From a discussion on the Electric Narrowboats group on Facebook, for those who don't use it but might be interested...
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There's still a lot of misinformation/misunderstanding about prop/motor choice including oft-repeated statements like "they're different to diesels" or "low torque at high speed changes things", so I'd like to try and clear this up.
There's no fundamantal difference; to get the full rated power out of a motor (electric or diesel) you need to match the prop size to the maximum power rpm. Overpropping means you can't reach full power/rpm, the rpm stops rising when propeller torque (proportional to rpm^2 -- power rises as rpm^3) hits the maximum motor torque.
For a typical electric narrowboat, to keep prop size up and noise down you don't want to go much over 1000rpm at full power, and for a motor rated at 14~15kW/130-143nm (e.g. Torqmar, Engiro) you end up with something close to an 18" x 12" prop (or 16" x 12" 4-blade, which I've got and so has Paul Sumpner -- and this was also the conclusion of the recent Ortomarine trials.
(Exact equation : Nm = 9550 * kW/rpm)
This is why not just the headline power of the motor matters, but also the rated rpm and torque -- many of the motors being sold for direct drive on canal boats are really too high-speed/low-torque, possibly because high torque at lower speed needs a bigger and more expensive motor, or the main target market for the manufacturer is faster seagoing boats where higher speed props are fine.
The reason "low-speed torque" doesn't matter is that propeller torque drops rapidly at lower rpm -- and this also affects efficiency. I've attached the efficiency plot for the Engiro 12013 (14kW/130nm/1080rpm), and this is what happens as rpm drops:
1080rpm : 14kw/130nm/91%
850rpm : 7kW/80nm/92%
650rpm : 3kW/46nm/92.5%
500rpm : 1.4kW/27nm/93%
If you put the same size prop on a lower-torque higher-speed motor, this will limit the power and rpm to below the rating of the motor. For example, a 15kW 1500rpm motor (e.g. Bellmarine 15/20kW) has 95nm of continuous torque, so with this prop will top out at 920rpm, at which point power will only be 9.2kW. Of course you can push more than this for short periods (e.g. short-term rating (30 seconds?) is 127nm), but that doesn't help you on a river (see below).
For many people with motors like this, such overpropping will be a better choice than the much smaller noisier "egg-whisk" matched prop for normal cruising, so long as you're aware that you can no longer achieve the full rated power -- a bit more than 60% in this case. Which will only matter if you ever need it, for example when travelling upriver against a current for any distance.
The more overpropped the motor is, the more that maximum power/rpm drops off -- put an 18" x 14" on the Bellmarine 15kW and it'll top out at about 8.5kW/95nm/850rpm, again fine (and quiet!) for normal canal cruising, but now down to not much over half the rated power should you need it on a river.
This downside of overpropping matters more on electric boats than on diesel boats since they have much less power to begin with -- an overpropped Vetus 10kW might end up only able to sustain about 7hp, which is very definitely on the low side for anything other than still water.
Of course all this only applies to direct drive motors, but that's what most electric canal boats use for various very good reasons...