How Fast are Domino Waves?

TL;DR

This paper develops a realistic theory for the propagation speed of elastic domino waves, accounting for finite stiffness and collision dynamics, supported by simulations that clarify collective interactions.

Contribution

It introduces a new theory considering finite stiffness and collision time, improving upon previous models that predicted infinite velocities and lacked realism.

Findings

Derived upper and lower bounds for domino separation distances.

Supported theoretical predictions with discrete element simulations.

Identified finite collision time as key to realistic wave speed modeling.

Abstract

The paper is concerned with the problem of toppling propagation velocity in elastic, domino-like mechanical systems. We build on the work of Efthimiou and Johnson, who developed the theory of perfectly elastic collisions of thin rigid dominoes on a frictional foundation. This theory has been criticised for the lack of correspondence with the experimental observations, in particular, prediction of infinite propagation velocity for zero spacing between dominoes, as well as the inability to represent the collective nature of collisions in real domino systems. In our work we consider a more realistic scenario of dominoes of finite stiffness and obtain a theory of fast elastic domino waves, taking into account a limit velocity of the perturbation propagation in the system of dominoes. Moreover, finite collision time allows to extract dynamic quantities of collisions and establish upper and lower borders for domino separations where the theory could still be applied. Our discrete element simulations support our theoretical findings and shed light on the nature of collective interactions in the nearly-elastic domino chains.