Originally Posted by SoNew
I'm trying to learn about about boat "weight" to engine HP while having the engine run in or at the proper RPM range for its size.
Thank you for any responses. http://www.benford.us/pcty/20supply.html
A good reference book is Dave Gerr's "Propeller Handbook" that will more fully explain the speed-power relationship. In there he describes his "displacement speed formula" which is:
Speed/Length Ratio = V/Lwl^0.5 = 10.665/(Displ/SHP at prop)^0.333
In words, this reads: Speed to length ratio equals 10.665 divided by the cube root of the quotient of displacement divided by the SHP delivered to the prop. For the engine horsepower, you have to increase SHP by about 5% to account for bearing, transmission, and internal engine losses.
So, applying this to the Baten: Lwl = 19.0'; Displacement at full cruise load is 4,600 lbs = 2.05 Long tons (a long ton = 2,240 lbs). So the boat weighs 2.05 long tons.
We can use the equation above because we know all of the factors except speed and SHP. So we pick speeds, and calculate horsepower. Displacement speeds will be anything below a speed/length ratio of 1.34, and a boat like this might travel at speed/length ratio = 1.10. We can also test 1.34, and let's try two more at 1.5 and 2.0. These latter two are in the semi-displacement or semi-planing range. When you get up to speed/length ratio = 2.5, you are generally considered to be in full planing regime. These numbers will vary slightly for different hullforms, but those are the basic ranges.
So, we specify a speed, calculate speed/length ratio (which I'll label V/L for simplicity) plug it into the equation, and turn it around to solve for the unknown, SHP:
V/L = 1.10; V = 4.8 knots; SHP = 5.05 HP; HP/Displ in L. tons = 2.46
V/L = 1.34; V = 5.8 knots; SHP = 9.12 HP; HP/Displ = 4.45
V/L = 1.50; V = 6.5 knots; SHP = 12.80 HP; HP/Displ = 6.24
V/L = 2.00; V = 8.7 knots; SHP = 30.34 HP; HP/Displ = 14.80
So here you can see the relationship between vessel weight, speed, and horsepower which is a pretty valid tool that we naval architects use.
Sometimes, if you are dealing with a particular class of hull shape, this formula may not work precisely, and you can modify the constant 10.665 to another number based on actual experience (empirical data). For example, on my Moloka'i Strait motoryacht designs, I reduced it to to 9.8 or thereabouts for the hull class in order to come up with more accurate predictions for intermediate hullforms based on actual test running of the boats we had already built.
I explain speed and power formulas more fully in my write-up that I did on this forum about 3 years ago called "The Design Ratios." I am posting it again here. You can also download this article from the ARTICLES section of my website.
I hope that helps.