EQUIPMENT

The equipment needed to play tennis is as simple as a racquet and a ball. Despite the seeming simplicity of the equipment, there are many concepts of physics involved. In additional, behind every racquet is extensive engineering done by complex computer programs.

[Physics of the Racquet]
[The Ball]
[Racquet Innovation]

PHYSICS OF THE RACQUET

On the face of the tennis racquet, there are actually four points of importance that could be noted. These four points on the tennis racquet are the centre of percussion, the vibration node, the dead spot and the best bounce spot (figure 6).

Figure 6; Four points of a tennis racquet
The four points on a tennis racquet that possess unique properties apart from each other include the centre of percussion, the vibration node, the dead spot and the best bounce spot.

Centre of percussion
The centre of percussion is one of the two “sweet spots” of the racquet. This is because at the point of impact between the centre of percussion and the ball, the hand can feel no impact. This is due to the fact that the centre of percussion is located near the centre of the face of the racquet. By the time energy from the impact of the ball reaches the hand, most of the energy will already have been scattered after traveling through the strings. As well, no impact is felt because hitting the ball at the centre of percussion will not provoke the racquet to spin on the handle’s axis. Impacting the ball at a point far away from the centre of percussion will provoke the racquet to spin more. The centre of percussion is generally 5-6 cm below the vibration node. The following is a more precise method of finding the location of the centre of percussion.

1. Suspend the racquet with the handle pointing toward the ceiling and the head pointing toward the ground. There should be about 3-4 inches of string beyond the point where the racquet is tied.
2. Swing the racquet.
3. Record the amount of time it takes for the racquet to swing forward and back once in seconds. This is referred to as the time of 1 oscillation.
4. Perform the following calculation: 9.77* (time of 1 oscillation)^2. This is the distance from the point where the racquet is tied to the centre of percussion in inches.

Vibration node
The vibration node is the other one of the two “sweet spots” of the racquet. At the point of impact between the vibration node and the ball, the hand does not experience a net force acting upon it. The vibration node is located at the very centre of the face of the racquet. By the time energy from the impact of the ball reaches the hand, most energy will already have been scattered after having to travel through the strings. As well, like the centre of percussion, no impact is felt because hitting the vibration node will not provoke the racquet to spin on the handle’s axis. The vibration node can be found by finding the centre of the racquet.

Dead spot
The dead spot is located near the top of the racquet. At the dead spot, the ball does not bounce off of the strings. Instead, the racquet absorbs all of the energy that the ball exerts on it. If a tennis player hits the ball with the dead spot of their racquet, they will feel maximum force from the impact of the ball. That is why it is not wise to attempt to return a fast serve with the dead spot of the racquet. Firstly, the racquet will absorb all of the energy of the ball. Secondly, the player will experience great shock in their hand.

Best bounce spot
The best bounce spots located near the throat of the racquet. At the best bounce spot, the ball rebounds the greatest distance at this point of the racquet. The racquet returns most of the energy that the ball exerted on the racquet during impact back to the ball. However, because the best bounce spot is located at an extremity of the racquet from the two sweet spots, the tennis player will experience a great deal of shock in their hand when utilizing the best bounce spot.

THE BALL

The standard tennis ball must have a 53-58% rebound height from concrete. This means that if the ball is dropped from 100 cm over concrete, the ball must bounce 53-58 cm back into the air. In other words, the ball must be designed to lose approximately 45% of its elastic energy. When the ball is dropped from 100 inches above concrete, its diameter should compress by about 6 mm. However, when the ball is dropped from 100 inches above a racquet, the ball will only lose approximately 30% of its elastic energy, while having its diameter compressed by 3 mm. It can, thus, be concluded that energy loss is relative to the amount of compression of the ball.

Prospective changes for balls used in international professional tennis
With the immense power and speed associated with modern-day professional tennis, it may be hard for certain people in the audience to enjoy the grace associated with tennis. In response to this, international professional tennis organizations are proposing to use bigger balls in the future. The diameter of the new balls is to be approximately 6% larger than the currently used balls. The method of construction is to remain unchanged. In using the new balls, a ball will rebound off the of racquet strings at the same rate as the currently used balls. However, due to the new ball’s larger size, the ball will be slowed down in the air by friction (figure 7). In doing this, the receiver of a serve will possess 10% more time to receive the lightning fast services of today’s game. As well, by slowing down the rallies, players are projected to have double the control and accuracy. This will result in the players ending rallies on more winners than faults. The duration of rallies is also supposed to increase by 10% as a result of the decreased speed of the new ball.

