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The Physics of Grass, Clay, and Cement

There are more than 160 different types of tennis surfaces. An investigation into how they impact play on the court.

The official rule book of tennis is 35 pages long. For the most part, the document is a case study in compulsive precision. Here are a few of the exacting guidelines:

  • If a tournament is played above 4,000 feet, pressureless tennis balls must be “acclimatized” for at least 60 days at the local altitude.
  • The cord holding up the net cannot be thicker than ⅓-inch in diameter, and must be covered by a white band between 2 and 2.5 inches wide.
  • The frame of the racket cannot exceed 29 inches in total length.
  • The organizers of tennis tournaments must announce in advance their ball-change policy.

Amid all this punctiliousness, however, the rulebook contains one glaring omission: There are no rules about the surface of the court. While the boundaries of the space are carefully specified — it must be a rectangle, 78 feet by 27 feet, with a one-inch-wide center service line — there are zero references to the different materials on which the game can be played. It’s as if clay, grass, and hard court don’t exist, as if the composition of the playing field doesn’t matter.

This oversight has profoundly shaped the development of the sport. Because there are no rules about court surfaces, modern tennis is played on a stunning variety of materials, from the crushed brick of Roland Garros to the manicured lawns of Wimbledon. In fact, the International Tennis Federation (ITF), the regulatory body overseeing the sport, currently recognizes more than 160 different kinds of tennis courts, including surfaces made of carpet, clay, gravel, concrete, wood, asphalt, and fake grass.

“No other sport is played on so many different materials,” says Jamie Capel-Davies, a senior project technologist at the ITF who oversees the assessment of court performance. “Furthermore, these surfaces really change the game. The same style of play that might work on clay won’t work on grass or acrylic,1 because the ball will behave very differently. As a result, athletes must constantly think about the type of court they are playing on. It’s a variable that can never be taken for granted.”

This was not always the case. For most of tennis history, there was only surface: grass. Although the sport began as Real Tennis, an indoor game played on wood floors and popular with the medieval nobility, it evolved into “lawn tennis” by the late 18th century. (One problem with Real Tennis is that it required an airy indoor space, which existed only in palaces and monasteries.) And so the court was lengthened and moved outside, to manicured fields etched with chalk lines. This remained the standard format until the 1940s, when the booming popularity of the game led to the invention of the cheaper hard-court surface, which was just a painted slab of concrete. In 1956, the Gallia Tennis Club in Cannes built the first modern clay court, a design that was easier to maintain than grass in the dry climates of southern Europe.

The multiplicity of tennis surfaces has been particularly relevant at the U.S. Open, which is the only tennis major to have experimented with three different materials. The first 93 years of the tournament were played on grass, before briefly shifting to the clay courts of the West Side Tennis Club in Forest Hills. In 1978, the Open moved to the USTA National Tennis Center in Flushing, where the courts consist of a hard-court surface known as DecoTurf II.2

Why does the surface matter so much? Why are there tennis players who can win only on grass or concrete? What does it mean to be a clay specialist? The answer to these questions is rooted in the physics of the sport, those laws of nature shaping the bounces of the fuzzy, yellow ball. During a typical rally, the ball will spend more than 99.5 percent of its time traveling between players, sailing through the air and ricocheting off the ground. It is in contact with the racket for the remaining fraction of a percent. The players control that fraction. Physics controls everything else.

But the physics of tennis — those impersonal forces shaping every shot — are not constant. Instead, they largely depend on three separate factors determined by the court surface.

