# Strip theory on Catamarans.

Discussion in 'Hydrodynamics and Aerodynamics' started by tea_floss, Apr 24, 2017.

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### tea_flossJunior Member

If I use Strip theory (maxsurf) to calculate catamarans coupled have and pitch, in head seas. will heave and pitch equation change?

Or just calculate added mass and restoring coefficients for one demihull and multiple by two?

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If you work out the WPA Inertia of a monohull..and multiply by 2..will it be the same as a catamaran..if not why not?

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### gonzoSenior Member

I think there is a new variable introduced, because the waves won't act simultaneously on both hulls.

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### tspeerSenior Member

First of all, is this a power catamaran or a sailing catamaran? One reason for the distinction is a sailing catamaran's demihulls are not loaded the same, so the boat is effectively asymmetric. This means you won't have two three-degree-of-freedom equations, but you'll need to treat the problem as a single six-degree-of-freedom problem.

I don't know about Maxsurf, but attached are my notes showing how I was intending to attack the problem of adapting a monohull seakeeping program to handling multihulls. My first assumption was the hulls were spaced widely enough that they didn't interact hydrodynamically with each other, so the coefficients could be calculated for each demihull separately, using conventional strip theory. Then the coefficients were transformed from the demihull reference centers to the ship reference center. The transformed coefficients could then be summed to generate the coefficients for the whole ship. Once the ship-based coefficients were calculated, then the equations of motion could be solved in the same manner as for a monohull.

There are actually two problems that are superimposed. One is the motion of a disturbed ship on a flat sea. This is taken care of by the transformation process. For example roll motion about the ship center results in both heave and roll motion for a demihull. (It is precisely this coupling between heave and angular motion that is the whole motivation for creating a multihull in the first place.)

The second problem are the forces and moments on a nonmoving ship due to the incident waves that provide the excitation for the motion. For a catamaran, the demihull excitation occurs at different phases of the incident waves, for all angles except sailing straight into a regular sea. So although the forces and moments of the wave acting on a demihull are similar to the monohull case, the catamaran has to take into account the phase difference in the excitation.

My notes are pretty cryptic, but I hope you can follow the development. I can post the Mathcad file if that would be of use to you.

#### Attached Files:

• ###### Transformh.doc
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### tspeerSenior Member

Actually, now that I read your question more carefully, I see that you have restricted it to just the headsea problem. In that case, I believe the answer is, "Yes."

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Tim

This is far too simplistic. A monohull, in terms of its hull shape and thus, what it is ‘designed’ to do, is very different hull form from that of a catamaran - this gives very different hull form coeff’s of a mono and a cat. A monohull will have more beam for example, simply to gain the stability it needs, in terms of statical stability. Thus very clearly the waterplane area (WPA) of a cat is not a simple equivalent mono times two. Ergo, since the WPA is not simply 2 x, the heaving will be very different as the heave period is proportional to the WPA, thus the damping will be different, i.e., not twice! Similarly the added mass owing to the difference in hull shapes between a cat and mono, the inertial force is not simply twice that of the mono – the hull shape also influences the added mass.

The interaction between two hulls is also significant. Assuming that the hulls are spaced far enough apart shall provide misleading results because of this too. Strip theory, if I recall correctly, assumes no flow interaction – which is clearly the case with a cat.

So the heave and pitching for a mono and a cat is not simply an order of magnitude of 2.

Thus, unfortunately, it is not a simple linear relationship between the coeff’s, in all terms. As a basic first hit – it may offer some guidance, but I wouldn’t go any further than that. Seakeeping is terribly complex.

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### tea_flossJunior Member

@Ad Hoc @Gonzo and @tspeer Thank you for your response and time. It is different for multihulls. More on this, in "Theoretical Manual SEAWAY" - Page 263. Here is the

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### gonzoSenior Member

Thanks for the link. Is there a correction equation for the interaction between hulls?

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### oataruJunior Member

In head seas, interactions between the demihulls are small and only occur at quite low Froude numbers, for catamarans where the demihull spacing is small.
However, note that the strip theory ignores the effects of overhangs and non-wall sidedness. In case of catamaran, such effect could significantly present on inboard sides of demihull.
Neglecting the above effects, I think the answer to your specific question is YES; demihull x 2 [but, not monohull x 2 as already pointed out by Ad Hoc above.]

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