Spin Ball: The Physics of Polyester String
Whipping his racquet through the air like a cesta in jai alai, Rafael Nadal produces such tremendous topspin that the ball sometimes seems to catapult off the court, creating a shot as challenging to combat as shrugging a shot-put off your shoulder.
When Nadal and Francesca Schiavone swept the men’s and women’s French Open titles last June playing with Babolat polyester strings, the repercussions of their success impacted already popular polyester string sales. One American racquet manufacturing exec estimates that polyester string accounts for more than 70 percent of string sold in Europe, and the majority of the world’s top juniors are polyester or co-poly string players.
“People often talk about how racquet technology has changed tennis, but I would argue the string technology has had a greater impact,” says former U.S. Open finalist Todd Martin. “In my era, Jim Courier hit a heavy ball with tremendous topspin and Jim would steepen his swing to generate heavy topspin. Today, you see guys like Rafael Nadal and Roger Federer able to generate heavier spin without significantly steepening their swings—you couldn’t do that with gut.”
To achieve the super-sized spin prevalent in today’s pro game, there are two factors to consider: The swinger of the string (the player) and the science behind the string. Dr. Rod Cross, an avid tennis fan who earned his PhD in plasma physics from Sydney University, co-authored the book Technical Tennis: Racquets, Strings, Balls, Courts, Spin and Bounce with Crawford Lindsey. (Amazon Link is here: ) The work explores the physics of tennis and exposes some misconceptions about the game.
Last spring, the pair collaborated on a study testing 16 different strings (primarily polyester and nylon) for spin. Using high-speed video analysis on balls fired from a ball machine at about 51 mph, the study concluded that “outgoing spin” from the selected group of polyester string was “25% greater, on average, than a sample of four nylon strings, at least under the test conditions.” (To read the study and view video analysis, click here.)
We caught up with Cross in Sydney for a deeper discussion on the subject of strings and spin.
TENNIS.com: Most research I’ve read shows the ball is on the strings for only about five milliseconds. A traditional theory was that string texture could somehow help produce spin by “gripping” the ball, but your study says less friction helps impart spin. Why?
Rod Cross: Less friction between strings allows the main strings to move sideways. As the ball is about to leave the strings, the main strings snap back and give the ball a sideways kick, thereby increasing the rate at which the ball spins as it comes off the strings.
TENNIS.com: Are there any other tennis misconceptions like that?
Cross: Almost everything in tennis is a misconception. For example, thin strings can be just as stiff as thick strings. Low string tension results in higher ball speed off the strings, but it is only 1% higher. String dampeners have no effect on elbow injuries. The sweet spot is about two millimeters in diameter, so one racquet can't have a bigger sweet spot than another—although some racquets vibrate less than others. And the friction force is greater on a ball when the ball slides on the strings. After the ball grips the strings, the friction force drops to zero and reverses direction. I could give you ten more examples, each of which is a story on its own.
TENNIS.com: Heavy topspin has been around since before the days of Bjorn Borg—Vic Seixas, for example—but Borg was playing with gut tightly strung in a small-headed Donnay wood racquet. Given the combination of today’s lighter, larger-head frames combined with polyester strings, how much more extreme can spin become in pro tennis?
Cross: Spin is governed by the tangential coefficient of restitution, typically about 0.2 for a tennis ball on tennis strings. The maximum possible value is 1.0 and that could double the spin. Spaghetti strings were like that. Given that strings must be woven, a practical increase would be 10%. But a player can get 20% more spin by hitting the ball 20% faster or hitting at a steeper angle, so the strings themselves are not the whole story.
TENNIS.com: Racquet experts generally say that string technology has impacted the game more than the racquet technology in recent years. Do you have any thoughts on the next wave of string technology and what it would mean to tennis?
Cross: The next best thing will be strings that don't break and strings that don't lose tension, but that would put string makers out of business.
TENNIS.com: Lastly, slightly off-topic, but I’ve always wondered: when the ball impacts the court, is it accurate to say that not all ball marks are identical? If that is true, then how does the line-calling technology used at the Australian Open and other majors account for this? If the ball strikes the court at a different trajectory with different spin, then wouldn’t it make a different mark, and if so, then how does line-calling technology account for that?
Cross: The ball mark depends slightly on the angle of incidence on the court. If the ball strikes the court at right angles, it will leave a circular patch. At a glancing angle, it leaves a mark about 4 inches long because the ball slides a long way before it bounces. The main problem with line-calling is that balls are fuzzy or hairy and have fibers extending up to 20 millimeters out of the ball. If one of those fibers touches the line then technically the ball is in, but technology and human eyes can't see it.