Math question

NorthCascades
NorthCascades Posts: 10,968 Member
in Fitness and Exercise
I went for a ride the other day, and didn't notice that my Garmin had my crank length at 172.5 instead of 175 mm. My PM is in my pedals. Did it over or under report power on that ride? I realize the difference is small, I'm curious though.

Replies

  • Jthanmyfitnesspal
    Jthanmyfitnesspal Posts: 3,522 Member
    Well, torque is force times radius, and power is torque times angular velocity. I assume the power meter uses your cadence to get angular velocity and the force from the sensor, so the error in the crank length will cause a linear error in the power. Only 1.4% in this case. No big deal.
  • BrianSharpe
    BrianSharpe Posts: 9,248 Member
    Jthanmyfitnesspal wrote: »
    Well, torque is force times radius, and power is torque times angular velocity. I assume the power meter uses your cadence to get angular velocity and the force from the sensor, so the error in the crank length will cause a linear error in the power. Only 1.4% in this case. No big deal.

    Parlez vous anglais? :p
  • magnusthenerd
    magnusthenerd Posts: 1,207 Member
    Seems like a physics question, really.
  • cmriverside
    cmriverside Posts: 34,416 Member
    I would say it over-reported.






    Bah. I had a 50/50.

    I'm wanting someone to answer though! I'm just going on a sense...

  • 99clmsntgr
    99clmsntgr Posts: 777 Member
    Thank you for tickling my engineer nerdiness.

    To echo @Jthanmyfitnesspal -

    Power (kW) = Torque (N*m) x Speed (RPM) / 9.5488

    Torque (N*m) = Push force (N) * crank arm (m)

    For all other variables held constant, the shorter crank arm setting will under report your power estimates for your ride. But, like jthan said, it's a 1.4% error. Fix your settings and move on without worrying about it.
  • NorthCascades
    NorthCascades Posts: 10,968 Member
    That's what I thought, longer arm would be more leverage so probably less power. Wasn't sure though and sometimes my hunches start me wrong.

    I'm not losing any sleep over it, but I'm a curious person and wanted to nail it down.

    Thanks everybody!
  • Jthanmyfitnesspal
    Jthanmyfitnesspal Posts: 3,522 Member
    NorthCascades wrote: »
    That's what I thought, longer arm would be more leverage so probably less power.

    This is where the physics teacher does a face palm.

    Doh2.gif

    The longer crank arm for the same force and cadence does more work and produces more energy. See above.

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