Article translated by Tommaso Villa
The Swedes followed Borg with his “grandchildren” Wilander & Co. Same with Germany, inspired by the Wunderkind, Boris Becker, and by Fraulein Forehand, Steffi Graf. The importance of leading by example.
Tennis is obviously an individual sport. Every player runs and strikes for himself or herself. However, it cannot be a coincidence that, in certain eras, players from the same countries have done well at the same time – a concept that applies the other way around as well. As to why this happens, here’s a few theories:
- It could be the leading example of a fellow countryman or countrywoman, someone who perhaps didn’t stand out as a junior player, allowing to understand that a champion is great, of course, but not superhuman – “if he or she did it, why can’t I?”
- Maybe it’s the fact that tennis players are not as alone as they used to be. They have coaches, physios, psychologists, tactical analysts, physicians, whole teams. And what do teams do? If they are friendly with members of other collectives, they collaborate, exchange information, foster the growth of each member. If they are not, they study each other, learn, and grow. What happens when a player’s team has success? Other teams emulate and study their methods. Very often, one’s achievement becomes everybody’s achievement. Within the tennis circles, it is then much likelier that people from the same country will enable each other – why would you antagonise people with which you can naturally cooperate, since they were shaped from the same mould?
- The media play an important role, perhaps, voicing and spreading the popularity of the game, positively influencing the entire movement, and encouraging the players to greater feats.
- Said national enthusiasm might prompt more kids to pick up a racquet and further stimulate the growth of the game in a given country, creating a positive cycle.
Tennis history validates all the above statements. I’m not referring to the epochs when the game was limited to a few select nations: before WWII, it was the Brits and Wimbledon, the French with the Musketeers, the Americans with Bill Tilden, Ellsworth Vines and Don Budge. Afterwards, and all the way to the end of the Sixties, tennis was dominated by the Aussies, followed (though not closely) by the United States. Between 1950 and 1967, Australia won the Davis Cup 15 times out of 18 (the competition was as important as a Major back then), dominating thanks to the presence of champions like Sedgman, McGregor, Rose, Rosewall, Hoad, Laver, Newcombe, Roche, and Emerson – the USA won thrice out of 11 finals.
Of course, both countries had a much bigger reservoir of young players due to a greater following, a following that was alimented by a winning cycle, so much that five consecutive American Davis Cup wins (between 1968 and 1972) took place in the same years when Agassi, Courier, Sampras, and Chang were born, three of them the children of immigrant parents who had discovered the game because of the national wins that made headlines and filled sports shows – this was also the time when the Slams were becoming more and more popular, especially the US Open and Wimbledon.
In the early Sixties, Italy reached two Davis Cup finals, in 1960-61, and, perhaps by chance, perhaps not (I believe not), four kids (they were born in 1949, 1950, 1951, and 1953) learned about the game after hearing about what Pietrangeli, Sirola, Merlo, and Gardini had done – they would later become Italy’s version of the Musketeers (Panatta, Barazzutti, Bertolucci, and Zugarelli), one of them the son of a tennis club’s custodian, another one the offspring of a Tuscan tennis instructor, two more the progeny of struggling families.
THE POST-BORG SWEDISH CASE
What happened in the early 1970’s? Borg Mania, the arrival of a racquet-swinging Beatle, that’s what happened. His popularity was immense – a bona fide superstar. He won a Davis Cup almost by himself, along with 11 Majors that included a triple Roland Garros-Wimbledon brace, back when grass was actually grass and players did not even have the time to assimilate the switch between the dirt and the lawns. The outcome of his domination? The media frenzy in Sweden spurred a bonanza of young children who elected to start playing, flooding tennis clubs in a small country that didn’t even have outdoor courts except in Bastad – all those kids braving the cold before dawn, they dreamt of becoming the new Bjorn Borg.
