Well...by definition, the coefficient of rolling resistance (Crr) is the ratio of retarding force divided by the tire load, i.e. Crr = RetardingForce/Wheel Load.

So, weight is already "baked into" the measurement. That's why it doesn't need to be repeated over varying loads.

Let's put it this way...if you measure Crr at a given wheel load, then you know what it will be at any other wheel load (for the same pressure). It just a varies linearly :-)

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Wow, mic drop. Thank you Tom.

Yup. Rolling resistance and Coefficient of rolling resistance are not the same thing, which is probably what's causing the confusion on the weight front.

That said, the point I think the OP is trying to make is Crr does vary by tyre pressure and lighter riders may typically use less pressure (and heavier riders more pressure). I suspect however the change in Crr over the range of pressures typically in question is not large and that the Crr v tyre pressure curve for most tyres won't differ much, with the bigger problem being at the over-inflated end of the spectrum and rougher roads.


As a complete aside, another way to think of Crr is that is has the same effect on power demand as adding gradient. In that way understanding impact of mass is easy conceptualise.

IOW a Crr of 0.005 is the same as adding 0.5% gradient.


Choosing tyres wisely is the same as riding up a less steep hill than someone else.




Below is more detail on why that's the case:

It's because power to overcome rolling resistance and power to increase potential energy take a similar physics/maths form, and "trig errors" at typical gradients are tiny:

Prr = Vg.m.g.Crr.Cos(i)
Ppe = Vg.m.g.Sin(i)


where Vg is ground velocity,
m = mass
g = acceleration due to gravity
i = arctan(gradient)


We can see that both have same factor of: Vg.m.g

and we are left with examining the differences between:
Crr * cos(arctan(gradient))
and
sin(arctan(gradient))



let's examine a Crr of 0.005 and a difference in power demand between gradients of 0% and 0.5%.


Prr ∝ 0.005 * cos(arctan(0.005)) = 0.0049999375

Ppe ∝ sin(arctan(0.005)) - sin(arctan(0.000)) = 0.0049999375

So on flat road, Crr = extra gradient.



At steep gradients, e.g. 10% and 10.5%:
Ppe ∝ sin(arctan(0.105)) - sin(arctan(0.100)) = 0.004922211

Prr ∝ 0.005 * cos(arctan(0.1)) = 0.00497518595

So even at steep gradients the trig error introduced by this simplification is only 1.6%

IOW we can for most intents and purposes say Crr has the equivalent effect as adding the Crr value to gradient.

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