# PropellerEfficiency

## Why we need big propellers at slow speeds

From Newtons laws we know that for every action there is an equal and opposite reaction. The push you get from a propeller is proportional to the change in momentum the propeller gives some water which is: mass * deltaV

where deltaV is the change in velocity of the water. So we can think about this in the frame of reference of the original stationary water, and ignore the frame of reference of the boat. The energy put into that water by the propeller is: 1/2 mass * deltaV^2

Because the energy goes up with the square of the velocity change and the momentum only with the velocity change, the most efficient approach is to push lots of water with a small change in velocity.

If a boat is going fast a propeller passes through lots of water and so can push a little bit on many different cubic feet of water and so only change the velocity of any given bit of water by a small amount.

A propeller that makes efficient use of 50 Hp at 15 MPH makes very inefficient use of the same power at 2 MPH. At slow speeds it goes through less water and gives it a much higher deltaV.

An efficient propeller for a slow seastead will be large so that it can give a small deltaV to a lot of water. Using a small fast propeller on a big slow seastead would take far more energy for the same push.

Power is energy/time. So the Hp or watts that we need will be higher if we do not design for an efficient use of the energy with a reasonable propeller.