What if it is a catamaran?

I have been reading Gerr's "Nature of Boats" to learn how to design a rather simple and small pontoon/catamaran. I am beginning to understand the major concepts. But, how do I figure out center of gravity/buoyancy, speed to length ratio, trim, et cetera when I have two identical hulls connected by a platform?

Dan

*Note: I am making a "camping boat" and decided upon a pontoon/catamaram because I thought it would give me the largest flat surface on which I pitch a tent with the smallest overall size. I also thought the initial stability would be good since I will frequently move about the deck either while at slow speeds (6-8 kts) or while not moving at all. If my reasoning is flawed, i.e. a different shape boat would work better for my purposes, please advise.

 

You figure out the center of gravity/buoyancy in exactly the same way as if it were a monohull, i.e. by finding the weight and center of gravity of all the parts that go into your boat and use them to establish the total center of gravity. The center of buoyancy will be exactly above or - most likely - beneath the center of gravity.
The total weight will be divided between the two hulls, so they should displace half of the total displacement each.
The same goes for all the other factors except the speed to length ratio, but you can forget about that one, because it's not really important in your case.

 

In part, it depends on the tools you have available. You can include both hulls in your section shape, pretending you have one hull that humps up in the middle. But many programs can't handle multiply connected sections.

If you can readily generate the hydrostatics for one hull, then make a table of displacement and longitudinal center of buoyancy as a function of sinkage and pitch trim, going all the way from zero displacement to fully submerged. The heel angles of interest for most catamarans are small, so you can get away with just using zero heel.

Now construct tables for the whole craft that is a function of sinkage, pitch trim, and heel trim. As the craft rolls about a given reference center (say, on the centerline, midship, at the design waterplane), each hull will move in heave proportional to its distance from the centerline. After all, this is the whole point of a multihull! The center of buoyancy will move fore and aft and side to side when any of sinkage, pitch, or heel varies. So you need whole-craft tables for buoyancy, longitudinal cb and lateral cb.

For a given height of the reference center, you go into your hull table with the appropriate heave for the heel angle, and interpolate the buoyancy and center of buoyancy for each hull. Add the buoyancies to get the total buoyancy. Multiply each hull buoyancy by its center of buoyancy to get the pitch moment, and by the distance from the centerline to get the roll moment. Add the moments together and divide by the total buoyancy to get the longitudinal and lateral location of the center of buoyancy.

Finally, interpolate the tables for the whole craft buoyancy to get the sinkage at the desired pitch and heel angle. Then use the same interpolation factor to get the longitudinal and lateral location of the center of buoyancy.

This can all be done in a spreadsheet. Since you have a catamaran, you only need to construct one hull table. A trimaran would need separate tables for vaca and ama.

Ultimately, you can produce a "multihull footprint" plot like this:

The blue lines show the location of the center of buoyancy, calculated by the process above. The black lines show the effective c.g. location of the applied load. For this sailing trimaran, the loads come from the sail rig, and their effective c.g. was calculated by dividing the aerodynamic pitch and roll moments by the total buoyancy.

In your case the applied load is the cargo and passengers moving about the deck. The footprint plot will show the initial stability very well. Capsize occurs when the displacement of one hull goes to zero, or when the center of buoyancy reaches one hull on the footprint plot. The tables will allow you to establish some margin (say, a minimum hull displacement) and figure out the limits for loading the craft to stay within those limits.