Battery babble: in general terms
A lithium cell, as in an 18650 cell, has a full charge voltage and voltage decreases as energy is withdrawn from the cell. 4.2 volts is generally considered full charge voltage. I use 3.5 volts as the lowest voltage I want to discharge a cell to. That said, I don't like to charge to 4.2 volts, but prefer to charge to 4.0 volts per cell. Charging to a maximum of 4.0 volts per cell and discharging to a only 3.5 volts per cell or higher than 3.5 volts per cell, is supposed to maximize battery life. My 13s, 4p battery is 3.5 years old and is doing just fine. Charging a lithium battery fully to 4.2 volts per cell and then letting it sit unused for weeks or months is bad for the battery.
A 13s battery, charged to 4.2 volts per cell, has a voltage of 13 cells * 4.2 v/cell = 54.6 volts. This is a stick of 13 cells in series.
A 13s battery, charged to 4.0 volts per cell, has a voltage of 13 cells * 4.0 v/cell = 52.0 volts
A 13s battery, discharged to 3.5 volts per cell, has a voltage of 13 cells * 3.5 v/cell = 45.5 volts
48 volts is sort of a figure of speech, or a nominal voltage, or a voltage under some load.
Voltage is a measure of push the battery has, pushing electrons through wires. A 48v battery will provide more power to a motor than a 36v battery...at full throttle, but we don't ride at full throttle. At a given power setting, a 48v battery will provide that power with less current (amps) than a 36v battery. As an example, if a bike has a 25 mph top speed and you are riding at 15 mph, the 48v battery would power the bike with less amps than a 36v battery. 36v/48v = 0.75, that is the 48v battery would send only 75% as many amps as the 36v battery, to produce the same power. That's the advantage of higher battery voltage. Note, it's easier for a system to handle higher voltage than to handle higher amperage.
Amp hours is a measure of battery capacity. An 18650 cell having 2.0 Ah capacity, holds less energy than a cell with 3.5 Ah capacity. One stick of 13 cells, each cell having 3.5 Ah capacity, still has only 3.5 Ah of capacity. Two such 13 cell sticks, wired in parallel has 2 x 3.5 Ah = 7.0 Ah capacity. This would be a 13s, 2p battery. Four such 13 cell sticks, wired in parallel, would have a battery capacity of 4 x 3.5 Ah = 14 Ah capacity. Note: battery capacity is a measure of how many amps a battery can produce for how long. Example, a 14 Ah battery can produce 14 amps for 1 hour, or 7 amps for 2 hours, or 3.5 amps for 4 hours, or 1.4 amps for 10 hours. There's a little more to it than that, but this is close enough for most ebike purposes.
Watt hours is a measure of how much energy a battery holds. As an example, a 13s, 4p battery is said to be a 48v battery, but really it is a 54.6v battery when fully charged to 4.2 v/cell, and a 45.5v battery when discharged to 3.5 v/cell. Voltage declining during use complicates the math, so we simplify by calling the battery a 48v battery. Volts times Amps = Watts. Volts x Amps = Watts. OK. Watts are the units of power, power causes speed, but not distance. To get distance we need energy, energy stored in the battery. Watt hours, Wh, is a measure of energy storage. As an example, a 13s, 4p battery of 48v and 14 Ah capacity, has 48v x 14 Ah = 672 Wh of energy storage. Now were getting somewhere, Wh are a valuable number for calculating things like range on a charge. Example: during 464 miles of riding, my average Watts of battery use were 163W.
Alright, if I divide my battery energy storage by my power average then I should get my range, right? Example: 672 Wh of energy divided by 163 W of power = hours of riding. 672 Wh / 163 W = 4.1 hours of riding. Woah, not so fast. Reason is that I can't use 100% of my battery energy and have long life from my expensive battery. To have long battery life my operating protocol is to use only about 40% of my battery energy. That is, I never charge to 100% which would be 54.6v, but only charge to 52.0v. Discharge never goes below 45.5v. Hmmm, I'm only using about 40% of my rated battery energy storage. So, 672 Wh / 163 W * 0.40 = 1.65 hours of riding. Now for distance: multiply hours of riding times average speed = distance. 1.65 h x 12.4 mph = 20.4 miles of range. About range, riding slower uses less power and thus increases range. For the 464 miles my actual speed average was about 11.0 mph and calculated average range was 22.6 miles.
So a battery that might give 50 miles range, going from full charge to low voltage cutoff ... is only used for 20 miles more or less? Yes, to extend battery life. If I want to go farther, and often do, I just ride slower or take a second battery.
Cost: My gas bike uses a 33cc Subaru Robin four stroke engine, it costs about 1.7 cents a mile to operate, for gas. The ebike costs only 0.10 cents per mile for electricity. But the battery cost is about 8 cents per mile, if the battery lasts 5 years. Batteries can be considered a consumable item, like gasoline, and an expensive consumable at that. Long battery life for this reason important.
Batteries have a lot of variables and there are many different ways of looking at them and their use.
I hope this helps. Keep us posted on what you get, what you do and how it works out.
Mike