QUESTION: So what's the situation re Diagonal Stability on multihulls?
This is somewhat complex to evaluate in finite terms, but lets take a look at the issues that affect it step by step.
Let's first clarify some assumptions. As a starting point, let's assume the sails are paid off so that the mean force from them is coming from a point approximately abreast of the mast and directed about 45 degree angle, 'NW' of that position (assume in plan view, that the bow is North and the wind is from the East). This would cause both a heeling and a pitching force, as it acts on a sail some 40% up, some distance above the water. At the assumed 45 degrees, both the forward and athwartship components of that force would be equal and each about 70% of the total force. Now the greater beam the boat has, the greater driving force it can support, and as the two force components are equal (in the case considered), the greater the forward pitching force would be.
This forward pitching force would be resisted by what we term 'the inertia of the waterplane area', which is effectively calculated by taking small areas of waterplane at different positions along the length of the ama or cat hull and multiplying each of them by their distance from the center of the whole waterplane area (cwp). So, the more wp area up front OR the longer the hull, the greater will be the waterplane inertia (summation of these multiplied areas), so it will be more able to resist the forward pitching.
Lengthening an existing cat for example, will increase the wp inertia and give more resistance to pitching or diving. If one could increase the beam, then the driving force that the boat could resist would be higher, but the pitching force would then also be raised.
Overall size and weight also plays a important part in deciding proportions. If the boat is light and the beam relatively low, then stability can be increased by lengthening the outer hulls. This will also add longitudinal stability too and such a boat will capsize athwartship far more easily that pitch-poling forward. (The unique Gougeon G32 is a cat of such configuration and even with water ballast, it was never that stable). Lengthening hulls is not as effective for heeling resistance as adding to the beam. In fact for a cat of ~25', it would require about 3 ft extra length, to give the equivalent heeling resistance of 12" more overall beam.
The balance between the two tendencies, has been found from experience to be roughly when a catamaran has a length of double its beam. A tri can accept a greater beam, because its main central hull is also providing resistance to pitchpoling (assuming it's still in the water!). With some sailing care and extra buoyancy forward, a multihull can accept the higher transverse force of larger beam and therefore be faster. Race boats have since demonstrated that too.
Articles have been written about boats being improved by lengthening and this has been tied to their improved diagonal stability. But there are several other factors at play here. Such boats will have higher speed potential from the added length and the improved slimness ratio (L/b). In fact their transverse stability will also increase and that means their ability to carry sail will go up too. That also means a higher potential force to cause pitch poling, but then, the longer hulls will be better able to resist it. The longer the hulls in the water, the higher the wp inertia and the more effective will be the buoyancy in their ends to resist pitch poling.
For boats designed to sail on two hulls, it's not actually that critical which hull is lengthened. In fact, lengthening the fattest one can easily be justified for speed, and the record-breaking Sodeb'O is just one example with a centre hull of 32 m (105') and amas about 20% shorter at the bow. However, smaller multihulls with more potential (or risk) to sail on one hull and therefore looking for more pitching resistance, generally (and should) have amas coming level with the bow and I anticipate it will not be long before some amas go even beyond the main hull, particularly for light 'flying' boats under 30'. This will not apply to the smaller day-sailing tris that have amas of relatively low buoyancy. These ultimately get pressed under and the longitudinal stability remaining comes mainly from the central hull. Their diagonal staability is quite seriously compromised in such a case and they will be more vulnerable to pitch-poling when their short ama is driven under.
As boats get longer, lighter and faster, the length of amas becomes very much a strength issue. Although beyond the scope of this article, let me just mention that for boats over about 50 ft, the slenderness of even 200% buoyancy amas makes their vulnerability to being snapped off like a pretzel stick, a real possibility. High strength, very stiff laminates of carbon fiber and lightweight core are brittle and therefore prone to this and sometimes these long amas have been designed too much like vertical beams (for pounding etc) with their sides lacking strong material in way of the forward aka to take rogue side waves that can be brutal on such a long cantilever. So, barring the installation of a McDonald's golden arch to the main hull, the better choice for really long tris, could be to let the main hull, whose cross section is much larger, take more of the longitudinal strength and shorten the ama to a point that it's no more vulnerably than the main hull—a fine balancing act that the Sodeb'O design seems to have achieved. As I hope I have pointed out, this is far less of a factor on smaller boats where the cross section of their amas are proportionally much higher than for the super light racing machines, compared to possible loading".
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