Tennis and physics: Are clay and hard courts slow or fast? It all depends on one factor - UBITENNIS
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Tennis and physics: Are clay and hard courts slow or fast? It all depends on one factor

Surfaces are different, but topspin makes them all the same. A (long) analysis of the physics of the tennis ball leads to an interesting discovery.

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Surfaces are not all the same. Every now and then someone surmises that this is not the case anymore, but there are data to show that differences that once seemed more evident still exist today.

Grasscourts have become slower than a couple of decades ago, this is confirmed, but the distance between clay and hard doesn’t appear to have altered. After all, while hyper-champions like Djokovic and Nadal have found a way to excel even on the surface that offers them fewer natural advantages, many others continue to struggle on courts that do not suit them. It turns out that hardcourt tennis is not identical to claycourt tennis, because the physics of shots are just different. If that weren’t the case, the performance of all players would be uniform, matches would be more or less the same, and the aces data – the best metric to indirectly compare the speed of the courts – would remain in the same range on all surfaces. Instead, Nadal’s career data state that the Spaniard hits an average of 2 aces per game on clay and 3.5 on hard courts (+75%); Federer 5.9 and 7.9 respectively (+34%); Djokovic 3.7 and 5.6 (+51%).

 

It follows that on clay, the elective surface of this part of the season, tennis changes. But how exactly? What is the best way to move on claycourts, and what is the yield of the shots as compared to other turfs? What are the difficulties that players face compared to hardcourts, and what are the advantages? It’s a long and complex issue, but before going deep into tactical considerations – where a bit of subjectivity takes over – we will explore the problem from a physical and theoretical premise in order to build a solid starting point for our digression. We will draw our conclusions in a second article, which will be published in the coming weeks.  

Special thanks for this article must be paid to Matthew Willis, who curates a very interesting tennis blog on Substack. He got us to discover the publications of Rod Cross, a former Physics Professor at the University of Sydney who has dedicated a large part of his career to the subject of physics applied to sports. If the topic appeals to you, some of his work can be found here, here and here. In the next sections we will try to summarise the main discoveries of his research, broken down into simple concepts. If you are not interested in physics and prefer to go directly to the conclusions, you might want to go straight to the second section.

FIRST SECTION: THE THEORY OF SURFACE BOUNCE PHYSICS

To put it very simply, the bounce of a tennis ball can be viewed as a physical system in which a spherical body has a speed that can be divided into two components: horizontal inbound velocity (vx1, it stems from hitting the ball with the racquet, measured in m/s) and the vertical inbound velocity (vy1, it stems from the stroke and ‘fights’ with gravity, measured in m/s). After the impact with the surface at a certain angle of incidence (θ1), the two outbound velocities are obviously reduced (vx2 and vy2); this means that the ball loses some of its thrust and speed and loses a little more or a little less depending on the surface on which it bounces.

Graphical representation of ball bounce (credit to Rod Cross)

Let’s start from the beginning. In 1984, Howard Brody developed the first model to study the physics of the tennis ball, imagining it as a rigid object which after the impact with the surface does not deform. This model, which turned out to be inaccurate and incomplete, assumes that the horizontal outbound velocity of the ball after the rebound is always 64.5% of that before the rebound, regardless of the surface and of the angle of impact, as long as it is greater than 16 degrees. 

In reality, the ball deforms after the impact. This is why the physics of the bounce are much more complex (the worst calculus final you ever had in your life,” according to the late, great David Foster Wallace) and consequently not all surfaces are the same. For a few fractions of a second, in fact, the ball – which possesses with a certain rotation – stops rotating and begins to slide on the court, covering a micro-distance (D as showed in the above figure) which corresponds to the displacement of the axis of force N, i.e. the one that fights with friction (F) to push the ball upwards. After this transitional phase, the ball resumes the rotation motion and takes off towards the phase following the rebound. The duration of this phase, and therefore the resistance that the surface offers to the ball, depends on the friction of the surface itself and the type of shot (we will get to that shortly). On the clay it lasts a little longer, so the distance D is greater and the surface “steals” more inertia from the slowed ball that comes out; on hardcourts it lasts less, so the distance D is smaller, and the ball resumes its upward motion more quickly, resulting faster after the rebound. Thus, the 64.5% rule fails. 

The premise is completed by specifying that two physical characteristics are attributable to the surface:

  • The coefficient of friction (μ), which measures the friction of the surface by subtracting the horizontal outbound velocity (vx2 after the bounce) from horizontal inbound velocity (vx1). Basically, it tells us how much speed the ball loses in the horizontal plane. The higher this coefficient is, the more the surface generates friction (as happens on clay) and consequently slows down the stroke.
  • The coefficient of restitution (e), which instead measures how much the surface “helps” the ball to bounce and is the ratio between vertical outbound velocity (vy2) and the vertical inbound velocity (vy1). The higher this coefficient is, the more generous the surface is with the bounce (like on clay).