The most important factor is the “coefficient of friction,” a measurement of the abrasive force between the ground and the tennis ball. Courts with high frictional coefficients interfere with the movement of the ball, disrupting its forward momentum. Think of a sluggish clay court. According to experiments performed by the ITF, a shot hit without spin and traveling at 67 mph will lose about 43 percent of its ground speed after contact with the clay surface, slowing down to a leisurely 38 mph. (The reason clay steals momentum is rooted in the friction of all that loose brick, which clumps around the ball. Each clump is like a little speed bump.) As a result, players have a few extra milliseconds to hit a return.3

In contrast, a shot on a fresh grass court — think of Wimbledon on opening day — will maintain a speed around 45 mph, which is 15 to 20 percent faster than clay. Hard courts are usually a smidgen slower than grass, although the speed of the court depends on the amount of sand mixed in with the acrylic paint. (There are at least 45 different kinds of hard court, some of which play slower than clay. The Australian Open, for instance, is played on a Plexicushion surface, which has a slightly higher frictional coefficient than the U.S. Open.) While grass courts become more sluggish over the course of a tournament — the exposed dirt plays more like brick — hard courts actually accelerate, as the soles of shoes wear down the surface friction, especially around the baseline.

But friction isn’t just about pure speed: It also influences the angle of the bounce. When a ball impacts a high-friction surface it undergoes a sudden increase in spin, as the bottom of the ball slows down more than the top. This burst of topspin redirects the momentum of the ball, transferring some of that horizontal velocity in a vertical direction. As a result, the ball seems to bounce straight upwards, hanging in the air.

These angles exaggerate the perceived speed of a court. The friction of clay leads to high bounces, which give players even more time to chase down a shot. In contrast, frictionless grass courts have a low “angle of rebound” — the balls maintain a flat trajectory — which leads players to perceive the court as even faster than it is. In fact, these rebound angles are typically more important in shaping the perceived speed of a court than the actual velocity of the ball. (Hard courts and grass courts often generate the same postbounce velocity, but grass courts seem faster because the ball bounces at a lower angle.) As Howard Brody, a physicist at the University of Pennsylvania, notes in his classic Tennis Science for Tennis Players: “The eye and brain are much better at gauging an angle than observing a slight change in ball speed. If the ball comes off the court at a low angle after the bounce, you conclude that the court is fast because you must act faster.”

The final factor influencing the court is the “coefficient of restitution,” a fancy way of describing the bounciness of the surface. Courts with less restitution — they’re not as bouncy — feel faster, since the ball bounces off the court at a lower angle and players have less time to reach it. Grass courts, for instance, have a very low coefficient of restitution, usually around 0.75. This lack of bounce, when combined with the lack of friction, leads to an exit angle roughly equivalent to the entry: When a shot collides with a grass surface at a 16 degree angle, it will rebound at the same slant. In contrast, clay courts have a high coefficient of restitution, usually around 0.85. This helps explain why when a ball collides with a clay surface at a 16 degree angle it will rebound at 20 degrees or more.

Rigorous tests by the ITF have documented these court characteristics. The tests feature an air-powered ball cannon and a pair of laser photocell arrays, which can precisely measure the velocity and angle of ball movement. These tools allow the ITF to rank every tennis surface in terms of its underlying physics, grouping courts in five distinct categories from slow to fast. (If you’re an ITF member, they’ll certify your court for $500.) Although there still are no rules regarding the performance of tennis court surfaces — the game can be played on anything — in January 2008 the ITF began regulating the speed of courts used in Davis Cup tournaments. Because the host country gets to choose the tournament location, the new rules prevent the use of extremely slow or fast surfaces. So far, only one court — a clay surface in Croatia, used in a 2008 match against Brazil — has violated the regulations.4

The physics of tennis might be interesting, but does it matter? Can it be used to improve performance? Or is it a useless description of the game, a complicated summary of a simple sport? In Tennis Science for Tennis Players, Brody insists that it’s possible “to take advantage of the laws of nature to win more points,” that players with an understanding of the game’s mechanics will have a decisive edge over their more ignorant opponents. “Knowing the physics,” Brody writes, “may enable you to gain a point here, a point there, and quite often, the single point is the difference between winning and losing a match.”

Needless to say, most players on the pro tour haven’t taken Brody’s advice. Roger Federer probably isn’t thinking about the angular momentum of his cross-court shot when approaching the net, just as Andy Roddick isn’t contemplating the “kinetic chain principle” before unleashing his serve.

