Soccer Ball Physics

When a soccer ball is kicked the resulting motion of the ball is determined by Newton's laws of motion. From Newton's first law, we know that the moving ball will stay in motion in a straight line unless acted on by external forces. A force may be thought of as a push or pull in a specific direction; a force is a vector quantity. If the initial velocity and direction are known, and we can determine the magnitude and direction of all the forces on the ball, then we can predict the flight path using Newton's laws.

This slide shows the three forces that act on a soccer ball in flight. The forces are shown in blue and include the weight, drag, and lift or side force. Lift and drag are actually two components of a single aerodynamic force acting

on the ball. In the figure, the ball is moving from the upper right to the lower left (in perspective), as indicated by the red arrow. Drag acts in a direction opposite to the motion, while lift acts perpendicular to the motion. Let's consider each of these forces separately.

Weight

Weight is a force that is always directed toward the center of the earth.

In general, the magnitude of the weight depends on the mass of an object as determined by Newton's law of gravitation. By rule, the weight of a major league soccer ball is one pound. A soccer ball is hollow and inflated with high pressure air, so the weight is distributed around the outside of the ball. But we can often think of the weight as collected and acting through a single point called the center of gravity. The center of gravity is the average location of the weight of an object. To first order, the center of gravity for a soccer ball is located at the exact center of the ball. In flight, the ball rotates about the center of gravity. Newton's laws of motion describe the translation of the center of

gravity.

Drag

As the ball moves through the air, the air resists the motion of the ball and the resistance force is called drag. Drag is directed along and opposed to the flight direction. In general, there are many factors that affect the magnitude of the drag force including the shape and size of the object, the square of the velocity of the object, and conditions of the air; particularly, the density and viscosity of the air. Determining the magnitude of the drag force is difficult because it depends on the details of how the flow interacts with the surface of the object. For a soccer ball, this is particularly difficult because stitches are used to hold the ball together. So the surface of the ball is not smooth. During the recent World Cup, 2010, grooves were added to the surface of the ball in an attempt to make the surface more uniform. To determine the magnitude of the drag, aerodynamicists normally use a wind tunnel to measure the drag on a model. For a soccer ball, the drag can be determined experimentally by throwing the ball at a measured speed and accurately measuring the change in velocity as the ball passes between two points of known distance.

Lift

Lift is the component of the aerodynamic force that is perpendicular to the flight direction.

Airplane wings generate lift to overcome the weight of the airplane and allow the airplane to fly. A rotating cylinder and a spinning ball also generate aerodynamic lift. Like the drag, the magnitude of the lift depends on several factors related to the conditions of the air and the object, and the velocity between the object and the air. For a spinning ball, the speed of rotation affects the magnitude of the aerodynamic force. The direction of the force is perpendicular to the axis of rotation as noted on the figure.

The orientation of the axis of rotation can be varied depending on how the ball is kicked. If the axis is vertical, the lift force is horizontal and the ball can be made to curve to one side. In soccer this is called "bending" the kick. If the axis is horizontal, the lift force is vertical and the ball can be made to dive or loft depending on the direction of

rotation.

The surface roughness of a soccer ball introduce some additional complexity in the determination of lift and drag. For any object, the aerodynamic force acts through the center of pressure. The center of pressure is the average location of the aerodynamic forces on an object. For an ideal, smooth ball, symmetry considerations place the the center of pressure at the center of the ball along with the center of gravity. But a soccer ball in flight is neither smooth nor symmetric because of the stitches. So the center of pressure for a soccer ball moves slightly about the center of the ball with time, depending on the orientation of the stitches. The time-varying aerodynamic force causes the ball to move erratically. This motion is also the source of the "dancing" knuckleball in major league baseball that confuses both batters and catchers alike. To account for the complexities when making predictions of the lift, aerodynamicists make an ideal prediction using theory, and then correct the prediction using experimental data. The lift coefficient - Cl for the soccer ball was determined by high speed photography of the flight of a thrown ball.

The motion of the ball through the air depends on the relative strength and direction of the forces shown above. We have built a simulation program that models the physical problem of kicking a soccer ball.