If it is easier to understand why the increase in the friction coefficient slows down shots (and therefore the game), it may be necessary to specify why a court that ‘returns’ more is considered slower: a higher bounce gives the player more time to execute the stroke and to find the ideal sweet spot for impact, whereas low bounces force the receiver to react in a shorter time span.

Lorenzo Musetti (Acapulco 2021 / photo AMT): example of impact below the level of the hips 

These two physical characteristics have been incorporated into a formula developed by the ITF to calculate the Court Pace Rating (CPR), an indicator of the speed of the courts. The formula is the following:

This rating, which basically tells us how much speed the ball has before bouncing and how much speed it has afterwards, is calculated in a laboratory under fixed conditions. Basically, a shot is hit at about 67,1 mph on a sample of the surface, without topspin and at a fixed angle of 16 degrees. However, this is a partial figure, because it does not take into account what happens when the ball hits the surface at a greater angle, namely when the stroke is executed with topspin – as previously implied, when the ball comes in with a lot of rotation, things are different. The above metrics is also not totally representative because it doesn’t take into account other factors that influence the speed of the court, such as weather conditions and all the layers composing the court beneath the upper surface.

CPR should not be confused with CPI (Court Pace Index), which is based on the same physical premises but is not calculated under laboratory conditions – it is simply inferred from the speed measures offered by Hawkeye data (used at Slam, Masters 1000 and ATP Finals levels). In some ways, it is a more truthful measurement, as it is based on matches data from played tournaments and on a larger sample of shots.

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Djokovic Isn’t Satisfied With The 20-20-20 Look

The world number one will be the overwhelming favourite at the US Open, but Berrettini is here to stay

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Now that Novak Djokovic has 20-20-20 vision, he says he’s not through.

 

He’s aiming to be the sole leader of the gang now that he has deadlocked Rafa Nadal and Roger Federer at 20 Grand Slam singles titles each.

But future Grand Slam titles might not come easy for any of the 20-20-20 gang, even  youngest member Djokovic. Italian muscleman Matteo showed on Sunday in his Wimbledon championship match loss to Djokovic that he has arrived as a legitimate Grand Slam tournament contender.

NOVAK BIDDING TO MATCH LAVER

Of course, Djokovic now has won three Grand Slams this year and has his eyes focused on winning all four Grand Slams in one year, matching something the great Rod Laver accomplished twice about half-a-century ago.

The U.S. Open awaits the challenge. Novak will be a huge favorite, although it would be great to see Rafa and Roger in New York again.

Who knows? These two legends hopefully are already out getting their games ready for the hard courts of Flushing Meadows.

MATTEO AGGRESSIVE, YET PASSIVE

Berrettini had his chances against Djokovic. But he was either too eager or too passive with his shots much of the afternoon. Unlike the 20-20-20 Gang, Matteo really doesn’t have great touch. But power? He has more than he needs.

Between the two traits, Berrettini didn’t take full advantage of his many opportunities. Had he cashed in on the majority of them, Wimbledon might have had a different champion, and Djokovic would still be looking up at Nadal and Federer.

But Novak was always there, ready to pounce on the smallest window of opportunity. He often turned opportunities for Berrettini into his own.

BERRETTINI: THE BIG MUSCULAR GUY

The preliminaries to the match were very English-like, much like the aftermath of the grueling 6-7 (4), 6-4, 6-4, 6-3 victory by Djokovic. Both players were somber as they made their way onto the court, each carrying green and white Head tennis bags and hand bags

Wearing his usual cap turned backward, the 25-year-old Berrettini looked like a movie star or a tight end with his 6-5, 209-pound figure, overshadowing the 6-2, 172-pound Djokovic, whose thin-man look enables the 34-year-old Serbian to be as nimble as an acrobat.

The first game lasted what seemed like a set as Djokovic survived two double faults and a break point to take a 1-0 lead. Novak broke in the fourth game and led 5-2 before Berrettini pulled his game together to survive the eight-deuce eighth game, then broke Novak and held service for 5-5.

TIEBREAKER BELONGS TO MATTEO

Berrettini surprisingly outplayed Djokovic in the tiebreaker and closed the door with an ace. But the Italian came down to earth and was broken early in each of the last three sets to allow Djokovic to take the title.