But is this a mistake? Could tennis players really improve their performance by knowing more about the equations of velocity and surface friction? To test Brody’s hypothesis, I met with the Caltech tennis team, arguably the smartest collegiate athletes in the country. (The average grade point average on the men’s team is 3.73, which is one of the highest team GPAs in the NCAA. And these players are taking Caltech classes.5) Despite this intellectual pedigree, the Caltech tennis players have struggled to win games: Last season, the men’s tennis team went 1-16.6 Although many of the players can rattle off abstruse physics equations with ease, they all insisted that their textbook knowledge was not an advantage. “To be honest, it doesn’t help at all,” says Devashish Joshi, a freshman on the team. “I never think about science while playing.”

The reason is obvious: The game is far too fast. Douglas Hofmann,7 a materials scientist at the Jet Propulsion Laboratory and Caltech and former assistant coach of the men’s tennis team, explains why the speed of tennis makes thinking about physics all but impossible: “Let’s say you’re returning a serve at 125 mph,” he says. “Given the length of the court, that means you’ve got about 0.4 seconds to execute your swing. It takes about .25 seconds just to execute a bodily movement. So that leaves just over a tenth of a second to actually think about what you want to do. If you’re trying to do some computations, the ball is going right past you.”

But this doesn’t mean intelligence is useless, or that pro players wouldn’t benefit from a crash course in Physics 101. As Hofmann points out, smarts are a crucial competitive advantage in the sport. “This is the paradox of the game,” he says. “Although there isn’t any time to think, the smarter guys still tend to win. Federer, Sampras, McEnroe, Connors, Agassi — these players weren’t always the best athletes on the court, but they won because they played more intelligently.”

And this returns us to the importance of the court surface. If the game were always played on the same material, and if this material always behaved the same way, it would be possible to dominate with a few master shots; intelligence would be far less necessary. “The sport would be a pure test of athleticism,” Hofmann says. “The better physical specimen would win every time.” Instead, success on the pro tour requires constant flexibility, an ability to tailor the game to an ever-changing set of surface conditions. (There is no such thing as a home court in tennis, no playing field that can be taken for granted.) As a result, players must always take the coefficient of friction into account, even if they don’t know what the coefficient is. “The top-ranked guys are all intuitive physicists,” Hofmann says. “They know how the ball will bounce even if they can’t explain why. This is what allows them to change their strategy based on the surface.”

Although some players make this adjustment process look easy, it’s actually one of the hardest parts of the modern game. The reason it’s so difficult, according to Brody and Hofmann, is because winning on a given surface requires players to fully embrace its idiosyncrasies, exaggerating the quirks unique to each material.

Consider the high friction of clay: It would be possible, of course, to hit through the surface, speeding up the court by hitting shots with backspin, thus minimizing the upward bounce produced by crushed brick. But such an approach is almost certainly a mistake. Instead, the best clay players, like Nadal, emphasize shots that magnify the very physical forces produced by the court. They slather on the topspin so that the ball kicks up even higher. They focus on consistency — winning on clay is often a matter of not losing — and rely on deep lobs when in trouble. In other words, they take advantage of the slow court by making it even slower.8

The same approach also applies to grass and hard court. That’s why the best grass players master the backhand slice, lowering the already low rebound angle, and hit aggressive approach shots that benefit from unpredictable bounces. (Grass courts are the hardest to measure, Capel-Davies says, as the surface is a living thing.) It’s why the best hard-court players hit flat and fast first serves — the slick court doesn’t slow down the ball — and learn to attack the net from the ¾ position, which requires a relatively high bounce. Hard-court players are also able to run around their weaker shots, turning potential backhands into forehand winners.

Such strategies are only possible, of course, because these players have undertaken a careful study of the varied surfaces, spending years learning the capricious habits of different courts. While Brody might have overstated the value of explicit scientific knowledge — there’s a reason the Caltech tennis team lost every conference match — he was right about the importance of physics. Because of that loophole in the official rulebook, tennis has become a game of strange variations in which the performance of a player can depend entirely on the performance of the court. Players don’t need to know the laws of nature. They just need to know that they can’t be escaped.

Jonah Lehrer is a contributing editor at Wired and the author of How We Decide.


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Filed Under: Sports, Tennis

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