Online: 17.05.2019

Wind of Change
Jarek Chrostowski

When we look at the techniques of today's tennis players, everyone seems to play according to well-known precepts. The perfect picture of modern knowledge is disturbed by Roger Federer. The uniqueness of the Swiss tennis master is commonly 'explained' by his exceptional talent. However, there is another, more interesting possibility. Federer does not have to be a freak of the gods. He may simply be the harbinger of a coming - yet invisible - revolution that is still hidden behind apparently insignificant symptoms.
A David Hume ship in the ocean of tennis.
It seems probable that most of the grand underlying principles have been firmly established, said Albert A. Michelson in 1894, referring to physics. Michelson was one of the most outstanding experimental physicists who ever lived and the first American Nobel Prize winner in science. Only a few years before saying this, he had conducted (together with Edward Morley) a certain 'unsuccessful' experiment. He wanted to measure, how changes in the velocity of the Earth in orbit around the Sun affect the measurements of the velocity of light. To the surprise of the entire community of physicists, he did not observe any changes. In 1905 Albert Einstein began to revolutionize our understanding of space and time. It is an irony of history that one of the two postulates used by Einstein to build the special theory of relativity was nothing more than a concise recapitulation of the Michelson-Morley experiment1.

There is a considerable similarity between the situation of physics at the beginning of the 20th century and the present stage of tennis evolution: everything seems to be well-known and beautifully arranged and yet a few details do not fit. Should anyone care?

Well, let's do it for a moment.

Riddle of the serve

In tennis, everything starts with a serve. The possession of a fast serve is considered an essential asset in today's game. A serve is judged to be very powerful when the velocity of the ball just after the hit is greater than 220 km/h. At the same time, a fast forehand would be one that exceeds just 160 km/h. Isn't that amazing? Someone might say: That sounds about right! If I hit a ball 'moving' at 0 km/h, I generate a 220 km/h serve. If the ball moves towards my forehand side at, let's say, 60 km/h, I must lose 60 km/h from 220 km/h just for hitting it back! The problem is that physics does not work this way.

In the physical reality of the world around us, it is not the velocity that is conserved, but the energy, linear momentum, and angular momentum. In serves, the initial velocity of the ball before the contact with the racquet is close to or equal to 0. Consequently, its momentum (product of mass and velocity) and kinetic energy (product of mass and square of velocity divided by 2) will also be close to or equal to 0. Forehands are different: before the impact, the ball moves at 50-70 km/h, and its momentum and kinetic energy are quite large. Therefore, in a system consisting of the ball, the racquet, and the tennis player, there is significantly more momentum and energy at forehands than at serves! In other words, the system with higher amount of energy/momentum (the player hitting the forehand) produces considerably less energetic output (slower balls) than the system with lower amount of energy/momentum. The question arises: why didn't we, the tennis players, win the Nobel Prize in physics for the discovery that conservation laws do not work in tennis?

The situation is even stranger. The serves are performed upwards, against the force of Earth's gravity. Forehands are much more horizontal and the work in the gravitational field of our planet is considerably reduced. A certain biomechanical fact seems also to be important: the human body is not adapted for effective swinging of the arms above shoulder level. Thus, there are many physical and biomechanical reasons for forehands being more powerful than the serves. If so, why are serves so radically faster?

Obscure rotation

In modern tennis, great importance is attached to controlling topspin rotation. On the courts we commonly hear advice like: Drop the racquet head! Under the ball! And pull it up now! In physical terms, we would talk about applying the force to the surface of the ball so that its direction does not pass through the center of mass of the ball. In an extreme situation, when the force applied to the point on the surface is tangential, we talk about a topspin stroke. The resulting moment of force rotates the ball - because that is what moments of force can do best.

Things become truly interesting when we notice that there is another mechanism for generating ball rotation: the tilt of the hitting surface. The ball is a spatially extended object. When it starts to collide with the head of the racquet tilted for topspin, the points at the top of the ball come in contact with the strings slightly earlier than the points at the bottom. This means that, although the bottom points of the ball bounce off the strings, the top ones bounce earlier. The consequence of this phenomenon is the emergence of a moment of force acting on the ball. It might seem that the rotation created this way will not be significant. However, anyone who has tried to hit the ball against a wall with dense horizontal corrugations knows that the rotations of rebounding balls can be extreme, especially when the initial strokes are quite powerful. Immediately, fresh questions are born. In contrast to 'pulling up', tilting the racquet head is an action that requires minimal effort. If we can generate a reasonably large rotation by that means, why is this method not generally taught by the coaches? Why is the efficiency of different combinations of both mechanisms not tested? Also, it is certainly easier to hit the ball with the tilted racquet head than brush it upwards. Why then are people so eager to use the latter method?

