How this instrument works
Rolling resistance is not sliding friction. Tyres flatten where they meet road, and rubber, being viscoelastic, hands back less energy than went into squashing it. That shortfall shifts ground reaction a few millimetres ahead of an axle, and that offset arm creates torque opposing rotation. Divide arm by wheel radius and out falls C_rr — one dimensionless number standing in for hysteresis in rubber, tread scrubbing across contact patches, plus modest bearing loss besides.
Coulomb rolled loaded cylinders across timber in 1785 and found resistance dropping as radius grew, which is that arm-over-radius picture in embryo. Modern figures come from ISO 28580: loaded tyres are pressed against a 1.7-metre steel drum spun at 80 km/h and force is read directly. EU labels grade car tyres from class A, at 0.0065 and below, down to E. Familiar magnitudes: steel rail under a train, 0.001; racing bicycle, 0.003; car on good asphalt, 0.01; that same car on loose sand, 0.3.
Two assumptions sit inside F_rr = C_rr·m·g. Ground is level, so normal load equals weight; and one coefficient covers all conditions. Point a car uphill and normal load falls to m·g·cos θ while gravity adds m·g·sin θ down-slope, terms that must be kept apart. C_rr drifts too — climbing with speed, falling as tyres warm through, rising sharply on soft pressure. Take a single coefficient as a sound first pass, never as a final word.
- Set Rolling resistance coefficient. Use 0.01 for a car tyre on dry asphalt, 0.005 for truck radials, 0.02 and up for gravel or wet grass.
- Enter Vehicle mass in kilograms, tonnes, or pounds — kerb weight plus passengers and cargo, since every kilogram presses down through those tyres.
- Read Rolling resistance force in newtons, kilonewtons, or pounds-force.
- Multiply that force by road speed in metres per second when you want power in watts, or by distance in metres for energy in joules.
Worked example — a 1500 kg hatchback on dry tarmac
A 1500 kg hatchback runs decent tyres at placard pressure, so C_rr = 0.01. Substituting gives F_rr = 0.01 × 1500 × 9.80665 = 147.09975 N — call it 147 newtons, near 15 kgf, roughly what a loaded shopping trolley asks of your arms. Crucially that force is there whether this car creeps across a car park or holds motorway pace.
Turned into energy it stops sounding trivial. At 100 km/h, or 27.78 m/s, 147 N draws 4.1 kW purely to keep rubber turning; across a 400 km run it absorbs 58.8 megajoules, which at a realistic 25 per cent engine efficiency burns close to seven litres of petrol. Aerodynamic drag on a car this shape only overtakes rolling resistance around 70 km/h — which is why tyre choice governs town driving and body shape governs motorway driving.
Questions
Is a rolling resistance coefficient the same as a coefficient of friction?
No, and mixing them up is the mistake people actually make. Coefficient of friction measures grip — how hard rubber can brake or corner before sliding, typically 0.8 to 1.0 on dry asphalt. C_rr measures energy lost to deformation while rolling straight ahead, around a hundred times smaller. A low-C_rr tyre is efficient, not slippery. Compound chemistry and casing stiffness let engineers tune both almost independently.
Does rolling resistance change with speed?
Hardly at all across normal road speeds, which is precisely why one flat coefficient earns its keep. Careful drum tests show C_rr creeping upward as pace rises, often fitted as C_rr = a + b·v², yet below roughly 120 km/h that correction stays within a few per cent. Higher still, standing waves in sidewalls make it climb steeply. Air drag, scaling as velocity squared, moves far faster and dominates long before this term does.
Why does under-inflation cost so much fuel?
A softer tyre flattens over a longer contact patch, so more sidewall flexes on every revolution and more heat is thrown away. Running 0.5 bar under placard pressure typically lifts C_rr by 10 to 20 per cent, turning 147 N into 165 N or worse. Checking pressure monthly is among very few fuel savings available for nothing but a gauge and two minutes.
How do I apply this on a hill?
Split those two effects apart. On a slope of angle θ, normal load drops to m·g·cos θ, so rolling resistance becomes C_rr·m·g·cos θ, while gravity separately adds m·g·sin θ pulling backwards. At a 5 per cent grade cos θ is 0.9988 and rolling resistance barely notices, but that gravity term piles 735 N onto a 1500 kg car — five times larger. Use this sheet for level ground, then add a grade term yourself.
What units does the coefficient carry?
None. C_rr is dimensionless, a bare ratio of retarding force to normal load. Geometrically it equals forward offset of ground reaction divided by wheel radius — millimetres over millimetres. So it reads identically in SI or imperial work; only mass and force need converting, which is what those unit menus handle.
Do heavier vehicles always meet more rolling resistance?
In direct proportion, yes: double mass and force doubles, because load and deformation scale together. Per tonne carried, though, big vehicles do rather well. Truck radials reach C_rr near 0.005, half a passenger tyre's figure, since tall stiff casings flex proportionally less. Steel wheel on steel rail manages 0.001 or better, which is exactly why bulk freight still travels by train.