Online: 10.07.2019

Dawn of a New Era
Jarek Chrostowski

Considered as the most technically versatile player in the history of the game, he impresses with the elegant style and fluidity of movements, surprises with the power and angles of his strokes. The winner of 20 Grand Slam tournaments, number one in the world singles ranking at the record age of 36! The closer to the end of the career of Roger Federer, the more voices are rising that for a long time we will not see such a complete and technically perfect tennis player. I am of the exact opposite opinion. Federer is not a unique phenomenon that crowns the splendor of the era. He is just the herald of a new one.

Technical differences between players are characteristic of modern tennis. When we look at the top of ATP or WTA rankings, all doubts disappear: players hit balls in their own distinctive styles. We should not be surprised. The human kinematic chain has many degrees of freedom and the number of ways that we can perform a seemingly similar sequence of motions is enormous. At the same time, among coaches, there is a strong - and so rational! - belief that the 'natural talents' of their adepts should be supported. As a result, the coaches share a certain foundation of tennis knowledge, but their final methodology is highly individualized. This situation leads to substantial technical diversity between their pupils.

The spectacular successes of Roger Federer have attracted the attention of almost every coach and player towards his most powerful stroke: the topspin forehand. For two decades Federer has been playing several dozen matches a year, recorded by many cameras, and watched by millions of tennis enthusiasts. Nevertheless, no one has ever succeeded in re-creating Federer's forehand! Of course, one in two coaches claims he/she knows the secret of the Swiss master's technique, and many players, especially amateurs, are strongly convinced that they use the 'Federer forehand.' But when we look closely at their technique, it turns out that although the external form of the stroke seems to be familiar, something in their forehands is wrong. Something is missing.

Here, an interesting question arises. If there are so many followers, why was no one able to copy such a well-documented stroke? Isn't that amazing? We do not need to be particularly sharp to notice that the number of hands, legs, and heads Roger Federer has does not differ significantly from the rest of humanity. Thus, if one kinematic chain is able to work under a certain regime, why aren't the others?

Sources of fixation

This is a fact: we have innate predispositions to replicate the behaviors we observe. In scientific experiments it has been shown that we copy in a thoughtless manner: while chimpanzees learn from others what makes sense for them, human children duplicate the actions of adults even when they are obviously pointless1. As adults, we rationalize own choices and build walls to keep out ideas that contradict those we endorse. But are we sure we have really eliminated this childish tendency of mindless copying? Being deeply immersed in the frameworks of reasoning sketched out by our predecessors, do we really face adversities of life in the most optimal way, or in a way just consistent with our current habits and deep faith in the value of our earlier (supposedly own) choices?

Some might say that only poor coaches urge their clients to adopt baseless axioms and that blind copying plays a marginal role in modern tennis. In reality, this is not the case. A wonderful example - one of so many! - is the most popular advice: 'Transfer your weight into the ball!'. Probably all coaches would sign up to it, whether they teach in local clubs or work with the elite of ATP players. The explanation we hear is always the same: during the collision - in the exchange of momentum, a physicist would say - the mass of the tennis player plays an active and important role. However, it is a scientifically proven fact, described in numerous publications2, that the effective mass involved in the collision with the ball is... smaller than the mass of the racquet. This is fully in line with on-court observations: corpulent gentlemen, playing for fun and transferring their not-so-small weight into the ball, certainly do not hit it harder than young, thin girls competing in national and international tournaments. On the contrary, these girls play significantly faster balls!

Efficiency, effortless power and aesthetics. Are they really reserved for the chosen? The author does not feel particularly special...

The physical reality tells us its own story. The contribution of the player's body motion is remarkably limited: it increases the velocity of the ball at the contact by a projection of the body velocity vector on the direction of the flight path of the ball after the hit. On the court, this increase does not exceed a few kilometers per hour, and in so-called open stances is close to zero. Moreover, during ATP matches we can often admire powerful strokes generated by players who are clearly moving away from the ball. The contribution of the tennis player's body velocity to the velocity of the ball after the collision with the racquet is therefore a few percent at best, and in most cases it is not important at all. Yet the advice to 'transfer your weight...' does really work! And - what a surprise... - nobody has ever asked: 'Why, if it has no physical sense?'3

A more or less subconscious human tendency for blind copying raises the suspicion that the difficulty in reproducing Federer's forehand may be a consequence of the fact that this specific stroke operates within a different regime than the one widely accepted between coaches. But is there a place in modern tennis for a paradigm that was previously unknown to anyone? One would guess that in a sport with such a long history there is no chance of this happening.

If we want to win in tennis, we have to be able to steal time from our opponent. This task can be accomplished in a variety of ways. The most obvious method is to increase the ball velocity, and thus the power of the strokes. The physical formula for power is a simple fraction. In the numerator, there is the amount of energy released, in the denominator - the time in which it was released. Clearly, the methodology of teaching in modern tennis is focused on increasing the numerator. Do you want to hit harder? Then you should increase the efficiency of your muscles, work more intensively, spend hours a day at the gym. And, of course, transfer your weight into the ball.

