Being a Mechanical Engineer, I've always been intimidated by electrical design work, but I've finally worked up the courage to take on the flowing charges and do some calculations!
As it turns out, determining our battery size is fairly simple. When we’re looking at batteries online, there is a lot of superfluous information that we don’t need to concern ourselves with. The 2 things we DO need to know about are the Voltage and the storage capacity (in Amp/hour or Ah).
Now, let’s assume our vehicle uses 22.35 Wh of electricity when driving at 15 mph. We’re using this as an estimated value only for our baseline calculation (data extrapolated from cyclone-usa.com test results for the same 500W motor).
As a base point, let's assume we want to travel 30 miles at 15 mph; therefore, we are going to consume 670.50 Wh of electricity during that trip.
Now to figure out how many Wh are in a battery multiply the voltage by the amp hour (ex: 12V x 75 ah = 900 Wh) The battery I'm looking at is HERE.
Seeing as that the motor we’re using is a 24V motor, we will need TWO 12V batteries to make a 24V system and our calculations are revised liked this: 24V x 37.5 ah = 900 Wh. (notice the Wh doesn't change when converting to a 24V system. This applies to 36V, 48V, etc. systems as well.)
Looking at these figures, it appears that we can get away with using just (2) 12V batteries and we will exceed our range/speed requirements; however, because we’re using sealed lead-acid batteries, we need to take into consideration that you can’t take lead-acid batteries below 50% capacity without damaging/degrading them and lowering the battery life substantially. Therefore, in order to meet the criteria set (minimum 1340 Wh total), we need (4) 12V batteries. At $158 a pop, that’s $632...
Now, I think 30 miles is probably a little excessive and since I'm planning on riding this bad boy at low speeds and on flat ground, I can probably get away with (2) 12V batteries; which if I back calculate, I'll probably get a little more than half the distance (15miles) or half the speed (7.5mph)...I think I'll be okay with that. Whew, that's enough electrical for me for one week. =P