A Raindrop Can Crack A Plane's Windshield, And The Same Forces Can Break Kidney Stones

The stresses caused by two sorts of surface wave are tracked using a high-speed camera (left) and compared to computer models of the phenomenon (right). These cracks can form on windshields flying faster than the speed of sound, and their counterparts help shatter kidney stones. Pei Zhong

Airplane windshields are designed to be strong enough to cope with hailstones or even birds, but sometimes even a humble raindrop can crack them. That's a problem for the aviation industry, but by understanding the physics that makes this possible, researchers are on the track of methods for shattering other things, including kidney stones.

In the 1960s when early commercial supersonic flights made the mistake of passing over rainforests some came back with small ring-like cracks in their windshields. In 1964 a broad explanation was published concluding the impacts produce surface waves, which spread in two dimensions, and therefore concentrate force far more powerfully than three-dimensional dispersal, which occurs in most situations.

More subtle details of the physics involved continued to elude physicists, but Professor Pei Zhong of Duke University has now filled in some of the gaps. Moreover, in Physical Review Research Zhong has shown we are already making use of the phenomena, and could probably do it better.

To break kidney stones down to a size where they can pass through the urinary tract, hospitals focus sound waves on the stones until the vibrations shatter them. Zhong placed one of the wave generators in water covered by a sheet of glass and observed the shockwaves induced in the water with a high-speed camera.

Although the initial waves were spherical, when they hit the glass some become two-dimensional surface waves depending on the angle.

The set-up allowed Zhong to observe the differences between two sorts of surface waves, known as leaky Rayleigh waves and evanescent waves. The leaky Rayleigh wave moves much faster, and Zhong found the maximum stress occurs as it pulls away from the slow-moving evanescent wave.

This divergence alone is seldom enough to crack a jet's windshield, Zhong found, but when the stress location coincides with an imperfection in the glass a crack is formed, which repeated after-shocks, such as subsequent raindrops, cause to spread out in a ring pattern. When Zhong etched out pre-existing flaws with dilute hydrofluoric acid the cracks stopped appearing.

Cracks formed from multiple impacts on glass caused by diverging surface waves. Zhang et al/Physical Review Research

"The challenge for treating kidney stones is to reduce the stones to very fine fragments so the doctors don't have to follow up with any ancillary procedures," Zhong said in a statement. "Based on the insight gained through this model, we may be able to optimize the shape of the shock waves and lithotripter design to create more tension on the surface of the kidney stones to open up the defects more efficiently."

The implications extend far further. Similar surface waves are also seen on ship propellers and wind turbine blades, so understanding how they spread could contribute to making both more robust.

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