# Back o' the envelope calculations-battery-powered bike

Discussion in 'Electronic Basics' started by JazzMan, Oct 29, 2005.

1. ### JazzManGuest

So, if I wanted to build an electric bike that would
be able to do at least 40mph, go 40 miles between charges,
and have decent accelleration above 20 mph, what would
I be looking at for batteries? I'm assuming either LiPo
or NiMh, no regenerative braking, and pedal power for the
first 10 MPH from stop signs. I have no idea where to
even begin. I'm assuming up to around 200 lbs for batteries.

JazzMan
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2. ### Fritz SchlunderGuest

I've heard the number claimed that an adult non-athletic fairly ordinary
homo-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:

http://data.energizer.com/PDFs/nh15.pdf

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.

http://avt.inel.gov/pdf/fsev/eva/genmot.pdf

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:

http://www.batteryspace.com/index.asp?PageAction=VIEWPROD&ProdID=945

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

3. ### JazzManGuest

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:

http://www.green-trust.org/2000/humanpower.htm
http://www.ebikes.ca/FAQ/

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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