I like to say 1 ah per mile at 36v, because my real world ride sometimes uses that much. It's not intended to mean you have to have that much. Just that it's SMART to have that much. Once in awhile, my 15 miles of uphill all the way home has a 40 mph headwind. On that day, I might need 1.5 ah per mile. Most days I get home on about .8 ah per mile, and if I have a tailwind of 40 mph, a lot less. Sure, most rides have less wind or hill to deal with. My route happens to follow a hilltop alongside the highway so there is no trees or houses to hide behind. Anyway, the battery will last longer if it has less stress on it so having the absolute minimum is not so smart in my opinion. A pingbattery 10 ah v3 should be plenty able to supply that motor if you have a flatter ride, but I still like the idea of a 15 or 20 ah pack for hills if you have them. The 1 ah per mile figure is just a very round number that can accept a lot of varaitions from the rider, like 300 pound weight, or 20 psi tires, or 800 ft of vertical gain without being totally wrong on the not enough side. This number is also based on no pedaling to start up, and riding full throttle with minimal pedaling effort. Obviously, if you pedal first a few hundred feet, and ride 3/4 throttle most of the time, you will use a whole lot less than an amp hour per mile. More like .5 ah. Not all of us want to calculate down to the last watthour. We just want a ballpark figure on what size would get me there, or there and back. This figure works on lithium or nicad batteries, not sla's, and is for bikes with speeds in the 20-25 mph range at 36v. Obviously motors wound different will perform different. This number of 1 ah per mile incudes a health reserve so you don't arrive at work with the bms tripping every day, and is way too much battery if you intend to ride less than 20-25 mph.
With a pingbattery, you don't need to charge right away, and the bms should stop you from discharging to the point where the cells get damaged. So you can ride to work, not charge, and ride back if you have the big enough size for that. Carrying the thing is another story. 48v-20 ah packs get a bit on the heavy side, and the package doesn't fit so good on the bike anymore. 36v-20 ah or 48v-15 ah packs will take you 20-25 miles minimum and still fit on a bike rack pretty nice. If you have a flat ride, a 36v 10 ah should be all you need, but having more is real nice. I'd buy enough to get to work and back so you don't have to bother with charging there, and then you have the capacity for longer weekend rides. It's a lot of money, but my pingbattery is the only ebike thing I have bought in the last year that has worked flawlessly for the entire year. Hopefully my brushless aotema motor will not give me trouble in the hot summer like the brushed ones did last year. But anyway, the pingbattery I bought a year ago has proven to be the cheapest per mile thing I have.