Stein,
Do some calculations on these models before asking more questions.
You are wrong in several aspects.
Counterexample :
A cube of volume 1 has a surface area of 6
A rectangular box of the same volume but a length of 2.0 has a surface area of 6.65 = 11 % more
A rectangular box of the same volume but a length of 5.0 has a surface area of 9.35 = 56 % more
A rectangular box of the same volume but a length of 5.5 has a surface area of 9.74 = 62 % more
So no nett change in volume still results in an increase of surface area. Clearly the shape of the box itself has an effect on the surface area. Exactly the same thing happens with catamaran hulls. See for example the last two lines in the calculations.
The reduction in wave making drag better be more then the increase in wetted surface area or else the overall drag of the boat will increase. Finding out where this transition point lies is important in beach cat design.
...For a 20 foot non-planing keelboat (monohull) the theoretical max speed is ca 6 knots. Beach cats easily sail much faster than that, hence it is obvious that we are often not in a pure displacement mode. ...
Actually the beach cats are always in displacement mode, even at high speeds. The contradiction you underline is actually caused by the theoretical max hullspeed theory being wrong. For some reason this myth is impossible to kill. Many people, including maritime engineers, inteprete Froude's law in the wrong way and thus think that the max hull speed law has a scientific basis when it does not. These rest of the errors can be directly trashed back to this fictious law.
However, going from a real short boat to 5.75 improves behavior in waves and reduces pitch-poling susceptibility immensely.
Also that is not a fixed law. It also ignores the role played by the width of the platform. It is not totally about the hull length. Such rules of thumb, while holding some element of truth, are often too crude to for usage in developping a superior beach cat design. Sorry.
Wouter
