Children set up lines of dominoes to topple them in visually interesting chain reactions, but university professors and students have converted domino chain reactions into serious business. The physics which affect chains of falling dominoes are subject to measurable physical forces, including gravity, momentum, and force vector analysis. The reaction is affected by the size and mass of the dominoes as well. As a result, determining the optimal rate of a domino cascade reaction requires serious mathematical analysis.
Time Between Impacts
If a domino were six feet tall, observers easily would be able to see how fast a domino falls, and the rate at which it strikes a neighboring tile standing a few feet away. A domino standing closer to the first one in a row would be struck sooner than one positioned farther away. Therefore, the rate at which an entire chain of dominoes will topple will be affected by how closely together the dominoes are positioned.
As a domino just begins to fall, it moves slowly, and therefore impacts the next tile in the row with little force. If the tiles are positioned farther apart, each falling tile pick will pick up more speed and, therefore, generate greater inertial force before it topples into the next tile. So, when the tiles are farther apart, the first tile hits the second one with greater force, and the chain reaction can be expected to accelerate faster than when the tiles are lined up closer together.
Force Vector Analysis
A moving object carries measurable forces, and in the case of falling dominoes, these forces can be broken down using vector analysis. The vector forces are a function of both the angle of the falling tile at the moment of impact and the speed of the falling domino. Using the example of a 6-foot-tall tile, if the tile begins to fall, a person standing next to it would exert less energy catching the tile just after it begins to move than he or she would if the tile were more than half way to the ground. Consequently, less force is applied to the adjacent tile by a slow-moving tile that is nearer to an upright position than a tile that's allowed to topple almost completely over before it strikes an adjacent tile. Therefore, the distance between the tiles affects the magnitude with which each tile hits the next one and, therefore, affects the speed of the entire chain reaction.
Measuring the Cumulative Effect
All of the variables that affect the speed of a domino chain reaction -- the amount of time between impacts, how much force each tile applies to the next, and the velocity with which a tile hits the next in the line -- are affected by the distance between the tiles. The key question, therefore, is at what distance, and at what angle, will a falling domino apply the greatest amount of force to its neighboring tile in order to topple an entire row of dominoes?