Abstract
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.
Highlights
In 1983, McLachlan et al.3 proposed a scaling law for the propagation speed v for dominoes with zero thickness spaced in a straight line
None of the previous investigations accounted for the domino width;2–13 perhaps, this is because the width was deemed to have little influence on the propagation speed
A universal scaling law for the propagation speed of domino toppling was formulated by using directed dimensional analysis
Summary
Szirtes and Rozsa used dimensional analysis to study dominoes with equal thickness δ, separation λ, and height h. From the Buckingham theorem of dimensional analysis, the authors obtained the dimensionless relation Π1 = f (Π2, Π3), namely,. This relation is similar to Eq (1) with an extra dimensionless parameter, namely, the separation-to-height ratio δ/h. II, we attempt to decode the function by using directed dimensional analysis, as proposed by Huntley and Siano.
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