Hi, this post is intended as a reference regarding various battery chemistries used for ebikes.
Please show me if I made a mistake or something, so I can fix it. Of course, I'll only edit it as time and will power permit. There's only lead-acid for now because I had to start somewhere, also they seem to be the most common type used.
1 - Do I want lead acid batteries?
2 - Care and feeding
3 - Capacity
4 - State of charge
1 - Do I want lead-acid batteries?
Well, Lead-acid batteries are cheap when you buy them compared to other types of batteries, 36V 12Ah will set you back about 75$can. This is as cheap as it gets next to other chemistries, but they're also very heavy compared to other types. You may have read that most people will buy other types of batteries, lighter ones, once they get into ebikes, but not all of them do. Beware that a 12V 12Ah brick will cost you about 4-4.5Kgs, so a 36V pack ends up weighing a bit less then 15 Kgs. Shopping locally can be advisable to avoid shipping charges... However, the cost accounted over their life span gets about comparable to some much lighter chemistries, because some of them last a lot longer. For an ebike in regular use, a Lead battery can be expected to last about a year, perhaps two depending on maintenance and such. However if it rarely gets used, say a trip per week or two, then lead batteries have an interestingly long calender life.
The main reason you may want lead batteries is that the battery pack is both an essential and expensive part of an ebike build, and lead is cheap so by buying lead bricks you can spread out the cost of building the bike over a longer period. For example you can get a really nice motor/controller etc. but with lead for the first year, and only the next year get better batteries. Now, some people are quite content to get around on lead batteries, but most people will want something better.
2 - Care and feeding
Lead batteries must be charged as soon as possible after having been used, even after only a light use like to go fetch bread at the store. If you don't, they won't last very long... The less they get discharged and the less they wear out.
These batteries form lead sulphate when they get discharged, and these crystals are easily reversible when they're fresh: Just charge the battery. But after a few days they get really damned hard and they may not dissolve back into the solution, for the ones that will, it'll take a lot more time and energy to persuade them to dissolve... Now give these crystals something like a week, and you've lost a significant part of the battery's capacity... Too bad for you. They're made of active ingredients that can no longer be used and worse still, the crystals cover parts of the lead grids so that the parts they cover can't be used anymore. A very badly sulfated battery is pretty cool to watch, it puffs up and cracks.
Batteries on regular use on a bike should get the chance to get a completely full charge at least once per week, just let the charger plugged in overnight, even if the light is already green. If you don't, they're not gonna last as long.
Thing is, they're made of 2v cells. This means a 12v battery has 6 cells, and of course some of them are weaker while others are stronger. This is why chargers have a float function, once the green light turns off it usually means the charging phase is complete, but the battery isn't completely charged. Some cells are slightly overcharged and others are slightly undercharged. What happens if you unplug the charger at this point is that the weaker cells never will get a complete charge. These undercharged cells will age like an undercharged batter - much faster, and when they die, they'll take the rest of the battery with them, like the weakest link on a chain. To prevent this, it's good practice to leave the charger plugged in overnite once in a while, this allows the weaker cells to catch up with the stronger ones (the stronger cells dissipate the surplus energy as heat).
A lead acid charger will give out something in the order of 14.4 to 14.8v @ 15°c, but only during charging stage. Once the battery is charged, the charger switches to equalizing stage where it will keep a battery at something like ~13.6v. Better chargers will also float batteries after about 20h of equalizing or so, this stage just barely keeps them fully charged. Beware of cheap chargers that often come with toys, they only have the charging stage. This means if you leave your batteries continuously plugged in, they'll bake and dry out, but you should be able to get away with letting it plugged in over nite once per week, or letting them a few hours after it turns green once in a while to keep your batteries equalized... A good charger such as a Soneil is expensive, but it has all three stages and not only makes your batteries last longer, but allows you to simply plug them in and forget about it until the next time you want to use them.
3 - Capacity
Soo... You got yourself some 12Ah bricks. Good for you! But what's that, you only get 8Ah out of them? Well sorry to break it to you, but that's normal. Let's talk about the Peukert effect... In a nutshell, if you take energy faster out of a lead battery, you can draw a lot less of it then if you took it out slowly. Now 1C would be the battery's capacity delivered over an hour, 1/2C or 0.5C would be the capacity over two hours. It's reasonable to expect you may suck your batteries dry within an hour or two or three on an ebike, but lead acid batteries are rated over 20hour discharges, that's 0.05C! So you understand, Peukert kicks ebikes in the balls as far as lead goes. It also means you have to juggle with capacity a bit, for example if you pull 20A out of a 12Ah pack, it'll give you more then double the capacity then a 7Ah pack would - it's 1.6C vs. 2.9C.
Here's a graph from the reputed maker B&B, you'll see that at higher amp draws you get nowhere near as much power out of a battery:
And here's a chard drawing out various flavors of lead batteries. If you're going to go with lead, this should help find a reasonable compromise between weight and power:
You can measure how much capacity a battery has left by getting something like one or two car headlamps of known wattage (say 2X55w) and letting a fully charged battery run down through them until the voltmeter reaches your cut off point, or you could just watch until the lamps grow dim, but do the math for power used vs/time and you'll get a capacity in Ah. Be careful not to forget them so they run all the way down, that would damage them.
Keep in mind that fresh batteries see their capacity increase over the first 20 cycles or so, so if you've just gotten new batteries, give them a few cycles before deciding what you think of them.
4 - State of charge
A voltmeter is all you need to tell a lead acid battery's state of charge, you can get simple 10$ multimeter for this, and nothing stops you from mounting that to the handlebars... Voltage drops off quickly when the battery is nearly full, then it reaches a plateau of voltage drop, where the drop is pretty linear, and once the battery is nearly empty the voltage will start dropping fast again. Keep in mind a battery that's been partially discharged but has been left sitting for a while will show a higher voltage, say you're walking out of the grocery store going back on your bike, but it will drop back down pretty much as soon as you use it.
This graph shows a single 2V lead acid cell:
According to this graph, a 12v battery would be charged at 12.9V, indeed once you unplug a battery from a charger that's pretty much where it goes after a while, and as soon as you start using it it drops to 12.4V, and is pretty much empty by 10.8V. In practice, you could say that above 12.5v a battery is charged, and below 11.5v it's empty. For longer life, a lower cutoff limit of about 11v would probably be a good idea.