Wave Theory and Tennis

The classic understanding of the tennis stroke is as a mechanical "rods-and-levers" contrivance vis: the legs turn the hips - the hips turn the shoulders - the shoulder turns the arm - the arm does some stuff to address the ball and get the racket head going in the right direction and presto! The ball is sent along to its target with unerring accuracy, irresistible power and screaming spin. That is the fantasy we carry around in our noggins, reinforced with terms such as the "kinetic chain" from the literature of tennis that reinforce such delusions. For some odd reason, this idea never seems to work out for us. Every time we adjust one cog in our corporal clockwork, it seems to throw our game into chaos. As an example, one might bend the elbow a bit to gain control over the position of the wrist to better guide the strings to the ball and avoid miss-hits. That makes sense - more control is good, right? The result is more mis-hits, a complete loss of pace, control, and spin, and a sore elbow. Is this beginning to sound familiar?. There are way too many objectives in tennis - adding spin, addressing the ball, creating pace and control, etc. to do it all with a series of tightly linked motions. Each of these objectives must be achieved by a system that is separate and distinct from the others in both time and space. Thus the muscles of the forearm are largely responsible for control while pace comes from the larger muscles of the shoulders, trunk, and legs. If you start tensing your forearm to get more pace, you lose control. If you fail to establish balance with your quadriceps muscles, your brain will recruit the muscles in your upper body and wreck the rest of your stroke. Each body unit in a stroke has its own set of responsibilities and is on its own schedule, and that schedule is not "first A completes then B starts, then B completes, then C starts ... " We achieve balance in the serve as the left hand is tossing the ball and the right arm is relaxed in preparation for the hitting sequence. They are independent of one another, and each has its own start and finish time. If each component has to wait for the other to get the energy and momentum it needs to complete its task then what you have is a house of cards, not a stroke.

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Theoretical Forehand Power Wave: Measured at the forearm. The shoulder and hips would see the same wave but would see it earlier. For example, the peak would come well before the load phase. The power is negative before and during the lock phase causing the hips to reverse-rotate creating the backswing proper. The wave also goes negative between the explode and follow-through phases as one puts the breaks on forward acceleration. This bi-directional behavior is typical of a wave and allows it to propagate through the body without resulting in excessive net twisting of the spine.

Each of the functional units of a stroke requires power to operate. Power is the ability to make things move, stop moving or change direction. It is a combination of energy and momentum. Energy for tennis stroking comes mostly from the muscles and a bit from gravity. Energy is necessary to influence the flight of a tennis ball, but it is also insufficient.

Power

One must also harvest momentum, mostly from the earth. If you have ever tried to hit a tennis ball while floating, weightless, in space ... sorry, bad example. You probably have not tried that yet. I have suffered from the delusion that I could stand flat-footed with no solid purchase on the court and hit a tennis ball 100mph with just the power of my muscles and my indomitable will.

Footwork is the primary source of momentum. Setting the back foot on a groundstroke, keeping the knees bent and the bodyweight bouncing from one foot to the next, orienting the feet so that the momentum generated is in a proper direction for the stroke are all essential for the production of power. Power must be created and distributed to each part of the body as that part needs it. Power is the raw material for pace, spin, and control. After all, what is control but the ability to direct a ball to the desired target; to change its momentum? Each component needs the power to reach it when the component need its and in the form that the component can use it. A mechanical linkage will not suffice. The power must be packaged and delivered in the form of a wave.

The Power Wave of the Topspin Forehand: Begins with a push-off against the earth and weight transfer from the front foot to the back foot (gold) during the unit turn which powers the lock (backswing proper). It propagates through the muscles as the first trough of the wave, rippling up the trunk, through the chest and shoulders and down the arm to the hitting hand where it is transferred to the racket, throwing the racket back away from the ball and helping set the tone of the forearm. Next one pushes off the back foot throwing the bodyweight to the front foot (green). This shift of weight produces the main peak of the power wave, and it accelerates the racket toward the ball to stretch-shorten the forearm muscles for directional control and spin and to develop racket head speed for pace. Finally, a weight transfer from the front foot to the back creates a final trough in the power wave which opposes the peak of the wave, terminating acceleration and thereby releasing the forces stored in the forearm. There is a delay between the production of power in the legs and the use of that power in the upper body, resulting in a troubling but unavoidable syncopation of the rhythm of the stroke.

I apologize if this all seems a bit too sciencey, but I truly believe that the "rods-and-levers" approach to sports is the poison that has sickened any attempt to make sense of this crazy game, so onward and upward!

Waves

Waves aren't passed from one part to the next. Instead, they propagate or flow through a medium. In tennis the medium is muscle. Bones and joints are not medium; they are a framework on which to hang the muscles and levers on which those muscles act. Muscles can pass the power along, use it to move things or store it for short periods for use after the power wave has passed.

