Scaling law for the propagation speed of domino toppling

It is essential for domino game players to have a quick estimate of dominoes’ propagation speed without engaging in complicated multi-body dynamics simulation. This research article uses directed dimensional analysis to propose a universal scaling law, v=λghf(δλ), for the speed of domino toppling motion. As an application, two approximate power laws were formulated by curve fitting of both theoretical and experimental data. The fitted power laws, v∼δλhg, show that the domino propagation speed is proportional to the square root of the domino separation λ, thickness δ, and the reciprocation of the domino height h. The obtained scaling law might not only be useful for players but also help them understand domino toppling energy transfer cascades.