Tennis Matrix
Exploring the Physics Behind Tennis
The Magnus Effect
Drag
In general, drag can be defined as a mechanical force generation by a solid object moving through a fluid. In the case of tennis, drag is a force that pushes the tennis ball backwards and slows it down. A ball traveling through the air experiences a backwards force. This is because the air pressure on the front of the ball is larger than the air pressure on the back of the ball. This is known as the drag force. The drag force is proportional to the ball speed square and is given by the formula:
Where r is the density of the air, A is the cross sectional area exposed to the wind, and v is the speed of the object. The constant C describes is called the drag coefficient.
A spinning ball sets the air around it in motion in a thin layer near the surface of the ball displayed in the diagram below. The air pressure on top of a spinning ball is decreased if the ball has topspin and is increased if the ball has backspin. As a result, if a ball is travelling horizontally, the ball experiences a downwards foce if it has topspin and it experiences an upwards force if it has backspin. The Magnus Force is defined as the force due to spin. It always acts at right angle to the drag force.
While playing tennis, if a ball with topspin is rising upwards at an angle to the court, the Magnus force is working by pushing the ball down onto the court and it pushes the ball forwards in a direction parallel to the surface of the court. Therefore, a ball with topspin falls onto the court a steeper angle, as mentioned in the topspin section, than a ball without top spin and a ball with backspin tends to float through the air and falls to the court at a shallow angle, mentioned in the backspin section.
