The unofficial soundtrack of every basketball, squash or hard-court tennis match is the constant high-pitched squeak or shreak of the players' shoes. But can this squeak be designed out of them while retaining the grip?
Author
- Gabriele Albertini
Assistant Professor in Structural Engineering, Department of Civil Engineering, University of Nottingham
That's the question an international team of engineers and applied physicists, including me, have been investigating. It sounds like a small design tweak. In fact, it cuts to a deep physics problem : how a soft body slides against a rigid one.
Perhaps surprisingly, the mechanism that produces sound when a soft solid slides against a stiffer one has long been the subject of scientific debate. Most theories are linked to the concept of "stick-slip" : when, instead of sliding smoothly, the sliding object rapidly alternates between sticking and slipping.
While it sticks, the soft body (such as a rubber sole) deforms and stores elastic energy. Then it suddenly slips, turning much of that energy into heat through friction - while also releasing rapid vibrations that radiate out as sound.
But this is not exactly what we observed in our experiments.
After Leonardo da Vinci
Our recently published study took inspiration from the simple-but-effective setup used by Leonardo da Vinci in his studies of friction from the late 15th century.
Leonardo used a wooden block resting on a flat surface. The block was subjected to two forces: a normal force (its own weight) and a tangential force which was applied using an additional weight attached to a cable.
By stacking and combining multiple blocks, Leonardo discovered the two fundamental laws of friction : that friction is proportional with how hard the surfaces are pressed together, and largely independent of the size of the contact area.
But Leonardo never published these findings, which were finally rediscovered and made public in the 19th century in notebooks scattered throughout Europe. In the meantime, the laws of friction had only been formally enunciated by French physicist Guillaume Amontons in 1699 - two centuries after Leonardo's studies.
Furthermore, these laws are empirical rather than fundamental, and in extreme cases they break down. This led us to the question of what makes a shoe squeak.
A surprising result
One of the biggest difficulties in friction studies is that the interface being tested (where a shoe sole meets a hardwood floor, for example) is hard to get at, and comes under a lot of pressure while slipping at high speed. Placing sensors at the interface is almost impossible - and even if it were, this would probably alter the frictional response.
Our solution was to use an optical trick : we replaced the hardwood floor with a transparent acrylic plate and mounted an array of LED lights along its sides. When each test object - including multiple rubber blocks - made contact with the plate, light would leak into the contact region, brightening up this area alone. That allowed us to visualise exactly which parts of the soft-rigid interface were in contact.
We used a high-speed camera, capable of capturing up to 1 million frames per second, to film how the contact patches evolved while the "sole" was skidding, and recorded the sounds being emitted with a microphone.
We found that at the point of contact, tiny wrinkles in the surface of the rubber block - known as "opening slip pulses" - were created, which then raced along the interface at nearly 100 metres per second. While most of the block remained stuck in place, these rapidly moving wrinkles created the sound in each friction test.
Surprisingly, even tiny geometrical features at the frictional interface had profound effects on the sound generated. When it was perfectly flat and smooth, the pulses were messy and generated a scratch-like noise of many different frequencies - closer to the sound of peeling adhesive tape than a clean squeak.
But when ridges were present, like those on the soles of sport shoes, the pulses were confined by the width of these ridges, making them very regular (not messy any more). This turned the sound into a more musical tone akin to the squeaks heard on a basketball court.
We were also able to determine what decides the precise pitch of a shoe squeak. In each test, it was largely unaffected by either the speed of sliding or magnitude of the force applied (which relates to the weight of a player).
Rather, the clearest link was with the height of the rubber block - or the thickness of a shoe's sole. Using this knowledge, we created a series of blocks of different heights in order to play a familiar melody, as shown in this video.
Our research lays the groundwork for controlling or suppressing squeaking in many mechanical systems involving soft-on-rigid friction. These range from brakes and tyres to hip and knee replacements, where polymer liners slide against polished metal or ceramic heads.
And yes, it could even lead to the development of squeakless sneakers. Designing intricate patterns that keep plenty of rubber in contact (so the grip stays high) but break the sliding into lots of tiny, out-of-sync microevents could kill the clean note of the squeak, and leave only a soft hush.
Table-top earthquakes
Beyond the realm of sports, this work also relates to much larger geophysical questions. Similar experimental approaches to ours have served as table-top models for studying earthquakes, during which ruptures and slip pulses spread along tectonic faults at extremely high speed.
If we can reproduce earthquake-like slip pulses in the lab, the next challenge is scaling - working out how those centimetre-scale measurements translate to what happens inside real faults in the Earth.
Achieving this could help interpret seismic signals more confidently: using waves recorded far from a fault to infer what has actually happened at the source. Better physics-based models could improve seismic hazard estimates and lead to more reliable hazard maps.
Meanwhile, we'll keep thinking about squeakless sneakers too.
Gabriele Albertini received funding from the Swiss National Science Foundation (SNSF), the Engineering and Physical Sciences Research Council (EPSRC), and the University of Nottingham.
