# Racquet Selection Map 2005

Our exclusive guide to help your customers find the perfect frame for their game.

## Weight Matters

The Racquet Selector Map plots power and swingweight. This seems pretty straightforward, but some explanation of what is behind these numbers is elucidating. The power formula used here is: (headsize × length index × flex × swingweight)/1000. “Power” refers to the intrinsic power potential of the racquet. This potential is primarily determined by the amount and distribution of mass, which manifests in the racquet in four very important ways: weight/mass (resistance to motion in a straight line), swingweight (resistance to rotation about an axis in the handle 10 cm from the butt), recoilweight (resistance to rotation about the balance point), and twistweight (resistance to rotation about the long axis from tip to butt). Racquet features that influence these are headsize (how far from the long center axis mass can be located) and length and balance point (how far from both the swing axis in the handle and the recoil axis at the balance point that mass can be located). All these “weights” are important to power for one very important reason — they determine the amount of energy loss that occurs when the ball pushes the racquet around in translation, rotation, and twisting.

## Energy Loss

“More powerful” actually means less energy loss. So, although racquet ads are constantly singing the praises of “more powerful” racquets, these racquets have no propulsion system. All the energy that is possible is present before the impact. That is the energy of motion in the racquet and ball approaching each other. The impact does not produce energy; it only loses it. Designing a powerful racquet is ALL about limiting energy loss, not about producing energy.

The most productive, even if not always the most practical, way to limit energy loss is to make the racquet “heavier” in all the ways listed above. This limits the energy that goes into translation, rotation, and twisting, making it potentially available to propel the ball. If you make the racquet 5, 10, or 20 pounds, it will give back much more energy. The only trouble is that you might not be able swing it fast enough to create as much available energy to begin with. Energy is directly proportional to mass and to the square of racquet velocity. So, if, for example, you double the mass of your racquet, you still have to be able to swing it at least 70 percent of the speed that you could swing the lighter racquet just to maintain the same racquet energy. Even if you could develop a racquet that lost almost no energy, you still have to be able to swing it fast enough to maximize the amount of available energy to begin with. Sometimes, losing nothing of a small amount of energy may not be as good as losing a lot of much more.

## Ultimate Power Potential

There is in fact an ultimate limit to how fast you can hit the ball. Even if you designed a racquet that lost no energy at all, the maximum attainable ball speed for a serve would be twice the racquet speed at the impact location. For a groundstroke, the maximum possible speed is twice the racquet speed plus the incident ball speed. The power potential of such a racquet would be awesome. But it would be too heavy to swing, and the power output would be nil — zero ball speed for a serve and the speed of the incident ball for a groundstroke, if the ball happened to collide with the unmovable racquet.

## Interpreting the Selection Map

How does this all relate to the Racquet Selector Map? Because twistweight and recoilweight are not easily measured, headsize and swingweight stand in for them in the power potential formula. Twistweight is increased more the farther the weight is from the long axis. So the bigger the head, the farther from the axis the weight will be and the greater will be the twistweight.

As to recoilweight, it generally moves relative to swingweight, so racquets sorted in order of swingweight will also be very close to being ordered in terms of recoilweight. So swingweight, which is easily measured on commercial machines, serves as a proxy for recoilweight in the power formula. Swingweight also shows up on the other axis as the maneuverability index. This is the real meaning of swingweight. Strictly speaking, it does not affect the intrinsic power potential of the racquet, except as a proxy for recoilweight, which does. But it does contribute to the final ball speed because it influences how fast you can get the racquet moving. But that contribution is due to swing speed, not intrinsic racquet power potential. If you can keep that straight, you won’t be confused by swingweight showing up in one way or another on both axes.

Finally there are flex and length. Flex is included in the power potential formula because stiffer frames bend less and thus lose less energy doing so. Length is actually already implicitly accounted for in swingweight and recoilweight because it influences those values by delineating the maximum distance from the axes that weight can be located. But it is also included explicitly in the formula because if you do hit the ball farther from your hand as a result of the longer racquet, then the impact location on the racquet will be traveling faster than a point closer to your hand and will add to ball speed (assuming swingweight didn’t increase too much with the extra length).

See all articles by Crawford Lindsey

**About the Author**

Crawford Lindsey is co-author of *The Physics and Technology of Tennis* and *Technical Tennis*

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