Tracking the paradigm

The value of each common fraction can be increased not only by increasing the numerator, but also by decreasing the denominator. Therefore, instead of increasing the amount of energy we put in, we could work on releasing it in a shorter period of time. If this time was short enough, energy production could be reduced reasonably, maintaining the power at a sufficiently high level. A reduction of time of energy release means that accelerations start to play a more and more important role. This article is too short to describe all physical details. Here, it is important to say that the structure of the human kinematic chain ensures that the increase in acceleration can take the form of a quite sharp peak: if the transfer of energy, momentum and angular momentum along the kinematic chain is appropriate, a microsecond spike in acceleration appears, many times larger than the spike in velocity4. At this point, it is worth noting that human senses have problems with detection of accelerations. When something moves fast, we are able to detect this fact immediately. Accelerations, especially those lasting fractions of a second, are much harder to see, even when they are significant5. We shouldn't be surprised that the strokes in which the accelerations play important role look effortless and surprisingly powerful.

If you want to increase power P, you can produce more energy E or release it in a shorter time t. Did you know that in tennis you have a choice?

A question arises as to whether a similar duality of paradigms can be seen in any other field of sport? The answer is: yes. Chinese martial arts have a very similar nature. They are divided into external styles, based on strength training (adepts work mainly on increasing the numerator in the power formula), and internal styles, where chi energy plays the main role. As long as the chi is embedded in Buddist mysticism requiring the fighter to achieve mental unity with the harmony of the Universe to perform a powerful stroke, it is difficult to take chi energy seriously. However, the internal styles work surprisingly well. In my opinion, it is possible because their techniques allow the fighter to shorten the time of the energy release. Internal martial artists work to increase power by reducing the denominator in the power formula6.

Let's go back to tennis. Would it be possible here to construct techniques around the idea of shortening the time of energy relaxation?

In 2011, being strongly discouraged by my own unsuccessful attempts at amateur reconstruction of the basic features of Roger Federer's forehand, I decided not to copy anyone anymore. Inspired by conversations with laser physicists, and using the ideas formulated during many years of my own thinking, I began - for pure intellectual curiosity - to develop a completely new theory of tennis techniques, built around the idea of the concentration of energy in space and time. I just wanted to see if it would be possible. When, two years later, the core of the theory was ready, I suddenly realized that out of all the strokes of all the tennis players I had ever seen - and I had been watching several players a day for years - all components of my theory can be found in one specific stroke. It is not difficult to guess in which one. At this special moment, I became convinced that my theory - something that was supposed to be just my private intellectual hobby - turned out to have a surprising and valuable outcome: it enabled me to describe and recreate the most famous stroke in the history of tennis! That's why I decided to devote the next few years to turn the theory into a coherent set of techniques. At the end of 2017, the techniques were not only ready; I could even demonstrate them in practice.

Inertial tennis

The description of inertial tennis techniques - called so because of the fundamental role of a broadly defined inertia - is far beyond the scope of this article (here is a brief introduction). What is important to note here is that in typical tennis techniques practically every component of a motion sequence, at any moment, is performed by a player, whereas in inertial tennis it is physics and biomechanics that are responsible to a large extent for controlling the most important aspects of the stroke. The player's task is not to perform the stroke sequence step by step, but to carefully prepare the best initial conditions. After the start of the sequence its actual state is controlled by the physics itself, within the biomechanical frames of the human body, in a way that is consistent with the expectations of the player.

The same goal, so different approaches. This short video visualizes the difference between the ideas behind modern and inertial tennis. In inertial tennis, physics does the work.

Inertial tennis has a remarkably specific property, which is crucial for the thesis that has been presented at the beginning of the article. With modern tennis techniques, the stroke sequence can be performed in many ways. This freedom is significantly limited in inertial tennis. Why? Imagine a long chain hanging from the ceiling. The last (lowest) segment of the chain is just above the floor, and there is a ball near it. We grab the free end of the chain and move it as high as possible. Now, how could we hit the ball? The first method is to move the hand holding the free segment down, near the ball, and then push it towards the ball. This can be done in many ways. The situation is similar to what we see in the techniques of modern tennis: the player has to perform the motion sequence from the beginning to (almost) the end. The second method seems to be much more interesting. High at the ceiling, the last segment should be carefully translated to the specific position, so that after its release it will fall freely to hit the ball, being controlled by physics only. In this regime the freedom of choice is limited. The number of places where you can initiate the free (and successful) fall is quite low, especially if the motion is to be as effective as possible. Inertial tennis works in a similar way. The stroke sequence must be prepared precisely, but then practically everything just happens on its own. This idea can be captured more vividly. In inertial tennis, it is not you who play tennis. It is the Universe that plays tennis using you.

In the light of the chain example it becomes apparant that, sooner or later, the tendency of modern coaches to support the 'natural talents' of their clients will lead to technical chaos. This is not the case with inertial tennis. Physics is always the same, which means that the initial conditions for every inertial stroke must be prepared identically. This observation should be properly understood. In inertial tennis, there are no hundreds or thousands of styles of forehands or backhands. Under the given conditions, the way to success is practically the same, because our Universe and our bodies work as they work. Therefore, everyone who knows how to prepare the initial conditions for a specific stroke will be able to reproduce this stroke in exactly the same form as other inertial players do.

