Power meters · Public discussion

inc^speed=power cubed for 40kTT

Started by grom · · Last activity · 6 posts · 1,444 views

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Power meters
Published
18 March 2006
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18 March 2006
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grom
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  1. robkit said:

    (frontal area .5m2, weight 75kg, gradient 0, cranks 172.5, all other inputs @ default)
    analyticcycling.comForcesPower Page.html
    mph met/sec watts increment factor increment time (mins) time (mm:ss) 1 mile
    20 8.9408 136 0 1.00 0.00 30.00 30:0 3:0
    21 9.38784 154 19 1.14 1.14 28.57 28:34 2:51
    22 9.83488 175 20 1.29 1.13 27.27 27:16 2:43
    23 10.28192 197 22 1.45 1.13 26.09 26:5 2:36
    24 10.72896 221 24 1.63 1.12 25.00 25:0 2:30
    25 11.176 247 26 1.82 1.12 24.00 24:0 2:24
    26 11.62304 275 28 2.02 1.11 23.08 23:4 2:18
    27 12.07008 305 30 2.25 1.11 22.22 22:13 2:13
    28 12.51712 337 32 2.48 1.11 21.43 21:25 2:8
    29 12.96416 372 35 2.74 1.10 20.69 20:41 2:4
    30 13.4112 409 37 3.01 1.10 20.00 20:0 2:0

    how does this relate to the power cubed statement/equation for increases in speed (change in speed is equal to power cubed???)
    ie if a 2mph increase in speed is equal to 2cubed then the change is2x2x2=8watts (which is so low its rediculous) and which here going from 221watts at 24mph then to 26mph the watts are275w( i believe to be correct), where is the cubing error because to go further and say 10 mph change is impossible to go to10x10x10=1000 watt change for 10 mph increase, and thanks robkit for the original data

  2. grom said:

    how does this relate to the power cubed statement/equation for increases in speed (change in speed is equal to power cubed???)
    ie if a 2mph increase in speed is equal to 2cubed then the change is2x2x2=8watts (which is so low its rediculous) and which here going from 221watts at 24mph then to 26mph the watts are275w( i believe to be correct), where is the cubing error because to go further and say 10 mph change is impossible to go to10x10x10=1000 watt change for 10 mph increase, and thanks robkit for the original data


    You're applying the math wrong, unfortunately. A 2^3 increase in power doesn't produce a 2mph increase in speed, but rather a *doubling* of speed. If you're going from 24 --> 26mph, that would be an increase factor of (26/24) = 1.0833. The power requirement should then be somewhere close to 1.0833^3 = 1.27 times. According to the data above, the actual power increase was (275/221) = 1.24.

    Also, note that the aerodynamic portion of the power equation increases by a cubed factor, but there are other portions that only vary by speed^1, so the true power curve will not be a perfect y=Cx^3 curve. Hope that helps.

  3. I was always wondering how come my speeds never match the speeds given power on analytical cycling.com. Are those speeds on time trial bikes? I mean 21mph at 155 watts?? Could someone please explain that. I tried surfing around on that site but to no avail thanks. 😕

    Alex

  4. Hoghunter said:

    I was always wondering how come my speeds never match the speeds given power on analytical cycling.com. Are those speeds on time trial bikes? I mean 21mph at 155 watts?? Could someone please explain that.


    According to some posters that claim to have seen real-world test data from pro riders, the AC.com defaults do represent a *very* tight TT position.

  5. frenchyge said:

    You're applying the math wrong, unfortunately. A 2^3 increase in power doesn't produce a 2mph increase in speed, but rather a *doubling* of speed. If you're going from 24 --> 26mph, that would be an increase factor of (26/24) = 1.0833. The power requirement should then be somewhere close to 1.0833^3 = 1.27 times. According to the data above, the actual power increase was (275/221) = 1.24.

    Also, note that the aerodynamic portion of the power equation increases by a cubed factor, but there are other portions that only vary by speed^1, so the true power curve will not be a perfect y=Cx^3 curve. Hope that helps.

    Hope that helps .. hope that helps... of course that helps, i was applying the aerodynamic portion to the entire change in speed thanks a bunch 🙂

  6. grom said:

    Hope that helps .. hope that helps... of course that helps, i was applying the aerodynamic portion to the entire change in speed thanks a bunch 🙂


    🙂 . Well, the aero portion is the dominant factor while riding on the flats, so the overall power curve does 'closely' resemble a cubed function, as the example above shows. On an incline, the weight factor becomes increasingly important, which is a linear function w/ speed, as is rolling resistance (which is typically minor).

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