Rolling Resistance & Grade
The two road-load terms that don't need a wind tunnel: the tyre's rolling drag and the weight you lift up a hill.
Underinflate your tyres by a third and your fuel economy quietly drops several percent. That invisible loss is rolling resistance — and it is one of the easiest road-load terms to quantify.
Where rolling resistance comes from
A rolling tyre looks round, but under load it flattens into a contact patch and the carcass deforms continuously as it rolls. The rubber and casing are not perfectly elastic — energy goes into deforming the tread as it enters the patch and is not fully recovered as it leaves. That hysteresis loss shows up as a small but persistent retarding force: rolling resistance. Remarkably, over normal driving speeds it is nearly proportional to the vertical load, so engineers lump it into a dimensionless rolling-resistance coefficient Cr and write the force as Frolling = Cr·mg. Passenger-car radials have Cr around 0.008–0.015; low-rolling-resistance 'eco' tyres push toward the bottom of that range; soft off-road tyres are higher.
On a slope, a second, larger effect appears. Gravity pulls the car straight down, and on an incline a component of the weight acts down the slope, resisting forward motion uphill (or aiding it downhill). This grade resistance is mg·sin θ for a road at angle θ to the horizontal. Road signs express slope as a percentage rise (a 10% grade rises 10 m per 100 m horizontal); for modest grades, sin θ ≈ tan θ ≈ grade fraction, so a 10% grade gives roughly mg × 0.10 of resistance — far larger than rolling resistance.
Compare the two at the same weight. Rolling resistance at Cr = 0.012 is about 1.2% of the car's weight. A 12% mountain grade is ten times larger — 12% of the weight pulling the car downhill. This is why a car that cruises effortlessly on the flat labours up a steep hill: the grade term, not rolling resistance or drag, suddenly dominates the road load. It is also why heavy vehicles need such low crawl gears on grades.
- Rolling resistance = Cr·mg = 0.012 × 1500 × 9.81 = 176.6 N
- Grade resistance = mg·sin θ = 1500 × 9.81 × 0.08 = 1177.2 N
- Combined low-speed road load = 176.6 + 1177.2 = 1353.8 N
- F_roll = Cr·mg = 0.010 × 1200 × 9.81 = 117.7 N
Check your understanding
- Rolling resistance ≈ Cr·mg, a fixed fraction of weight (passenger radials Cr ≈ 0.008–0.015) from tyre hysteresis
- Grade resistance = mg·sin θ ≈ mg × grade fraction for modest slopes
- On a steep grade, grade resistance dominates total road load (a 12% grade ≈ 10× a typical rolling term)
- These two form the speed-independent part of road load; aerodynamic drag is quantified in Module 11