Stress relaxation of tennis strings
- Harsh Bhundiya
- Feb 27, 2023
- 4 min read
You might have heard of stress relaxation – the phenomenon where a material loses its strain energy due to internal dissipation. But have you ever thought about it occurring in the strings of a tennis racket?
If you’ve ever played with a rubber band by stretching it and holding it stretched for a while, you might have noticed something interesting: when you let go, it doesn’t return to its initial shape. What has happened is that rubber band has undergone stress relaxation, a phenomenon where a material loses its strain energy due to internal dissipation. This lost energy has caused the material to “relax” over time. In other words, the restoring force of the band has decreased as you were holding it.
Stress relaxation and its complement “creep” (which refers to the case where the rubber band keeps stretching due to a constant applied stress) are both phenomena associated with viscoelasticity, the tendency of a material to “flow” viscously as a liquid and deform elastically as a solid. Indeed all materials are viscoelastic: the rubber in car tires, the concrete in buildings, the glaciers at the poles, and even cheese. However, the time scale of their deformation is different, and that’s why some materials (especially plastics) appear more viscoelastic than others. Hence in some cases viscoelasticity can actually be a failure point and therefore needs careful consideration.
One of my favorite examples is in the field of space structures, where long booms of fiber reinforced plastics are routinely used to deploy parts of a spacecraft (e.g. antennas, solar arrays, and solar sails). For these applications, the booms are tightly stowed inside the spacecraft, sometimes months before launch. Then once the spacecraft launches and reaches orbit, the booms are released and unfurl from their stored elastic energy. However, if the booms have been stored tightly for a while, they likely have undergone stress relaxation and therefore do not unfurl to their desired shape. Indeed stress relaxation of this kind has caused anomalies in the past, including for the MARSIS spacecraft launched in 2006 and the recent Lucy spacecraft launched in 2021. Clearly viscoelasticity needs careful consideration from the engineers at JPL.
Besides spacecraft, viscoelasticity affects objects in our day-to-day life, too. Today I want to talk about stress relaxation occurring in an object close to my heart: the tennis racket.
If you’ve played tennis before, you know that the strings in your racket can greatly affect your game. So much so that many professional players (like the great Roger Federer) hire a dedicated stringer who travels with them and whose only job it is to string the rackets in a particular way. Tennis strings come in various materials, shapes, and sizes, but the key factor which affects your game is the tension, i.e. how tightly the strings have been attached to your racket. And guess what: since most strings are made of a polymer material, stress relaxation can affect your game – by decreasing the tension over time! Check out this plot of tension vs time for two tennis strings, one made of polyester and the other made of natural gut [1]:
We see that over time, the tension in the strings decreases, and that too quite quickly. The measurements suggest an exponential decrease in tension over time, with up to a 30% drop for the polyester string in 24 hours. The natural gut string doesn’t lose its tension as quickly, but it too decreases over time. Note that this data is measured for a single string and not a full racket; however, the trend translates to the strings in a full racket too. While the tension drop isn’t as dramatic, rackets lose their tension quickly as well, around 10% in the first 24 hrs after stringing.
What’s going on here? Well it’s exactly the viscoelasticity we discussed earlier: after the strings are attached to the racket, they are subject to constant strain and undergo stress relaxation. Depending on the string material, this occurs at different rates as bonds break between the long-chain molecules. And this leads to a tension drop in each string and therefore the overall racket.
This tension drop can actually affect a player’s game. Generally a higher tension corresponds to greater control over the ball’s spin and direction, so for experienced players a decrease in tension can lead to different shots than expected. It can also cause a decreased force on the ball during impact and lead to slower shots (more time for your opponent!). For these reasons, most professional players try to avoid stress relaxation in their strings and opt for stringing only a few hours before their match. This way they know how their racket will behave.
The material of the strings also affects their stress relaxation. As the plot above shows, natural gut strings (made from cow intestine) generally relax less than polyester. However, these strings come with a tradeoff in stiffness and do not impart as high of a force on the ball [1]. For this reason, some pros opt for a half polyester/half gut combination. Today, synthetic gut (i.e. nylon) strings are also popular and offer a good balance of stiffness, stress relaxation, and cost. Another string material, Kevlar, offers even less stress relaxation but comes with a tradeoff in the tension drop after every hit of the racket. The high stiffness of Kevlar also results in a greater force on the player’s hand and is more prone to causing injuries. In the end, it comes down to the choice of the player and the “feel” they prefer. Personally, I haven’t experimented much with different materials and usually choose the cheapest nylon strings…but after writing this blog post I think I’m going to be more picky.
To summarize, tennis strings (and for that matter strings used in any racket sport) offer a great example of stress relaxation. Over time the viscoelasticity of the string material decreases the tension, which can affect the feel and performance of the racket. So next time you play tennis with the old racket that’s been in your closet for years, remember your misses may actually be a result of stress relaxation and not your rusty skills. 😉
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