# Multi speed/length relationship?

Discussion in 'Multihulls' started by RHough, May 17, 2008.

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### RHoughRetro Dude

I'm sorry if I've missed this, but I've been searching for information about the relationship between length and speed for multihulls.

For displacement Monos, 1.34 x Sqrt LWL = knots

Is there a similar formula or relationship between length ans speed for multi's or do they have the same the extreme SA-D and D-L ratios that make the mono formula useless for sport boats.

Should a 40 foot cat or tri be faster than a 20 foot boat? How much faster? Why? and how do you predict by how much?

Thanks,

Randy

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### TeddyDiverGollywobbler

It's basicly the same with multihulls as mono's. The things that matters when one's want's to overcame "hull speed" are Displacement/Length Ratio and the actual Hp giving the thrust.

S/L ratio = 8,26/ (D/L ratio)^0.311 or = 10,665/(Disp lbs/Hp)^0,334
D/L ratio = Displ longtons/(0.01*Lwl)^3 ; longton = lbs/2240

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### RHoughRetro Dude

Thanks, not exactly what I'm looking for, but good information.

Try this:

20ft Cat with lower D/L and higher SA-D
40ft Cat with higher D/L and lower SA-D

Will the 20ft Cat be faster than the 40ft Cat? Why and by how much?

or

20ft Cat and 40ft Cat with equal D/L and SA-D. Will the 40ft Cat be faster? Why and by how much? If top speed is a pure relationship between power and weight, is there any reason to build larger boats?

Is the relationship similar to a mono?

20ft LWL = 6 knt
40ft LWL = 8.47 knt

The 40 foot boat is 41% faster in displacement mode. Given equal D/L and SA-D will the 40ft Cat be 41% faster than the 20ft Cat? Is it possible to predict the approximate top speed of both boats?

My gut feeling is that between two multi's with equal D/L and SA-D ratios, the larger (longer) boat should be faster. Is that just a notion I have because it is true for monos or does it apply to multi's also?

4. ### Doug LordGuest

I was told a long time ago that the speed length ratio for a high(14-20/1) L/B ratio hull would be approx. 4 times the square root of the waterline length.

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### marshmatSenior Member

Hi Randy,

There really isn't any difference between multis and monos as far as this subject goes. (As an alternate way of looking at it, picture two identical monohulls cruising side-by-side; do the mathematical principles surrounding each boat change?)

The speed/length ratio (or, for engineering/physics types, you can think in Froude number) is basically just relating the wavelength to the speed. The commonly cited S/L of 1.34 is for a non-breaking wave moving freely in open water. It's a practical value to use for relatively wide or heavy boats because, if these try to go faster than their wake system naturally wants to when the wavelength is the same as the ship's length, the resistance really starts to climb.

When we look at a slimmer, lighter (for its length) hull, the exact same math still applies. But where the fat heavy boat (typical mono) saw a sharp increase in resistance at around the maximum natural speed of its wake, this increase is a lot more gradual in the skinny boat. So while it sees an increase in resistance when it exceeds 'hull speed', this increase is not necessarily enough to stop it from accelerating further. VSVs, cats and tris all tend to have skinny hulls; thus, the "1.34 barrier" is not as pronounced.

While you will see an increase in power requirements and fuel use above 'hull speed' in the multi, it's not necessarily a hard limit. S/L of 2, 3, even 4 or higher is not unheard of in a slim hull while still in displacement mode.

All other things being equal, an increase in the length of a cat or tri will still result in an increase in speed potential proportional to the square root of the waterline, just as with the wider hulls found in monos. (In a sailing vessel, of course, linear scalings of all factors are impossible (area with the second power, weight with the third and stability with the fourth- they never all reconcile). But all else being similar, longer is always faster.)

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### TeddyDiverGollywobbler

Fastest sail boat ever is (i think) a sail board so there's allways exceptions and Yes smaller craft can be faster but all depends on how much different they are. Just take some specific boats and do the math, then compare the results to manufacturers information about the speed.. Remember to take only half of the displacement when counting cats..

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### oldsailor7Senior Member

So far all that has been posted in this thread is irrelevant.

The limiting speed for monohulls is governed by their wave making properties.
Their high displacement and low waterline beam/length ratio causes a bow and stern wave pattern which --to put it simply, locks the hull in a trough between the two waves which it can't climb out of.. As a result, in boats of this hull type the longer a boat is the faster is its limiting hull speed.

