There probably is a Wiki, but the basic concepts re pretty simple.
Let's work an example just for fun. Go to the motor simulator at: http://www.ebikes.ca/tools/simulator.html and set up a system.
On the left where it says Clyte 3540, click and there is a choice of motors -- choose eZee 250rpm -- this is a good example of a good quality low-end e-bike motor.
Now down in chart options (lower left) choose mph for speed and click "simulate".
There you have your first example of an ebike. With the eZee 250rpm, a 20 amp controller and an eZee 36V 14Amp hour (Ah) battery you can go 20.9 mph at 100% throttle on level ground.
That is where the power required, called Load in the graph (the black line that swoops up at higher speed) crosses the red line (Power)the power that the motor can output at that speed. And while we are at it, the green line (efficiency) tells you that at this speed, the efficiency of the system is ~80%, that is, 80% of the power pulled from the battery makes it into driving the bike forward. The rest goes into heat in the battery, controller and motor.
So, looking in the "electrical" box at the bottom of the graph, we see that the power being drawn from the battery is 462W. (37.8 volts x 12.2 amps) -- battery nominal voltage x amps. So we are drawing 462W continuously from the battery.
How far will the battery take us ? Well, it is 37.8 (nominal) volts and it holds 14 amp-hours (Ah) of current. The total stored energy is: (37.8 V) x (14 Ah)= 529 Watt-hours (Wh) of energy.
So we have 529 Whr and we are using it at a rate of 462W --- it will last : (529Wh) / 462W = 1.145 hours.
And how far do we go ?? Well, that's easy (1.145 hours) * (20.9 mph) = 23.9 miles before the battery is empty. Want to go twice as far, double the battery Ah and get a 36V 30Ah battery.
While we are at it, we used 529 Wh to go 24 miles. (529Wh) / (24 miles) = 22 Wh/mile. And that number (Wh/mile) is a good measure of e-bike "efficiency". Lower numbers are better and 22 Wh/mile is pretty decent for a mountain bike at 20 mph.
As a quick experiment, go back to the simulator for a moment. Reduce the throttle to 60%. Now we go 13.1 mph and we draw only 159W from the battery and instead of 24 miles, we can now go 46 miles on the same battery. And now our consumption is down to 12.1 Wh/mile which is a REALLY good number. The simple moral: speed kills (batteries).
When you buy a battery, you are buying Whr of electrical storage. a 36V (nominal) battery with 14 Ah has (36*14)=504 Wh of storage. A 48V (nominal) battery with 10Ah has (48*10) = 480 Wh of storage and will cost just about the same amount. as the 36V 14Ah battery.
If I want to charge a battery, obviously I need a charger with the right voltage, but what about the wattage of the charger? Most LiFePO4 and LiMn batteries like to be charged relatively slowly. And that brings us to the arcane topic of C-rating.
The C-rating of a battery is an indication of how quickly it can be discharged without reducing the battery cycle life in the long term. So what the devil does the C-rating mean ?? A battery with a C-rating of 1 can be safely discharged at a continuous rate in a period of 1 hour. So to take a specific example, let's say that 36V 14Ah eZee battery we used in the example e-bike has a C-rating of 1. Then we can draw 14 Amps continuously for an hour and then the battery will be empty. Or, in Watts, we can draw (37.8 nominal volts) * (14Amps) = 529Watts continuously for the hour and the battery will be empty.
Notice that this is actually close to the example we worked and, in fact, the C-rating of the eZee 36V 14Ah LiMn battery needs to be at least 1 and it probably actually has a C-rating of 1 or no more than 2, and that would be typical of most LiFePO4 and LiMn batteries.
Now, back to battery charging. Most LiFePO4 and LiMn batteries want to be charged slowly (say in the range of 0.2c to 0.5c max). That is, if I could charge at a continuous rate, those batteries want it to take between 2 hours (0.5c) and 5 hours (0.2c) to fully charge the battery. So, thinking about it simplistically, if I need about 500Wh into the battery and if I want it to take 5 hours, then I need roughly a 100W charger. Actually, chargers are not 100% efficient, and I really don't charge at a continuous rate (the charging slows down as the battery gets full). So that 100W charger will take 6-7 hours to charge a 500Wh battery if it starts from empty. Those numbers are actually pretty typical of commercially available e-bike batteries and the chargers that come with them. That relatively slow 6-7-8 hour charge is conservative and will do a good job preserving the cycle-life of the battery.
So what have we covered:
Power in Watts --- a measure of how fast we use the energy (Wh) stored in a battery
Energy (Wh) = (V nominal) * (Amp hours) is a measure of the energy stored in a battery
Consumption (Wh/mile) -- a measure of ebike efficiency -- goes UP if we go faster
C-rating -- a measure of how quickly a battery can be discharged (or charged).
Hope this gets you off to at least a start.
