>>Fineness Ratio: Hull fineness ratio is simply LWL divided by max hull width at the waterline. The equation in many books for the hull speed limit of a displacement hull is:
Vel max = 1.4 X sqrtLWL. This equation seems to work for keelboat monohulls that have a hull fineness ratio of around 4:1 or so. In this form it sure doesn't work for beach cats. What I have found is that for displacement hulls the 1.4 coefficient varies with hull fineness ratio. For beach cats this coefficient varies between 4 and 5 depending on hull design.

This formula of Vel max = 1.4 X sqrtLWL is directly derived from the Froude law and make a link between the wave length of the created (bow - stern) wave system and the waterline length of a given hull.

This formula givens the speed at which a given length hull needs to travell throught the water in order to have a single wave spanned along it hulls. With a crest at its bow and a crest at it stern.

In heavy vessels this wave system is a huge boundery as drag suddenly increases rapid at this speed and hardly any engine and no sailing rig is powerfull enough to overcome this rapid increase in drag.

Please note here that the factor of 1.4 (in this form of the formula) is a constant determined by the way waves on a water surface behaves. It has a very clear physical interpretation, A free wave travelling at the given speed has the same wavelength as the hull waterline length. The adjusted factor of 4 to 5 HAS NOT. This adjusted factor is nothing more than an imaginairy factor that someone dreamed up to make the froudes law useable for situations where it really doesn't apply. Such a case are catamarans. What has been done is that the end result has been determined and a factor is calculated from that that gives this end result at a given speed. This is a circular reasoning.

In catamaran design the situation that Froudes law describes (wavelength of bow-stern wave = waterlinelength) is found at the speed which the formula Vel max = 1.4 X sqrtLWL gives. However because of the special qualities of the catamaran design (maily very light weight) this wave system is much much much less significant from a overall drag point of view. In fact the drag is there (make no mistake about that) but it's magnitude so small in comparison to the other forms of drag on a catamaran design that its effects are not noticed on cats. Cats simply power through into the force mode state and continue to accellerate much longer till they reach much higher speeds where the other forms drag have grown to such a magnitude that they are big enough to stop further acceleration.

Simply put adjusting froudes law to cats is useless. Froudes law works very well in heavy displacement vessel (Heavy crusing cat design MAY be included here) but in general it is misapplied in light weight vessels like sport cats and some navy ships. Continiously adjusting the factor to make the formula work is fooling oneself.

Bills eaxmple is correct with the excepting that bill doesn't account for the reduction in overall drag due to the same reduction in weight.

The following statement

>> The boat is 130 pounds lighter than a Tornado so the platform righting moment is well down from the Tornado, like 40% less.

is simply misleading.

It the combination of Platform and CREW that is important here and not the platfrom alone. When looking at this combo the righting moment has only been reduced by 13 % and not 40 %.

See the math (in SI units) ; assumption centre of effort of the crew id 1 mtr (3 ft) up from their feet.

Tornado + 150 kg crew : 170 kg's * 1/2 * 3.0 mtr. + 150 kg * (3 + 1) mtr = 855
Lightweight Tornado + 150 kg crew 170 - 60) kg's * 1/2 * 2,9 mtr. + 150 * ( 2,9 + 1) = 744,5

744,5 / 855 = 87, 1 %

Wouter