How do you calculate energy to go differnet speeds.

Discussion in 'Cycling Equipment' started by Bill Smith, May 28, 2003.

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  1. Bill Smith

    Bill Smith Guest

    Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18 mph
    vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more energy
    to hold the pace at 20 or 22 mph.
     
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  2. Bill Smith wrote:
    > Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18
    > mph vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
    > energy to hold the pace at 20 or 22 mph.

    From a physics point of view you are interested in how much *power* it takes to maintain that speed
    - the rate of energy use per second.

    Ignoring second-order effects and whatnot most of your power when peddling at constant speed on
    level ground goes into overcoming wind resistance - and assuming a constant windspeed relative to
    the ground your power output increases with the square of your speed. It's four times as hard to go
    twice as fast, and going from 18-22mph is an increase of (22/18)^2 or about 1.5 times as much power.

    It might *feel* like even more if this level of exertion causes your muscles to switch from aerobic
    exertion to anaerobic - it's pretty subjective and dependant on your body.

    Others may disagree.

    Adam
     
  3. Ron Hardin

    Ron Hardin Guest

    Jacobe Hazzard wrote:
    > Ignoring second-order effects and whatnot most of your power when peddling at constant speed on
    > level ground goes into overcoming wind resistance - and assuming a constant windspeed relative
    > to the ground your power output increases with the square of your speed. It's four times as hard
    > to go twice as fast, and going from 18-22mph is an increase of (22/18)^2 or about 1.5 times as
    > much power.

    Actually it's the cube
    --
    Ron Hardin [email protected]

    On the internet, nobody knows you're a jerk.
     
  4. Dr. Dave

    Dr. Dave Guest

    Bill Smith wrote:
    > Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18
    > mph vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
    > energy to hold the pace at 20 or 22 mph.

    http://www.kreuzotter.de/english/espeed.htm
     
  5. Ron Hardin wrote:
    > Jacobe Hazzard wrote:
    >> Ignoring second-order effects and whatnot most of your power when peddling at constant speed on
    >> level ground goes into overcoming wind resistance - and assuming a constant windspeed relative
    >> to the ground your power output increases with the square of your speed. It's four times as hard
    >> to go twice as fast, and going from 18-22mph is an increase of (22/18)^2 or about 1.5 times as
    >> much power.
    >
    > Actually it's the cube

    How is that? I would have thought that the drag force is proportional to the speed so...
     
  6. Ron Hardin

    Ron Hardin Guest

    Jacobe Hazzard wrote:
    > How is that? I would have thought that the drag force is proportional to the speed so...

    You're right, but the power is the force times the speed.
    --
    Ron Hardin [email protected]

    On the internet, nobody knows you're a jerk.
     
  7. Ron Hardin

    Ron Hardin Guest

    Ron Hardin wrote:
    >
    > Jacobe Hazzard wrote:
    > > How is that? I would have thought that the drag force is proportional to the speed so...
    >
    > You're right, but the power is the force times the speed.

    Sorry, I misread your ``would have thought'' - the drag force is the square of the speed; you hit
    twice as much air twice as hard.

    and then the speed multiplies force again to get power.
    --
    Ron Hardin [email protected]

    On the internet, nobody knows you're a jerk.
     
  8. Ron Hardin wrote:
    > Ron Hardin wrote:
    >>
    >> Jacobe Hazzard wrote:
    >>> How is that? I would have thought that the drag force is proportional to the speed so...
    >>
    >> You're right, but the power is the force times the speed.
    >
    > Sorry, I misread your ``would have thought'' - the drag force is the square of the speed; you hit
    > twice as much air twice as hard.
    >
    > and then the speed multiplies force again to get power.

    Yeah you're right of course. My assumptions were wrong.

    Adam
     
  9. Velocat

    Velocat Guest

    Bill Smith wrote:
    > Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18
    > mph vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
    > energy to hold the pace at 20 or 22 mph.

    From: http://www.analyticcycling.com/ForcesPower_Page.html

    you can find the answer to your questions.

    18mph = 103.5W 20mph = 135.8W 22mph = 174.7W

    These use the default assumptions about weight, wind, etc.
     
