# Bell Spanload Implications for Sailing?

Discussion in 'Hydrodynamics and Aerodynamics' started by lunatic, Nov 19, 2017.

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### Mikko BrummerSenior Member

Erwan, I thought the main difference between airplanes & sailboats was that the first one flies in the air and the second floats in the water ;-). The classical paper by RT Jones tells us that when root moment constrained, the downwash distribution (not the span loading) should be linearly decreasing, which leads to a bell-like span loading. For an elliptical span loading, the downwash would be constant.

For sailboats, it was shown in the 70'ies that for best performance in heavy air, the loading should go negative in the top of the sails, the top part supporting against heeling with a long "lever arm", despite the obvious extra drag associated. This leads to a negative camber in the head - look at the top battens of these Star boats sailing in a breeze - heavily overcanvassed, they could not handle a breeze like this in heavy air, without recurring to this special trim.

Last edited: Dec 13, 2017
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### ErwanSenior Member

Thank you Mikko for this correction , I was confusing spanload distribution and downwash,
distribution.
I have to check the position of a Bell distribution's CoE , I will probably have to make revision on integral calculations and primitives functions.

Thank again for this opportunity to sharpen my Fluid Dynamics understanding.

Regards

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### ErwanSenior Member

FastSailing,

AFAIK, Naval Architects, have to choose a True Wind Design Speed, in order to design their boats with full righting moment/ full power at this TWDS.
10-12 knts is often the prefered (or mean) TWDS, with some standard deviation around this mean, according to the type of sailing boat:
An A-Cat or a 18 feet Skiff have probably a lower TWDS while a family keel boat an higher one.

Regards

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### philSweetSenior Member

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### Ben GJunior Member

Mikko while I understand the implications of downwash and heeling moment point to the benefits of a pin-head sail, I think Square tops have a practical performance benefit beyond just mast length limits. I agree the difference between a well set up pin head and square top sail isn't as large as some may think.
The Star is likely to be one of few boats highly optimised for a pin head main. (tiny mast tip with no spinnaker load, and finely controlled mast bend)
Some benefits to Square tops:
In yachts, the drag at the tip of the mast itself is likely to be significant, mast's don't taper that much at the tip, so a larger sail chord will give that upper one or two feet better aerodynamics.
In other boats, the range of the rig is likely to be better from a square top. It can be difficult to get the correct twist in the head of a pin head sail across the range, ie. not to overload the upper leech down range, and be able to flatten the head sufficiently up range - especially boats that cannot access sideways tip bend due to mast head rigs etc.
If setup properly the square top achieves both of these - controlling the camber and twist of the sail more readily to the conditions at hand. Up range, the head should be completely flat and twisted off, while leaving the lower third with camber. The downside will be the extra skin friction of the square top, less so the incorrect downwash.
Also fanning and incidental dynamic response during manoeuvres could be a large benefit.
It would be interesting to compare the CFD video you have of a boat (star?) through waves, showing vorticity and loading changes as the rig pitches, to a correct aeroelastic model of a square top. (I imagine this would be impossibly difficult to model)
I have seen some wind tunnel studies on square tops, but what I saw didn't show the twist setup correctly etc.
I also agree that rule constraints often create 'overdone' square tops, ie big rigs on 18' skiffs.

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### ErwanSenior Member

Squared Top were interesting for A-Cat with a tear drop mast, in order to fly a hull earlier windward and to sail the "Wild Thing" earlier downwind.
As illustrated by Mikko's pictures for the Star, it deserves to be mentionned, that A-Cat have been using the top sail inversion for a long time, even when we were sailing aluminium masts.
It was striking to see the difference, from an overpowered situation, you just had to pull the mast line in order to bring the mast orientation from 45° of the boat's centerline to something like 15°, then the 2 or 3 top battens got inverted, then the windward hull stopped climbing, the boat accelerated while staying flat on the water with the windward hull just kissing the waves, the cost was a few °'s give up windward, but the boat speed was so much better that at the windward mark, the "pointers" were behind the "runnners" with no brainer.

Thank You Phil for your suggestion, I remember Tom Speer's workpaper : Optimum Sailplan", written and published many years ago, and if I remember well the Bell Shaped distribution was addressed as well.
Thanks again the wake-wash link, I will dig into it with great pleasure, even if I will probably not understand everything.

Regards

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### Mikko BrummerSenior Member

Ben G: Obviously, both pin head & square top will need a different mast and correct trim to perform at its best. When the question about classic vs square top sail raises, I usually point to the JPK 998 case: The builder had 2 boats built and optimised, one for a classic main and the other for a square top, and sailed a whole summer (with different skippers & crews) with both. At the end, the classic rig was chosen, being easier to handle (one permanent backstay vs. 2 running), always performing a little better upwind (pointing a tad higher), and similar off the wind.

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### Mikko BrummerSenior Member

I've run simulations (quite a while ago) on fat heads & square tops, on the same mast length and sail area. In these, the fat head & square top did perform marginally better, but the mast length was the same. When over trimmed, with it's wide top, the square top has a large area stalled above the hounds, the classic sail a lot smaller area. I believe, like the plumb bow, it's much fashion.

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### markdrelaSenior Member

What's the reason for having the hounds below the tip? Aerodynamically it doesn't make sense, since it promotes local tip stalling as your calcs show. This is why a leading edge slat on a wing always goes all the way to the tip.

