Sebash4 wrote:Jim, that's a lot of info which will take me time to digest.
SEBASH--the relationship between boat speed and horsepower is really as simple as my one-sentence description. More horsepower makes a moderate speed planing hull boat go faster, but the rate of increase is only to the 0.5-exponent, and that is only if the weight is constant. Maybe if I give you another example it may help:
If the horsepower on a moderate speed planing hull boat is doubled, the boat speed does not double. The boat speed increase is in proportion to the horsepower increase, but only to the 0.5-exponent. If the horsepower ratio is 2, the speed ratio will be 2
0.5.
It may also aid understanding to mention that raising any number to the 0.5-exponent is also the same as "taking the square root" of that number. I use the exponential notation because it is just about impossible to write mathematical formulas in HTML text with the radical sign that often is used to denote taking a square root or other root. You just can't create simple HTML text with radical sign notations in formulas.
I hope that helps you understand the relationship between propulsion horsepower and boat speed.
I also mention weight. Boat speed is inversely related to weight. I think this is really intuitive. The more weight added to a boat, the slower the boat goes. I don't think anyone has a notion that adding weight makes the boat go faster. The effect of weight is again to the 0.5-exponent, or perhaps I should say 1/weight to the 0.5-exponent. The weight is the TOTAL BOAT WEIGHT, not just the engine weight. This is intuitive, too, as the engine has to also push the boat weight, not just its own weight. You don't calculate just the engine weight change but the total boat weight change.
The boat speed is always in proportion to the ratio of power to weight. So more power makes the boat go faster, and more weight makes the boat go slower. Because not all propulsion engines have the same weight, and because engines with more horsepower are often larger engines and weigh more than smaller engines of less horsepower, you need to consider both the change in horsepower and the change in total boat weight. Maybe another example will be helpful:
If a boat weighs 2,000-lbs with its present engine and a new engine weighs 100-lbs more than the old engine, then the new total boat weight will be 2,100-lbs. In making a speed estimate we use the weight change as (2000/2100)
0.5, or 0.976, that is, the boat speed with the new, heavier engine will be 0.976-times the old speed with the lighter engine.
Now if you don't want the boat to slow down by a factor of 0.976 when you in add 100-lbs, then you have to increase the horsepower. How much more horsepower? You have to get 1/0.976 speed increase of 1.025. This means the horsepower will have to increase by a factor of 1.025
2, or 1.05-times.