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Back o' the envelope calculations-battery-powered bike

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

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  1. JazzMan

    JazzMan Guest

    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.

    Please reply to jsavage"at"
    Curse those darned bulk e-mailers!
    "Rats and roaches live by competition under the laws of
    supply and demand. It is the privilege of human beings to
    live under the laws of justice and mercy." - Wendell Berry

  2. 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

    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

    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.
  3. JazzMan

    JazzMan Guest

    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. :)

    Please reply to jsavage"at"
    Curse those darned bulk e-mailers!
    "Rats and roaches live by competition under the laws of
    supply and demand. It is the privilege of human beings to
    live under the laws of justice and mercy." - Wendell Berry
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