Oar+Some - Physics Diversion

This is a diversion into some of the physics involved in water propulsion - and how it affects Oar+Some's design. Just for fun.

Why not use a screw, or water jet, or some mechanism that more naturally fits a pedalling action - with perhaps continuous rotation?

There are two good reasons.

Firstly, these alternatives require additional mechanisms or power transmission elements (chains / belts / gears etc. ) - and these all sap power, and add overall weight.

Secondly there's some fundamental physics involved, that comes out in favour of paddling or rowing - which is what I survey below.

It's called Froude Efficiency. I believe this was named after William Froude. To honour his work, not because he discovered or formulated it.

Basics
Screws, water-jets, paddles, oars etc. all drive a boat along the same way - as far as physics is concerned. They all take some water that was sitting there perfectly still until you came along, and push it backwards - creating what is effectively a continuous, rearwards flow of water. You can't push something backwards without it pushing you back the other way - ie forwards by exactly the same amount. One "Isaac Newton" is pretty un-equivocal on this - viz. Newton's Third Law. This is what make your boat go along.

The problem
The problem is that creating thrust by setting some water in motion wastes power. There is absolutely nothing we can do about it. It is a fundamental fact of physics to do with kinetic energy. If the water was still before, and you made it move - you have given it kinetic energy. Period. And there's only one place that energy could have come from. Your legs. This kinetic energy does nothing to propell our boat. It is pure waste. We'll come back to this. One thing is sure - we need to look for ways to reduce the amount of kinetic energy we give the water!

What about the thrust?
Newton to the rescue again; this time his second law! This law when applied to liquids, says that the thrust we are going to get goes up in line with how fast we make the water flow backwards, and also with how much water we do it with. So if we turn a blind eye to our kinetic energy problem, we want to get as much water as we can, going backwards, as fast as possible.

So we're stuck then?
Oh no we're not. 'Because of a square law'. It turns out that increasing the speed of the flow has a far worse effect on kinetic energy losses than the benefit it gives to increasing thrust. This is because kinetic energy goes up with the square of the speed. What that means in practice is that we must find a mechanism that creates a flow with the maximum possible amount of water, but with only a miniscule speed of flow.

Enter the oar or paddle
Oars and paddles are not just a happy coincidental evolution. The physics is with them! When you think about it, a big oar or paddle graps a great lump of water on each stroke and pushes it backwards. In so doing it is creating a rearward flow - but a nice slow one. Theoretically the bigger the paddle the better as that gets closer to the perfect physics solution - but practical limitations come - like the ease and comfort of handling. If oars and paddlles don't 'slip' a little in the water as you pull them - it feels all wrong.

Exit the screw and water jet
These are the opposite of oars and paddles in this context. They catch only a relatively small volume of water, but create a very fast rearward flow. This makes them gravely inefficient - but then that doesn't matter if your motive power is an engine, not a pair of legs.