Volts and Amps
Volts, Amp, Amp hours, watts and watt hours, what do they mean for an e-bike?
These are the units of measurements for batteries, controllers and motors. Lets dive into what each means in detail:
Volts is directly related to max RPM for a given motor. For a given battery voltage will slowly decrease as it discharges (See https://cdn.discordapp.com/attachments/734563841228275763/787404431360000001/unknown.png for chart).
Current (measured in amps) is directly related to the torque of your motor. You will often see a controller specify its 'battery amps' and 'phase amps'. Phase amps are your peak torque at lower RPM, where the controller can exchange voltage for amps to give you extra torque at low speed. Battery amps are what will be drawn from the battery. You absolutely must have a battery rated for the same or more amps then your controller is rated to use or you will damage your battery when the controller draws too much.
Voltage * battery Amps = Watts. Watts are your power. In fact it takes 745.7watts to make one horsepower. While voltage determins your absolute max RPM, without more watts you won't go any faster unless you where limited by the motor reaching its max RPM before you ran out of watts.
Amp hours are how many amps your battery can give for one hour. For example if it was 10 amp hours, it could give 10amps for one hour, or 20 amps for 30 minutes, or 5amps for 2 hours. You might be mistaken into thinking that amp hours are equal to range, but that is only true for a given voltage as watt hours are the true unit of energy storage.
Watt hours are Amp hours * Voltage. They tell you the true power capacity of a battery. In fact you will often find electric vehicles energy efficency expressed in watt hours per KM or mile. (wh/km or wh/mi). For a very rough idea, you can assume about 10wh/km for very slow riding at 25kph or below on flat ground, 20wh/km for fast riding up to 45kph or on slightly hilly ground, and up to 40wh/km for very fast riding at up to 60kph or on very hilly ground. Exact figures vary greatly but this gives you a rough idea.
Cells have what is known as a C rating, this is basically how quickly they can be discharged, with 1C being the current needed to fully discharge the cell in exactly 1 hour. You can calculate the peak discharge current by multiplying the AH rating and C rating hence for a 3.3Ah cell, 1C would be 3.3A and take 1 hour to discharge at that current. For a 2.5Ah cell, 1C would be 2.5A and also take one hour to discharge. a 2.5AH cell at 2C would fully discharge the cell in 30 minutes and at 5A current, 4C is the rate that would fully discharge the cell in 15 minutes at 10A for a 2.5AH cell, and so forth.
Note that the C rating is only the maximum you can safely draw from the cell, if you only draw at a lower current the cell will take as long to discharge as a lower C rated cell of the same Ah value