Torque required on boat motor to reach velocity

Question

The resistance against a boat is proportional to the velocity. It needs 22 hp to keep the boat moving at 34 km/hr. The boat's engine turns at 2.3 rev/min when the boat is moving at 48 km/hr. What is the torque on the shaft which drives the propeller? (You may assume that the propeller is 100% efficient.)

Answer 1

Hello Lucy B....

First of all, your question brings up some questions-- the first is whether you are solving this for 48 km/hr or 34 km/hr.?

You can solve for either, since the resistance is proportional to the velocity. So the first thing I assume is that you need to solve for the 48 km/hr situation. So since there is no energy lost in this whole system (in the propeller or the motor, etc.) you need to find the hp applied when it is going 48km/hr. that's just two fractions: a/b = c/d, with both horsepowers (one known, one unknown) in the numerators.

Once you solve for that, you just need to convert Horsepower to torque. It's kind of a hairy conversion factor, but it can be reduced to 1HP = 5252 rpm x Torque(ft-lb) I'll let you do the manipulations and algebra.

Cheers!

Mike