Electric Bikes - Motor Power vs Battery Power Confusion

I've searched and I've searched but I'm confused. As an example I've seen two kits:

250w 24v motor with 2x 22ah 12v batteries
500w 36v motor with 3x 10ah 12v batteries

Now I always thought watts = amps x volts. So the batteries in the first kit supply 528watts when in series, and the second supplies 360watts in series. This makes no sense to me considering the motors power rating. Does this mean the kit with the 500w motor will never make 500w because the batteries simply cannot provide it? Is the 22ah 12v batteries in the 250w kit overkill?

My basic question is, what sort of aH and volt rated batteries should you match with your motor?

Oh and also, people talk of increasing the volts to the motor. Would supplying 48v to a 36v motor not break it?

Cheers!

You're confusing battery capacity with amp draw. In the first example the motor should draw 10.4A @ 24v to have 250W input power. The second should run 36v and 13.9A to make 500W, but high discharge rates with lead batteries will reduce their useable capacity quite a bit.

48v on a 36v motor is usually ok, but depends on heat dissipation and where in the efficiency range the motor is running. Very low RPMs + high voltage and current = lots of heat.

You're confusing battery capacity with amp draw. In the first example the motor should draw 10.4A @ 24v to have 250W input power. The second should run 36v and 13.9A to make 500W, but high discharge rates with lead batteries will reduce their useable capacity quite a bit.

48v on a 36v motor is usually ok, but depends on heat dissipation and where in the efficiency range the motor is running. Very low RPMs + high voltage and current = lots of heat.

So, in theory the 500w kit would only last around 43min before the battery fully discharged? I understand in reality it would probably be even less, say 30min. Now the motor would not run at 500w all the time, but surely this is a bad configuration... the first kit could last 2hrs or so at full power. But would the more powerful motor mean you wouldn't need to use it as much? If its twice as powerful you would only need to use it half as much?

I think the battery choices are not really comparable. I'd say you'd be lucky to get 20 min of full throttle with the 500W setup with SLAs, where the 250W would go around 95 min.

Yeh, it looked rather poor.

when you see "##Ah" that refers to how many amp-hours the battery stores, not how many amps the battery can put out. (amps and amp hours are quite different.)

Quite often, the batteries are capable of putting out power faster than the motor can use it.

(Power is be their amps [not amp hours] rating times voltage)

It's a limiting-factor thing: the maximum power output of your motor or your battery, whichever is lower, will be the maximum power output of the system.

The maximum on a motor or a battery is to some degree flexible-- higher quality items can often be pushed higher than their rated power, while lower quality stuff may be unreliable unless you use it below manufacture-recommended maximum power. How long you want it to last may determine how much power you use from a battery or motor.