Python Simulation of Washboards Formation on Unpaved Highways

Discrete washboard road simulation.

Authors

• Spyridoula C. S., [email protected]
• Cristian Estany B., [email protected]
• Andreas Radke, [email protected]
• Dani Salgado. R. [email protected]

Abstract

Several simulations and models have been purposed till the date, ranging from mathematical analysis to experimentation and simulation, everything with the purpose of gaining some insight about the washboard phenomenon, which has been classified as a complex dynamical system with some chaotic component.

In this project we propose a two dimensional, discrete mathematical model which is translated to an iterative algorithm that tries to reproduce the washboards dynamics observed in the experiments by several authors \cite{riley1971road, TheDynamicsofGranularRipplesFormedbyRollingWheels}. As an starting point, the basic discrete model purposed by David C. Mays and Boris A. Faybishenko in 2000, \cite{discretepaper}, is considered. The lack of realism of that basic model has motivated us to propose new improvements and models for the processes that seem to contribute to washboards formation. To model the road-surface interaction, we propose a probabilistic model for the so-called digging and piling process. To model environmental effects such as diffusion due to wind \cite{continuouspaper} and bump stability due to gravity \cite{modelpile,ontheshape,discretepilemodel}, a road smoothing strategy that model these kinds of phenomena is proposed.

The dependence of the road profile after some vehicle passes on the initial profile, and the dependence of model parameters on the road surface patterns obtained with our model are also studied and analysed. In addition, a methodology to estimate the wavelength of possible periodic or quasi-periodic regions in the obtained patterns of the road's surface is also proposed.

Program guide

To be continued.

References

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