The stones used in the domino game made a completely different career many years ago. They are no longer put together according to the rules, but are placed upright in the possible long series. The clever arranging finds its conclusion in letting the first stone fall against the second. This triggers a tipping shaft that runs through the entire system in a chain reaction. The energy to drive the spectacle comes from the height energy of the dominos.
Before the start, each stone is in a stable balance. Its centre of gravity is located vertically above the contact surface, and according to its size, the domino has high-altitude energy. In order to tilt it over its edge, the center of gravity must inevitably be raised a little before the stone falls. Then the altitude energy is converted into kinetic energy. This is partially transferred on impact to the next erected stone and knocks it over, whereby now the next one in the row is overturned and so on. One goal is to trigger the fastest possible wave by placing the dominoes appropriately. As a rule, it is implicitly assumed that the friction with the ground is so great that the stones on it do not slip away. This is usually guaranteed with the usual surfaces.
But it can also be different. This is shown, for example, by a video of youtuber Destin Sandlin recorded with a high-speed camera. The experiments documented on his channel "SmarterEveryDay" have inspired David Cantor from the Polytechnique Montréal and Kajetan Wojtacki from the Research Institute for Basic Technology of the Polish Academy of Sciences in Warsaw to conduct more detailed investigations. With the help of computer simulations, the two physicists brought down chains of up to 200 dominos. They varied the distance between the stones and the frictional forces with the substrate as well as with each other.
A realization from this: At a small distance between Dominos, if the edge of the stone stone bounces high up to the neighbor, the wave spreads slowly. On the one hand, the kinetic energy is still small as a result of the low height difference. On the other hand, the foreheads slide together for a long time during the tilt together, that is, the frictional power has a relatively large route, which converts a lot of kinetic energy into heat.
A slippery surface also slows down the chain reaction, because the stones slide slightly backwards as a result of the impact in the near-ground area. Conversely, the shaft becomes faster when the friction with the ground increases and the track losses due to such slipping decrease. In practice, the dominos usually have good grip on the ground.
Interesting behavior results in a larger space up to triple stone thickness. Here you can no longer observe the backwards - regardless of the strength of friction with the floor. The lower impact point overturns the neighbors less effectively. However, the large fall height ensures more motion energy, and this largely prevents the stone from slipping back. The two opposite effects are partly balanced, and the speed of the shaft remains about the same at a certain distance area.
However, if the gap width exceeds three times the thickness of the stones in the simulations and the friction between the dominoes increases and decreases with the substrate, the wave becomes unstable. Because with such a combination, the stones sometimes slide back so far that they can no longer reach their neighbors.
In addition, the speed of reproduction changes only slightly as soon as the coefficient of friction between the dominoes exceeds a certain value. Presumably, the stones then hardly slide off each other anyway, and a kind of saturation effect occurs. There are similar phenomena when the influence of friction on the angle of the slope of a stable pile of sand. Therefore, the two researchers suspect a universal phenomenon behind the behavior.
The fastest wave expansion is available with a configuration in which the domino stones stand together relatively tightly and exert a large friction with the floor and a small one. Cantor and Wojtacki determined a top speed of 2.25 meters per second.
Such simulations help to explore and visualize the behavior of a domino chain up to practically no longer realizable constellations. However, this does not necessarily understand all aspects of complex dynamics better. For example, in the video of Destin Sandlin, there are, for example, on the side of Destin Sandlin, in which individual stones seem to dance out of the row if they have not been perfectly initiated in the middle. The virtual tilting of Cantor and Wojtacki does not cover such an effects. The manual setting up has some fascinating aspects on the computer. It's more fun anyway.
