What determines how quickly dominoes fall? Two engineers determined this by working with virtual dominoes.

Until 2009, dropping as many dominoes as possible was an annual phenomenon – and with the new program Domino Challenge this hobby has made its comeback on Dutch television. But how exactly do dominoes fall? Strangely enough, we don’t really know. The Canadian Engineer David Cantor and his Polish colleague Kajetan Wojtackic have changed that with more than a thousand (simulated) domino falls.

Distance and friction

Cantor and Wojtacki were inspired by this videoin which vlogger Destin Sandlin goes to work with dominoes and frankly admits:This has broken me. I don’t understand dominoes.†

And Sandlin is not alone in this. “There has been no systematic analysis of the distance and friction between dominoes themselves, and between the dominoes and the surface,” Cantor and Wojtacki write in their paper. scientific article, published in the journal Physical Review Applied†

Weirdly close together

Cantor and Wojtacki picked up the gauntlet and dropped two hundred dominoes 1,210 times. That is, they had a computer simulation do it. They varied the distances between the stones and the friction they experienced as a result of each other and the subsoil.

The latter is the main added value of this research, says physicist Hans van Leeuwen (Leiden University), which previously dealt with the subject himself† “In most studies, the friction with the subsurface is set to infinity.” He calls the new research “worthwhile, but not a revolution”.

Cantor and Wojtacki’s simulations show that it is easy to go wrong if the dominoes are bizarrely close to each other. In other words: if the distance between the stones is only 0.5 to 1 times as large as the width of the stones. Then a number of dominoes can be pushed against each other, so that they no longer tap the next tiles.

Smooth or rough floor

Furthermore, things go wrong if the distance between the dominoes is more than three times as great as the width of the stones, and moreover, the surface is smooth and the friction between the stones is great. “Under those conditions, the rocks can slide backwards, stopping the tipping over,” Cantor and Wojtacki write.

If such exceptions are not taken into account, a formula can be drawn up that reflects the speed of the falling rocks. This appears to be virtually independent of how great the friction is between the stones and the surface. In other words, whether you place the stones on a smooth or rough floor, it makes little difference to the speed at which they tip over each other.

The friction between the stones does play a significant role. The higher it is, the slower the stones fall. However, that effect does become smaller if this friction becomes greater than a certain limit value.

messy reality

As a result of the fact that Cantor and Wojtacki used computer simulations, their dominoes were identical, perfect blocks, spaced exactly the same distance from each other. In reality, of course, you are dealing with stones that differ from each other – even if only slightly – and distances that will always vary somewhat.

The two engineers don’t seem to have any plans to include that messy reality in a follow-up study. They do, however, cordially invite others to do so. “Readers can download our model and conduct their own experiments.” The software that Cantor and Wojtacki usedis free, so that is no obstacle to getting started yourself.

If you don’t trust the computer, you can of course get a box of real dominoes. Although it will take some time to put down those 1210 times and make them fall over – without knocking them over prematurely, of course. Moreover, you would actually have to make both the surface and the stones a little rougher, and, like vlogger Sandlin, arrange a moving high-speed camera. Good luck!