Stein,

Your comments are correct to the extent of what I've learned over time but I would like to make one comment :




This is a typical example of a statement that is so tortured because the original source wants to cling onto an orginal concept that is so obviously wrong (or misunderstood). In this case that the max hull speed myth.


There is no "fooling" or "assuming of longer waterline length". You can't "fool" a law of physics and neither does such a law "assume" anything. It is not an object with a information processing unit like a brain that can be "fooled".

The foundation of all this torture logic is the misunderstanding that Froude's law says anything about a hull. And indeed, I've have encountered many well educated persons who make this mistake as well while the way out of this situation is sooo obvious.



And now too all :

Again, Froude's law doesn't say anything about a given hull, it ONLY says something about the speed a given wave length travells across the watersurface for a given set of temperature, pressure and water density. That is all.

So why is the Froude formula referred to so often ? Because the pressure distribution around a hull travelling through the water is dependent on the wave system around it and therefor dependent on the wavelength of a wave system that is travelling along the hull at the SAME speed as the hull is travelling.

Obviously, a wave system with multiple crests along the hull will result in a rather symmetric pressure distribution. Such a situation leads to the lost energy (drag) incurred on the front part of the hull to be won back (drive) at the rear part. OFTEN, this leads to lower hull drag. When the hull starts to move faster then there will be fewer and fewer crests along the hull till the last crest moves behind the stern, resulting in a much more a-symmetric pressure situation along the hull where basically there are only pressures working against the movement of the hull (drag) left and there are no more positive pressured (drive) that recouperate some of the loses.

For very heavy boats like frighters and ballasted keel yachts the hull drag (excluding wetted surface drag) makes up a very large portion of the total drag, so when that component increases rapidly then it will quickly use up all available power (drive) from an engine or sails and thus stop accellerating. It will then have reached max. speed. Again for heavy craft this point happens to coincide often with a distanced travelled per second (=boatspeed) that is a fraction longer then the wavelength of the wave travelling alongside the hull (as caused by the bows and sterns). This leads to the misapplying of Froude's law as a formula to calculate max. (hull) speed for any given hull length. Of course for some situations (heavy boats - low power) this works rather well but for many others it is simply wrong. As in the past we only had "heavy-boats with lower power", people began to believe the errornous intepretation of Froude's law.

So what happens on a design like a beach cat ? Exactly the same as descibed above, with only one very important exception. The overal fraction of the hull drag in the total drag of a beach cat is MUCH smaller. For wave-inducing drag it is something like 10-15% of the total where it could be over 50% for a heavy yacht. Now, you can easily double 15% and have the beach cat hardly notice much difference while you can't double 50% or more and expect the yacht to keep travelling at that speed. It will need (alot) more drive then the sails can produce. On a beach cat the increase in boatspeed leads to INCREASES in saildrive that are LARGER then the increases in hull drag when acquiring higher hull speeds. I know this sounds weird but that is exactly what is happening. On a heavy craft this situation is reversed. Here an increase in hull speed increases hull drag more then it increases saildrive. Therefor when surfing off a wave it will pick up speed beyond Froude's inpired max hull speed but then slow down later. A cat however will keep accellerating even without the help of a wave till a point were the aerodynamic limits of the rig stop any further accelleration (increases in sail drive have topped out). And this is why so many forced displacement catamarans and planing dighnies are so close in overall speed. Their real obstacle is aerodynamic performance of their rigs, not so much the drag of the hulls. Just an example, on a beach cat aerodynamically related drag is 25-30% if the total and as good as twice as large as the wave-making drag component of the hull. (Miss Nylex C-class data that using a highly drag efficient wingsail).


So summerizing :

Froude's law equates wave-travelling speed to wave-length for a typical wave on earth on the surface of a body of water with density around 100kg/m3. Nothing more, nothing less. It is certainly not explicetly saying anything about a hull. The fact that Froude discovered this law by looking at ships doesn't change this fact.

Froude's REAL law is : Wave-speed = 1.34 * square root of wave-length

The coefficient 1.54 that is used often is nothing more then designers trick when designing a "Heavy Weight - Low Power" Boat. Remember the earlier comment on how a hull of such a design would typically travell a tad bit faster then its surrounding wave system. The difference between 1.34 and 1.54 is that tad bit. Basically these designers made Froude's law fit their experience with such boats instead of the other way around where the experiences fit the formula. Some people like to use a coefficient of 5 for beach cats but that is just more of the same tweaking of the formula to fit a particular set real life experience. And for each new design you have to redo this, meaning the formula is useless in such roles as it will only reflect what you already know and not predict what you don't already know. And why use any formula when you already know what the result is going to be ?

For only a portion of hull design (heavy craft - low power) this Froude formula coincides closely to the maximally attained speed in real life because in these situations the accompanying wave system (that DOES follow Froude's law in all instances) is so important in the total amount of drag.

In a very large portion of other designs Froude's law still applies to the accompanying wave-system but as its related drag describes only such a small part of the total system that it is of very limited practical use. Beach cats fall into that category.

Wouter