Figure 7; Balls Used in the Future
Balls used in the future are to possess a diamter 6% larger than currently used balls. By doing this, the velocity of the ball will be decreased by air friction. This will allow spectators to watch a more enjoyable match, as there will likely be longer rallies as tennis players are given more time to react.

RACQUET INNOVATION

When tennis was first invented, wooden racquets had always been used. The usage of wood racquets lasted for decades, until the 1970s. In the 1970s, metal tennis racquet frames were introduced for the first time. These metal frames quickly replaced the old wooden frames, as many advantages could be spotted with such a change. Firstly, as manufacturers experimented with mixing different types and proportions of metals together to construct the frames, the racquet frames became stronger, but also lighter. Currently, most racquet manufacturers mix graphite with another metal, such as titanium, to form composite metals. Because the frames became stronger, larger heads were possible. Large heads were not possible with wooden frames, because they would not have strong enough to keep the longer strings under tension. In fact, a large-headed wooden racquet would snap. With strong and light metal frames, oversize racquets about twice the size of the average wooden racquet can be constructed. The larger string area of the racquet allows a player to benefit from a larger sweet sport, resulting in more accurate shots. The increased size of the racquet also decreases the likelihood of the racquet wanting to spin on the handle’s axis as the ball is struck. A racquet’s polar moment of inertia is a racquet’s resistance against this spinning. The formula to calculate a racquet’s polar moment of inertia is:

The decreased mass of the racquet will, unfortunately, decrease the polar moment of inertia. However, this is compensated by the large size of the racquet.

Racquet engineering
When designing racquets, a manufacturer must be able to incorporate both desirable

• Playing properties- power, ease, control, comfort; and
• Mechanical properties- mass (total mass, balance, inertia), stiffness, damping (string, frame, grip, dampener)

Mechanical properties are especially complex with the incorporation of composite metals. The following discusses the three major categories of mechanical properties: geometric properties, rigid body properties and vibration properties. (Hughes et al., 1995)

1. Geometric properties- These properties involve the dimensions and shape of each section of the racquet. Sometimes, design is limited by league rules, such as restrictions on head surface area. Design may be based upon beauty or the manufacturer’s trademark template.
2. Rigid body properties- Here, mass, balance, polar moment of inertia and centre of percussion are considered. a) An increase in mass usually results in an increase in power and control, but a decrease on versatility and comfort. b) The balance of a racquet has to do with the position of its centre of gravity. The position of the centre of gravity determines the swing type of the racquet. The closer the centre of gravity is to the head of the racquet, the more power the racquet will have. The lower down toward the hand the centre of gravity is, the more comfortable the racquet. c) The greater the polar moment of inertia has, the better the racquet will be able to resist spinning of the racquet on its axis in the handle. An increase in the polar moment of inertia will increase stability of the racquet, resulting in greater control. Increasing the mass both sides of racquet can increase the polar moment of inertia. d) Having a large centre of percussion will increase the comfort of the racquet. However, the centre of percussion decreases as the centre of gravity is closer to the head of the racquet. Manufacturers may utilize computer programs to visualize the finished product in light of the rigid body properties. Vrije Universiteit Brussel has designed two computer programs to perform this task. “RIGID” requires the manufacturer to input the racquet components’ positions and mass properties in order to generate a visualization of the racquet. “PROFILE” requires the manufacturer to input material properties and dimensions of section to compute mass properties of each section of the racquet.
3. Vibration properties- Each racquet design has unique mode shapes. Mode shapes are slight vibrations of a racquet during impact depending on the position of impact. To lessen the forces of vibration on the player, a designer may choose to add a damping device. The addition of a damping device is the only modification that will improve all playing properties, as this improves power control and comfort.

After a prototype of the racquet design has been produced, it is tested in the laboratory. Many times, tennis players are also asked to assist in assessing tennis racquet designs.