About this Article
Written by: Yohan Chang
Written on: November 4th, 2005
Tags: entertainment, mechanical engineering, sports & recreation
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About the Author
Yohan was an engineering student at the University of Southern California at the time of publication.
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Volume VIII Issue I > The Science Behind Tennis Racquet Performance and Choosing the Right Racquet
The quest of finding the perfect tennis racquet can be very arduous. There are so many factors to consider when choosing a racquet. One's playing style along with various features of a racquet should all be taken into consideration. The sweet spot, moment, torque, torsion, impulse reaction, shock, work, power and control are important aspects that rely on the relationship between the fundamentals of tennis and the multiple facets of the racquet.


The racquet is one of the most fundamental tools necessary for the game of tennis. The length, composite materials, grips and strings all affect the player's ability to play the sport. Choosing the right tennis racquet is quite a challenge, and there are many factors that lead people to make the wrong choices. Fans of the sport choose racquets used by their favorite players, not knowing that the racquets are often just designed to look like their sponsor's racquets without taking into account the physics that go into every reaction of a swing.

Sweet Spot

When purchasing a racquet, the sweet spot should be one of the biggest deciding factors. The physics and science behind the sweet spot are important to understand, in order to not get taken in by the hype of large sweet spots. The "sweet spot" of a racquet is not really an area, but rather a point on the racquet. There are actually various types of sweet spots; the center of percussion, vibration node, and center of oscillation [1]. All these areas are not the same and have different properties that make them a sweet spot (Fig. 1). There is a rotational force that exerts a torque on the hand every time a tennis ball is hit. This causes a force going in one direction of the upper part of the hand while a reaction force in the opposite direction is exerted on the bottom of the hand. The point where these forces cancel out is where the ball is hit in the center of percussion. The vibration node of the racquet is where the ball can be hit and no vibration is felt in the racquet or the hands. The center of oscillation is the area on the string bed where the racquet's bounce is maximized. All three sweet spots are independent of each other and are located in different areas.
Figure 1: There are multiple points on a racquet that can be categorized as the sweet spot.
There are multiple points that can be categorized as the sweet spot; however, the general consensus for the sweet spot is the center of percussion. The location of the sweet spot is much better if it is higher on the racquet face. There are many ways to be misled because racquets come in many different lengths. Comparing q values (the distance from the hand to the sweet spot) directly should not be done, because a racquet that is longer will more than likely have a higher q value. To remedy this, one must take the distance of the C.O.P. from the top of the racquet to that point. There is a simple formula that is used to find the center of percussion on a racquet:
q= I / Mr(1)
'Q' is the distance from one's hand to the center of percussion (which is in cm). 'M' is the racquet's mass in kg. 'R' is the distance from one's hand to the center of mass. 'I' is the racquet's swing weight about the hand, which is also known as the moment of inertia. Using this formula to solve for 'q' gives you the location of the center of percussion [2]. The sweet spot, however, is not that important when considering which racquet is best for you.

Moment, Torque and Torsion

The weight and specifications of a racquet are important because the moment, torque and torsion generated by the racquet can greatly affect your play. The moment is the cross product of the force of the ball and the distance from the axis of rotation, i.e. your hand. The moment is very important for consideration because a racquet with a high moment can increase difficulty when volleying and returning, making the racquet very difficult to hold while maintaining good positioning. The moment and torque generated give rise to torsion, which is the rotational twist that one feels around the handle's centerline that results from each impact [3]. High torsion can be bad for younger players and can contribute to the pain of tennis elbow. The impact of the ball also affects the torsion.

Impulse Reaction

An impulse reaction is a push or a pull on the hand resulting from an impact. Impacts above the center of percussion will be defined as a pull (negative force) on the hand and below will be a push (positive force). A positive impulse reaction is considered to be better because of the fact that it leads to less impact force. An impact at the sweet spot, i.e. center of percussion, leads to an impact reaction of zero [2]. An impulse reaction is calculated in units of force, because it is a translational force, like a push or a pull on the axis of rotation, i.e. the hand. The unit of measurement of force in the metric system is the Newton (1 Newton = 0.2248 lb force). These forces, from the impact to the racquet, generate shock.