Coincidentally (but it’s not a coincidence) those years saw the emergence of Wilander, Nystrom, Sundstrom, Jarryd, and Edberg. A grassroots dynasty with seven consecutive Davis Cup Finals between 1983 and 1989 – and three titles. The glory days lasted until Edberg’s retirement in 1996, when his team lost the final in Malmoe against the French led by Arnaud Boetsch (now a Rolex man), who saved three match points against Niklas Kulti in the decisive tie. Unfortunately, Larsson, Kulti, Gunnarson, and Gustafson didn’t have the talent or the charisma of their predecessors. Therefore, the sacred fire of tennis in Sweden was extinguished, and it hasn’t come back to this day – at the moment, the best Scandinavian player is a Norwegian, Casper Ruud.
Midway through the 1980’s, a new champion emerged in Europe – Boris Becker, born in 1967. Actually, the young Teutonic studs were two, because a few years later Steffi Graf (born in 1969) broke onto the scene as well, and in a far more emphatically dominating way. At the beginning of the ensuing decade, when Boris had already become the most popular German along with his peer, nicknamed Fraulein Forehand, the German Chancellor Kohl said: “If Becker decided to run, he’d easily win the elections” – that was around the time when, in 1991, he lost the Wimbledon final against a fellow countryman, Michael Stich.
Coincidentally (but it’s not a coincidence) Germany notched its first two Davis Cup titles in those years (out of three finals played between 1985 and 1989), and the wins snowballed into a generation of very good players, such as former world N.2 Tommy Haas, N.4 Nicolas Kiefer, and N.6 Rainer Schuettler. However, a guy like Haas, who didn’t reach the top spot and wasn’t reared in Germany but rather in Florida by Nick Bollettieri, wasn’t enough, and the flame was extinguished in Germany as well, with the galore of tournaments (Munich, Stuttgart, Frankfurt, Essen, Hannover) trickling down to almost nothing, the population losing interest due to the lack of new great champions.
NADAL, SPAIN, AND THE FRENCH TENNIS MOVEMENT
As soon as the German fandom started dwindling, Ion Tiriac moved his Masters 1000 event from Hamburg to Madrid, where the Caja Magica was built and Rafa Nadal dominated, spearheading a national movement that was already great – the years of Santana, Orantes, and Gimeno were the same when Bruguera, Albert and Carlos Costa, Moya, and Ferrero were born or grew up in, another coincidence/not coincidence – the latter even became the first man to lead Spain to a Davis Cup triumph.
I don’t want to become repetitive, even though there are dozens of examples, such as in France, where the generation of Noah, Forget and Leconte was succeeded by Grosjean and Clement, who were in turn up-staged by the contemporary, ageing quartet of Tsonga, Monfils, Gasquet, and Simon, or in Argentina, where the duel between Vilas and Clerc caused the emergence of Jaite, Coria, Gaudio, Del Potro, or in Croatia, where Ivanisevic spawned Cilic and Coric, and so on.
THE ITALIAN CASE, FROM SCHIAVONE TO CECCHINATO
The history of Italian tennis is further confirmation of the generational theory: after years of drought, Francesca Schiavone won the French Open at 30 years old, reaching the final again the next year, perhaps an even greater achievement. Before her, Silvia Farina had reached the 11th spot in the rankings, but she had never broken through at a Slam, thus not spurring a winning wave. Coincidentally (but it’s not a coincidence!) Schiavone was immediately succeeded by another Italian in the Parisian final, Sara Errani, a player very few believed in – certainly not the national federation, judging by the press releases of the time and by the fact that she had opted to move to Spain to train with Pablo Lozano, but still, right on her heels, Flavia Pennetta won at Indian Wells and then at the 2015 US Open, defeating Roberta Vinci, another Italian who hadn’t done much early on in her career.
How can this multiplicity of great players be explained if not by acknowledging the veracity of the theories I laid down at the beginning of this op-ed? Why the Italian women managed to ratch up these wins while their male counterpart couldn’t? The answer is simple: because no man was able to convey a positive message to the younger generation for over 40 years, no Italian male player was able to go deep into a Major nor to win some big event.
