Physics of the domino effect toppling speed
What determines the propagation speed of a wave of toppling dominoes, and why does it approach a roughly constant value regardless of how hard the first domino was pushed?
History and references
Partly settled. Some of it is understood, some is still argued about.
The domino effect is a familiar demonstration, but explaining why a chain of toppling dominoes settles into a roughly constant propagation speed independent of the initial push requires modeling the rotational dynamics and collisions of each rigid domino, not just simple energy transfer. Efthimiou and Johnson's 2007 SIAM Review paper built a theory of perfectly elastic domino-on-domino collisions on a frictional foundation and derived closed-form expressions for the limiting wave speed as a function of domino spacing and dimensions. Subsequent experimental and theoretical work (including 2020s papers using sound recordings and elastic-collision refinements) found this classic model's predictions diverge from real measurements in some regimes, particularly at small spacing, motivating ongoing refinement of the theory. The basic phenomenon (a constant asymptotic wave speed) is well established, but the precise quantitative model is still being improved.
A row of falling dominoes settles into a steady marching speed no matter how gently or violently you tip the first one, a small everyday example of a system finding its own natural rhythm.
Explanations that circulated
- Simple energy- or momentum-transfer 'toy' models that ignore each domino's rotational dynamics predict the propagation speed should increase without bound (even diverge to infinity) as domino spacing shrinks toward zero, which does not match real measured domino-wave speeds
References
- Domino Waves, Christopher J. Efthimiou, Matthew D. Johnson, SIAM Review, 2007
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