A novel approach to velodrome track design 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 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 radius of the bends. Particular solutions to the design problem are obtained using a least-squares minimization of an objective function, within the framework of numerical optimization. Symmetric and asymmetric designs are presented to demonstrate the versatility of the approach. The resulting formulation may be used to design velodrome tracks of any UCI Category and track geometry specification.
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