Granular Matter

, 21:15 | Cite as

Measuring the coefficient of restitution for all six degrees of freedom

  • J. E. HighamEmail author
  • P. Shepley
  • M. Shahnam
Brief Communication


The coefficient of restitution is a cornerstone empirical parameter of any model where energy is dissipated by particle collisions. However, completely determining this parameter experimentally is challenging, as upon collision, a particle’s material properties (such as roughness, sphericity and shape) or minor imperfections, can cause energy to be shifted to other translational or rotational components. When all degrees of freedom are not resolved, these shifts in energy can easily be mistaken for dissipated energy, affecting the derivation of the coefficient of restitution. In the past, these challenges have been highlighted by a large scatter in values of experimental data for the restitution coefficient. In the present study, a novel experimental procedure is presented, determining all six degrees of freedom of a single, spherical, nylon particle, dropped on a glass plate. This study highlights that only by using all six degrees of freedom, can a single reliable and consistent coefficient of restitution be obtained for all cases and between subsequent collisions.


Particle characterisation Coefficient of restitution Particle tracking velocimetry Rotational moment 



The first author funding provided by Oakridge Institute for Science and Education. Second author with funding in part through the Engineering and Physical Sciences Research Council, UK (Grant No. R/147129).

Compliance with ethical standards

Conflict of interest

The authors can confirm there are no conflicts of interest associated to this work.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Geography and Planning, School of Environmental SciencesUniversity of LiverpoolLiverpoolUK
  2. 2.Department of Civil and Structural EngineeringUniversity of SheffieldSheffieldUK
  3. 3.National Energy Technology LaboratoriesUS Department of EnergyMorgantownUSA

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