Thus, as a rule of thumb, big monohulls are faster than smaller monohulls.

Edmund Bruce, in the 1960's, had the UK national tank testing facilities at his disposal. He extensively researched hull L/B ratios.

He found that at high L/B ratios the wave making effect was reduced and at about 8/1 L/B the wave making phenomina was greatly reduced. Above 11/1 it virtually disappeared and the limiting hull speed with it.

However there was a downside.

Long narrow hulls can't carry as much weight as fatter hulls unless their draught increases. That increases the wetted surface, and thus drag. The answer is of course to keep the boat light.
Impossible in the average monohull with its heavy keel, (typically half of the total displacement.)

Enter the Multihull.

This type of sailboat is lighter, by way of replacing STABILITY BY WEIGHT, with STABILITY BY BOUANCY.

Also the weight can be distributed between two ---or three hulls.

For cruising multis, which have to carry more "Stuff" an L/B ratio of 8/1 is good, and because the wetted surface is reduced, they have improved light airs performance.

For racing multi's much experimentation has been done with L/B ratios up to 20/1. However the law of diminishing returns comes into effect here and such boats, like the Tornado for instance have to be very light to get their screaming speed. However super light cats capsize too easily unless their overall beam is increased, which in it's self can bring on other problems.

The best compromise for performance seems to be between light weight, good hull shape (form drag), and an L/B ratio of around 11/1.

Given these parameters, which have killed the Wavemaking Dragon, it is a fact that well designed SMALL multihulls can go just as fast as BIG multihulls------------just so much as they have same Bruce Numbers.

Which is another story altogether.

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### Capn MudJunior Member

Small multi-hull speed

Oldsailor,

If you had told me that prior to last Saturday I would not quite have believed you. What happened on Saturday? I took my new Weta trimaran out on the bay and hit over 12 knots in what seemed to be 10 to 12 knots of breeze (maybe a bit more in gusts - I didnt have an anemometer with me).

What I do know for sure is that my F27 wouldn't have acheived anything like the same top speed in that wind.

Interestingly this isnt reflected exactly by the Texel Ratings refer http://boatdesign.net/forums/showthread.php?t=21565&page=21 which seems to show:
where lower is better.

However perhaps the Texel spreadsheet may assist to give a first pass estimate of which of Randy's catamarans would be faster? Plug in the numbers in the spreadseet randy and see what comes out.

(And before someone shoots me down - I dont claim to be an expert on this - all I know is that it is amodified version of the Texel formula that has been used to develop the OMR - Offshore Multihull Rating - handicapping system)

Cheers,
Andrew

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### oldsailor7Senior Member

Congratulations Andrew. Now you have proved it to yourself by first hand experience.

IE:- Suck it and See.

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### Capn MudJunior Member

Suck and See

I used to know a guy who lisped and his Ss sounded like Fs....

We were always trying to get him to say that

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### oldsailor7Senior Member

Lol.

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### RHoughRetro Dude

How is the Bruce number calculated?

Would a 45 foot multi be as fast as a 90 foot multi?

I'm obviously looking to understand the new boats for the America's Cup, a sloop rigged boat can be anywhere between 44 and 90 feet LWL. If a 44 foot boat with a higher/lower Bruce number would be as fast or faster, why build bigger?

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### RHoughRetro Dude

Okay ... I did my own homework ... the Bruce number is just another SA-D ratio. I'm not ready to buy that a 45 boat with the same SA-D will be as fast as a 90 foot boat.

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### oldsailor7Senior Member

Exactly. :?:

The Bruce Number is only a rule of thumb, all be it a good one.

Other factors come into it---like for instance the ability of the bigger boat to handle rough water better and also that the taller rig is operating higher up in the wind gradient.

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### Richard WoodsWoods Designs

Take a model yacht 1ft long weight 1lb, 2 sqft of sail area. What is its Bruce Number???

Will it be as fast as a 90ft boat????

The original F40 multihulls were scaled up Tornados (2 x length, 8 times weight and 4 times SA)

It will indeed be interesting to see if a 130ft tri can beat a 90ft cat MATCH RACING.

The last UK America's Cup boat failed BECAUSE IT COULDN'T SAIL BACKWARDS VERY WELL

If you've ever done any match racing (I have and also lots of team racing) you'll know pure speed has nothing to do with winning a match race.

Just a thought

Richard Woods of Woods Designs

www.sailingcatamarans.com

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