Re: can 50hp engine push 16ft. bass boat?
Well? It?s like this:
Power is a function of thrust, velocity and time. The pump laws relate thrust (pressure head of the prop) as the first integral of power with respect to time and speed is the second integral. The same way as torque in an engine is the first integral of power with respect to time and rpm is the second.
Think about it? Say your skiff will go 20mph with a 25Hp motor. Given that the drag curve for the hull is a fixed property of the hull for a given displacement; on a whim you decide you want to make your skiff go 40mph. Guess what? If the efficiencies are the same and the displacement of the boat is constant (drag 1 = drag 2), then you will need a motor with (N2/N1)^3, or a 200Hp motor to achieve you goal. That?s why fast boats need so much more power to go only 20 or 30 mph faster. My boat will go 30mph with 750Hp (34? Carver Montego) while my friend requires 2200Hp to go 70mph (35? Baja). Our displacement is different but by far the biggest factor is the relationship of power required being proportional to the speed cubed for a given configuration.
Looking at it from the other end:
Distance is a zeroth order function. It is simply the displacement from your origin.
Velocity (speed in a given direction) is the first derivative of displacement with respect to time.
Acceleration (change in velocity per unit time) is the second derivative of distance and the first derivative of velocity.
Acceleration can be related to a force by the relationship F = m * a where m = mass of the object, and F = the force applied. Differential pressure (Dp) of a prop or other pump element can be related to force by the relationship Dp = F/A where F = the applied force (thrust) and A = the area of the active element (effective prop area). So, by doing some substitution and a bit of math, we can say that Dp is by function the second derivative of distance and the first derivative of velocity.
Energy is defined as moving something through a distance using an applied force yielding units of length*force like ft-lbf.
Power is the first derivative of energy with respect to time, in other words, how much energy can be produced per unit time.
Since we already related thrust (force) and pump speed as well as force and energy we can now relate power to speed and thrust to speed by the relationships:
P ~ N^3
And
Dp ~ N^2
Where ~ means ?is proportional to?
What this all boils down to is:
To double the boat speed if the prop efficiency is constant you need to double engine speed. In doing this you are generating four times the differential pressure across the prop thus requiring eight times the amount of power to do so. There is the relationship in a nutshell.
I hope this helps?
Enjoy!
PatDaddy67
Here is a link to some useful info:
http://www.engineersedge.com/fluid_flow/pump_laws.htm