On technical considerations of UCI-regulated velodrome track design

TL;DR

This paper introduces a mathematical model for velodrome track design using differential geometry, enabling the creation of UCI-regulated tracks with customizable geometry through numerical optimization.

Contribution

It presents a novel differential geometry-based approach for designing velodrome tracks, incorporating safety zones and transition curves, adaptable to various UCI specifications.

Findings

Successfully modeled velodrome surfaces with differential geometry

Generated computer renderings of symmetric and asymmetric designs

Demonstrated versatility for different UCI track categories

Abstract

A novel approach to velodrome design for UCI-regulated tracks is presented. The mathematical model uses differential geometry to form a three-dimensional ruled surface. The surface accounts for the safety zone, blue band, and track region, the latter of which is comprised of three types of segments: straight lines, the arcs of circles, and connecting transition curves. Following a first-principles approach, the general expressions are derived from the Frenet-Serret relations, as a function of the banking and curvature profiles, lengths of curve segments, and turn radii of the bends. Given the underdetermined nature of the design problem, particular solutions are obtained using a least-squares minimization of an objective function, within the framework of numerical optimization. Computer renderings of two designs, a symmetric assembly of quadrants as well as an asymmetric one, are presented to demonstrate the versatility of the approach, which may be used to design velodrome tracks of any UCI Category and track geometry specification.