Effects of Friction and Spacing on the Collaborative Behavior of Domino Toppling

Inspired by the high-speed camera experiments of YouTuber Destin Sandlin (SmarterEveryDay) [D. Sandlin, Dominoes – hardcore mode (2017), [Online; accessed 15-Jul-2021].] on the toppling speed of dominoes over different surfaces, we performed discrete-element simulations of this process, varying the spacing between adjacent and evenly spaced blocks (dominoes). We also varied the block-block and block-surface friction coefficients over a wide range of values to have a complete picture of the behavior of these cooperative, dissipative mechanical systems. We found that a steady wavefront speed $v$ exists for a specific interval of spacings between dominoes and coefficients of friction. Surprisingly, while $v$ is more affected by the domino-domino friction, the domino-surface friction determines whether or not toppling anomalies can appear and stop the wave. Finally, our observations led us to propose a scaling law that is able to predict $v$ based on the domino configuration and friction coefficients, and to correctly reproduce experimental tests.

Figure 1

(a) Screenshot for one of the tests with spacing between dominoes ${\delta }_d=3$ and geometrical characteristics of the dominoes. (b) Wavefront stops under narrow spacing because of vertical stacking. (c) Wavefront stops because of backwards sliding of dominoes under low domino-surface friction (i.e., slippery surface).

Figure 2

Wavefront speed in $\mathrm{m}/\mathrm{s}$ as a function of the coefficient of friction between dominoes ${\mu }_{dd}$ and between domino and surface ${\mu }_{sd}$, for varying spacing between dominoes from (a) ${\delta }_d=0.5$ to (j) ${\delta }_d=5$ in steps of $0.5$.

Figure 3

(a) Relation (2) versus the measured wavefront speed $v$. (b) Scaling proposed in Eq. (4) versus $v$ for a wide range of spacings and friction coefficients between dominoes.

Figure 4

Comparison between experimental data from Larham [18] (circles), McLachlan et al. [17] (squares), and Stronge and Shu [3] (triangles), the model proposed by Shaw [19] (orange line), the collision model by van Leeuwen [5] (green line), and the scaling law proposed in this work (red line). The shaded red zone corresponds to the spacings between dominoes that typically show anomalies.