  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.
