RE the first post, I did not check your math, but if you take the same cells and reconfigure them to a higher voltage pack, you did not add one bit of more energy to that pack. it will have the same watt hours it had before. But, if your amps was too high at 48v, then it can potentially deliver more watt hours if you lower amps, because it was too much before. If it was not too much before, then no gain will be seen. You wanna get more from any battery, lower its discharge rate by making each cell deliver less amps. The practical way to do this is to add cells. If you enable yourself to pull 3000w from the pack instead of 1000w, you will hammer that pack into dogshit.
The higher voltage can increase distance too, if you don't change speed, or rate of acceleration.
But you WILL.
And then you will go less distance. And risk hammering that pack to dogshit.
You can ride slow with a high powered, high speed rig, and get very close to the same distance. If you do actually go slow, often only doable by some kind of limiting by CA or whatever means, then basically what happens is the wind resistance at 18 mph is the same no matter what the voltage, and it just comes down to watt hours you have, (ah). If you get 20 watt hours to the mile at 18mph, then you go 5 miles on 100 wh. ( about 3 ah of 36v)
There will be some differences in efficiency, but in general nothing you could not make up by coasting or pedaling slow for a half mile.
So bottom line is this, there is no real penalty in distance, if you must ride slow and get distance, you can. You wont without a lot of effort or a limiter, but you can. And its great to have some speed when you want it.
One thing to avoid though, is going so high in voltage you can't control the throttle to ride slow at all. More than 72v I would not go there, and really 60 v might be plenty of speed anyway, depending on your wants and needs.
And whatever you do, or want, you still have to limit your amps to a reasonable rate, so the cells don't get hot. just make your 48v pack bigger. Get another one, and parallel them. Then you will see more watthours from both, and go amazing distances. I learned this on the road, doing 60- 80 miles between charges. It works. And 48v is generally fast enough for the open road. In a city, 72v might be worth it to keep up, but on the open road, 48v speed is enough.