Minimising resistance is a matter of interest to most cyclists. These forces arise from passage through air (‘drag’) and interaction with the road surface (‘resistance’). Recent work recognises that resistance forces arise not only from the deformation of the tyre (‘rolling resistance’) but also from irregularities in the road surface (‘roughness resistance’), which lead to power dissipation in the body of the rider through vibration. 

The latter effect may also have an adverse impact on human health. In this work we offer a quantitative theory of roughness resistance and vibration that links these effects to a surface characterisation in terms of the International Roughness Index (IRI). We show that the roughness resistance and the Vibration Dose Value (or VDV, the usual vibration dosage metric) can be expressed in terms of elementary formulae. In common with other recent reports, we find that almost any cycling activity will breach public health guidelines relating to Vibration Dose Value.