# Catamaran Speed

Discussion in 'Boat Design' started by Deering, Jul 20, 2012.

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### DeeringSenior Member

I'm trying to understand how a displacement catamaran can seemingly violate the Froude's Law.

All boats create a transverse wave, which is perpendicular to direction of travel. That wave is a function of the waterline length of the hull and the speed of the boat. Froude identified the wave and the mathematics associated with it back in the 1800's.

Once the boat speed reaches the wavelength of the transverse wave, the hull is stuck in the 'trough' between two wave peaks, and the boat is perpetually trying to climb out of that trough. Adding more power (for a displacement monohull) is futile at a certain point.

Why is it that catamarans (and other slender boats) can seemingly defy Froude's Law? They create transverse waves too. And those waves are a function of length and speed - the physics still apply. So how can catamarans climb out of that trough?

I understand that it's a function of displacement and hull slenderness, and I assume that the wave height a catamaran generates is much lower than a monohull's, but can someone explain the theoretical underpinnings of it?

Many thanks.

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### Mr EfficiencySenior Member

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### DeeringSenior Member

Not really. What are the theoretical underpinnings for that? You know, math and the like.

4. ### FrostyPrevious Member

Ive never been one to accept the application of maths to the movement and actions of water to varying hull shapes.

I think thats why they use so much tank testing as would I.

I think this can be eloquently put when architects seem delighted when a new built vessel attains the speed designed. Why such a surprise?

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Firstly, you need to understand what you mean by Froude's law. (It is not a law by the way). Thus if you define it, as you understand it, what does it say?

A boat is not "stuck" between the waves as you put it. Since define what you mean by a boat to be stuck?

There is no universal rule that covers all, from low speed to high speed. However, there are "rules" that define how we understand the behaviour at different speeds and then, how we can interpret this to understnd the mechanisms at play.

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### DeeringSenior Member

OK, not a 'Law'. Here's what I think I understand:

Basic wave theory says that the wavelength of the transverse wave is: 2*pi*V^2/g

At a certain hull velocity, the hull length equals the wavelength. As velocity increases, the crest of the bow wave is in front of the bow, and the stern is settling into the trough between the crests. The bow is trying to climb up the face of a wave that gets steeper as more power is applied. At some point adding more power becomes futile and results in little increased velocity.

As the speed-length ratio gets larger, much above 1.4, the resistance increases dramatically. Or at least that's what I'm reading.

So how can a 40 ft (OK, 13m) catamaran run efficiently above 10 kts?

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### Mr EfficiencySenior Member

Needless to say the Polynesians didn't worry their heads about the theory, but they found that slim hulls with fine entry don't push up the sort of transverse wave amplitude that creates the barrier you speak of.

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### DeeringSenior Member

Probably not. But they weren't running 25 kts either.

Look, this is the boat DESIGN.net Design, as I understand it, involves understanding some fundamental principles and applying them to new problems. If we fail to do that, we don't progress much beyond log hulls, as efficient as they may have been for the Polynesians.

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### Mr EfficiencySenior Member

I don't know how fast the Polynesians were going, but they amazed old Capn. Cook. Ad Hoc is your man, he's a catamaran expert.

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### yipsterdesigner

you may also try leo-lazauskas MICHLET

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### FAST FREDSenior Member

"As the speed-length ratio gets larger, much above 1.4, the resistance increases dramatically. Or at least that's what I'm reading."

That is fine for a fat boat with a 3-1 length to WL beam ratio.(L/B)

Once you get over 6-1 L/B or better 8-1 L/B the bow wave is so small that the resistance does not go anywhere as high.

So the multi-hull.

The problem is then that skinny hulls don't carry much weight , so the boat will need to either be lighter , or longer , to carry the same load.

At speed the fat boat uses most of its energy pushing water aside as it makes a failed attempt to climb its own bow wave.

The skinny boat tops out when you run out of HP to pay for the skin friction.

Want to go fast? climb out of the water (plaining boat) , but that's not cheap either

FF

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### yipsterdesigner

yet if you want to stay in the water and sacrifice on speed but want to pass a fround nr and save on fuel
Fiona Sinclair made a basic calculator that nicely shows how wave resistance rises over viscious with speed
was once working as java aplet online but cant upload here as such so here the remains i saved in zip, still working!
start HULL RESISTANCE CALCULATOR press calculate button, modify hull, enter datas (as for example weight) etc and watch the graphs when changing these variables

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### philSweetSenior Member

Deering.

The most famous bit of theory/math on the subject is discussed here in a paper by Tuck.
The math is gnarly, though. The discussion gives some good insight into the relative importance of beam, thinness, and slenderness.

link won't stick. I don't know why. Google the following--- the wave resistance formula of J. H. Michell.

Last edited: Jul 27, 2012
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### yipsterdesigner

hi phil, want to check that link ?
i get: File not available. [S0334270000006329a.pdf] time=1342878891 [eopocc=1342883607]

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### AlikSenior Member

This question is too general and can not be answered separately from design task.

One should understand that cat is designed to have its own weight and to carry certain payload at specified speed. Having done these (not in optimistic manner as it is done for some 'ultralight attractive designs'), one needs to choose proper demihull shape and spacing for efficiency. Here on the picture is some insight: we compare round bilge shapes with chine shapes, for different relative lengths l=LWL/V^0.333, where V is volume displacement in m^3; LWL is waterline length in m. Horizontal axis is volumetric Froude number FnV; vertical axis is resistance R. One can note that for lighter cats displacement shapes keep being efficient at higher Froude numbers.

Designer can also play with other parameters and shape features depending on tools he has. Beam of hull should be at least enough to fit the engine

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