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.
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 . 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.
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 . 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 . 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.
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 . 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.
Although in engineering there is no clear accepted definition of shock, for our purposes we will define it as the sudden difference in kinetic energy after impact, which then generates frame vibrations. The change in kinetic energy refers to how a racquet is decelerated when it makes contact with the ball .
Energy is used before impact. Energy is spent to speed up the racquet for the swing, and more energy is expended when the ball is controlled during the swing. The tennis ball receives part of the lost energy while the rest of the energy then becomes internal energy, wasted and absorbed by the bending of the frame .
When choosing a racquet it is important that the frame is not too stiff and light because the energy that usually gets absorbed by the frame’s bending will end up being absorbed by the arm holding on to the racquet. Also, do not think that getting a rubber string vibration dampener will help. Rubber string vibration dampeners do not work well because their masses are too small to do much besides diminish lingering vibrations from the strings. This is nothing more than a minor annoyance. (When the author played tennis in high school, he used a rubber band tied around the bottom of the middle two strings in order to get rid of string vibrations.) Vibrations of the racquet itself are too great for the small mass dampener to absorb. However there are other alternative methods to alleviate the vibrations.
The most useful vibration dampener is a handle end weight that is filled with a bag of shot or sand. This added mass dissipates a lot of the excess energy. There are also other effective methods of vibration damping like the Pro Kennex Kinetic system that incorporates particulate masses in the racquet head . The level of work and power generated by the racquet also affect shock. Racquets that generate high power tend to generate more shock.
Work and Power
Work is the energy used to generate a certain ball speed. Work is also a measure of how energy-efficient the racquet is. A racquet that has low work is good, whereas high work is unfavorable. A racquet with high work will require a player to swing and the hit the ball much harder in order to achieve the same ball speed and power as a low work racquet. It is simple enough to say that because the player has to swing and hit the ball much harder to get the same type of ball speed and power. Work is a measure of the racquet’s power; the less work the player has to generate, the more powerful the racquet. Tennis players may put in a lot of effort and energy to generate high ball speed but the power is generated by the player and not the racquet. In the game of tennis, power and work are inversely related. Low work means that the racquet is high in power while high work means the racquet is low in power.
Head heavy racquets tend to require a lot more work to hit the ball fast, which causes a strain on the wrist, arms and shoulder. A heavy head, light racquet with a high swing weight is the most ideal work/power racquet. It is efficient and gives the user the best work for power output, which also leads to better control.
The debate over what is considered control rages on. There is no clear way to quantify or define control. Some people argue that it is the racquet’s maneuverability, while others say it is the stability of the racquet, and finally some argue that it is the inverse relation of power. There are many ways to try and explain control. For our purposes we will choose control to mean the level of difficulty of executing accurate shots.
A large head size could lead to the illusion of better control, because people think that it has a bigger sweet spot and so the bounce will be more accurate. There is some truth in that argument; however the larger head causes the strings to deform more if the ball is hit off center, which causes players to spray balls left and right. Based on the author’s experiences, a mid-sized head with a handle-heavy setting is ideal for overall control.
There are many things to consider when deciding to purchase a racquet. Hopefully, the science behind the reaction of the ball and racquet will help each player choose which racquet is suitable for them. The general consensus seems to be that heavier racquets are better in the long run. The pick-up appeal of the light-weight racquet had been the reason for its dominance in sales, but for the true tennis aficionados, a heavier, head-light racquet with a high swing weight is the best racquet to use. All top pros add weight to their racquets and professionals definitely know a lot more about what works.
The facts all lead to the conclusion that a heavier head-light tennis racquet with a high swing is the most ideal racquet to use for power, control and longevity. It reduces injuries, and offers better play than the other types of racquets available.