Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Scaling Law for the Velocity of Domino Toppling Motion in Curved Paths

Version 1 : Received: 7 December 2020 / Approved: 9 December 2020 / Online: 9 December 2020 (10:24:23 CET)

A peer-reviewed article of this Preprint also exists.

Guangkai Song, Xiaolin Guo, and Bohua Sun, Scaling law for velocity of domino toppling motion in curved paths, Open Physics 2021; 19: 426–433 Guangkai Song, Xiaolin Guo, and Bohua Sun, Scaling law for velocity of domino toppling motion in curved paths, Open Physics 2021; 19: 426–433

## Abstract

The arranged paths of dominoes have many shapes. The scaling law for the propagation speed of domino toppling has been extensively investigated. However, in all previous investigations, the scaling law for the velocity of domino toppling motion in curved lines was not taken into account. In the present work, the finite-element analysis (FEA) program ABAQUS was used to study the velocity of domino toppling motion in curved lines. It is shown that the domino propagation speed has a rising trend with increasing domino spacing in a straight line. It is also found that domino propagation speed is linearly proportional to the square root of domino separation. This research proved that the scaling law for the speed of domino toppling motion given by Sun (2020) is true [B-H. Sun, 2020. Scaling law for the propagation speed of domino toppling. AIP Advances, 10(9),095124.]. Moreover, the shape of domino arrangement paths has no influence on the scaling law for the propagation speed of dominoes but can affect the coefficient of the scaling law for the velocity. Therefore, the amendatory function for the propagation speed of dominoes in curved lines was formulated by the FEA data. The fitted amendatory function, $\varphi_{revise}$, provides the simple method for a domino player to quickly estimate the propagation speed of dominoes in curved lines.

## Keywords

Scaling law; velocity; domino toppling motion; curved paths

## Subject

Physical Sciences, Acoustics