## 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

## POWER AND VELODROME

Filippo Ganna, by Roberto Lauciello (2020)

For a moving bicycle, the power can be modelled as a response to the propulsion of the centre of mass of the bicycle-cyclist system.

On a velodrome, an accurate modelling of power requires a distinction between the trajectory of the wheels and the trajectory of the centre of mass.

We formulate and examine an individual-pursuit model that takes into account this distinction. Using this model, we can calculate the power required to achieve a desired time or, since the relation between power and speed is one-to-one, the time achievable with a given power. Also, for repeated laps, we can estimate model parameters from the power and speed measurements. The method proposed to estimate these parameters is specific to velodromes.

Among conclusions quantified by this model is the fact that a constant-cadence approach to an individual pursuit does not minimize the required power.

Christiaan Huygens confident of a centripetal force, which he mathematized in 1659, by Roberto Lauciello (2020)

## LEAN ANGLE

In examining the lean angle, it might be natural to ask about the effect of the track inclination. Invoking a noninertial reference frame, we show that the lean angle is independent of the track inclination; it depends only on the speed and the radius of curvature.

## POWER EXPENDITURE

Straightening upon exiting the curves of a velodrome entails increases of both kinetic and potential energy, which require work. This is beyond the work done against such factors as air, rolling and drivetrain resistance.

To quantify the work expended to increase mechanical energies we use the calculus of variations.

## REFERENCE PUBLICATIONS

Slawinski, M.A., Slawinski, R.A., Stanoev, T. (2020) On modelling bicycle power for velodromes: Part I Formulation for individual pursuits, 2005.04691 [physics.pop-ph]

Bos, L., Slawinski, M.A., Slawinski, R.A., Stanoev, T. (2020) On modelling bicycle power for velodromes: Part II Formulation for individual pursuits, 2009.01162 [physics.app-ph]