1.34 x square root of the LWL. In this case 6.14 knots. (There is more than a little quibbling about the coefficient, but the standard deviation of the quibbling results in negligible differences anyway.)
OK, THANKS FOR THE HELP BUT NOW I HAVE TO SHOW MY IGNORANCE. THE HULL SPEED IS THROUGH THE WATER. GPS HAS SHOWN A STEADY BOAT SPEED OF UP TO 9 MPH AND AT TIME A STEADY 7. WITH MOTOR RUNING IN CALM I CAN CRUISE APPROX 7.5MPH. SO IS THIS RATIONAL OR WHAT?
The calculation yields an approximation, but it should not be that far off. The more interesting of the two measurements you supply is the motoring in calm water example. That one precludes surfing or lengthening the effective LWL through angle of heel and thereby increasing theoretical speed. The first place to look is at the GPS measurement. Was there a favorable current running (tidal or river)? Remember GPS is measuring Speed Over Ground (SOG) not through the water which the calculation approximates. Also is the GPS measurement recent, i.e since GPS selective availability has been turned off (May 2000 I think)? Is your GPS a differential model using beacon or WAAS? The tighter geolocational accuracy of differential also yields more accurate velocity calculations.
I do not know a simple formula for a cat. As you know the catamaran is not restrained by displacing water - which the simplistic formula is based on. The ability to plane in a catamaran frees you of all that stuff. I suppose a much more complex formula based on drags (hydro and aero) and power is possible but it would be less general in nature i.e. requiring very specific measurements for your boat.
Actually, most Catamarrans do not plane. Most Cats and certainly cruising cats are really displacement vessels than operate in that grey zone of ''semi-displacement'' speeds. The typically quoted formula for Hull Speed equal to 1.34 times the square root of the waterline length is based on the wave making of the hull.
The faster a boat goes the bigger its stern and bow waves become. Also the faster a boat goes the further aft that the bow wave migrates. At some speed around 1.34 times the square root of the waterline the bow wave and stern waved meet and combine creating this big wave that the boat must climb onto to go any faster. Boats that are on a plane have climbed up on to the top of this wave and have ceased to be in displacement mode (where the weight of the boat equals the weight of water displaced). Boats that are surfing are on the downward inclined plane of a wave and the force of that downward incline offsets the force needed to climb up on a plane.
Climbing up on a wave is only one way to assault the limits of hull speed. The other way is to make smaller waves. The shallow and very narrow hulls of a multihull, (or high speed monohulls for that matter) produce smaller waves and so it takes less force to push the boat beyond the theortical hullspeed. Many modern race boats will routinely travel at 1.5 times thier hull speeds and Cats can reach speeds of 2 to 2.5 times their hulls speed without actually planing.
The other issue in terms of speed is the amount of time spent at or near hullspeed. The easily driven hulls of lighter and narrow boats spend a lot more of their sailing time at or near thier theoretic hullspeeds that heavier, deeper and wider boats with the same theoretical hullspeed which is why lighter boats tend to be substantially faster than heavier boats.