Background
Propeller design is a complex topic which I am sure has been the life's work for many engineers. The difficulty is that a propeller has many parameters which are all interdependent. There are diameter and pitch (the distance the blades will travel through the water if the propeller turns once, like a corkscrew), the area of each blade and the number of blades. Once these are determined, and the blade profile chosen, the speed of the boat will depend upon the hull characteristics and the weight of the boat.
Let's get back to first principles. The whole point of Perseverance is to cruise quietly. Smoothly. Without fuss. Therefore I opted for a 4-bladed propeller as more blades give a smoother ride. I also found that standard propellers have a limited range of area ratios, so that reduces the number of unknowns further. I tried to use charts to find out the propeller performance, but some are fiendish like this one:
The wake caused by a large propeller moving more water more slowly will be less turbulent, and hence quieter, than a small propeller moving a little water more quickly. For this reason, I opted for an 18in propeller, and using a chart like the one above I settled on a 14in pitch.
As a sanity check, I asked lots of people for advice, used on-line and downloadable propeller sizing tools, and plotted all the information I could gather on a chart of diameter vs pitch. Fortunately my 18x14 choice was in the middle of the range which provides reassurance.
The actual propeller and sterngear can be seen in Sterngear Vlog, and Why Waste Money addresses the different types of power plant which could be used.
2022 Update
Well this didn't work out as expected. The propeller certainly shifted lots of water and was wonderfully silent in use. I did many measurements, and in fact the thrust for the bollard pull test was so great, it bent a steel bar used to connect to the tensiometer.
The snag was that by 660 rpm the motor reached its torque limit (82Nm) so we were only using about 6kW to move the boat from a motor rated at 12kW. Half the speed means half the power. This performance was good enough to see us complete the autumn 2021 cruise to the Odiham, Godalming, Brentford and back to Napton, but sometimes we would have liked to speed along a bit more.
Back to the drawing board, and I decided to start again from scratch, this time using a computer. From data gathered from the cruise and other tests I now know the drag charactersistics of Persy and adapted the standard form cubic drag equations to match. Then with some polynomials I encoded the Wagningnen chart as shown above. I blew the cobwebs off my old textbooks and set up an optimization process that fiddles about with the variables to find an optimal solution, and added motor performance boundaries to avoid demanding more power or torque than is available.
The end result allows you to type in the hull length and displacement and the motor limits. Then you can either optimize the propeller for the highest speed, or for the lowest power at a selected speed. This process has since been used to select the propeller for some of the newer Ortomarine boats.
My first stab at using this software was aimed at getting the highest speed out of the boat. The original propeller was 18 x 14 in, 4-blade, and the optimized one was was smaller diameter, and a lower pitch than the original, at 16 x 8 in and still 4 blades. The result was mixed; although the motor could reach maximum power and, even allowing for the less efficient propeller, the boat speed increased, the mechanical noise of the shaft spinning at higher speed and the more turbulent wash made the experience less pleasant.
Of far greater significance was that over the cruising range of propeller speeds, the propeller "sang" terribly. All propellers have mechanical resonances - just like a bell - and if one matches the input disturbances experienced on that boat, the prop will ring. We could stand it just long enough to shout "Quick! Get me another prop".
With this experience, I ran the program to find an optimal propeller aimed at a lower speed and (because I can't help tinkering) I chose a 3-bladed prop. A 3-bladed prop will be slightly more efficient than a 4-bladed design, and optimizing for a speed of 3 mph I selected a 18 x 10 inch prop. Here are the second (just come off) and third (just fitted) props.
The new new prop didn't sing, so we happily did some test measurements and went off cruising to Dudley and back. The midway selection of area and pitch does give a midway performance - higher power and faster than the original without the noise and excitement of the smallest prop (remember, excitement is a bad thing on Perseverance). One downside is that the 3-blade prop appears to be more prone to collecting weed, and its stopping power in locks is very poor.
I have yet to do the sums to quantify these differences, but already I can feel prop 4 coming on... After all, this boat is a big boy's toy, and I like playing. Oops - that should read "I enjoy the engineering challenge" (sounds more grown up!).