Formula for battery capacity

Discussion in 'iPod touch' started by ivanlul, Mar 18, 2009.

  1. ivanlul

    ivanlul New Member

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    I was thinking about the iPod's battery for a while and I came up with a formula to model it's battery capacity ( the amount of "charge" it can hold from it's original state ), I used y = Ce^(kt) to model it.

    Here it is:

    ln(%/100)/(ln(4/5)/400)=c

    The variables are % and c

    % = the percent of change you are aiming at multiplied by 100 (i.e 50% = .5*100 = 50, so the percent without the percent sign)

    c = how many charges it will take to reach that capacity percent

    Now with than and simple algebra you can figure out when your battery reach a desired capacity.

    How I got the formula:

    First, things I assumed:

    1. Battery capacity exponentially decreases
    2. Battery capacity goes from 100% to 80% in 400 charges
    http://www.apple.com/batteries/ipods.html

    OK, here is the math stuff:

    y = Ce^(kt)
    or
    % = Ce^(kc)

    Plug In the info we know

    80 = 100e^(kc)
    80 = 100e^(k400)
    (80/100) = e^(k400)
    ln(80/100) = k400
    (ln(80/100)/400) = k

    again

    % = Ce^(kc)

    % = 100e^((ln(80/100)/400))c
    %/100 = e^((ln(80/100)/400))c
    ln(%/100) = ((ln(80/100)/400))c
    ln(%/100)/(ln(80/100)/400) = c

    80/100 simplifies to 4/5

    ln(%/100)/(ln(4/5)/400)=c


    Ohfoohy made a program for this formula:

    Click here
  2. Alok

    Alok New Member

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  3. ivanlul

    ivanlul New Member

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  4. Deadhead

    Deadhead New Member

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    Colud I get a bit more detail? Where did (4/5)/300 come from? I haven't seen this used in a long time(at least 15 years)
  5. ivanlul

    ivanlul New Member

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    Sure, I'll update the first post
  6. FluffyofDoom

    FluffyofDoom Member

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    wow i raised one eyebrow and was scratchin my head while i was scrolling down

    im still 13 almost 14 in 2 days i dont think ive gone over this lol
  7. Duykur

    Duykur Banned

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    too bad the equation looks horrible on a computer
  8. ivanlul

    ivanlul New Member

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    yeah lol
  9. john_van1

    john_van1 Banned

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    hahaha are you gonna make an app for this huge formula?hmmm
  10. bluepigster

    bluepigster New Member

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    Now this would be useful if it could actually help us, but no....

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