Only one conclusion can be drawn here: to control the ball rotation, modern players do not use rational thinking, they use blindly-learned habits. Deprived of real knowledge, these players, standing in front of Roger Federer, are suddenly surprised by the amount of rotation produced by his seemingly flat and visually so natural strokes. His tennis is out of this world! they say. Or maybe it's not Federer who plays cosmic tennis, but the rest of the players play tennis that has been created on incomplete fundamentals?

Accelerations are passe

Coaches often talk about 'dynamic strokes'. When it comes to practice, however, they use phrases like: Increase your racquet head speed! It is obvious that they overlook accelerations and the important questions that follow. Should the acceleration phase end just before contact with the ball? Should it be present during the collision? Does this make any difference? We should not be surprised at these absences. Accelerations are overlooked even in scientific papers about the physics of tennis. But are the accelerations really useless?

The effects of acceleration are greater the longer it acts on an object. In many scientific sources we can read that the shortest contact time between the ball and the racquet is close to 3 ms. Would a human be able to produce the acceleration that could in such a short time significantly increase the ball velocity? The mass of the tennis ball is ~57 g. The largest increase in velocity occurs during the serves and exceeds 250 km/h (~69 m/s). To increase the velocity of the mass 57 g by 69 m/s in 3 ms, the force would have to be: 0.057 kg * 69 m/s / 0.003 s = 1311 N. That seems to be a big value - until we start to think about it.

The force generated during a handshake can exceed 400 N (woman), or even 700 N (man)2. In 1985, a heavyweight professional boxer, Frank Bruno, performed a punch at peak force close to 4,100 N3. Also, we should not forget that when we strike a ball with a tennis racquet, its head moves at much higher velocities and accelerations than our palm. Furthermore, most players would be delighted with a coach who would be able to use accelerations to increase their stroke velocities not by 250 km/h, but just by 20-30 km/h. The above facts suggest that accelerations during the contact between the racquet head and the ball can indeed be meaningful, at least potentially. Then why are they so regularly ignored?

What does the ball collide with?

Conservation laws are responsible for the course of the collision between the ball and the racquet. Now we know that if accelerations are present, their contribution should also be included. From the physicist's point of view, everything looks so simple: we know the velocities of the ball and the racquet head, we know the masses and we use these values in an appropriate formula, voila! The problem is that neither the ball nor the racquet have the knowledge of the physicist! Until they come into the contact with each other, one object 'knows' absolutely nothing about the other. The ball must therefore mechanically 'feel' the mass it is colliding with, and it can 'learn' this only during the collision time.

At this point, things are heating up. The contact time between the ball and the racquet is not constant. In 1979 Howard Brody measured4 that it changes with the relative velocity between the ball and the racquet. When the relative velocity is small, the contact time can be as long as 10 ms. The lower limit seems to be close to 3 ms, at relative velocities larger than 100 km/h. Changes in the nature of collisions (from elastic to deeply inelastic) and the fact that the strings get stiffer the more they deform, are probably responsible for this effect - and it carries enormous consequences. It means that the effective mass of the racquet (that is, the mass that the ball 'senses' during the contact with the racquet) must be different at different relative velocities! At low relative velocities the ball has much more time to detect the mass of the object it collides with, and the more time it has, the more 'aware' it can be of the masses of the player's racquet and body.

In the light of the above facts, it becomes clear that depending on the material characteristics of balls, strings, racquets, and the relative velocity between the ball and the racquet head, tennis strokes occur under different physical regimes for different combinations of these parameters, and the collisions are more or less elastic. Nevertheless, practically all physical and biomechanical analyses are conducted as if the regime was only one! What's even worse, it is the norm that conclusions from experiments performed with one set of tennis equipment, at low relative velocities, are uncritically extrapolated to all situations on the court, even those where the players hit very powerful strokes using quite different equipment!

Body magic

All the coaches, whether on working with beginners at local clubs or leading ATP players, speak with one voice: Transfer your weight into the ball! Why? The common replay is that when we 'go into the ball', the mass of our body helps us: it significantly increases the ball velocity. But is this really the case?

