Thanks Jeramy, tbh a lot of that went over my head. Il re-read it a few times and try to get to the bottom of it
I'll try and give you a few facts and figures and examples that might help you to get a better understanding how it all works. These are only generalisations.
Most 250w so-called legal bikes have 250w motors and they have controllers set between 12 and 15 amps. They can do about 18mph, but are unlikely to get up a medium hill without pedalling.
The more amps you have, the steeper the hills you can climb. You can often modify the 15 amp controllers to give 20amps, which is about the maximum for a 250w motor, and will give better hill-climbing, but not much change to speed on the flat.
A 350w motor (apart from the Q100, which is more like a 250w motor) can handle 20 to 30 amps and will get you up a medium hill without pedalling, but you will have to pedal a bit on steep hills.
A 500w or more motor will get you up fairly steep hills without pedalling with more than 30amps
The speed of the motor depends on what speed it's designed to spin at, and has nothing to do with power; however, it needs power to maintain speed. The higher the speed, the more power it needs. A 250w motor at 15amps can maintain about 18mph, a 350w motor at 22 amps about 22 mph and a 500w motor at 30 amps about 25mph. All the above estimates from the beginning are at 36v.
If you used the same motors at 48v, they would try to spin 33% faster, but would need about 33% fewer amps to maintain the same speed as at 36v, so you can now see that your actual speed depends firstly on the design of the motor, which affects the speed it will spin at at any given voltage. then how many volts you use, and finally having enough amps to give the power to maintain any speed. therefore the final speed depends on which battery you have, which speed version of the motor and the amps rating of your controller. Your battery must be powerful enough to give the amps that the controller allows, so if you want to run at say 25amps, you need a special high discharge rate battery or at least 20aH capacity.
It's much better to decide, what speed you want to go, and then find a motor that's designed for that speed, then a controller and battery to match. At the same time you need to bear in mind your weight and the steepness of the hills you'll be going up. When looking at a motor, your first question should always be: How many rpm does it spin at with say 36v? 201rpm equates to about 15mph, so 25mph is about 335rpm.
Let's say you decide that you want to go 25mph. You need a motor that will reach 335rpm at 36v. You also need a controller and battery capable of giving 25 amps. Alternatively, you could use a 36v 250rpm motor with a 48v battery and controller at about 20amps. These figures are very approximate. Or, you could use 335rpm 48v motor controller and battery at 20 amps. In all cases the motor needs to be rated at 500w or more.
Finally, big motors and batteries weigh a lot, and you soon find that they spoil your ride and make it less like a bicycle, so then you find that you have to make some sort of compromise.
