Actually, it is not so difficult to understand, I'll try to keep it simple.

Assume the fulcrum of rotation is in the middle of the hull, this results in each small volume of floation to get an increased leverage of 6.5 %. That is your first gain.

But there is more. Giving a 3.90 mtr hull a down sloping angle of say 1 degree puts 6.5% more volume below the waterline then the 3.66 mtr hull. Why because rotating a 6.5% longer lever through the same angle results in its tip reaching 6.5 mtr lower. So at each stage along the hull 6.5% more volume is pressed into action.

This is a magnifying effect. => we now have more volume displaced for a given dive angle, which results in a large restoring force that ALSO acts on a longer leverage. 106.5% * 106.5% = 113.4% gain so far.

Note that this gain already allows us to carry 7.0 * 113.4% = 7.94 sq. mtr. of sail area for the same dive feel. That is a whole square meter more sail area.

I'm not sure if I should proceed with the other magnifying effects, it will get detailed and the general feel for the causes has been established already. Suffice to say that by this increase in power one can widen the hulls a little bit ansd still be faster with the 7.94 sq. mtr. rig. These increases will again improve dive resistance so that we can again allow the sail area to be entlarged (and the mast length with it). This trade-off is so favourable that the increase in sail area is so much larger then the invested increases in drag that the boat becomes faster with each additional increase in hull length not because of waterline length increases but because the max size sail that can be carried increases disproportionally.

This is a commonly accepted principle in sail yacht design. Large yachts can carry disproportionally larger sized rigs. Disproportionally meaning that say a hull length increase of say 6.5 % allows 20% more "sail-area-times-mast-length" when keeping the same dive resistance ratio to be carried (a third power dependency). Of course the opposite effect also applies, meaning when you reduce hull length.

Note how a F18 at 5.52 mtr hull length and 21.15 sq. mtr. sailarea roughly coincides with a 7.00 sq. mtr. sail on a 3.75 mtr F12 when applying this 3rd power law ?

7.00/21.15 = 0.33 = almost = 0.31 = (3.75/5.52)^3

If you do the same to the US I-20 and the F12 you see the numbers match up quite well again. Same if you do the F18 to US I-20 etc. So this law does indeed predict a very large portion of the differences in sail area from one design to another. It is actually strongs dependencies like this one that make the measurement system based handicap systems work, even though none of these rules were used in the creation of these systems ! But that is a whole different topic.

Now a 3rd power relationship is quite strong, it is the same as increases in enclosed volume when you entlarge a fluid container. Scaling up a bottle in every direction by a factor of 2 will increase it contents by a factor of 8.

I hope this clear enough.

It was also one of the laws that allowed me to quite accurately predict the F16 and F14 performances in relation the F18 design before prototypes of both had been sailed alot. In the F16 case it told me what kind of potential the Taipan design truly had. Remember back in early 2001 there was not much Taipan to F18 race data at all to do a statistic race data analysis of the same accuracy.

Just more useless mathematics I guess !

Wouter