In 2018, Marco Cecchinato reached the semi-finals at the French Open, 40 years after Barazzutti. Suddenly, every Italian player who had played and perhaps even beaten Cecchinato (sometimes just in training sessions) realised that his achievement could be emulated. Moreover, the national tennis federation (the FIT) also came to a sudden realisation, finally understanding that financing private teams is a good thing, because it creates financial benefits for the entire movement.
What happened next? Fognini won in Monte-Carlo in 2019, after years of high-level play but with no satisfaction, finally breaking into the Top 10, while Matteo Berrettini reached the fourth round at Wimbledon and then the semi-finals at the US Open, qualifying for the season-ending ATP Finals. The pandemic slowed down the growth of the movement, but at the moment both the two highest-ranked players born after 2001 are Italians, Jannik Sinner and Lorenzo Musetti.
This doesn’t mean that Italian tennis will dominate the next decade. Spain had as many players in the third round of the men’s French Open as Italy, five apiece, their N.1 player is also the favourite to win the men’s tournament, and they are already assured of a spot in the fourth round thanks to the Carreno-Bautista derby. Moreover, the Italian women’s movement seems to have meanwhile withered (hopefully not for 40 years). But negative and positive cycles are not a coincidence. So, tennis is an individual sport, but maybe not that much. Don’t you agree?
Looking Back at Madrid and Forward to Rome
Alexander Zverev stated his case in the Spanish capital – will Djokovic and Nadal re-assert their claycourt supremacy in Italy?
We have been witnessing a fascinating clay court campaign in a multitude of ways over the last several weeks. The first major development was when Stefanos Tsitsipas secured his initial Masters 1000 crown in Monte Carlo by toppling Andrey Rublev in the final after Rublev had stunned eleven time victor Rafael Nadal in the quarterfinals. Novak Djokovic suffered an even more astounding upset loss there to Great Britain’s Dan Evans in the round of 16.
Then Nadal was victorious in Barcelona, capturing that highly regarded ATP 500 title for the twelfth time, rescuing himself from match point down in the final against an inspired and somewhat unlucky Tsitsipas, prevailing in three hours and thirty eight minutes of suspenseful and riveting tennis. That same week in Belgrade, Djokovic was beaten in the semifinals of an ATP 250 event in his homeland, narrowly falling short against the surging Aslan Karatsev. The following day, the top ranked Italian Matteo Berrettini ousted Karatsev in a final set tie-break to claim that title.
And soon the stage was set for the second clay court Masters 1000 tournament of the season this past week in Madrid. Once more, there were a good many surprises over the course of the week. For starters, 2019 champion Djokovic chose not to play. Tsitsipas was knocked out in the round of 16 by a perspicacious Casper Ruud. Overflowing with confidence coming into the tournament, Tsitsipas never found a way to contain Ruud from the backcourt. He seemed constantly ill at ease coping with the Norwegian’s heavy and penetrating topspin forehand. Ruud kept Tsitsipas at bay with his high bounding shots off that side.
That match turned late in a first set settled in a tie-break. That crucial sequence was locked at 3-3 when Tsitsipas punched a backhand volley long to give Ruud the mini-break. Ruud took control off the forehand to stretch his lead to 6-3, and then came through to take the tie-break 7-4 when Tsitsipas missed a forehand inside-in wide.
The second set went to 3-3, but Tsitsipas was broken at 15 when he double faulted and pressed off the forehand, netting his down the line shot off that side. Ruud was too good with the lead, holding at 30 for 5-3. Two games later, Ruud served for the match, meeting that challenge with temerity, holding at the cost of only one point. Victory was salvaged deservedly by Ruud 7-6 (4), 6-4, who connected with nearly 80% of his first serves and largely set the tempo in this meeting. He was so good that Tsitsipas was frequently discombobulated, pressing and beating himself down the stretch.
