Hi Jake,
First let's review a little bit.
Using the Tornado Sport as a chinning bar, to have equal speed in light winds a boat,X, must have equal sail area to weight ratio than the TS. That means if boat X is heavier than the TS by 10%, for example, then boat X must have 10% more sail area than a TS just to be equal in sail area to weight ratio or power to weight ratio. The highest performance way of adding sail area for sailing to windward is to add mast height and increase sail aspect ratio at the same time as the sail area increase. Let's say this results in boat X having a mast 10% taller mast than the TS. The centerboard area on boat X needs to go up by 10% also to keep the sail area to centerboard area in balance. Now we have boat X powered up to the same sail area to weight ratio as the TS and it took a 10% increase in sail area, mast height and centerboard area to get there with no further increase in weight.
Now let's look at the righting moment situation. The TS with a 10 ft beam has 6100 ftlbs of righting moment and 251 sqft of sail area for a righting moment to sail area ratio of 24.3. Now we want boat X to have at least an equal righting moment to sail area ratio as the TS so it will have equal speed when the wind blows over 12-15 knots. Boat X has 10% more sail area than the TS, therefore its max righting moment must be 1.1x6100 = 6710 ft lbs. If boat X is 8.5ft wide and the compliment in righting moment is gained with wings, then the wings must be an additional 3.6 ft outboard of the hulls and not weigh anything. So at this point boat X, which is 10% heavier than a TS, must have 10% more sail area, 10% taller mast and 10% more centerboard area and also have 3.6 ft wide wings on each side to be competitive with the TS in 'all' wind conditions. Now we have a boat X that might stand a chance of being competitve with the TS.
So how about the pitchpole tendency of boat X??? Boat X has 10% more sail area than the TS and that sail area is 10% higher above the center of bouyancy than the TS. Is it more prone to pitchpole than the TS???
First let's understand pitchpole. Two criteria must be met before pitchpole can occurr. 1) The pitching moment from the forward component of the sail force must be equal to than the restoring moment from the hulls. This is called 'verge of pitchpole'. 2) A very sudden and abrupt increase in hull drag occurrs and trips the boat and makes the boat rotate in a violent forward cartwheeling motion, sterns over bows. When this happens, we sailors call this pitchpole. This very sudden and abrupt increase in hull drag occurrs when the fore deck goes underwater and the sleek bow that was splitting the water becomes very blunt as the foredeck becomes the bow and parts the water. The cartwheeling motion of pitchpole is a result of the the conservation of momentum, Physics again. The boat system mass times velocity of translation is converted into rotational momentum, mass times rotational velocity. This can only occurr when criteria #1 and #2 are met. Now let's go back and look at criteria #1 again.
Boat X has 10% more sail area and that sail area is 10% higher above the center of bouyancy in the hulls. This tells us that boat X has 21% more max pitching moment than the TS. This is pro pitchpole for boat X. Now let's look at the max restoring moment of boat X relative to the TS. The restoring moment is the sum of the platform restoring moment plus the people restoring moment. The restoring moment, in general, is equal the the weight times the distance from that weight to the center of bouyancy in the hull. Now the boat naturally tries to resist pitchpole. As the forward component of sail thrust increases, the resulting moment forces the bows down and this makes the center of bouyancy migrate forward in the hull and increase the distance between the center of bouyancy and the weight, platform and people. This is an automatic increase in restoring moment. If boats were long enough and bows were tall enough, catamarans would never pitchpole. (Look what they did to Playstation's bows.) Back to boat X and the TS: Let's assume that boat X and the TS have similiar bow heights, therefore both boats, hull shapes, can make the center of bouyancy migrate the same distance forward toward the bows. If the rigs, main beams, on both boats are at the same fore and aft location along the hull, 10 ft for example, then it is likely that the center of gravity of the two platforms are in the same place. Now remember that boat X is 10% heavier. This means that boat X has 10% more platform restoring moment, platform weight times distance from the center of bouyancy to the platform center of gravity, than the TS. This is more pitchpole resistance for boat X. Now let's consider the people restoring moment. At the verge of pitchpole the sailors are usually as far aft as they can possibly get on the boat. Let's assume that the sailors are at the same aft position. Since the centers of bouyance of these two boats are equally forward at verge of pitchpole, the restoring moments, people weight times distance from center of bouyancy to their center of gravity, are equal.
So in summary on the pitchpole question we can say that boat X has 21% more max pitching moment due to the larger sailplan and 10% more restoring moment due to its heavier platform which is only 3% in total restoring moment. Therefore Boat X has an 18% greater tendency to pitchpole than the TS. Another way to put it is to say that boat X will pitchpole with 18% less forward component sail thrust than the TS.
Bill
PS Jake, there is alot more to this which I will get into another time.