Grand Slam titles didn’t always come so often for Djokovic. After notching his first Grand Slam title at the 2008 Australian Open, he watched Rafa Nadal and Roger Federer win 10 of the 11 Grand Slams before Novak got in the winner’s circle again in 2011.

EVERYTHING GOING NOVAK’S WAY

But now as Nadal and Federer appear to be struggling with their age, Djokovic has won eight of the last 14 Grand Slams. Overall, he has won 20 of the last 54 Grand Slams.

While all of that has been happening, Djokovic has won five of the last seven Wimbledons, and six in all.

Everything appears to be going Novak’s way, but the young guns of the tour obviously are getting anxious to win Grand Slams. And Novak can’t look like Superman forever.


See James Beck’s Charleston (S.C.) Post and Courier columns at postandcourier.com (search on James Beck column). James Beck can be reached at Jamesbecktennis@gmail.com

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Why Are So Many Tennis Players Skipping The Olympics?

It isn’t just the COVID-19 pandemic which are putting players playing off going.

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On Monday Canada’s Dennis Shapovalov joined the growing number of tennis stars who have decided not to play in this year’s Olympics Games.

 

In a statement issued on social media, the world No.12 said his decision was due to the COVID-19 pandemic and doing what he believes was best for the safety of his team. Japan, which is where the Games are being held, has been dealing with a surge in cases in recent weeks with a low number of the population to be fully vaccinated. Whilst the country has banned international spectators from attending amid fears of the virus being spread, organisers say up to 10,000 domestic fans will be allowed to attend the Olympic venues.

“After careful consideration I wanted to let you know that I will not be participating in the Olympics this year. Representing Canada means the world to me, but due to the current situation my team and I have decided this is the best decision for everyone’s safety,” Shapovalov wrote on twitter.

Shapovalov’s concerns related to the pandemic aren’t the only thing which is deterring tennis players from attending the Olympics. Over the past week, two top 10 players from the men’s Tour also confirmed that they will not be participating. Rafael Nadal is missing the event in order to take a break from the sport following what was a demanding clay court swing. Meanwhile, Dominic Thiem says he doesn’t want to travel to Tokyo and instead wants to focus on his title defence at the US Open.

This year’s tennis calendar doesn’t favour the Olympics. The Wimbledon Championships concludes two weeks before it begins and the US Open starts five weeks after. Two of the biggest events in the sport which offer the highest amount of prize money and ranking points per round. At the same time as the Olympics two ATP 250 events are taking place in Austria and America.

So much has to depend on where a player is in their career. Have they won an Olympic medal before? How important is it to them? Do they want to travel to Asia in the middle of the summer? For every player I think it is very individual how seriously they take the Olympics,” former Olympic champion Lindsey Davenport told The Tennis Channel in 2020.

Tennis was officially reintroduced into the Games back in 1988 after being showcased as a demonstration sport four years prior. It is different to Tour events with no official prize money on offer. However, some countries such as Russia have previously issued financial rewards for athletes who win medals.

Another sticking point is there being no ranking points available for players participating. Back in 2019 the International Tennis Federation told UbiTennis they were ‘open’ to allowing points being awarded but no progress has been made. Perhaps due to the complex governance of the sport with the Olympic event being run by the ITF. Meaning they will have to form an agreement with both the ATP and WTA for such an incentive to happen.

“Currently, the WTA and ATP do not award points for the Olympic Qualification Pathway. We (the ITF) are always open to discussion on the matter.” The ITF said.

Another issue concerns the location. Players face having to travel from Europe to Asia and then North America within a month. A journey made substantially more difficult than usual due to restrictions related to the pandemic.

Chile’s Christian Garin says his decision not to go to Tokyo is because he feels athletes will not be able to get the full experience due to the current restrictions in place.

“Due to the instability of this year and added to the fact that the established conditions will not allow me to live the real experience of what the Olympic Games mean, that is why I have made this decision,” he wrote on Instagram.

When it comes to other Olympic absentees, a contingent of Spanish players will not be attending due to what newspaper Marca describes as ‘calendar issues and a logistically difficult trip to Tokyo.’ Those skipping the event are Roberto Bautista Agut, Albert Ramos, Feliciano López, Jaume Munar and Carlos Alcaraz. Norway’s Caper Ruud, Serbia’s Dusan Lajovic and Bulgaria’s Grigor Dimitrov will also not be playing.

Despite the surge in withdrawals which will most likely increase in the coming weeks, other top names have committed to playing. Novak Djokovic, Naomi Osaka, Daniil Medvedev, Victoria Azarenka, Aryna Sabalenka and Andy Murray have all confirmed they will play.