The Norwegian eventually lost in the semifinals 6-4, 6-4 to a top of the line Berrettini after ousting Alexander Bublik 7-5 6-1 in the quarterfinals. He is beginning to make a habit out of showing up for the latter stages of Masters 1000 tournaments. He lost to Djokovic last year in the semifinals of Rome and a few weeks ago advanced to the same round in Monte Carlo. Ruud has the game to keep advancing deep into these draws at elite events.
Meanwhile, Daniil Medvedev returned to the ATP Tour after being sidelined by Covid-19. He won a match but was then taken apart by the seasoned Christian Garin of Chile, a seasoned clay court player who was not intimidated in the least by taking on the world No. 2. He came through 6-4, 6-7 (2), 6-1 for perhaps the biggest win of his career. Medvedev looked out of sorts and ill at ease through most of this encounter. The 25-year-old Russian was candid both before and after losing about his inner confusion concerning how to make his game work effectively on the dirt. The 2019 U.S. Open finalist and 2021 Australian Open runner-up has never won a match at Roland Garros in four appearances. He will have his work cut out for him to recover his finest tennis this week in Rome.
Clearly the most pivotal moment of the week in Madrid was the quarterfinal departure of Nadal at the hands of Zverev. The Spaniard looked composed and secure on his way to the appointment with Zverev. He was outmaneuvering his tall adversary in the early stages of this contest, building a 4-2 lead, putting himself two holds away from taking the first set. He reached 30-30 in the seventh game but Zverev stung him severely with a pair of excellent passing shots to get the break back.
Down break point in the following game, Zverev gamely held on to reach 4-4. Nadal had a game point for 5-4 but he could not cash in on it. At deuce, he double faulted, and then he netted a backhand passing shot. Zverev was rolling now. Serving for the first set, he started with a double fault but swept four points in a row from there with a flourish, lacing a backhand winner crosscourt, coming to the net to pressure Nadal on the next two points, and then acing the Spaniard down the T.
Zverev had captured four consecutive games and he never looked back as a desultory Nadal could not recover his form. Zverev played beautifully and dictated his share of the points. His serve was magnificent as Nadal only broke him once. For his part, Nadal was far too negative once he dropped the opening set. He fell behind 4-2 in the second set and held on there from 15-40, but Zverev maintained the upper hand to win 6-4, 6-4, stopping Nadal for the third time in a row.
Nadal, Tsitsipas and Medvedev were not the only major casualties in the tricky high altitude conditions on the Madrid clay. Dominic Thiem— absent in Monte Carlo and Barcelona and moving through something of a mid-career identity crisis—managed to fend off the sport’s most fearsome server in John Isner. Isner had cut down both Roberto Bautista Agut and Rublev in final set tie-breaks and he nearly halted Thiem. But when the industrious Austrian erased four break points against him at 2-2 in the second set, he altered the course of the match and Isner’s soaring confidence was soon diminished. Thiem rallied admirably for a 3-6, 6-3, 6-4 triumph and a place in the semifinals.
That was not a bad start to his 2021 clay court campaign. But he looked rusty and uncomfortable against Zverev in the semifinals, and the 6-3, 6-4 scoreline is somewhat misleading. It was not as close as that. Zverev was far more self assured and consistent amidst the swirling winds and he had another very good serving day. He never allowed Thiem to settle into any kind of rhythm from the backcourt. The win for Zverev was all the more gratifying considering that it was their first clash since meeting in the U.S. Open final. Zverev led two sets to love in that match and later served for the match in the fifth set, but he faltered in the crunch and endured a nightmarish setback.
