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  1. #1
    mtbr member
    Join Date
    Jul 2011

    Weight weenie calculations

    Maybe this has been raised before, but I will put it up just in case it hasn't.

    Found this web page with regards to extra mass on the wheel.

    Now as an example; consider
    A. a bike that weighs 13kg, of which 3kg in rotational mass (wheels/tyres).
    B. same bike using 0.5kg less in rotational weight due to lighter rims.

    Using the formula in that document you will calculate an improvement of 6.3% by going with combo B.

    My question is; why isnt the riders (kitted) weight included as part of the translational component? After all, the bike doesnt ride itself. If you assume a riders weight of 100kg then the improvement of B. is only 0.9%. And as the document says this advantage is only realised on accelerations!

  2. #2
    mtbr member
    Reputation: sissypants's Avatar
    Join Date
    Sep 2016
    You are correct that the rider weight should be included as translational mass IF you are assuming the rider's mass is rigid and fixed to the bike. The formula for the fold change in kinetic energy required for acceleration after removing a mass of "x" from rotational weight would then be:

    fold change in kinetic energy = 2x/(total bike mass + rotational mass + rider mass)

    Where rotational mass is defined as anything with significant rotational momentum, such as rims and wheels (not hubs, cassettes), assuming rotational mass on the cassette, rotors, and spokes is negligible.

    Suppose you are 80kgs, ride a 10kg bike, have 350g rims and 650g tires and will upgrade to 280g rims and 540g tires (rotational mass = 2.7kg, x = 0.360 kg), the fold change in kinetic energy required to accelerate will be:

    2*0.360kg/(80kg+10kg+2.7kg) = 0.0078, or 0.78%.

    That seems negligible.

    But you are not a rigid body of mass affixed to your bike. You are a dynamic mass capable of pumping, pushing, pulling, and jumping. This is not something that is easy to describe with simple physics equations, so the easiest way to get a quantitative measurement of the effect of rolling weight is to use a power meter.

    When you have a power meter, you can ride the same segment of trail, output the same amount of watts, and ride it repeatedly on either wheelset. After getting a statistically satisfactory sample size, you can compare how much extra power that additional weight took. Power is just energy divided by time.

    To make this experiment more reliable, I would plot actual average power for that segment against speed. Then perform two linear regressions, one for the dataset with heavier wheels, one with lighter wheels. Then pick a given wattage that is representative of the dataset and calculate the power from those equations. You can also get confidence statistics as well.

    Ultimately, each rider will have a unique exponential coefficient that can be experimentally determined. This coefficient can be placed into the standard equation for fold change, and will be proportional to their handling skills and bike setup.

    Bike wheels are the most important place to shave weight, but this difference will only be more substantial than the rest of the bike when accelerating, not when travelling at constant speed. Other very important aspects of the bike involve reducing tire tread rolling resistance, drivetrain friction (bottom bracket bearings, chain/chainring interface, chain/cassette interface aka derailleur alignment, derailleur pulleys, derailleur cage alignment (not bent), hub drag (good bearings and efficient freehub mechanism), and brake pad rub (a good bleed can help). Finally, don't underestimate aero benefits even on an MTB. A sleek posture, skinsuit, more aero helmet, and aggressive form make a difference when bucking headwinds or traveling quickly.

    Weight weenie-ism is just a small part of the equation.

  3. #3
    mtbr member
    Join Date
    Jul 2011
    appreciate the reply Sissypants. Wished I thought this through properly years ago. Doh~!

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