You could just bump your other thread instead of launching a new one. http://endless-sphere.com/forums/viewtopic.php?f=2&t=58413
You linked to a fleabay cheap controller in one of your other threads. It was rated at 24V, 500W and said to have a limit of 28A. Not much else is known about it except a cheap price.
So at 24V from the battery, 500W requires 20.8A. Right? Just use's Ohm's Law extension; P = V * I. So 20.8A is the rated battery current for the controller. One would expect the controller to operate at 20.8A or less of battery current for long periods of time without overheating.
The 28A value is a current limit or maximum current. The controller allows current in excess of its rated value for short durations. This is experienced during accelerations or going uphill among other reasons. The controller will impose this limit. It accomplishes this by sensing the current and reducing the output voltage (to the motor) in order not to exceed the limit value.
Since the current limit of 28A is greater than the rated 20.8A, one can not expect the controller to run very long at that condition, usually less than a minute, but this depends on the temperature at which you start. A good controller will sense the temperature of its critical parts and cutback further this limit current when it gets too hot or simply turn off until it cools down, thereby preventing overheat damage. A cheap controller may just fail.
All of the above just concerns the controller. It says nothing about the battery or the motor. If you have a 500W, 24V rated motor it will likely survive in good shape with that controller. If your motor is rated lower, you may be able to overheat it with that controller.
You had even another thread recently about the motor where you were looking for the maximum current. So I'll talk about that a bit. Let's continue to use the numbers from above. Say the motor is rated for 500W at 24V. Then rated current is 20.8A. But the maximum current the motor can draw when 24V is applied to its terminals is much greater. The maximum current occurs at stall (zero RPM) and is called stall current and can be calculated by dividing the applied voltage by the motor resistance. Let's pick a number for the motor resistance: 0.24Ω. So if you applied 24V to the motor to launch your bike from standstill, the motor would draw 100A at first. Without a controller between the battery and motor, that 100A would come from the battery.
Now when you put that controller in there, and launch at WOT (wide open throttle), the controller will prevent 100A from being drawn from the battery. It will limit the current to 28A.
Now; here's where it gets messy. Is the 28A current limit battery current or motor current? They are not the same. Motor current is always greater than (or equal to) battery current. The controller works by reducing the voltage from the battery. Neglecting the small loss in the controller, use a power balance of power-in equals power-out of the controller. So battery power (Vb * Ib) = motor power (Vm * Im). Solve for motor current: Im = (Vb/Vm * Ib). Since Vm is always less than (or equal to) Vb, Im is always greater than (or equal to) Ib.
If the controller current limit of 28A refers to motor current, then motor current and battery current will never exceed 28A.
If the controller current limit of 28A refers to battery current, then motor current can exceed 28A but battery current will stay below 28A. So what is the maximum motor current in this case? You can find that if you know the motor resistance. Im = √(Ib*Vb/Rm) So for a motor with resistance of 0.24Ω, a 24V battery, controller with 28A battery current limit, maximum motor current will be 52.9A.
This method I used ignores battery droop (due to internal resistance) and controller inefficiency. And as you found out in a previous thread, motor resistance is a difficult parameter to pinpoint. Long answer to a short question, but I hope you understand a bit better. My history deals with larger EVs and controllers in that field. Those have always used motor current for current limit specifications. I was surprised to find that controllers for bike motors sometimes use battery current limit. Hence my explanation on both methods. That fleabay controller you showed did not specify which.
But a worthwhile investment. The more data; the better :wink:
