# Metacentric Height of Multi-Hull Vessel

Discussion in 'Stability' started by Rounak Saha Niloy, Sep 8, 2022.

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### Rounak Saha NiloyJunior Member

What should be the range of metacentric height for catamaran and trimaran passenger ships? I know, GM should be greater than 0.15. But what is the maximum permissible GM for a passenger catamaran/trimaran?

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### bajansailorMarine Surveyor

How big are these multihull passenger ships?

I think that pretty much any multihull will have a GM much greater than 0.15 (I presume you are talking metres here?).
Usually the area of concern is a minimum GM, not a maximum.

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### jehardimanSenior Member

Generally, for human factors, you want a roll period between approximately 10 and 12 sec for a passenger vessel. You do not want to exceed 0.1g lateral and 0.2g vertical at the most extreme operator/passenger location.
The still water roll period is T=(2*pi*K)/(g*GM) where T is the period and K is the radius of gyration.
For calculation of vertical and lateral g loads anywhere in the vessel, see MIL-STD 1399, Section 301a.

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Depending upon the type and size of catamaran, but as a ROM guide, anything from 5 to 50m...

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Hi Niloy,
If you have access to some basic information of the vessel, I am pretty sure that you can calculate the value of maximum GM for your project within engineering accuracy, say +/- 10%. Let me explain it in the following:

GM = (KB + BM) - KG

If you know the demi-hull dimensions (L, B) and draft (T), you can get the KB value and vessel displacement. By knowing the demi-hull spacing and with the dimensions (L, B) you can roughly calculate the water plane inertia I, and BM=I/disp. The only thing that will be left is KG. You can consider the vertical centre of gravity of the catamaran on it's deck. However, as you are interested in the maximum value of GM (require lower KG), you can consider this value on the water plane. This is how you can get the max GM for your vessel.

Now, let us look into the problem from crew/passenger comfort angle. If GM is very high (as of now we do not know how high is very high!) then the vessel will be very stiff and it will try to be upright too quickly when subjected by any external force, for example, wind, wave, passenger heeling etc. Thus, to my understanding, if you can calculate the roll period of the vessel, Tn4 = 2*pi*sqrt((mass + added mass)/stiffness) you shall be able to see something useful. Although, calculating added mass requires vessel information and access to a PF (potential flow) solver.

Cheers!

Last edited: Jan 13, 2023
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