The system I am looking at has a smallish battery pack as standard (300wh 52v according to the website ) a user of the same system posted the following details found printed on the battery pack itself (14S2P18650 6Ah 50.4Wh 302.4Wh XE31)
given that, it's 14 pairs of 18650 cells in series. the cells are each 3ah. don't know which cell, but you just need to find one that can provide a minimum of 3ah capacity, and is capable of the required current.
so that's 28 cells. if each cell is 65mm long, and you have ot put them in single file, then you will need 28 x 65 = 1.82 meters of tubing length space for just the cells, not including the casing, cell holders / caps / wiring / etc.
if you can put htem in pairs, then you need half that length. if triples, 1/3. if quads, 1/4.
etc.
I'm not sure of the current requirements but the motor is 750w if that helps.
what is the controller current limit?
assuming it is matched to that motor, then 750w / 52v = 15a (rounded up). so the cells need to be able to suppply a continuous 7.5a.
at 7.5a continuous rate, if they are 3ah cells, they will be drained in 3 / 7.5 = 0.4h or 24minutes. this matters because:
I'd not need more capacity than the provided battery pack as my current commute would only involve partial motor assistance for max 10km for the return trip home up a steep windy mountain road.
jsut for numbers' sake, if you use the full power of the system on that section, then unless you are riding faster than 25km/hour the whole way, you'll run out of power before the end of it.
and that is only when the pack is new. as it ages it will become less capable of providing current, and it will lose capacity, so there will be less and less assistance available for a shorter and shorter time.
i'd recommend sizing hte pack so that you have at least 25-50% more capacity and capabilty than you actually need, so that over time it will still do what you need it to.
I'm not sure about whether a bms is required.
a bms (or something that does that job) is required if you don't want to take the packs out of the frame and test them periodically (possibly frequently, if the cells are not perfectly matched in characteristics) for "balance", and balance them manually. you'd also want to verify somehow that no cell drops below it's safe empty limit, or rises above it's safe full limit. (per the spec sheet of the cell).
a bms, if you get one with balancing built in (nto all have this) will handle the balancing for you during charge, usually at the end of charge, if you leave it on the charger long enough for this to happen. it will also do the checking for balance, and disconnect hte pack from the system / charger if cells go too high or too low, etc,. to protect them from damage that can lead to a fire.