## Mathematical constraints of Backus averaging

## Mathematical constraints of Backus averaging

## Mathematical constraints of Backus averaging

## Mathematical constraints of Backus averaging

## Mathematical constraints of Backus averaging

#### MODELLING OF BICYCLE MOTION

The goal of our research is to increase the efficiency of bicycle performance.

We do this in the context of applied mathematics, mathematical physics and classical mechanics, which—for us—constitute the bicycle science.

Quantifying relations among the values provided by cyclocomputers, as opposed to just looking at the values themselves, is essential in optimizing a performance.

We are doing this by working on:

Fausto Coppi by Roberto Lauciello (2017)

POWER AND RESISTANCE

Coefficients of air, rolling and drivetrain resistance and their relative importance for hilly and flat rides, based on power-meter measurements, including an optimization for a downwind and upwind time trial

VAM

Maximization of the mean ascent speed (VAM) as a function of weight, slope and power, including the gear-ratio and cadence considerations

POWER AND VELODROME

Quantitative models of power expenditure on velodromes, including the effects of lean angle, centre-of-mass height, and track geometry

Commonly, a performance is evaluated in a qualitative manner. This is not sufficient. It is obvious that the lighter and the more powerful a rider, the faster the ascent up a given hill.

But how a change of a kilogram, a percent of a slope or a watt would modify the speed? What about two kilograms or three? The relation is not linear!

Commonly, our theoretical models grow from qualitative observations by riders and coaches. Models allow us to quantify and, hence, to evaluate the efforts and improve the results. We work hand-in-hand with coaches: a pattern recognized by the eye of a coach prompts a refinement of our models, while the predictions of our models provide the tools and strategies to the coach.