  10. Bill Smith

    Bill Smith Guest

    So are you guys saying that to go from 18 mph to 22 mph it would be
    (22/18)^3 or 1.8 times more energy. It feel like that but I would not have thought theoretically
    it would be.
     
  11. "Jacobe Hazzard" <[email protected]> writes:

    [snip]
    >
    > Ignoring second-order effects and whatnot most of your power when peddling at constant speed on
    > level ground goes into overcoming wind resistance

    Agreed so far.

    > - and assuming a constant windspeed relative to the ground your power output increases with the
    > square of your speed.

    The wind resistance _force_ increases with the square of the speed, hence the _power_ needed to
    overcome it increases whith the cube of the speed.

    > It's four times as hard to go twice as fast,

    Eight times as hard.

    > and going from 18-22mph is an increase of (22/18)^2 or about 1.5 times as much power.

    By doubling your power output you can increase your speed by approximatly 1/4.

    >
    > It might *feel* like even more

    Indeed, trust your feelings, in this case they coincide with classic physics.

    > if this level of exertion causes your muscles to switch from aerobic exertion to anaerobic - it's
    > pretty subjective and dependant on your body.
    >
    > Others may disagree.

    Yes.

    >
    > Adam
    >
    >

    --
    __o | Øyvind Røtvold _`\(, | http://www.darkside.no/olr/index.html (_)/(_) | ... biciclare
    necesse est ...
     
  12. [email protected] (Bill Smith):

    >Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18 mph
    >vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
    >energy to hold the pace at 20 or 22 mph.

    Well, there's bikepwr.c by Ken Roberts, see http://www.mystrobl.de/ws/fahrrad/bikepwr.htm,
    for example.

    A year a go, I ported this to Python for better readability
    http://www.mystrobl.de/ws/fahrrad/PyBikePower/bike_pow.py and made a portable graphical version
    using wxWindows/wxPython: http://www.mystrobl.de/ws/fahrrad/PyBikePower/pybikepwr.html (sorry, this
    page is German language only - the program itself has English messages). For MS Windows there is a
    .msi package available at http://www.mystrobl.de/ws/fahrrad/PyBikePower/bike_pow.msi

    --
    Wir danken für die Beachtung aller Sicherheitsbestimmungen
     
  13. On Wed, 28 May 2003 20:36:19 GMT, [email protected] (Bill Smith) wrote:

    >Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18 mph
    >vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
    >energy to hold the pace at 20 or 22 mph.

    www.analyticcycling.com
     
  14. There is an article in the Rivendell reader (RR27) entitled "Force, Horsepower, Speed, Math, and
    Climbing" by Michael Barnes. Mr. Barnes' primary focus is how much more energy is required to climb
    per extra pound carried. However, he provides a link to a really nifty spreadsheet of his own
    creation. With this spreadsheet, you can build your own scenarios to model the effects of weight and
    wind on your output:

    http://www.ucop.edu/~mbarnes/bike.xls

    Trevor

    "Bill Smith" <[email protected]> wrote in message
    news:[email protected]...
    > Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18
    > mph vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
    > energy to hold the pace at 20 or 22 mph.
     
  15. Bill Smith

    Bill Smith Guest

    I was unable to find this article or go to this web site. Could you provide me with some additional
    information?

    Bill Smith

    On Sat, 31 May 2003 02:29:59 GMT, "Trevor Taylor" <[email protected]> wrote:

    >There is an article in the Rivendell reader (RR27) entitled "Force, Horsepower, Speed, Math, and
    >Climbing" by Michael Barnes. Mr. Barnes' primary focus is how much more energy is required to climb
    >per extra pound carried. However, he provides a link to a really nifty spreadsheet of his own
    >creation. With this spreadsheet, you can build your own scenarios to model the effects of weight
    >and wind on your output:
    >
    >http://www.ucop.edu/~mbarnes/bike.xls
    >
    >Trevor
    >
    >"Bill Smith" <[email protected]> wrote in message
    >news:[email protected]...
    >> Does anyone out there know how to calculate the amount of energy it takes to pedal a bike at 18
    >> mph vs 20 or 22mph? I know I can keep a steady pace of 18 mph but it sure seem to take a lot more
    >> energy to hold the pace at 20 or 22 mph.
     
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