First off, let me introduce you to one of the best tools for figuring out your power needs: http://www.kreuzotter.de/english/espeed.htm
This takes wind resistance into account. Put your conditions and speed desired and it'll spit out the power needed "at the wheel". Then, to figure out how much power you need "at the battery", divide this by the motor's efficiency (a good ballpark number would be .85). Then, figure out how long you need to go at that speed and multiply that time in hours to find out how many watt-hours of energy you'll need. Lithium batteries are good for about 90% or their rated capacity, so then divide that number by .9 to find out what watt-hour capacity rating you'll need. To go from watts to amps, divide by the pack voltage if you need the capacity in amp-hours. For example, one Dewalt pack it 33v, 2.3Ah or 76WH.
I think I will try my hand at a chain drive system as long as they are able to be competitive with hub mounted motor solutions. Do you know of the best way to go about it? Would the way I described earlier work properly? Or are there much better ways to do it?
If you want to go for it, then more power to you. Everything is the same as a hub setup except for the motor and the silly bits between the motor shaft and the wheel hub. I'll say, though, that I have never built a chain-drive setup. Though, I can share what I know. The drivetrain will add some noise, but how much will vary. I can't tell you too much about the motor options other than the Etek, which is notorious for being overkill for a bike, as it's a 15hp motor that can draw hundreds of amps (for more information, search for insane-a-cycle, or look here: http://www.electricrider.com/custom/index.htm
). Anyway, someone more qualified can help you with motors.
You'll have to work out where to mount your motor. You'd want to decide on a motor first to know its dimensions. You'll need to know its RPM in its most efficient part of its powerband and gear it so that it is around this RPM at your most common cruising speed and so that its maximum rpm correlates to your desired top speed. If you want, you could work out multiple gears and a derailleur system of one sort or another. Just be warned that a bicycle chain won't be strong enough.
...since not every single road here has room for bikes, or a sidewalk.
You mean that you have to go offroad because the roads are not suitable for bikes in some places? If the road, if you could ride on it, would be preferable to riding offroad, just VC it. http://en.wikipedia.org/wiki/Vehicular_cycling
The idea is to take the lane and behave as if you were a motor vehicle... which you would be. It's perfectly legal, and usually more legal than riding on sidewalks, let alone safer. Since you'll be able to keep up, you can negotiate traffic just as if you were a little motorcycle. Just remember your hand signals and helmet.
For batteries, forget about A123 and stick with lead-acid.
Well, I'll have to disagree. I'd say get a small a123 pack now and build it out as you go. Still, a123s are very expensive. And SLAs are
dirt cheap. However, that is the only way that they are preferable to lithiums. They're heavier, bigger, will only provide ~60% of their rated capacity, perform poorly in cold weather (erm, Florida...), have much shorter lifespans, take longer to charge, require immediate charging after being drained, steadily loose voltage as they drain (while lithiums stay close to their nominal voltage until near the end). SLAs are just a bad investment.
However, if your were to build a trike, or other vehicle that would be more forgiving as far as mounting the large batteries and the weight not hindering its handling, SLAs would be a good choice. You could load them up with a lot of lead and get a whole lot of range on the cheap.
Your budget, though, leaves plenty of room for lithium batteries. Still, a123s are very expensive, but doable. For ~500USD you could get 4 Dewalt 36v (33v 2.3ah) packs for $130 each or 6 Milwaukee 28v (28v, 3ah) packs for $85 each. After the above corrections for motor efficiency and 90% depth of discharge, at 25mph on a mountain bike the Dewalt setup would give you about 14 miles of range while a Dewalt setup would yield about 22 miles. The downside, of course, is that the Milwaukee packs can only discharge at half the C rate and charge at about a quarter the rate. Still, such a pack would be able to discharge at a rate sufficient to throw a mountain bike at 50mph.
I mean, at peak discharge rates, a 66v 4.6ah 30C a123 pack could provide 9100 watts, while an 84v 6ah 15C e-moli pack could "only" provide 7500 watts. (That is, without voltage sag on either, since I don't know what the sag on a123s at that rate are. And correct me if I'm incorrect about the a123 peak rate... thought it was 20 continuous/30 burst, but it might be 30/45).
But I digress. Buy quality lithium cells now, and add more capacity later as your gas savings allows.
A side note: let me explain about the C rate. The C rate equals the fraction of one hour in which a cell can be fully discharged without damaging the cell. A 1C cell can be safely drained in an hour, and a 4C cell can be drained in 15 minutes. To calculate how much current that is, multiply the C rate by the battery's capacity in amp-hours. A 2.3Ah 30C a123 cell could safely provide 69 amps. Two a123 cells in parallel would have a capacity of 4.6ah and this be able to provide twice the current.