Not so in Madrid. On the clay he was often masterful, driving his two-handed backhand deep down the line for winners, opening up the court with his forehand, and approaching the net at all the right times to keep Thiem unsettled. He demonstrated in this match— as he had against Nadal—that he is as formidable on clay as he is on any other surface. Zverev was a worthy winner of the Madrid Masters 1000 tournament in 2018 after winning Rome the previous year. He also won the Canada hard court Masters 1000 tournament at Montreal in 2017. Those string of triumphs are abundant proof that he can win big tournaments as well as perform with comparable excellence on all kinds of courts.
For Zverev, the final this time around was a chance to reaffirm his greatness while Berrettini was searching for a breakthrough and a validation of all the progress he has made since he climbed into the world’s top ten in 2019 and reached the semifinals of the U.S. Open. He had never reached a Masters 1000 final before, but this was a chance to get on the board and prove that he belongs among the sport’s elite.
Berrettini acquitted himself well in a hard fought opening set. He gained the first break of the match for 4-3 but Zverev retaliated immediately to make it 4-4. They settled that set in one of the most bizarre tie-breaks of the entire tennis season. Benefitting from a stream of unforced errors from Zverev, Berrettini built a commanding 5-0 lead, with two service points to follow. But the Italian tightened up, losing the next four points, giving away three with unjustifiable mistakes.
Yet Berrettini unleashed a forehand inside in winner for a 6-4 lead, with two set points at his disposal. Once more with the lead, Berrettini faltered and Zverev moved in front on a run of three consecutive points, serving an ace for a 7-6 lead and a set point. But Berrettini produced a pair of fine first serves and took control off his explosive forehand to regain the lead at 8-7. Although Zverev made it back to 8-8, he foolishly gambled by going for a huge second serve ace down the T, double faulting that point away. Now Berrettini secured the set on his fourth set point with a service winner to the backhand.
The charismatic Italian had survived a considerable ordeal to salvage a set that almost got away, but Zverev refused to be preoccupied by an agonizingly narrow failure. Across the last two sets he was the decidedly better player. At 4-4 in the second set, Berrettini was burned by allowing Zverev to read his drop shot with ease. The German scampered forward and chipped a backhand winner out of reach for 15-40. Shaken, Berrettini double faulted and Zverev had the critical break for 5-4. Zverev served it out in the tenth game to make it one set all.
The Italian had one more opportunity early in the third set when he had a break point for 3-1 after Zverev went for another second serve ace down the T and double faulted. But Zverev saved the break point with a massive combination of a big serve that set up a forehand winner behind Berrettini. He held on for 2-2 and never looked back, breaking in the fifth and ninth games to record a 6-7 (8)), 6-4, 6-3 victory for his fourth Masters 1000 singles title. The only active players who have won more are Djokovic (36), Nadal (35), Roger Federer (28) and Andy Murray (14).
Most importantly at the moment, this was Zverev’s third Masters 1000 crown on clay. That puts him in very good stead for Roland Garros. Zverev now must be considered a top five candidate to take the world’s premier clay court title. Nadal remains the clear favorite, followed by Djokovic, Thiem and Tsitsipas. But Zverev is now right up there on the clay with the Serbian, Austrian and Greek stylists. Winning this title could not be more timely or uplifting for the tall German performer, with or without a strong showing in Rome this week.
Zverev coming through so convincingly in a tournament of such prestige only augers well for him in Paris. But what about Rome? Who is best positioned to be victorious this week on the Italian red clay?
Those are not easy questions to answer. One would think that Nadal will be very eager to make amends. He has won only one of his three clay court tournaments this year en route to Roland Garros, losing a pair of quarterfinals. Even his lone triumph in Barcelona was a narrow escape as the Spaniard saved a match point in the final set before holding back Tsitsipas in a rousing title round showdown.
This week in Rome, Nadal’s draw is not easy by any means. Seeded second behind Djokovic, he may have to face the hard working and wildly ambitious Jannik Sinner after a first round bye. He could meet Zverev for the second week in a row in the quarters. Zverev would have nothing to lose after eclipsing Rafa in Madrid, and the Spaniard could be both eager and uneasy if he does indeed face Zverev again.
