The physics of selecting a tennis racket

So you finally decide to replace your old, tired tennis racket, and you hit the sports stores. The first thing you notice after picking up a few is that the new rackets seem incredibly light. Oh, the technology! Carbon fiber is even lighter than graphite! I will be able to swing this like a matchstick! You imagine yourself at the net, deftly hitting winners. You are about to whip out your credit card. You know this racket will really improve your game.

Except that physics says you're wrong, and so do the choices of most professional tennis players. Light rackets are not a good idea. In fact, there are many ways in which they are a very bad idea.

What the pros use

"But", I hear you protest, "I've seen (insert favorite tennis player) using this racket. I even checked in a tennis magazine to be sure of the model." Ha. You have been duped by the giant tennis merchandising machine. The racket may have started out the same, but the pros modify their rackets significantly. In particular, most of them add weight to their rackets at the base, using what is called a 'tailweight' cap. In the case of some of the male players the added weight makes their rackets as heavy or heavier than the old wood rackets your parents played with. Pete Sampras plays with a 14-ounce Wilson, and if you watch you can see him choke down on the racket (increasing the 'swingweight') when he puts the ball away. Why make the racket heavier? For one thing, physics.

The physics of a tennis swing

First of all, think about a tennis swing in the abstract: you are moving a heavy rod in an arc, and making a semi-elastic collision with a ball, hoping to impart speed and perhaps spin to the shot.

Now imagine that you are playing against Sampras, who has just stepped in from the baseline and hit the snot out of the ball. You now have to do three things quite quickly: (1) get to the ball, (2) move your racket to prepare your swing, (3) stroke away, hoping he didn't make it to the net. Getting to the ball (#1) is your problem; we'll assume you made it.

Say for the sake of argument that you have a racket made of (insert space-age material) that is unbelievably, impossibly light: two ounces. You will be able to bring that baby back in record time, and swing the head faster, but when you make contact with the ball it's going to knock the racket out of your hand, because your end of the collision has no mass (think of trying to hit a baseball with a child's plastic 'whiffle' bat), and what's important in the collision is momentum: mass times head velocity. If you do somehow manage to hold onto it, you're going to take most of the force in your arm and shoulder, because what you were banking on is the angular momentum of the racket swing to propel the ball back over the net. Taking that force in your arm causes tennis elbow and other tennis-related injuries. So you want to be swinging something of reasonable mass.

Weight distribution

The mass of your racket is not the only consideration; the center of mass is what is important in a moving object, so you should be concerned not only with the mass of your racket but how it is balanced. You have three choices: centered, head-heavy (weight toward the head), or head-light (weight toward the base). The best choice is head-light, because it moves the mass center closer to the axis of rotation of your swing. This is important because:

• It reduces the moment of the racket, defined as the mass times the moment arm, the distance from where you hold the racket to the mass center. The moment measures roughly how difficult it is to hold the racket out parallel to the ground, and hence move the head to the ball.
• It reduces the torque (the screwdriver-like twisting force around the shaft from impact), and the torsion (or longitudinal torque, the bending force in the direction of the ball due to impact). These are the major contributors to tennis elbow and other tennis-related injuries, which are now being reported in huge numbers: the site I used to research this node reports that half of tennis players over 30 now develop tennis elbow.

Power and control

Power, as we observed above, comes from the momentum involved in the collision: mass times velocity. But we would also like control, loosely defined as the ability to impart spin on the ball and direct it to where we want it to go. Several factors contribute to control:

• impact time and ball mash. This is how long the ball stays on the racket, and how much it mashes down on impact; more of each gives more control. It is a function of momentum (higher momentum = more mash), string tension (higher = more mash) and racket stiffness (stiffer = lower impact time).
• swing speed.The faster (and harder) we have to swing, the more difficult it is to guide and spin the ball.

These are more arguments for a heavier racket. More mass means we don't need a high swing speed to achieve the same momentum.