Simulation
Tyre Rolling Resistance Modelling
A first-principles rolling resistance model for pneumatic bicycle tyres using Maxwell viscoelasticity, Persson's contact theory and quarter-car dynamics, deriving a closed-form expression for rolling resistance coefficient in terms of tyre width, pressure, load and road roughness.
Links & Resources
The Received Wisdom
The engineering literature on rolling resistance in pneumatic tyres largely concludes that first-principles modelling is not feasible, and that empirical correlations are the best available tool. This conclusion deserves scrutiny.
The Model
Combining three established components produces a tractable analytical model. Maxwell's viscoelastic constitutive model describes the hysteretic energy loss in the tyre rubber under cyclic deformation. Persson's rough-surface contact theory provides the framework for computing the contact mechanics between tyre and road texture. Steady-state quarter-car dynamics couples these to the macroscopic tyre-road interaction including the suspension compliance effects.
The result is a closed-form expression for the rolling resistance coefficient as a function of tyre width, inflation pressure, vertical load, road roughness, and rolling speed. The derivation avoids empirical fitting parameters and relies only on measurable material and geometric properties.
Key Findings
At constant tyre stiffness, the effect of tyre width below 25 mm is below the just-noticeable difference for amateur performance purposes. Heavier riders pay a small rolling resistance premium on smooth road surfaces; on rough terrain, the relationship reverses as the larger contact patch distributes road roughness excitation more favorably. The model suggests that for the road quality typical of Belgian roads, tyre pressures considerably lower than the traditional "1 bar per 10 kg" rule are justified.
The practical implication extends to competitive cycling: a pressure-switching system that responds to road surface quality in real time — effectively operating as a dynamic tyre-road contact management system — can exploit this variation during a race, offering an advantage on mixed-surface stages.
Scope and Limitations
The model covers rolling resistance only. Grip and cornering stiffness are separate phenomena requiring different treatment. The quarter-car suspension model represents a single corner; full bicycle dynamics adds chassis coupling that can modify the effective load spectrum at each tyre.