Exact relationship between IRI and the roughness PSD coefficient G_d(n0)

Derive an exact analytical relationship between the International Roughness Index (IRI, in m/km, measured per the Sayers et al. protocol) and the road elevation roughness power spectral density coefficient G_d(n0) at the reference wavenumber n0 = 0.1 m^{-1}, replacing the current approximate mapping IRI ≈ 0.22√G_d(n0) that is used to convert measured roughness indices into model parameters for vibration and resistance calculations.

Background

The paper models road roughness via the International Roughness Index (IRI) and uses a standard power spectral density form G_d(n) = G_d(n0)(n0/n)^2. Although IRI includes measurement protocols yielding G_d(n0), the author notes that the exact mapping from IRI to G_d(n0) is not established and instead employs an approximate relation IRI ≈ 0.22√G_d(n0).

An exact relationship would improve the precision of translating field measurements (IRI) into the PSD parameter G_d(n0), which directly feeds into the model’s expressions for roughness resistance and vibration dose, thereby strengthening quantitative predictions and comparisons across roads and bicycles.