Stability Considerations Part 1
This series of articles is based on a lecture I gave a few years ago at a MOCRA symposium. For simplicity I write about catamarans, but most is also relevant to trimaran stability.
When I was a student studying electronics at London University I had a maths lecturer who used to write a lot of gibberish on the blackboard and then say "clearly it is obvious that" or worse "well that's straightforward I needn't bother to explain it" One reason for the apparent gibberish is that to save time and space mathematicians use simple symbols or letters to describe more complex ideas (perhaps the best known simple equation is E=mc2 which sums up the whole universe in five symbols). If you don't know the code you can't read the equation so first I will try and explain the code for stability before going into the specifics. I am afraid, as in life, it gets harder as I go along, so if you are confused at first you'll be baffled at the end. Take it slow, print out this article and then read it at your leisure.
So lets start simply.
Well, as you can see, that's straightforward, I needn't bother to explain it! Seriously, generally in science people observe the world and then try and explain it. Even Adam and Eve knew fruit fell from trees, but it was only 300 years ago that someone worked out why. We know that multihulls are very stable, but explaining why they don't capsize is actually quite hard. At its most basic, stability is like a see saw, balancing the forces of the wind trying to turn the boat over against the weight of the boat trying to keep it upright.
This is usually expressed as: HM = RM or: Heeling Forces = Righting Forces
Technically they are moments, but that sounds complicated so I'll carry on calling them forces. If heeling forces increase then the see saw becomes unbalanced and the see saw (or boat) tilts until a new equilibrium position is reached and the see saw stops moving. If it can't find a new stable equilibrium then one end of the see saw will hit the ground (or the boat capsizes)
Heeling forces are easy to understand as we all know we have to reef if there's too much wind. These heeling forces are dependant on three things: One sail area, two the height of the centre of effort (ie the height of the centre of the sails above the water). This equates to the length of the see saw lever. Three the speed of the wind. But because we are actually interested in the wind FORCE we need to know not the wind speed but the wind speed squared. I won't explain why, please just accept it. Similarly I won't explain how we decide how heavy the wind is, nor how much of the wind is pushing the boat along, and how much is pushing it over. In the trade they are called fiddle factors.(FF)
Now if we put all the above words into a formula we get:
HM = SA x Hce x Va x Va x FF
Now to stay stable these heeling forces have to be balanced by the righting forces. As on a see saw the righting force is a combination of weight and distance from the pivot point. On a catamaran the fulcrum (or pivot) is actually at the centre of buoyancy of the lee hull, but because the hulls are narrow compared to the overall beam we usually assume that the lever is the same as the hull centreline spacing and to simplify further we say all the weight is in the two hulls and ignore the mast and bridgedeck cabin. Similarly because most catamarans will fly a hull at under 15 degrees we can assume that we don't need to compensate for the angle of heel.
So putting all that in one formula we get:
RM = 0.5 x Disp x CL Spacing
And now we can combine the two (because the see saw must balance).
But kept as it is that's not very useful. What we want is to know when to reef, ie at what apparent wind speed should we reef.
So we have to fiddle around with the formula a bit more, but then we get:
Va = SQRT( (0.5 x D x Cl spacing)/(SA x Hce x FF)
This is the formula that explains in a few symbols all that I've written already and is a formula you may well have seen before, even if you did not know how it originated. As I said at the beginning, at first sight it looks complicated, but that's only because you don't know what the symbols mean.
In Part 2 I look at the concept of stability curves and why Hobie Cats can fly a hull safely yet narrow cruising catamarans cannot.