To the smallest details, the inertial forehand is a result of rigorous logical reasoning. The similarity of its visual shape and dynamics to the so-called Federer forehand is a strong indication that Roger Federer is just the first (but unaware) user of inertial techniques. This fact has enormous consequences. As long as the efficiency and power of the strokes depend on the player's athletic preparation, amateurs were unable to hit the ball on the level typical of professionals. In inertial tennis, the powerful strokes are not the effect of athleticism, they are the result of pure physics - and physics is the same for everyone. That's why there is no significant differences in efficiency and power of strokes between the twenty-fold winner of Grand Slam tournaments - the professional player considered as one of the greatest in the history of the game, and one of the richest sportsmen in the world - and a pure amateur at the age 50+, who has never took a single tennis lesson and during his tennis 'career' won exactly 0 $.

Time to reach the final conclusion, and it is quite surprising. There is no such thing as the 'Federer forehand'. There is the inertial topspin forehand, and Roger Federer is just its first user - and, quite ironically, one who is unaware of the deep theoretical background behind his stylish signature stroke7. Thanks to the enormous intuition of his first coaches, and certainly his own too, he retained and then extended many inertial features of his original, childish techniques, developed during early on-court lessons with racquets that have been heavy in comparison to his body mass. By using inertial techniques on a large scale, he is now a beneficiary of being a pioneer: he does not have to compete with other inertial tennis players8. Against the background of modern tennis he presents all the advantages of inertial tennis. Until now, it seemed that his tennis was perfect and unique. But inertial techniques are not limited to forehands and are not reserved for the chosen few. Inertial tennis is not a gift from the gods, it is knowledge. And knowledge can be passed between people. That's why I have no doubts: when Roger Federer puts his racquet in mothballs, a certain era in tennis will end...

...and a new one will begin.

In inertial tennis, it is not you who play tennis. It is the Universe that plays tennis using you.


Jarek Chrostowski, Polish physicist, popularizer of natural and technical sciences (over 30 years of experience), author of several hundred popular science articles in national media, science journalist and editor promoting in Poland and around the world achievements of the leading Polish scientific institutions, such as the Faculty of Physics of the University of Warsaw, the Institute of Nuclear Physics of the Polish Academy of Sciences, the Institute of Physical Chemistry of the PAS, the Institute of Experimental Biology of the PAS and others. He has been playing tennis since he was a child, always as a self-taught amateur who has never participated in any tennis lessons. Inspired by creative conversations with other physicists, in 2011-12 he created the inertial theory of tennis and within the next five years transformed it into the first in history of the game internally coherent set of tennis techniques, based on the phenomenon of inertia and conservation laws.

1 Causal knowledge and imitation/emulation switching in chimpanzees (Pan troglodytes) and children (Homo sapiens), V. Horner, A. Whiten, Animal Cognition (2005) 8: 164-181, DOI: 10.1007/s10071-004-0239-6.

2 For example: The Physics and Technology of Tennis, H. Brody, R. Cross, C. Lindsey, Racquet Tech Publishing 2002, San Diego.

3 A really deep explanation of the effectiveness of this advice would require a separate article. Here we will confine the answer to the statement that the rule works for biomechanical reasons, not purely for physical ones. It should also be noted that it is physically impossible to 'transfer the weight'. In physical systems we can transfer energy, momentum and angular momentum - and momentum, as a product of mass and velocity, has nothing in common with the weight.

4 It should be emphasized that this statement is the author's hypothesis. Large peaks in acceleration have already been described in the scientific literature, for relatively simple physical systems, e.g. various types of pendulums. With regard to the human kinematic chain, the author is not aware of any publication analyzing this problem with sufficient diligence. However, it is hard to believe that a significantly different physics works inside human bodies.

5 Bruce Lee is an excellent example. To this day, it amazes everyone how he could break the boards by hitting them from a distance of one inch. He barely moved his hand! A mythical power of the Universe? The Force? No. Small velocity, but large acceleration.

6 But what are the sources of belief that Buddhist mythology is needed to control the flow of chi? The explanation is quite simple. It is practically impossible to master techniques that are built on a very short-lived physical phenomenon, if the adept is not aware of the existence of this phenomenon. In the past centuries, who had enough free time to work out blindly, for years, to develop strokes based on acceleration peaks produced by concentration of energy in a small volume and its relaxation in a very short time? The answer is: monks, spending their lives on meditation in monasteries. The correlation was obvious: the longer meditations, the more powerful strokes. Only one conclusion could be drawn from this observation. Bad luck, a wrong one.

7 If he was aware of physical and biomechanical principles behind his forehand stroke, he would use them in his topspin backhands and serves. Meanwhile, these strokes, albeit remarkable, do not look as unique as his forehand. It is not surprising: they are not inertial.

8 In fact, 20 Grand Slam titles are not the greatest achievement of Roger Federer. Every year brings us four winners of Grand Slam tournaments, and there were hundreds of them before Federer. Roger Federer is so exceptional because he is the first inertial tennis player in the history of this game.


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