Watts = Amps x Volts.
A motor watts rating is simpy a measure of maximum CONTINUAL watts allowed. Ie before something melts. So if you were to wrap a towel around a 250 watt motor, it then cant lose as much heat. So it might be good for 125 watts. Or add a heat sink, or water cooling, or just a fan, ot may be safe at 500 watts continuous.
What a "watt" rating does not tell up is how many watts a motor takes! Or how many Amps it will pull at a given voltage.
So you can take 2 identical looking motors, with identical efficiency ratings, that have say 2 turns of the windings, or 20 turns. Both may be 250 watts. The 2 turn one will take 10X the Amps at stall. And so ten times tha watts. And 10x the torque. Yet its still 250 watts AVERAGE.
Take a typical 4 pole wheelchair motor rated at 350 watts. Actual figures may be:
With a 120A R-net controller, it CAN take 24V and 120A at max acceleration, at around half speed, so that is then 2880 watts. With a 60A controller limitation thats then 1440 watts. With no controller limit it may be 3k watts peak or much more dep on impedance. A lot different from its rated 350!!!
So as you can see, max motor power in watts is Max stall amps, x the battery voltage. So that as you can see, impedance, and battery voltage x motor efficiency at a given RPM determine motor power. That 350 watts tells is absolutely nothing useful. Its entirely possible that a 200 watt motor gives more way more power than a 1500 watt motor. Just not continually. Depends on impedance and motor efficiency.
The problem I have is that the legislation states that the motor is limited to 250w and top speed before assist cuts out is 15.5mph. Batteries are measured in watt/hours ot Ah.
So the moron that typed the legislation was a solicitor, or a civil servant. And no clue how motors or controllers work, so its pretty much meaninless drivel. It doesent tell you anything useful! They are not engineers. I suspect that they really mean that the peak power of the whole system, is 250 watt peak. In which case the only way to achieve this is to use a nominal battery voltage of x and a current limited controller of Y which when multiplied together cannot provide a motor with more than 250 watts. So the actual motor used as long as its of low enough impedance is completely irrelivant. A 10,000 watt motor will then be limited to 250W. But its to complicated for them.
And batteries are measured in watt hours because they are all different voltages. A 48V 10Ah battery is the same amount of storage as a 24V 20Ah battery. So we measure them in watt hours. My BM3 is 3240 watt hours. The two batteries in the example above are both 480 watt hours.
They are equally stupid when it comes to power limits on int combustion engines. A new biker that has not passed his test is limited to a bike with 11 horsepower. But in typical idiotic fashion thats all it says! A 18 horsepower engine gives 18hp with no ancilliaries like water pump, or generator etc. Do they mean that? Because it may be left with 11 afterwards. Or do they mean at the wheel? Generally aprox 20% is lost through the transmission. So the same engine loses another few, and reads 9bhp on the dynamometer at the wheel. Is it meant to include windage losses, and does it take temperature and pressure or altitude above sea level into account? Doesnt say. So again another easy 10%variability. And then theres correction factor standards. Which one should I use? SAE 1340? Din 70020? ISO? Again all give a different figure, or P.S. figures? They dont say... I had various cops bring me bikes to test to see if they were "over the legal limit" in the past to my automotive dynamometer. When I asked the these questions I was met with a blank stare? So depending on what I felt like I could give them half a dozen wildly different figures, and all were correct! The civil servants do not understand these things and so cannot write legislation correctly.