Catamaran Hull Speed
More efficient single hull boats are designed to travel with a low Froude number, which reduces but does not eliminate the drag barrier. This drag limits hull speed based on a relation involving length at waterline, given by the formula V=(gL/(2pi))1/2, where g is the gravitational constant and L is the waterline length. This is the theoretical limit for single hull displacement craft. Note that ships can sometimes exceed this theoretical limit, but to do so requires a very large power source.
The calculations for a catamaran are more complicated. The formula for catamaran hull speed is 1.34*(wetted length)1/2; however, this drag formula is generally not the limiting factor for catamaran hull speed. This is because boats with waterline length to beam ratios greater than 8:1 are not limited by hydrodynamic drag factors, whereas smaller boats need to plane to do so (planing requires enormous amounts of power for displacement hulls). A more important factor to consider is the prismatic coefficient, Cp. Cp = V/(LBP*Am), where V is the volume of water displaced by the hull, LBP is the length between perpendiculars, and Am is the area at midship.
Very fast boats actually require a high prismatic coefficient, which in turn requires a less-narrow boat. However, narrower hulls can get away with a lower prismatic coefficient. The ideal range of Cp for a catamaran is between 0.61 and 0.65. There are a few ways of increasing the prismatic coefficients: sailors can use bulb bows, a wide planing aft segment, or a flat hull rocker in conjunction with a bustle aft. Though high prismatic coefficients increase drag at low speed, at high speeds they can reduce drag by as much as ten percent.