The power wave typically starts as an oscillation in the feet. The bodyweight begins on the front or offsides foot - the foot opposite the hitting arm. As we transfer weight to the on-side foot, the hips reverse-rotate - they turn away from the oncoming ball. This is the backswing proper or lock. After the back foot accumulates bodyweight and is planted firmly onto the court, weight transfer is reversed and travels from the back foot to the front. This weight transfer is not an isolated movement but is part of a constant shifting of weight from one foot to the other to create dynamic balance. During the instant that bodyweight is moving from one foot to the other and is more or less evenly distributed between the feet, the feet push off against the court in opposite directions starting a powerful rotation in the legs and pelvis. There are always two rotations; one back to set the hitting foot and create the backswing proper, followed by one forward, generating the power used to load the muscles of the arm for control and spin and accelerate the racket head for raw, unadulterated pace. Finally, there is another reverse-rotation that puts the brakes on, triggering the explode phase and ultimately putting the brakes on the follow through. This back-then-forward scenario plays out throughout the game of tennis and typifies the wave nature of this and every sport. The crack of a whip is back-forward-back. That oscillation creates the wave that propagates the power of the swing along the whip culminating in a miniature supersonic boom at the tip.

As the tennis power wave propagates through the body, power bleeds from the wave, either inadvertently wasted or harvested for creating spin, pace or control. Although a huge amount of energy and momentum pass through the body, the wave does not throw us off our feet. Waves leave the medium through which they propagate largely unchanged, like a cork on a stormy sea. If one is thrown off balance by the wave, it may indicate that one invested it with too much energy. I call this problem overmodulation.

Applying the Wave Concept

Let us take a concrete example to demonstrate the value of the wave concept. Why is the two-handed topspin backhand (2HBH) so consistent? Why is it that you can hit the shot as hard as you want and not wreck its control? Why is pace sometimes lacking? Of course, the answer to the first two questions must be "Because you have two hands on the racket ... duh!" I like a little more meat on my analysis if only because I am more interested in the third question - how do I hit the two-handed backhand with pace? The presence of two hands on the handle of the racket in the 2HBH presents both challenges and opportunities. There is an opportunity to store an enormous amount of control and spin force in the muscles of the two forearms. This surfeit of forearms is the source of the superior control and consistency of the 2HBH compared to all one-handed strokes. The immediate challenge presented by all this stored force is holding it in the muscles of the forearm until it is needed.

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Short Stroke Power Wave: Compact and brief, the short stroke version of the power wave shows the absence of a lag phase and a hitch in the upstroke reflecting two sources of power; an early bump from the legs and hips followed by a late contribution from counter-rotation by the non-hitting hand , especially important in the two-handed backhand.

All strokes use the inertia of the racket head, being dragged behind the wrist during the acceleration phase of the stroke, to wind up the forearms,storing those forces and keep them bottled up. With two hands on the racket, we have twice as many "springs" to use for power storage. Keeping those springs stretched requires a power wave of twice the amplitude, meaning we need to maintain twice the acceleration going until we are ready to release the stored forces into the ball. We can't generate a power wave sufficient to create and hold that much acceleration for any length of time. The only solution is to shorten the stroke, eliminate the lag phase and dump the control and spin forces into the ball immediately after we store them. The amount of racket head speed that we can develop is dependent as much on the duration of the acceleration phase as it is on the peak acceleration. In short, the very brief acceleration phase stunts the pace of the shot, no matter how violently you lean into it.

The answer to the "pace problem" of the 2HBH is the additive nature of waves. Two waves that meet at a point in space and are "in sync" with each other, aka in phase, aka peaking at the same moment, will add together and combine forces. The additive quality of waves allows one to use the leverage provided by having both hands on the racket to enhance the power wave using energy from the shoulders and momentum generated by counter-rotation of the wrists. If one can manage to resist the temptation to enlist the forearm muscles in this process, the enhanced power wave will propagate through them without disturbing the precious control and spin forces stored there. In short, you can have it all; superior control, spin and pace. All you need is lots of fast twitch fibers and an exquisite sense of timing.

Granted, the truly talented figured all this out a long time ago without resorting to wave theory. They did it by feel, sound, and superior muscle memory. What they could not do is convey to you the important and non-intuitive details such as counter-rotating viscously with your shoulders while keeping your forearm muscles completely relaxed, or synchronizing the shoulder's contribution to the arrival of the main power wave. For that, you have to know what you are up against. Then it is only a matter of summoning up the sources of power available to the two-handed backhand through proper stance, balance, weight transfer, counter-kicking, incorporating the deep shoulder muscles (by reaching back in the unit turn), counter-rotating the wrists and timing all of that so the power of each source reaches the racket at the same, very brief instant. Sounds impossible, I know, but it isn't.