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I just noticed that ship's propeller in this thread, so here's a recent rant:
When asked to build a better pedal-propeller system for small boats, I knew that the physics were such that similar shapes worked in air and water, just at different sizes and speeds. Instead of designing and carving my own propeller, I just tried model aircraft props, with instant success in racing. The prop pictured is modified with a tail fairing that is fully streamlined, producing a single, continuous trailing edge to minimize drag.
There are two reasons why marine propellers usually have such stubby blades. One is packaging - they just take less room, don't hit bottom in harbour, require less gearing, cost less, and so on. The other is probably historic, arising from the day that an early screw-propeller builder was challenged to a competition with a paddlewheel steamer. The ships were to be tied stern to stern, and the loser dragged backwards. Operating in still water, a prop causes circulation, and that strictly limits the efficiency available. This Betz Limit also applies to windmills - how much can you take from the wind before it just goes around instead?
Once under way, however, there is a continuous supply of fluid available to push on, and we try to disturb it as little as possible, so that we are not pushing on something that is running away from us. For this, we use the Froude Equations. Unfortunately, these have not penetrated into Marine Architecture, and the boffins there are still patting themselves on the back over beating the Betz Limit by a few percent, which should itself tell them that their theory is misapplied.
Like a wing, an efficient propeller blade is long and thin, so that little fluid is lost over the tip. We don't need a full disc of blades, because each one has a large, invisible wake. Looking at the front view of an airplane with the prop circle shown vs a boat gives an idea of the change in proportions that should be made. Larger, slower propellers should increase mileage about 20% between ports, but will usually have to be stowed one way or another near land. This is not nearly as ungainly as paddle wheels or sails, but it will look odd at first, and the first few will be expensive. We have to get the word out to the people who pay the bills, and those who fight oil use. A windmill gearbox or two might work for a coastal freighter, to keep costs down for prototypes. Propeller shafts that are extended and geared down for a large propeller, and hinged to swing up for shoal waters would be the first configuration I'd try.
Re: Square tips in ducts, etc. If you have a diameter limitation, it is better to prevent loss over the blade tips with a ring of material, but if not, that material does more good as more blade length.
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