I will approach this from the motor perspective and try to keep it somewhat simplistic (also because selfishly my understanding is limited and i dont want anyone to find out
)
1. Extreme example - 3000W peak motor.
current Bafang and Archon supported batteries are 48V or 52V. So to get to 3000W
- 48 V battery will need 3000/48 =
62.5 A discharge current (bookmark this number - we will address this later)
- 52 V batter will need 3000/52 = 57A discharge current.
2. Lower bound example 750W motor.
- 48 V battery will need 750/48 = 16A A discharge current
- 52 V batter will need 750/52 = 14.5A discharge current.
This tell us that all things remaining the same, to support a motor with X wattage, a 52Volt pack will need lower discharge current than a 48V battery pack.
But wait - It doesn't matter what the battery can discharge at, the BMS (battery management system) is the actual gatekeeper of the battery health. Most BMSes only support limited discharge currents (25A continous, 35Peak), regardless of what underlying battery you use, to protect battery health etc etc..
Watt Wagons BMS supports 40-45A continuous with a burst/ peak of
60A. (notice the 60A number?) . Larger capacity BMS also typically means larger size plus need for better thermal management since higher current is flowing through the wires.
Limitation of the 48V pack - notice that to support 3000W we need the 48V pak to discharge at
62.5A... but the most any current ebike BMS can do is 60A! So we end up in a scenario that with the current state of BMS it is not possible to support a 3000W motor with a 48V battery pack. Current BMS tech is pretty good.. and going beyond 60A burst is not needed for 99.999% cases.
Addendum - So how do we support higher (say 4000W peak) systems ? Well.. we use a higher voltage battery like 72V or even 96v !
so 4000W/72 = 55A, and 4000 / 96 = 41A... both of which can be managed by the BMS.
Addendum 2 - Bafang and Archon X1 only support 48 / 52V... so we are at a hard limit of ~3000W peak with current tech.
There is clealy more nuance to this whole this, and battery / BMS junkies will murder a philistine like me for advertising a 50.8 volt system as 52V etc etc.. but you get the overall idea.
TL;DR It is not just the size of the battery - it is the base voltage, the BMS capacity, and the types of cells needed to support the motor wattage you need. More money will get you a battery system that can do 750W to 3000W with ease. Also Star Wars > Star trek.