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### Mikko BrummerSenior Member

It's a control thing - easier to bend the mast with the backstay when the forestay doesn't go all the way up. With the masthead rig, you need to add a "babystay" (inner forestay) to be able to bend the mast properly. For control, a fractional ratio of 75-80% is the best, as that kind of rig will work automatically: When a gust hits, the mast top will bend aft and the mid-mast forward (with the hounds as a pivot point), effectively flattening & twisting off the mainsail. The masthead rig as well as the current 9/10 rig lack this automacy, requiring manual adjustment as the pressure changes. You need a long enough topmast, to have the "lever" to bend the mast automatically with the leech pressure.

Very much about sailboats is dictated by rating rules. In 1970's-80's, the IOR rule dictated how sailboats looked like. The era started with masthead rigs, aerodynamically most efficient, but with time the masthead rig was replaced with a fractional one, more versatile to trim and outperforming the stiff masthead rig. The mast is to the sailboat what suspension is to a race car - when it gets bumpy, the bendy fractional rig outperforms the stiff masthead rig. One reason is that with the masthead rig, the foresail gets so large - the foresail shape is more difficult to control (no mast), and the mainsail is producing most of the heeling moment. So a larger mainsail will provide more scope to power control. Sail trim is in essence power control.

Attached (historical) rig types illustrated.

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### CT249Senior Member

I was going through some old Seahorse magazines the other day and the repeated theme (as of course you know very well, Mikko) was the influence of mast and in particular sailcloth technology on the choice of masthead rig compared to fractional. Guys like Bouzaid, Bertrand and Dubois were talking about the flexibility of the fractional rig in smaller boats in the '78-'83 period, and of the difficulties in getting them to work over 42 ft due to the weight and stretch of the larger mainsails.

It's also interesting to see that even designers who didn't follow rating rules, like NZ's John Spencer, tended to go to masthead rigs for some time in the '60s and '70s. Although he was a dinghy designer, from his writings and the spars he had on his boats it appears that Spencer didn't think that the technology allowed offshore-style boats to use mast bend effectively and therefore to obtain flexibility in different conditions he relied on the masthead rig where changing headsails had more effect. Given the tech of the day, he may well have been right - although today the same hulls can carry fractional rigs and go dramatically faster we are using very different gear. Looking at something like this early '70s video of top NZ ocean racer Whispers, sailed by top dinghy sailors (The Hum | Short Film | NZ On Screen https://www.nzonscreen.com/title/the-hum-1974 ) underlines how hard it would have been to get a big fractional rig to work given the technology of the day. Even top class big-budget crews like that on Prospect of Whitby (the '73 one) had no luck getting an early '70s fractional rig to work offshore on a big boat.

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### Mikko BrummerSenior Member

As you may recall, the fractional rig era started with the Bruce Farr quarter tonner 45° South... the French quickly adapted the fractional rigs into half tonners, 3/4 tonners and 1 tonners. For bigger boats, it depended on how & where they sailed: Inshore on windward-leeward courses, the masthead rig with big spinnakers was good, while offshore, with fetching and reaching and bumpy (waves), the fractional rig was unbeaten. The large genoa of a masthead rig is not very good as soon as you ease the sheet - too full in the foot and too open in the head, while a large mainsail with a long boom and vang works much better. Then waves matter a lot: While pitching in waves, the pressure on the sails varies easily +- 30% in a 1-2 sec. period - here the fractional rig with its automacy easily outperforms the masthead. In waves, size matters - in 20 kn, the waves are large for a 30 footer, but an 80-footer power right through them without notice. I guess this is one reason why bigger boats still sport masthead rigs more often.

In the late 80'ies, even maxi boats got fractional: In the Whitbread 89-90, I sailed on Belmont Finland, with a fractional rig, like all others... In the pre-racing/practicing, we sailed against round-the-buoys IOR maxis on windward-leeward courses, with no chance against them, finishing often almost half a beat behind. On the other hand, when we did a practice race across the Atlantic, the same masthead maxis were 3-4 days behind us - of course, there were other differences, the heaviest round-the-buoys IOR maxis weighed 40 tons, while the offshore maxis were 25 tons or so.

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### lunaticSenior Member

Brummer's negative loading at top and Erwan's top sail inversion would indicate a reversal of downwash, does this transition effect the tip vortex? is there a benefit beyond heel reduction? The upwash of bellspan loading would add to heel, seems too costly even with the 15% more thrust for 15% increase height of Erwan's paper. The Horten HXc wing of the NASA project has a unique twist perhaps not applicable to a sail, but nice to see a tip vortex manipulated to some advantage. Brummer's sail pitching in waves with pressure on sail +- 30% in a 1-2 second period might reduce drag by the Katzmayr effect, there have been times beating upwind when progress seems not to have been earned.

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### CT249Senior Member

It's interesting that you say the era started with 45 Degrees South. I know many English-speaking commentators say the same thing but I wondered whether someone from Europe may also have been interested in the earlier fractional rig 1/4 tonners like Listang and Quarto. Obviously their fractional rigs were of very different proportions to 45 Degrees, but one of them won an early worlds and the other lost in '74 only on protest so both showed good speed.

I completely agree with all you said about the comparative performance of the rigs, of course, and it's very interesting to get information on Belmont Finland, which was a lovely looking boat. The fractional rigs had such an impact on us down here that it took me some time to work out how and why they didn't work all the time in the big boats.

Years ago I did an interview on trimming Farr 40 sails with Grant Simmer, after he had won the worlds. He thought that basically, the stiffer the mast the better and I note that the Farr 40 seems to have about as high a forestay as the X41, yet you appear to thing the X41's forestay is too high. Have techniques and materials caused changes, or is the difference related to the greater weight etc of the X41 and the possible difference in sail shape, acceleration etc?

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### JoakimSenior Member

Farr 40 fractionality is 88% and X 41 94%, which is a huge difference for trying to control forestay without runners. At 88% you really need a stiff mast for that!

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