We already understand that the effective mass involved in the collision with the ball can vary, but we have not tried to estimate it. High-frame-rate videos, especially those showing serves, can be helpful here. With serves, the horizontal component of the ball velocity before contact with the strings is close to zero and so it is easy to observe in the ball the propagation of disturbances caused by collision. It turns out that if the final velocity after the serve is 230 km/h or so, the part of the ball that is the most distant from the strings starts to move horizontally after more than half the time of the collision duration5! The internal structure of the strings and the racquet is more rigid than that of the ball and the disturbances here spread faster than in the ball. However, we should not expect a dramatic difference, and video analyses of the propagation of racquet deformations confirm this thesis. As a result, it seems reasonable to say that, with the longest contact times, the effective mass may include the mass of the entire racquet, and even part of the hand, while with the shortest contact times it is close to the mass of the racquet head. In reality, even in the case of experienced amateur players we can expect that the effective mass becomes smaller than the mass of the racquet.

If the effective mass is less than the mass of the racquet, it becomes obvious that the mass of the tennis player cannot affect the course of the collision with the ball. Not without reason, corpulent gentlemen transferring their not-so-small masses into the ball do not hit it harder than slim young girls competing in junior national championships. The mass of the body is not important during the ball-racquet collision! The rule 'Transfer your weight into the ball!' is, however, widely used, because it works - not only in groundstrokes, but also in serves. Great, but why does this principle work if physics says it should not work at all6?

Here, another pervasive belief needs to be mentioned: that the power of strokes 'comes from the ground' and flows through the whole body, from the feet to the hand and then to the racquet. Virtually every coach justifies this thesis with 'reaction forces'. The concept of reaction forces was introduced in the 18th century by Isaac Newton. In his approach, reaction forces are results of other forces, they never act alone. Meanwhile, in modern tennis, reaction forces are said to initiate the action, but that is a clear contradiction of its original use! Coaches can be somewhat justified, because it is easy to distort an unclear idea, such as the concept of magically emerging reaction forces. In modern physics it has been abandoned. Instead of reaction forces, today we talk about the conservation of momentum. It is easy to understand then that when, somewhere in the system, the momentum appears, it must disappear somewhere else. You immediately know what the cause, and what the result is - and therefore no rational physicist will ever say that the source of power in tennis is hidden somewhere in the ground.

Outdated view

Time to reveal probably the biggest flaw of modern tennis. It is the widespread tendency of players, coaches and tennis scientists to interpret observed phenomena in the received spirit typical of naive Newtonian mechanics. As a result, people do not think about the efficiency of the production of energy, nor do they care how to transfer and release it. They do not practice methods of reducing energy losses and do not consciously use conservation laws. The reality is cruel: the driving forces of modern tennis are archaic physical concepts dating back to the beginning of the 18th century, provoking the use of the simplest mechanical solutions and analogies. Today, for example, advanced kinematic models take into account the existence of muscles and tendons, yet these parts work within a strictly mechanistic paradigm, as simple springs. They may modify details of a well-defined system, but they are never able to change its nature. Meanwhile, we know from our own everyday experience that we can modify our movements, more or less, in different ways, practically at any phase of motion!

The situation is exacerbated by the current state of measurement techniques, by means of which it is especially easy to collect data about linear or angular velocities. As a consequence, almost every publication in the field of the physics or biomechanics of tennis is full of numbers: we see bending angles of joints, their rotational velocities and linear velocities of individual links of the kinematic chain. In this approach, a human becomes a construction of more or less inertially moving sticks. Experimental 3D analysis of accelerations, especially their rapid changes, combined with the recording of muscle activity of the body parts involved in the stroke, is still ahead of us. The results are tragic because the simplest interpretations of incomplete measurements are used to construct tennis techniques and methods of teaching them, often leading to players' drama7.

The essence of these arguments is perfectly illustrated by a simple experiment. Let's grab a tennis ball in one hand and throw it up to the height of the head, in such a way that it falls into the other hand. Obviously, only the gravitational field of Earth shapes the motion of the ball. Now, let's repeat the throw and try to follow the ball with the palm (please do it as freely as possible and do not touch the ball). Have you succeeded? Certainly. The palm was at the ball all the time, so to describe its motion we can use the same physical equations we use in the case of the freely moving ball. In other words, with a small activation of muscles, we recreated an ordinary projectile motion in the gravitational field - something that cannot be described by any system of freely-moving double or triple pendulums used today to describe movements of the upper limb with the racquet. How many contemporary researchers, looking just at the motion of the palm, would come up with the idea that they see an analogue of a simple gravitational projectile motion? Practice suggests not one. This trivial experiment shows how the prevailing mechanistic approach radically limits the construction of theories of efficient tennis strokes.

