Thrifty Reservoir: A Phenomenological Concept Model for Cycling

Abstract

Thrifty Reservoir (TR) is a phenomenological model of field behavior of a rider, both in training and racing. The main component of TR is an energy reservoir; a stream of energy enters the reservoir, and an output stream propels the bike at the will of the rider. A control is exerted on the reservoir level. It is a PID (Proportional, Integral, Derivative) control, as it is usual in process engineering. Generally speaking, the control effect is to reduce the power available to the rider as much as the reservoir content is depleted. This property is a sort of thrift and therefore the model is named thrifty reservoir. This feature of TR, as far as the author knows, is a real novelty in cycling modelling as it imports concepts from process engineering into the cycling field. The model is mathematically described by a couple of equations: a differential equation for the dynamics of the reservoir and an algebraic equation for the control. TR is easily applied to training session with intermittent exercise or race conditions where intensity of effort is very variable in time as in a race or in a road training session. In this capacity TR differs from models based on explicit formulas, which work only on average values and have difficulties with intermittency. TR differs also from W'bal models which have no control mechanisms on reservoir content, and therefore have difficulties in identifying maximal effort points, while with TR they are easily identified. TR predictive capacity may be applied day by day to road training sessions and races without any need to run specific tests to determine its parameters. TR development may lead to a valuable tool available to trainers in their work, for instance in monitoring training progress, in designing more effective training sessions, and race strategy as well.