If Nadal survives a potential confrontation against Zverev, he will be very likely to reach the final. No. 3 seed Daniil Medvedev is on his half of the draw. I don’t believe Medvedev will make it to the penultimate round, but perhaps Diego Schwartzman will break out of a recent slump of sorts and try to reprise his winning form against Nadal last year at the same tournament.
There is no doubt Nadal could use a boost going into Roland Garros. He has yet to strike peak form these last bunch of weeks on his favorite surface, but claiming a tenth title in Rome would do much to improve his state of mind and carry him into Roland Garros feeling more like himself.
And yet, as much as Nadal wants to raise the level of his game this week in Italy, Novak Djokovic is even more in need of a morale boosting tournament. Djokovic, of course, commenced 2021 in style with his ninth Australian Open title run and an 18th Grand Slam title victory. But in his two clay court appearances this spring, he has not found a winning formula.
In Monte Carlo, playing Dan Evans for the first time, Djokovic was way off his game in a straight set defeat. He then suffered the disappointing loss to Karatsev in Serbia. Those subpar results are precisely why Djokovic must be determined to win his sixth Italian Open this week—or at least reach the final. That will be no facile feat. He could meet Evans again in his opening match if the British competitor beats Taylor Fritz in the first round.
The seedings project that Djokovic will meet the No. 5 seed Tsitsipas in the quarterfinals (if Tsitsipas can defeat Berrettini), and that one could be a blockbuster. Also on his half of the draw for a potential semifinal encounter are Thiem and Rublev, who should clash in the quarterfinals. My feeling is that Rome is even more important for Djokovic than it is for Nadal; a great week in Italy could propel the estimable Serbian into Paris and make him believe in his chances to win Roland Garros for the second time, but an early round loss would be a serious setback.
So there you have it. I have a hunch that we are in for some more surprises this week. Rublev might explode and take his first Masters 1000 title. Zverev will be ascendant after his heroics in Madrid. He will be loose, confident and happy to be sparkling in the springtime. Perhaps it is asking too much of him to win back to back Masters 1000s in successive weeks, but perhaps not. I would also not be stunned to see Tsitsipas step back up after his loss in Madrid and put it all together again.
To be sure, Nadal must be the favorite this week. He can be exceedingly dangerous when he is disconcerted with his game, and that could well drive him to dizzying heights in Rome. I feel the same way about Djokovic. He has too much pride and professionalism to accept anything less than a stellar showing this week as either the champion or the runner-up.
But what makes it all so intriguing at the moment is the unpredictability of the last three Masters 1000 tournaments. Hubert Hurkacz struck down Sinner in the Miami final; neither player had ever been in a Masters 1000 final before. Tsitsipas took his first of these elite prizes in Monte Carlo by toppling Rublev in the final. And then Zverev triumphed deservedly in Madrid, coming from behind to oust Berrettini, who was appearing in his first final at one of these elite events.
So take nothing for granted. Look for Nadal to be almost defiant. Expect Djokovic to be as motivated as he has been in a long time. Be anticipating as well that one of the emerging superstars of men’s tennis will be in the thick of the proceedings and unafraid to confront the icons of the game at the second most important clay court tournament in all of tennis.
Steve Flink has been reporting full time on tennis since 1974, when he went to work for World Tennis Magazine. He stayed at that publication until 1991. He wrote for Tennis Week Magazine from 1992-2007, and has been a columnist for tennis.com and tennischannel.com for the past 14 years. Flink has written four books on tennis including “Dennis Ralston’s Tennis Workbook” in 1987; “The Greatest Tennis Matches of the Twentieth Century” in 1999; “The Greatest Tennis Matches of All Time” in 2012; and “Pete Sampras: Greatness Revisited”. The Sampras book was released in September of 2020 and can be purchased on Amazon.com. Flink was inducted into the International Tennis Hall of Fame in 2017.