Inertial techniques of a pure amateur versus techniques of the most advanced and successful professional tennis players in the world.

The facts presented above led the author of the article to make an attempt to formulate an internally coherent theoretical description of all tennis techniques that is free from drawbacks discussed here. The goal was ambitious: to check whether starting with 2-3 axioms one can create a logical structure, based on reliable scientific facts and the principles of modern physics (including the fundamental role of conservation laws). The theory, created in 2011-12, can now be identified as an inertial theory of tennis8. Something that was originally supposed to be just an intellectual entertainment of a slightly-bored amateur, suddenly revealed its real value. It turned out that in modern tennis just one groundstroke is performed according to the key physical and biomechanical rules of inertial tennis: it is the Roger Federer's forehand. This observation has become a strong motivator for further work. Over the next five years, the theory was expanded by a set of clearly defined techniques of strokes and movement. They were created on such a well-defined logical structure that it can be objectively demonstrated they are currently the only techniques reproducing the Federer forehand not only visually, but also based on the laws of physics that determine the uniqueness of this stroke. More importantly, inertial techniques use these laws not only in forehands but also in any other type of strokes.

World at the edge

The lack of reliable explanations of the phenomena described in this article and the existence of working inertial tennis techniques, built on coherent theoretical foundations, and having a radically different character from the techniques that are currently popular, are factors indicating that the scientific background of modern tennis, its techniques, and teaching methodologies, require a thorough reconstruction. It should be emphasized here that this necessity does not result from the fact that the current foundations are clearly wrong, or that their creators were ignorant. On the contrary, it only means that thanks to the perspicacity, patience, and meticulousness of generations of tennis enthusiasts, we were able to gather enough experience and facts to identify increasingly accurate general structures. Such an evolution of knowledge is typical of reliable science, evolving from one conceptual revolution to another. New concepts do not entirely negate the value of previous ones, but determine their domain of applicability more clearly and suggest more general solutions. After all, the most important feature of any scientific revolution is the fact that it opens up new possibilities.

Albert A. Michelson, the physicist I quoted at the beginning of this article, participated in international tennis matches at Newport and was an active tennis player until he was over 70. Few people know he was actually born in Strzelno, a small town just over 50 km south of Bydgoszcz, the capital of the Kuyavian-Pomeranian region of Poland9. And Bydgoszcz is the city where this article was written and where inertial tennis was born. History obliges. It should also teach us, so let's conclude with the following summary: In tennis, it seems probable that most of the grand underlying principles have NOT been firmly established.

In other words: the time of change is coming.

The driving forces of modern tennis are archaic physical concepts dating back to the beginning of the 18th century

ABOUT THE AUTHOR: 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 It is something Einstein, nota bene, did not mention in his Annus Mirabilis paper.

2 Man-Systems Integration Standards, Volume 1, Section 4: Human performance capabilities; Revision B; NASA, July 1995.

3 The Damaging Punch; J. Atha, M.R. Yeadon, J. Sandover, K.C. Parsons; British Medical Journal, Volume 291, 21-28 December 1985.

4 Physics of the tennis racket; H. Brody; American Journal of Physics, 1979, 47: No. 6.

5 This means that the parts of the ball farther from the strings collide not only with the racquet head but also with the ball parts already rebounded from the racquet.

6 ...and let us skip the fact that weight could never play any important role because it is something totally different than mass.

7 A whole generation of American players could see it for themselves. Frequent injuries of the shoulder joint are nothing more than the consequence of the popular belief that in serves the internal shoulder rotation must be a critical source of power.

8 Inertial theory of tennis is not a mathematical structure, it is a set of causal sequences between well-known physical and biomechanical facts.

9 Michelson's father was born in Fordon, currently one of the largest estates in Bydgoszcz. Polish readers can learn more about Michelson's scientific achievements from a lecture given by the author in 2019 at the City Hall of Bydgoszcz during his fight for Albert A. Michelson Street:


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