Clay, I think We're in vilolent agreement
thrust ( or force) IS a function of velocity squared. Power, by definition IS force x Velocity. therefore HP (power) is a function of velocity cubed.
1 horse can lift 550 lbs at 1 ft/sec. that same horse can pull 1100 lbs at .5 ft/sec = both are one horsepower. the force is doubled in one case, while it's velocity is halved.
Torque x rpm is the equivelent to force x velocity. 600 ft-lbs of torque at 3000 rpm is 1/2 the power as the same 600 ft-lbs turning at 6000 rpm.
through our boating experience we have come up with "emperical calculations " that approximate these physical equations and in many cases are more accurate because they take into acount efficiencies and such that we choose to neglect in the physics calcs. things like prop effeciency chances, trim angle, aero lift in cats, etc.
ie 15 hp per mph. for an example. but this estimate applies only around say the 400--500 hp range, or 60 mph range. At 70-80mph it is a difference story because the drag is not linear.
(61mph/60mph) cubed = 1.05
1.05x 300 = 315 !!! there's the 15hp needed.
(81mph/80mph) cubed = 1.037
1.037 x 600 = 622.
22 hp more from 600 to get 1 mph
any of the calc mentioned in this string will give you an estimate to stat with. I'm an engineer so I like to try to take the physics approach to understanding this. hopefully saving my money by reducing or eliminating trial and error. One thing that is evident here . It takes a lot of HP to gain a little speed.
Where's Tomcat. He always has insight