Battery Range/Capacity testing

Well you could pray a lot for the infinite organizing wisdom of the universe (who you might know as 'God') to teach you how to intuitively read the charge state of a battery. (you think I'm kidding)

I take it from what you say that your bicycle has lead-acid batteries?

Lead-acid batteries do, during discharge, deeply dip in voltage and towards the end of the discharge they'll dip really deeply. If I recall right the safe discharge depth tends to be about 11 volts per battery under load. So, yeah, if you ride far enough that the power from the motor is weak, then you will have discharged the battery pretty deeply.

It's best to have something like the Watts Up meter - I have several of them - you can learn a lot about EV operation by watching the display while riding the vehicle. I recently ordered a Cycle Analyst unit because it's featureitis is much better than the Watts Up.

However other battery chemistries don't act the same during discharge as do SLA. They tend to not dip their voltage so deeply and instead they'll provide the same level of power until it feels like you dropped off a cliff.

I agree, a watts up is the only way to really know how an ev is doing. If you are like me, though, you bought the hub to save as much money as possible. Too bad they aren't a $25 item. I went ahead and took my WE 12ah batteries to the limit with a brushed hub on a schwinn trike. I knew I was going to get a LiFePO4 asap so I wasn't too worried about toasting the lead. For me, at full throttle on a run that was slightly uphill for 4 miles and back down 4 more, I was getting about 6 miles at full throttle,and just making it 8 if I held back. After a few weeks it seemed to get better, and by peadaling a lot I got 10 miles a couple times. Going down a huge hill to work, I could just make it all 12 miles there. Recharged and going back uphill, about 7 miles. On those runs I was pedaling like mad to stretch the range.
I tried a 4th battery, and found I just got the same distance but climbed the hills faster. I guess whatever I saved on the flat, I just used up on the hill. I found it a bit hard to go slow once I had 48 volts, and found it harder to know when I was getting low since the trottle lights are calibrated to 36 volts. Anyway, I did find that you could actually get quite a distance with the low battery light lit if you did a lot of pulsing and peadaling. Toward the end of my commute, it's nearly flat and I could actually milk that low battery a lot more than I expected. The lead will recover just a little bit if you rest it for 5 or 10 minuites. Occasionally running the lead real low will not ruin the batteries overnight. From what I've read the really important thing is lot leaving them that way any time at all.
You will definitely feel some voltage drop before the throttle lights up. For me it was noticable at about 3 to 4 miles distance, and would gradually get less and less till the yelllow light went on on the throttle. A ten buck voltmeter from the hardware store let me know that the light went on at about 31 or 32 volts, but I could still get usable power out of the batteries down to close to 24 volts. Since I knew I needed Lifepo to make my commute, it was kinda cool to go ahead and see just whether I could kill the lead batteries. No doubt I have reduced the number of cycles, but I have not seen any less range after at least 20 cycles of this kind of abuse. If range is an issue, I can only say that I am really happy so far with a ping 36 volt 20 ah. It takes a long time to charge if drained a lot, but If I had about a 7 or 8 mile commute I'd be able to even leave the charger at home. The charger It came with claims to be 2 amp but the specs say it can take 5. Hopefully soon a 4 amp lifepo4 charger will be avaliable. Then I could charge more without working a long day.