To add a bit to an above post, the formula I've most often seen is Maximum hull speed (displacement) equals The square root of the water
line length times that vessel's hulls K value. The K value for many monohull
cruising boats this may be about 1.34, but it will be very different for most catamarans - mostly higher K values which means a faster hull. My understanding is most cruising catamarans don't plane, they just have very high k values. However, one must also note that with less buoyancy, for a given length, adding weight to a catamaran
will greatly increase the wetted surface as well as other characteristics which will slow down potential speed more than a monohull
of comparable length.
Charles Kanter goes into how hull shape and other factors contribute to the K value as well as moving characteristics in his book: "Cruising in Catamarans"
As one approaches the theoretical maximum displacement speed, resistance increases more and more, so you get less speed gain for a given increase in power. At slower speeds, wind
will play a larger role. I think it's hard to talk in terms of maximum efficiency without knowing more. Your most fuel efficient speed to cross an ocean in a power cat is probably to get into an ocean current
and prevailing wind
, throw out a sea anchor
and turn off the engine
. The most efficient speed for you will include how important your time is to you. What I think you really need to do is get out in your boat and test the fuel efficiency at different speeds and decide what trade-off you are happy with.
I know in a previous outboard
powered pocket cruiser
I had, I could go about 7 knots at full throttle with a 10 HP outboard
, but there was a lot of pressure on the rudder
and the boat did not behave well. At less than 3/4 throttle, I could still do 6 knots comfortably with a notable savings in fuel. That was my typical cruising speed under power.