Back o' the envelope calculations-battery-powered bike

I've heard the number claimed that an adult non-athletic fairly ordinary h*mo-sapien sapien can pump out about 60W on a quasi-continuous basis on a bicycle generator (IE: uses primarily leg muscles instead of hands or arms). I find this to be a quite reasonable figure considering adult humans need around 2000 food calories (kilocalories of energy) per day, which works out to an average sitting around energy of 100W.

I would also estimate a human can move somewhere near 20 mph on a decent bicycle in good condition (IE: paved dry roads, clean properly lubricated chain, properly inflated tires) without over exerting themselves.

So we should be able to make the assumption it takes around 60W of useful energy to move at a rate of 20mph on a properly configured bicycle under decent conditions. Efficiency will drop off at higher velocity, so lets makes the simplifying assumption that the bicycle will only be about half as efficient at 40mph than at 20mph. So, this means the bicycle probably needs very roughly 250W (1/3 horse power) continuous useful energy delivered to the wheels in order to sustain 40mph on level terrain.

If we assume a motor plus motor controller combined efficiency of roughly

70%, this means we probably need a 1C battery energy storage of around 350 watt hours. This assumes fairly high efficiency at delivering motor output to the wheels. This is probably a reasonably good assumption if your motor drives the chain or is hub mounted on the wheel. If the motor drives the wheel(s) with a "tire scrubber" approach, expect distinctly lower efficiency still.

So, how much does a 350 watt hour battery pack weigh? Well if you built it from off the shelf high capacity 2500mAh 1.2V nominal AA NiMH cells such as these:

Then you would probably need around 120 cells, if we assume each cell stores around 3 watt hours of energy at a 1C drain rate. Each cell weighs around

1.01 oz plus support material for a full battery pack, so the battery needs to weigh around 7.5 lbs (plus battery pack structural support material). Maybe round that off to 10 lbs.

So it would seem you don't need anywhere near 200 lbs of battery for your application (assuming you don't go the lead acid route). The original GM EV1 had a claimed efficiency of 115 watt hours/mile at a constant speed of

45 mph.

If you had 200 lbs of high capacity NiMH cells like those Energizer AA sized batteries, then they would store around 9500 watt hours. That would be enough to power the GM EV1 full sized electric car a good 80 miles at a constant speed of 45mph.

Decent lithium ion cells may provide even better performance still, although perhaps with a higher price tag:

These are of course back of the envelope calculations and they could pretty easily be off by a factor of two or more, depending.

That's a lot less batteries than I was visualizing. I hadn't thought of human power in terms of watts since to me watts is strongly associated with electrical concepts. I did some looking around and found these links of interest:

I'm thinking more of an electric motorcycle than a bike, though I would leave pedals on it to avoid having to register it as a motorcycle. In my my state if it has pedals and a motor smaller than 50cc it's exempt, and the rules say nothing about electric motors at all. 40 MPH would cover me on most of my route to work, and it's around 14 miles each way. If I could get a range of 30-40 miles out of a single charge then I would have ample reserve margin assuming I could get a partial charge at work.

If I just ballpark the above numbers I think that 1HP motor (for accelleration reserve) and a 1kWh battery pack that weighs in around 40 lbs with controller would be the ticket.

Ultimately I'd like to add regenerative braking as there are several significant hills on the route and it would be a shame to waste that energy as brake heat.

Time to bust out the TIG and start fiddling. :)

JazzMan

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