|Eolian's low aspect ratio propeller|
I've been thinking about propellers lately. A lot.
No, I can't explain that. Perhaps it is a residue of our recent election. Or something.
Now, I am not a trained Naval Architect. But still, I have thoughts which seem coherent (to me at least, but then the judge may be biased), some brought on by casual observation of a rooster tail following a heavy cruiser. Even riding on a ferry you can see evidence of a jet of water that eventually surfaces astern.
To me, the whole idea of thinking of a propeller as a water screw is, well, screwed.
Imagine that the that theoretical speed of a boat which would be determined only by the pitch of the prop and its RPM is called St. In the common parlance, "slippage" - that condition when the boat is moving at less than St, is considered to be an inefficiency.
But imagine that a boat is moving thru the water at exactly St... there is zero "slippage" - the prop is a perfect screw. But then the only force on the prop is drag, as it completes its revolutions thru the water. So how then is any force created* to move the boat forward?
How about this instead: Newton's Third Law: For every action there is an equal and opposite reaction. Imagine now that the prop's mission in life is to throw as much water astern as it can... in a sense the boat becomes a rocket, propelled by the water being thrown away aft. This theory would have as a consequence that "slippage" is required for propulsion. If the boat reaches St, from the boat's perspective NO water is being thrown aft... NO propulsion. This also says that a boat will never reach St, because the closer it gets, the less propulsive force is available - a hydraulic version of Zeno's Paradox.
Given a fixed amount of horsepower applied to the shaft, the product of the amount of water discharged and its speed are fixed. If you want more water discharged, then for a fixed amount of horsepower input, the discharge speed of the water must be decreased. And vice versa. So, if you want a high speed discharge jet (high St), you must compromise with less water in the jet. Therefore, assuming the same Chevy V8 engine, installed in a high-speed racing hydrofoil, you'll need a comparatively small diameter prop with a HUGE pitch. With that same engine in a tug, a large, slow-turning prop will give you humongous thrust, but with the compromise of a low top speed. Variable pitch props do not solve the problem because they only allow their pitch to be changed, not their diameter.
What do you need for your boat? I bet that you want the most speed you can get. So: the highest pitch prop that still provides sufficient thrust to get you somewhere near St for that pitch. Still a guessing game, tho empirical formulae do exist.
*I said that at St there would be no thrust. That is not (at least theoretically) true. Since the beginning of flight, aircraft propeller blades have had an airfoil cross section. That is, they are really rotating wings, not only generating thrust by virtue of their pitch, but also using the pressure differential the airfoil creates between the front of the prop blades and the rear: lift. An aircraft propeller, even operating at (or above!) St still delivers thrust because of this. It strikes me that there is a lot of room for hydrodynamic improvement in water propellers, specifically in improving their lift/drag ratios. Aircraft wings and propellers (and sailboat keels!) long ago gave up the low aspect ratio shape that today's boat propellers still retain. Continuing with that thought, boat propellers, it would seem to me, would be well served if they moved toward narrow high aspect ratio blades with a cross sectional shape derived from hydrofoils. Another trade-off: enough "meat" will need to be retained in those thin blades to handle the thrust forces...