How do you calculate the power required for underwater propulsion?

Question

OK, another newbie question that may have hundreds of variables but I wondered if there is a simple, or fairly simple application I could use that would allow me to work out, on a given craft that is underwater (at say 3 metres depth), I know the weight and buoyancy, what power output of the motor would need to be to achieve a speed of say 2 knots?

Is there an easy way to do it or even a method that gives a range in which to work?

Answer 1

Andy,

The power requirement goes up by the cube of the speed. If you have neutral buoyancy it will not be a factor in calculations.  If you have positive or negative by greater than five percent it will require proportionally more power for the planes to maintain depth.  It requires about 150 Horsepower to move a submarine that carries nuclear ICBMs at two to three knots.  It takes over 20,000 Hp to move it at twenty knots.

Answer 2

First calculate the thrust required, then multiply by the speed to get power.

Thrust = 0.5*rho*V^2*A*Cd

rho = density of water

V = velocity (m/s)

A = cross sectional area

Cd = Coefficient of drag (start with 0.5, this depends on how well streamlined the hull is).

This only gets complicated if you want an accurate value for Cd, but actually it does not vary as much as you might think. 0.5 will give you a good approximate answer.

Everything must be in SI units,of course.