“It’s going to be my first Olympic Games. We have a great team so we can do some doubles, mixed doubles, everything,” Medvedev said about playing.
“Going to be amazing experience. Of course, with COVID maybe it’s not going to be the same like every year.”

The Olympic tennis event will be held at the Ariake Coliseum and get underway on July 24th.

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The Other Side of Press Conferences

American author and journalist Mike Mewshaw gives his take on the controversy that surfaced at this year’s French Open

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After Naomi Osaka’s withdrawal from the French Open, the debate about press conferences keeps cropping up.  Pressers have been analyzed from more angles than Rafa’s forehand or Serena’s backhand.  Players, both active and retired, have weighed in with their opinions, along with coaches and sports therapists.  The consensus is that tennis reporters are insensitive, disrespectful, sexist, racist, and eager to provoke controversy.

 

The constant threat of illness, the absence of fans, the isolation, and loss of income has certainly added to impatience with reporters.  Venus Williams tartly suggested she maintained her composure during interviews by realizing she could beat any hack in the room; none of them could hold a candle to her. 

But this sort of disrespect runs in both directions.  While players view reporters as pesky publicity machines, at best, or gossip-hounds at worst, some journalists regard players as spoiled high school dropouts who couldn’t write a grammatically correct paragraph if their endorsement contracts depended on it. With all due deference to Naomi Osaka, I would urge her and her colleagues on the ATP and WTA tours to view things from a different perspective.  The coronavirus has wreaked havoc on the press just as it has on them.  Plenty of tennis reporters have lost their jobs.  Almost all of them earn less income.  They face the same risks of infection and submit to enough Covid tests to leave them as red-nosed as Rudolph.

Under the circumstances, reporters who travel the tour, along with those covering matches remotely from their basements, have done a creditable job.  Sure, they sometimes sound testy, just as the players do.  Of course their questions can be repetitious, just as the players answers can be. 

Over the past four decades, I’ve covered more press conferences than I now have white hairs on my head.  I’ve heard racist comments, sexist remarks and massively insulting accusations.  But more often than not, the putdowns were aimed at reporters or at other players.  In the old days, these seldom made it into newspapers, and the really offensive quotes and admissions of rule breaking were deleted from press conference transcripts.  In that politically incorrect era, Arthur Ashe, for instance, came in for a raft of prejudice.  Ilie Nastase openly referred to him as negroni.

Although it’s now largely forgotten, Billie Jean King’s sexuality was accepted by the press long before many on the women’s tour spoke up in her defense.  While male journalists can be appallingly insensitive—Italian Hall of Fame journalist Gianni Clerici used to print Steffi Graf’s menstrual cycle in La Repubblica—it would be difficult to find anything less “woke” than Martina Hingis’ description of Amélie Mauresmo as a “half-man” who “travels with her girlfriend.”  Or Lindsay Davenport’s comment after Mauresmo beat her, “I thought I was playing a guy.”

Predictably, both women walked back these quotes, accusing the press of taking their words out of context.  That’s an ancient canard on the circuit—shoot off your mouth, then claim you were misquoted.  I remember Buster Mottram, then the British Number One, complaining about rowdy fans in Rome, accusing Italians of being animals.  At his next press conference he carefully parsed the remark.  Suddenly the voice of reason, he observed that human beings were all, anthropologically speaking, animals. 

If Buster had won a few majors, his quotes might have been immortalized, like Andre Agassi’s wisecrack at the French Open, “I’m happy as a faggot in a submarine.”  That line made the list of Esquire Magazine’s annual Dubious Achievement Awards. 

John McEnroe’s infamously objectionable conference quotes could only be contained on a wall as vast as the Vietnam War Memorial.  Even if one had the space and energy to chisel them in stone, many would have to be bowdlerized.  One that barely passes the censor’s blue pencil is his barbarous backhand at a female reporter who had the impertinence to question him.  “Lady, you need to get laid.”

In some cases actions speak louder and more loathsome than words.  After a match in Milan, a local female journalist asked Jimmy Connors, “Why do you always touch yourself in a particular place?”  Jimmy shoved a hand down his shorts and gave his genitals a good shake.  “It feels good.  You should try it.”

To repeat, I empathize with Naomi Osaka’s aversion to press conferences.  More than she might imagine I agree that they can be frustrating, stress producing, depressing, and borderline transgressive.  I accept the sage advice of deep-think editorials and socially conscious scribes that reporters need to raise the level of their game.  But so do players who could profit from sensitivity training, anger management, and basic etiquette lessons.  With mutual respect for all those who share a rough road toward an uncertain future, the tour could become a better place for everybody.


Michael Mewshaw is the author of 22 books, among them AD IN AD OUT, a collection of his tennis articles, now available as an e-book.

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