When I sourced the replacement motors for Divecat I had no idea what propellers would be needed. Of course, these second-hand Yamahas came complete with a set of 15½ by 17-inch propellers (15½-inch diameter and 17-inch pitch) but those were suitable for the boat that they were originally fitted to. As anyone who has been down this route knows, selecting the right prop for your specific boat and desired performance is part science, part mathematics and, perhaps, part dark arts and personal preference.
The hull design, weight and waterline length are of course all factors in the ultimate performance of the motor and hull. If you have a production boat, then the manufacturer will generally have a good idea on what are likely to be a good motor and propeller configuration. But even if that is all known, there are different requirements for racing, fishing, water-skiing or towing (very relevant for Coastguard, who once owned my motors). Fuel consumption, speed, loaded weight and acceleration at different RPM ranges
