. It's always interesting to see a Laser (smaller rig, similar wsa, more beam, less LWL) hanging in with a Canoe on square runs and broad reaches in light winds.

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Originally Posted by CT249

Frosh and Rhough, I agree with you and actually I'm up on that stuff - I just wonder what Brian, the man who is most involved with pushing the mast-aft rig, has to say about all the good reasons you have given.

Originally Posted by CT249

If jibs are more efficient, why have A Class and C Class stopped using them? Why is a guy like the world's fastest Canoe and C Class sailor so convinced of the speed of cat rigs that he's experimenting with them in Canoes?

I think Rhoug answered this one very well:

If the rig can be sized so that CL over about 1.6 is not needed (upwind), there is no reason for a multiple element sail plan. Windsurfer, foiling Moths and Cats all have very high righting moment to sail area ratios. There is little need to control the heeling moment with low aspect ratio rigs, or splitting the area between main and jib.
On single-handed dinghies the added workload of trimming two sails to work properly probably slows the boat more than any extra power from the rig gains. On boats that always sail with the apparent wind forward of the beam wing-sails are a logical choice.

Originally Posted by Frosh

With the A cat I believe that very high aspect mainsail (almost the identical planform to a high performance glider wing) overcomes any advantages of sloop rig due to sufficient RM to support the greater heeling force.

Originally Posted by redcooprs

However, the design of sailforms is very much a practical nature.

In terms of sailing, the feel is that our jib supplies the driving power - and wind tunnel tests also show that it has a very large Cl compared to the main. The main on the other hand, is very responsible for the righting moment and general tuning of the boat. Skippers know that if they constantly communicate with their mainsail trimmers while sailing upwind they'll do well - the jib trimmers are mostly left to following their tales.

So ultimately, what I am saying is that for a sailboat, instead of thinking of a design point for a Cl, think instead of a large plateau in which you can spill enough wind out of your sails to maintain a stable platform. In 8kts of wind, you may be able to get 5kts of boatspeed. In 15kts of windspeed, you may need to start easing out the main to get 6kts of boat speed. What most designers want is a boat which quickly gets up to near designed boatspeed and then gradually increases afterwards.

So the reason many boats use a fractional rig is because all sailing is a compromise. A nice roach on a main will supply power at very low wind speeds. In high winds, you can simply ease the traveller and let the jib with its lower CE do the work

I’ve said before in another posting,

Originally Posted by book

A disadvantage of the masthead rig which is often referred to for smaller boats, is the difficulty in trimming the mast properly

Or in other words, on many boats the capability to utilize the bendy characteristics of the mast to reshape the mainsail for a variety of conditions does not lend itself to the masthead configuration. Many racing classes depend upon this mast shaping feature and thus utilize fractional rigs. Or in the case of multihulls with rotating mast, the fractional jib is practically a necessity.

But this should not be taken as an across the spectrum endorsement of the fractional rig, nor a condemnation of the masthead rig from a purely aerodynamic standpoint.

[CT 249]

Ok, thanks.

I agree with much of that. However, just as a suggestion unless I'm reading it wrong (which is of course possible) some of your promotion of the mast-aft rig can be seen as a little more one-eyed than the way you have put it here. Maybe that's a good way of promoting the rig, but it may also get people's backs up (as it did with me).

I still can't see how the jib is a necessity with rotating mast cats, since As, Cs, some fast old Bs, some F16s and T 4.9 1-ups don't have jibs and perform very well. But I won't worry you about the point further.

[brian eiland]

Originally Posted by CT 249

I still can't see how the jib is a necessity with rotating mast cats, since As, Cs, some fast old Bs, some F16s and T 4.9 1-ups don't have jibs and perform very well.

I'm not saying jibs are necessary for a rotating mast rig, but rather that if a jib is to be used with a rotating mast, it needs to be a fractional one because of the staying arrangment.

[Vega]

Excellent work guys, very good thread. I have been following it, but not posting here, simply because you guys seem to know more than I know about the issue

Thanks for the résumé Brian, very well done.

I have a question. There is a rig that can utilize only one sail and it is not the cat rig. It is an old one, the Latin sail. It is obvious that the rig is not practical for a number of reasons (reefing, tack, etc) but I have seen some Latin rigs in the Canary Islands (racing traditional boats) that look very sharp in what regards performance (even if they don't use high-tech materials).

I am curious about it. Can someone make an evaluation of those high developed Latin rigs?

[gggGuest]

There are pros and cons to just about every possible rig that has been widely used.

For ultimate performance per square foot of cloth I wouldn't have a triangular planform, nor would I have a loose foot. I'd also have doubts about the dynamics, things like gust response.

On the other hand there are more knowldegeable folk than I who state that the angled leading edge has some neat advantages, notably the way that leading edge vortex creation gives high lift (but high drag) at large angles of attack without stalling. Bethwaite is a good reference on this.

[MAINSTAY]

Brian Eiland,
The diagrams of Rick Loheed (#151) are good demonstrations of your theory. It shows very little contribution to the drive from the main.

If the diagrams were to show a non-rotating mast it would be even more in your favor.
Larry