I believe amp hours means how many hours you get 1 amp.
So it wouldn't matter if you ran a motor or a headlight, it would still be the same amp hours for that battery.
Amp hour is the rating used to tell consumers how much amperage a battery can provide for exactly one hour. in theory a 10Ah battery can provide 1 amp of power for ten hours or 10amps for 1 hour
Amps is a measure of the current any electrical device – in our case an e-bike motor,
so in the OPs case. 1500watts and a 48v motor = 1500/48. = 31.35 amps. So if in fact his motor is pulling 31 amps then a 30ah battery would last approx 1 hour at full throttle (if full throttle was being provided 100% for the full hour). The Bafang 750watt motor actually peaks at 1500 watts but doesn’t maintain that wattage consistently and doing so for long periods of time will burn out the motor, So technically that motor is running 750/48 = 15.6 amps. Most of the time. However I have personally tested several Bafang 750watt Motors on a bench and discovered that they are very inconsistent in their peak ratings, I have never tested one that actually got above 1200 watts.
however we also have to take into consideration any BMS (battery monitor system) installed within the battery, typically those are 15amp or 30amp. In the case of most Hailong, they are 15amp, so the battery will not allow a draw of more than 15amps before the protection kicks in and kills the battery. You will find in most of these type batteries if the BMS kicked in, that connecting it to a charger and disconnecting after 2-3 seconds, the BMS resets and you still have a lot of battery left.
In the case of mine as I posted above, the BMS would kick over at about 11 miles, if I plugged in the charger and removed it I would get another 10 miles out of the battery, multimeter reading showed it was at 45-46 volts after 11 miles, but the BMS kicked in.
I subsequently replaced the 15amp BPM with a 30amp BPM that prevented this issue from occurring, as the OEM batteries from Cyrusher come with a 30amp BMS. However even doing so I never got more than 20 miles out of a rated “20ah” Hailong That i bought on Alibaba regardless of the PAS settings but the 17ah from Cyrusher gets 48 miles using the same PAS settings and all things being equal (i.e. same path to work, same stop and go, same speed, same PAS, etc.)
I work for an Electric car manufacturer, and have access to some testing equipment and a lot of smart people that know about how all of this works, I have done some real world research as to fine tune my e-bikes for the best range and speed I can get.
I own the following e-bikes.
Cyrusher XF800. Bafang 750watt - peak 1,283 watts (from my testing)
Cyrusher XF650. generic 1000watt - peak 1,012 watts (from my testing)
Bikonit HD750. Bafang 750watt (same motor model as the Cyrusher XF800) peak 1,145 watts (from my testing)
Custom made Tandem with Bafang 500watt - peak 1045 watts (from my testing)
each of these bikes (except HD-750) are using the exact same controller (Bolton Rad Power upgrade 30amp controller) and display (bolton Rad Power KT-LCD8H). They are all programmed exactly the same. Meaning that the P and C settings are identical on all of these bikes as the motor specs are the same (number of magnets, tire size, etc). The HD-750 has the bikonit controller, but the settings are the same as the other bikes.
I have tested and documented the following: testing done using exact same route and circumstances
On the Cyrusher XF800 I can hit a max speed of 37mph (peddling) on flat land and get a range of 22 miles in PAS 5 and 48 miles in PAS 3 with the OEM 17.5ah battery
On the Cyrusher XF650 I can hit a max speed of 27mph (peddling) on flat land and get a range of 28 miles in PAS 5 and 52 miles in PAS 3 with the XF800 17.5ah battery
On the Bikonit HD750 I can hit a max speed of 32mph (peddling) on flat land and get a range of 51 miles in PAS 5 and 78 in PAS 3 on the dual 15ah batteries
On my tandem I can hit a max speed of 34mph (two people peddling) on flat land and get a range of 32 miles in PAS5 and 55 miles in PAS3 on a 20ah dorado battery (two people total weight of 350lbs)
All of these bikes have the C5 setting set to “5” which prevents the motor from exceeding 750watts, they never peak at the Bafang rated “peak“ of 1,500 watts, I am more concerned with range than I am with speed, I rarely throttle only except to assist getting up a hill so I don‘t lose momentum. The Tandem only peaks at 610 watts as it has a smaller 500 watt motor.
I weigh 220lbs and all of these bikes have upgraded gearing (53T crank and 11 speed mag) except the Bikonit, it still has the OEM 42T crank.
the primary difference I see in range and speed is the overall weight of the bikes,
Unladen weight of each bike
XF800 - 76lbs
XF650 - 64lbs
HD750 - 71lbs
tandem - 98lbs.
hopefully this info is helpful to someone. I was bored this morning, so y’all get to read my long winded post.
FWIW max speed (while peddling) is entirely person dependent. I have topped out at 37mph on my XF800 and my daughter can’t get it above 26mph under the same circumstances.