How a quarter-car model computes IRI
IRI is just the suspension's relative travel rate, integrated over distance, when a standardized two-mass car drives over your road profile at 80 km/h. The simulation below is the standard golden car running live — drag the bump amplitude up and watch IRI climb.
The trick: don't measure the road, measure how a car reacts to it
A road profile is just elevation vs. distance. Two roads can have the same RMS roughness but feel completely different to drive — one rattles your teeth, the other lulls you to sleep. The reason is that a vehicle's suspension is a filter: it cares about wavelengths that excite its sprung-mass and axle resonances, and ignores wavelengths outside that band.
So instead of computing roughness from the profile directly, you simulate driving a standardized car over the profile and measure how much its suspension worked. That's IRI. The standardization matters: everyone in the world uses the same fictional vehicle (the "golden car") with the same parameters, so two engineers running the same profile through their own code get the same number.
The simulation above runs the standard golden-car ODE with parameters $k_1 = 63.3$, $k_2 = 653$, $\mu = 0.15$, $c = 6.0$ (Sayers' normalized form), at 80 km/h, integrated with a 1 ms timestep. The IRI readout is the running average of |ż_s − ż_u| divided by distance traveled — exactly what the standard defines.
Versus measuring the profile directly
| RMS of profile | IRI (quarter-car) | |
|---|---|---|
| What it measures | Statistical roughness of the road surface | Suspension work the road forces a car to do |
| Sensitive to wavelength? | No — all wavelengths weighted equally | Yes — band-pass shaped by golden car dynamics |
| Two roads with same answer feel… | …sometimes very different to drive | …similar to drive, by construction |
| Standardized? | Depends on profile sample interval | Yes — fixed vehicle, fixed speed, fixed band |
| Used by | Internal QC, profile validation | World Bank, FHWA, every DOT, contract specs |
Where you'll meet it
Pavement contracts ("must deliver IRI < 1.5 m/km on completion"), pavement management systems prioritizing rehab, ride-quality acceptance criteria, and — relevantly to heavy-truck testing — establishing whether a test course represents the operating environment. The ASTM E950 / E1926 family of standards specifies how to compute it from a measured profile; HDM-4 uses it as the input to its rolling-resistance and vehicle-operating-cost models.