*This is a somewhat lengthy post, but for those who might benefit from it it might be worth the read:
I've always thought one of the problems with electric bicycles (besides their dorky look) on the market today is their lack of some kind of variable transmission. You car doesn't have just one gear--why should your e-bike?
When a bike has only a single gear, the rider must choose his gear with the knowledge that he will not have the most efficient gear at certain speeds. Going fast down hills he will begin to spin out; if he tries to up the gearing to address this, he'll quickly notice how much more effort is required just to spin the crank one revolution.
The thing is, there is no reason for this...not since the advent of the dérailleur at least. Being able to change gear ratios means being able to adjust to varying amounts of torque at a given rpm and allows for higher top speeds by turning the wheel at a higher rpm.
It's simple physics. A motor typically reaches its point of maximum power at 50% of max rpm; At 80% of max rpm, a motor is operating at its most efficient speed. My most recent project is a street cycle built from bicycle parts with a 900w motor with a rated speed of 2600rpms. So for the sake of this argument, let us assume that this is the motor being used and 2600rpms is the top speed rather than the rated speed. Assuming 26" wheels, multiply 201 by gear ratio (chainring/sprocket) to give you top speed. This is how fast your bike (with 26" wheels)" will be traveling when the motor is spinning at its maximum rpms. *note: this is my own modified formula for determining mph of 26" wheels.
So if you have a 10t sprocket on the motor and 60t sprocket on the rear, your top speed at maximum motor rpm (2600rpm) would be:
If your bike was a typical e-bike with one gear, you would top out at 33.5mph. The thing is, the higher you gear the bike for speed, the less torque you have for quick starts and tackling hills. With a multi-speed transmission, you can retain your high gear for those times when you need it while having other gears to use if conditions change (stops, hills, headwinds, etc.)
A bicycle's 'transmission' is relatively simple. It consists of 2-3 rings in the front and 5-10 cogs in the back. Using a shifting mechanism (a derailleur, adjusted with a shift lever), the chain hops up and down these two sets of sprockets to create different gear combinations (ratios). Contrast this with a car or motorcycle which uses a 5 (sometimes 6) speed internal gearbox in the front and a stationary cog afixed to the rear wheel (note that you do not have the ability to 'freewheel' on a motorcycle the way you can on a bicycle, since the sprocket is bolted to the wheel). This method uses planetary gearing to change the gear ratio, but also requires the use of a clutch to engage/disengage the flywheel. A clutch is not required on a bicycle; one advantage of this is that no power loss is experienced as in a car (try shifting from first to second in a car without putting in the clutch and you'll see what I'm talking about). Another is that it makes shifting that much simpler.
Bicycles are not restricted to external gearing, however. The old '3-speed' English bikes are an example of a bike with variable gearing which takes place inside the rear hub using planetary gearing. Recent developments in this area by companies like Shimano, SRAM, and Rohloff have put 5,7, and even 14 speed internal hubs on the market. Although they have not gained a huge following, they do have the advantage of being completely sealed and relatively maintenance free, having a cleaner look, and being able to shift while at a stop. New companies like Fallbrook Technologies are springing up as well with creative solutions to the shifting 'problem,' including a CVT hub called the NuVinci.
Now, since all of us here are DIY folk, we know that we have the advantage of being able to build stuff for ourself that mainstream manufacturers might not be able to get away with. Top end speed and motor size restrictions legally tie the hands of companies that would otherwise like to put out a faster, more powerful e-bike. We don't have that problem. But even for those companies, the use of gearing would allow manufacturers to get more bang out of the relatively small motors they are using.
It is (again) one of the laws of physics that a vehicle will only be able to go as fast as the horsepower propelling it. Wind resistance is the primary force working against propulsion. If you hunch lower on your bike and maybe put some fairings on, you will notice that you either don't have to work as hard to maintain a certain speed or you can go faster at a given level of exersion. But even with these techniques, you can only go so fast before the force of the wind stops you from going any faster.
You want your top-end gearing to coincide with the maximum hp that your motor is able to produce at max rpm. There is a somewhat involved formula used to determine this, but Walter Zorn has made it easy with his interactive webpage used to determine bicycle power and speed:
If you find that the gearing you have chosen allows you to travel 33.5mph, but you are only using a 250w engine, then you will find that you only have the horsepower to reach a top speed of 22mph. In this case, gearing down your bike allows for a wider range in gearing, which results in more torque at low speeds--something no one would complain about having.
The more gears you have, the wider a range you can have. Take a mountain bike for instance with a 42/32/22 up front and a 11-34 in the back. Low gear (22/34) produces a (gear inch)GI value of 17; High gear (42/11) would be 99. That's a pretty descent spread. Road racers who are more concerned with speed than low-end torque will typically run a 52-53/39-42 up front to increase GI and, thus, top speed.
So what possibilities does this create for DIY e-bike builders? Well, lots. Like I mentioned earlier, I'm working on a streetcycle made from bicycle parts and a 900w motor. I'm making it a simple 3-speed using an old sturmey-archer hub as a variable-jackshaft, but really i could run 2 or 3 of these for a 6 or 9 speed. if i wanted to I could combine that with a 6,7, or 8 speed rear freewheel and derailleur, or a triple chainring in the front. Too much gearing can get unnecessarily complicated, but having enough to maximize torque and top speed can really help you squeeze as much performance out of your little motor as possible so you can smoke those Harley dudes off the line...with a fraction of the horsepower.