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Rolling resistance coefficient (Crr) in cycling: what it is, what it costs and how to measure it on the road

Equipment6 min readBorja Alfaraz

Rolling resistance

9.5 W

That is the cost of going from a Crr of 0.004 to 0.005 at 40 km/h with 85 kg of rider and bike.

Over a 40 km time trial at 250 W and CdA 0.30 m², that difference is 51 seconds. Model calculation.

Summary. The rolling resistance coefficient (Crr) sums up how much energy tyres lose as they deform against the ground. We explain its role in the power equation1, what it depends on (tyre, pressure, load and surface3) and how to estimate it on the road with a power meter2.

Crr is a dimensionless number, typically between 0.003 and 0.006 on the road, which multiplied by weight gives the force resisting motion due to rolling. Unlike air drag it does not grow with the square of speed: the power it consumes grows only in proportion to speed and weight.

How much power does rolling resistance take?

The power required is P = Crr · m · g · v, divided by drivetrain efficiency1. With 85 kg at 40 km/h:

20304050600.0030.0040.0050.006CrrW
Figure 1. Power consumed by rolling resistance at 40 km/h with 85 kg of rider and bike, by Crr. Model calculation.

Every thousandth of Crr is 9.5 W at that speed. That is the same order as many aerodynamic equipment upgrades, and usually cheaper to achieve: a top tyre with a good inner tube or tubeless setup can save more watts than many aero parts.

What does Crr depend on?

  • The tyre: casing, compound and tread thickness. Differences between race and training tyres are large.
  • Pressure and load: on a smooth surface, more pressure reduces deformation and Crr, and more load increases it3.
  • The surface: on rough tarmac the tyre and rider vibrate, and beyond a certain pressure the result stops improving or gets worse. That is why the optimal road pressure is rarely the maximum.
  • Temperature: warmer rubber loses less energy, so the same tyre rolls a little better on a hot day.

How do you measure it on the road?

Crr and CdA can be separated with a power meter because they depend on speed differently: rolling force is almost constant while aerodynamic force grows with the square of speed. Riding several constant speeds on the same flat, windless stretch and plotting force against speed squared gives a straight line: the slope gives CdA and the intercept gives Crr2,4.

  1. Pick a flat stretch with uniform tarmac and no traffic, on a windless day.
  2. Ride constant-speed passes at 4 or 5 speeds, for example from 20 to 40 km/h, in both directions.
  3. Calculate the average force of each pass (power divided by speed, corrected for the drivetrain).
  4. Fit a line of force against v². Intercept = Crr·m·g; slope = ½·ρ·CdA.

This method detects small changes in CdA and Crr with bike-mounted power meters2. Chung’s virtual elevation method does the same with a single variable-speed ride and is easier in practice (see how to measure CdA without a wind tunnel). To separate Crr well, the ride must include low-speed sections, where rolling resistance weighs more.

Rule of thumb: to compare two tyres, test both on the same day, on the same stretch, at the same pressure, alternating them. Crr changes with temperature and tarmac more than between many good tyres.

What is known and what is not

Crr’s role in the power equation is solid, and models that include it predict road power well1. What is uncertain is the exact value for each combination of tyre, pressure and tarmac: lab drum tests rank tyres well but do not reproduce the roughness of a real road. That is why it pays to measure on the tarmac you will race on.

Frequently asked questions

What is a normal Crr for a road bike?

Between 0.003 and 0.004 with race tyres on good tarmac, and between 0.005 and 0.006 with training tyres or rough tarmac.

Does more pressure always roll faster?

On a smooth surface, yes. On rough tarmac there is a point beyond which more pressure stops helping, because vibration increases.

References

  1. Martin JC, Milliken DL, Cobb JE, McFadden KL, Coggan AR. Validation of a mathematical model for road cycling power. J Appl Biomech. 1998;14(3):276-91. doi:10.1123/jab.14.3.276
  2. Lim AC, Homestead EP, Edwards AG, Carver TC, Kram R, Byrnes WC. Measuring changes in aerodynamic/rolling resistances by cycle-mounted power meters. Med Sci Sports Exerc. 2011;43(5):853-60. doi:10.1249/MSS.0b013e3181fcb140
  3. Grappe F, Candau R, Barbier B, Hoffman MD, Belli A, Rouillon JD. Influence of tyre pressure and vertical load on coefficient of rolling resistance and simulated cycling performance. Ergonomics. 1999;42(10):1361-71. doi:10.1080/001401399185009
  4. Debraux P, Grappe F, Manolova AV, Bertucci W. Aerodynamic drag in cycling: methods of assessment. Sports Biomech. 2011;10(3):197-218. doi:10.1080/14763141.2011.592209

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