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.
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.
Old-Timers’ ‘Big Three” Face Unpredictable Future
This past weekend, both Nadal and Djokovic were pushed to the limit – will they be the men to beat for much longer? Long-time tennis columnist James Beck gives his take.
Dominic Thiem broke into the party at last year’s U.S. Open.
But Rafa Nadal came right back with his answer in the moved-back French Open and Novak Djokovic opened this year by winning the Australian Open.
And, suddenly, everything looked okay for the old-timers on the men’s tennis pro tour.
But is it?
IS EVERYTHING OK FOR OLD-TIMERS?
Sure, Nadal came through again on Sunday to do his part for the old-timers by out-lasting young Greek Stefanos Tsitsipas in the Barcelona final, taking his 12th title there on a court named in his honor.
It isn’t that Nadal looks tired or anything, except maybe in allowing Tsitsipas to come back from two sets down in the Australian Open and then looking un-Nadalish in a loss to Russian budding superstar Audrey Rublev in the Monte Carlo tournament.
Just this past week, Russian tour rookie Aslan Karatsev pushed Djokovic all over his home court in Belgrade in the Serbia Open.
And, of course, no one probably remembers when Roger Federer was last seen in a showcase situation.
TIME TO START WORRYING?
So, maybe it is time to worry about the old-timers, 39-year-old Federer, 34-year-old Nadal and 33-year-old Djokovic.
If Nadal and Djokovic can hold off the new crowd through the French Open and Wimbledon, that might be about the best that fans of the old-timers can hope for.
The U.S. Open probably is a toss-up between the three Russians (that’s including maybe already superstar Daniil Medvedev), Tsitsipas, young German Alexander Zverev and Thiem.
These young guys (Medvedev, Thiem, Tsitsipas, Zverev and Rublev, Nos. 3-7, respectively) occupy the last five places in the top seven positions in the latest world rankings, with old-timers Djokovic and Nadal serving as guides at Nos. 1 and 2, respectively.
Of course, you can’t overlook Matteo Berrettini and 19-year-old Jannik Sinner, a pair of Italians that appear capable of joining the “Russian Trio” in dominance of the tour, with help from Thiem, Zverev and Tsitsipas.
RAFA FANS CAN’T RELAX
In the case of Nadal, fans never knew when to relax, sort of like the Los Angeles Dodgers who have gone from “Wonder Men” to “Wonder What’s Next Men” during the past 10 days of major league baseball in the United States.
The Dodgers were up 7-1 late in a game and end up losing in extra innings to the San Diego Padres? Of course, Nadal failed to close out Tsitsipas while holding a 5-4 lead and two match points in the second set in the Barcelona final. After that, fans were never quite sure of how famous-finisher Nadal might end up against the fiery, hard-hitting, highly athletic 22-year-old Greek.
TSITSIPAS MAY BE BIGGEST CHALLENGE
Although Rublev manhandled Nadal in the Monte Carlo quarter-finals, it now appears that Tsitsipas might be Nadal’s biggest challenge to overcome in winning a 14th French Open title. Yes, even ahead of Djokovic, who appeared to run out of gas against the steady, big-hitting Karatsev.
A year from now, we may be talking about Karatsev in the same breath as Thiem, Medvedev, Rublev and Tsitsipas.
As for the “Big Three” old-timers whose combined age of 106 is nine years more than that of the quartet of the possible future “Best Four” of Thiem, Medvedev, Rublev and Tsitsipas.
Yes, the upcoming French Open is critically important to the immediate future of Nadal, and maybe Djokovic. Go three steps further to Wimbledon, the U.S. Open and next year’s Australian Open, and the top of men’s tennis might have an entirely different look from the current one.
James Beck’s columns are available on the Charleston (S.C.) Post and Courier newspaper’s web-site at postandcourier.com. He can be reached at Jamesbecktennis@gmail.com.
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