What are the factors involved in the capsize of catamarans
John Shuttleworth covered that in a talk available on his web site, complete with equations:
Considerations for Seaworthiness https://shuttleworthdesign.com/NESTalk.html
The equations are:
Terms of these equations ordered by what makes capsize more or less likely, and what you can control, with my comments in brackets.
What contributes to capsize:
- Ei = energy transferred during impact. (Can be controlled by limiting impact moment and increasing roll moments of inertia)
- Mi = impact moment (some of the terms contributing to impact moment, in the second equation, can be controlled by either the designer or the skipper)
- A = area of hull superstructure
- Cd= coefficient of drag of hull superstructure.
- r = impact moment lever.
- vi = velocity of impact (mostly out of your control, except to the extent that you can let the boat skid sideways)
What resists capsize:
- Ir = roll moment of inertia of the boat
- Ia = inertia of water entrained by the hull (known as added mass)
What is out of your control:
- t = time
- d = density of seawater
Considering the factors involved, how would you mitigate the effect of each factor?
If you design from scratch to resist wave-induced capsize, minimise the area and drag to sideways impact of the weather hull, maximise the rotational inertia, and fiddle with the impact moment lever by controlling the direction of the force of impact. The easiest way to do so, without having to deploy devices like a Jordan series drogue to increase the inertia of entrained water, would be a very wide Pacific proa (because rotational inertia increases with the square of the distance of mass from the point of rotation) with an ama that barely floats (small area for its mass) or is even dense enough when flooded to be submerged at rest, to that it is below where breaking crests impact. It can't have any impact drag if the impact passes by above it. Wind drag on the rig and leeward hull would still prevent windward capsize. A lowered Bruce foil or L-shaped foil to windward would increase entrained mass, but resists sideways movement and needs to be assessed for how it changes the impact moment.
If you have a catamaran, choose a hull shape that deflects impacting water up and over the boat, rather than deflecting down and lifting the windward hull (the force of the impact is a vector, and its direction determines the impact moment lever). Install mass that is fixed to the boat in the hulls, not the bridgedeck. Moveable mass goes into the windward hull.
So a catamaran designed to minimise the effects of wave impact might have hulls with very low freeboard for much of their length (to reduce impact drag), rising up at the ends for longitudinal stability. Where you need accommodation in the centre, the outside of each hull would have tumblehome above the waterline to deflect breaking crests up and over the boat. The hulls can flare out on the inside, because the lee hull being lifted by an impact is not a problem. Or have high freeboard and outside tumblehome across the whole length. But keep the hulls wide and shallow so the boat can slip sideways, reducing impact velocity a bit.
Disclaimer: I haven't tested any of this, I am not a naval architect, but my advice is absolutely free and worth every penny you pay for it.
