Power: Does the Racquet Matter?
Crawford Lindsey, Tennis Warehouse, San Luis Obispo, CA, 93401

#### The Ingredients of Power

A racquet's power potential is determined in the lab by measuring ball velocities and calculating the ratio of the ball's outgoing bounce speed to its impact speed. The impact speed is defined as the combined speed of the racquet and ball just prior to collision.

Impact speed = ball speed + racquet speed

For a given hitting location the power potential is always a fixed percentage of the impact speed, is a different percentage for each location, and generally varies from racquet to racquet.

For example, if the power potential is 40% in the center of the racquet, then the ball will bounce from the racquet at 40% of the impact speed.

Bounce speed = power potential x impact speed

The speed of this bounce is determined by the "local" weight, frame stiffness, and stringbed stiffness at the impact location.

However, the bounce speed is only one component of the final shot speed. The other component is the swing speed. The bounce occurs off a racquet that is already traveling at a given speed. The bounce speed is added to the speed of the racquet from which it bounces to get the shot speed:

Shot speed = bounce speed + racquet speed

#### How Much Racquet, How Much Player?

We will see that the bounce speed is the racquet's contribution to the shot and the racquet speed is the player's contribution. These contributions relate to each other in interesting ways resulting in some unexpected conclusions.

To see how bounce speed and racquet speed work, consider first that impact speed can be made of an infinite combination of ball and racquet speeds. For example, lets consider several ways to add up to an impact speed of 70 mph:

Case Number Ball Speed Racquet Speed Impact Speed
Case 1 0 70 70
Case 2 10 60 70
Case 3 30 40 70
Case 4 60 10 70
Case 5 70 0 70

In each case the impact speed will be 70 mph. If the power potential is 40% at the impact location, the bounce speed will be 28 mph in each case (.4 x 70 mph = 28 mph). In other words, the power potential built into the construction of the racquet will deliver 28 mph of bounce speed to each of these 70 mph impact scenarios. The racquet delivers the same number of miles per hour to the shot in each case.

But here is the key. The shot speed is different in each case. Remember that bounce speed is only one component of shot speed--we have to add the swing speed to the bounce speed to get the final shot speed:

Case Number Bounce Speed Swing Speed Shot Speed
Case 1 28 70 98 mph
Case 2 28 60 88 mph
Case 3 28 40 68 mph
Case 4 28 10 38 mph
Case 5 28 0 28 mph

That is a huge difference in shot speed given that the ball strikes the exact same location at the exact same impact speed in each scenario. Obviously the swing speed has a huge influence on the speed of the shot. The racquet adds a fixed number of miles per hour to the shot for any given impact speed, whereas the swing adds a variable amount.

You can see that, in this example, the 28 mph added by the racquet in each case represents a different percentage of the final shot speed:

Case Number Racquet Contribution
Case 1 28 / 98 = 28.6%
Case 2 28 / 88 = 31.9%
Case 3 28 / 68 = 41.6%
Case 4 28 / 38 = 73.7%
Case 5 28 / 28 = 100%

The faster the swing speed compared to the ball speed, the less the contribution of the racquet to the shot speed. The slower the swing speed compared to the ball speed, the greater the influence of the racquet design to the shot speed.

We can summarize the above into one completed table as seen below.

Case Number Ball
Speed (mph)
Racquet
Speed (mph)
Impact
Speed (mph)
Bounce
Speed (mph)
Racquet
%
Player
%
Case 1 0 70 70 28 28.6% 71.4%
Case 2 10 60 70 28 31.9% 68.1%
Case 3 30 40 70 28 41.6% 58.4%
Case 4 60 10 70 28 73.7% 26.3%
Case 5 70 0 70 28 100% 0.0%

There is a lesson here. The faster the racquet speed compared to the incoming ball, the less influence the innate properties of the racquet have on the ball. And contrariwise, the slower the racquet speed compared to the incoming ball speed, the more contribution the racquet has to ball speed. So, bunters, pokers, and patty-cakers rejoice! You get more out of your racquet than do the swing-for-the-fence animals using the same racquet. You get much more for your money! The racquet is worth more to you.

Using the power potential measurements of each racquet, we can determine each racquet's contribution to any shot scenario. The interactive tool above (linked in the "See Also" box) allows you to do just that. Using the drop down menus, choose a ball speed, racquet speed, and impact location. Press the "go" button to see how every racquet compares.