# “Book domino” propagation speed?

I was watching this video on the Guardian website. As it can be seen, the "wavefront" of the fallen books travel with a fairly constant speed, which I guess depends on the mass of the book $m$, on its height $h$, and of course on the spacing between two neighbour books $l$.

How would you estimate the "collapsing front speed" of the books?

## 1 Answer

Efthimiou and Johnson (See PDF) developed a formula for the propagation speed of falling dominos. Given a chain of stiff, identical, uniformly separated and parallel dominos, then under the assumption that the collisions are elastic, the dominos do not slide during the collision and no energy is dissipated, then from dimensional analysis the propagation speed has the form

$$v = \sqrt{gl}G(\frac{d}{l})$$

Where $g$ is the acceleration due to gravity, $d$ is the domino separation and $l$ is the domino height.

The function $G$ is given on page 8 of the article in terms of elliptic integrals.

• The function G derived by Efthimiou and Johnson does not fit the measured data very well, IIRC this reference : J. M. J van Leeuwen,The Domino Eﬀect, arXiv:physics/0401018v1 generally does a better job – Conrad Turner Jan 6 '15 at 5:33