I think the formula your using assumes a displacment hull with a small engine and a deep reduction gear turning a large prop. We are talking about a planning hull with 2 large high output engines running a light reduction gear and a small prop. A boat that's designed to go fast not displacment speed.
You really can't use only weight and LWL there are lots of other considerations like beam and hull form. Also when your talking low speed fuel consumption on our boats you need to remember your grossly overpowered. When your taking 60 or so HP from an engine that's rated at around 400 thru a fixed pitch prop (very lightly loaded for the RPM) Then you waste a lot more fuel it can be as much as a 40% loss.
Brian
Oh, I totally agree that these baots aer WAY over powered and under propped for fuel efficient displacement speed powering. But that forumula does indeed accurately show how little power is really needed as long as you don't ever care to get more than displacement speeds out of her. If you really wanted to go slow and efficient, a Hat 43 wowner would repower with twin 75hp diesels, Maybe 85s if you want a lot of reserve power. Hatt 53 owners would use twin 100-125s. If you wanted a decent "reserve" on a Hat 53, go with twin 150s and you'll cruise along effortlessly at 3 gallons per hour at 8-9 knots. In the LONG term, when my original DDs die, I may very well do that. I went with a Hat 53 for the layout and live aboard space...not the speed.
I thought the list might might enjoy knowing where the formulas for
power required and anchor drag forces come from. It is all beginning
physics.
For fluid flow that is not turbulent the basic pressure (i.e. force
per unit area) exerted by the fluid on any surface goes like 1/2 times
the fluid's density times the square of the fluid speed. You may have
seen this called Bernoulli pressure. To get the quantitative number
you need a fudge factor that is determined by the geometry of the
surface. The drag coefficient is typically about 1.
Since pressure is force/area, you get the force by multiplying the
pressure (given by Mr. Bernoulli's term) by the area. Now you know how
to estimate the wind force on your boat when it is blowing. You also
know how to determine the force on your hull due to the water flowing
past it.
Now since the force varies like the speed squared and power is given
by force times speed you can see that the power required to move a
boat at some speed must vary as the speed cubed. That is the essence
of the formula realting hp to speed.