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Mathematical Model Predicts How Stones Skip Across Water

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Researchers have found a mathematical equation that can predict how stones will behave when thrown on the water’s surface. The mathematical model is in different sizes and shapes of rocks, as well as the angle of the throw and the pressure of the water.

The model can reliably predict how thrown stones will skim across the water. The researchers found that the flatter stones can look for longer across the surface of the water, while the fatter stones elicit a ‘super-elastic’ response from the surface and can jump higher. While stone skippers tend to prefer flatter stones, the larger, heavier, and curvier ones can also do a great job.

The researchers have discovered that there is no single optimal shape for making stones skip.

Lead researcher of the paper, Ryan Palmer says “Our research shows the role of a skimmer’s mass and shape in determining whether it successful skips out of the water or sinks into it. It also reveals a relationship between these two characteristics, with a more curved underside enabling heavier bodies to skim that would otherwise sink if they were flatter.”

The equations can predict how various designs will behave when planes land. Other practical applications include ensuring that the aircraft can shed particles of ice on the exteriors when flying through clouds to ensure that they do not accumulate. The researchers were modeling the behavior of objects skimming on water, and the ability to predict thrown stones was just a happy byproduct.

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