When a soccer ball is
the resulting motion of the ball is determined by
Newton's laws of motion.
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
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
of a single
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
lift acts perpendicular to the motion.
Let's consider each of these forces separately.
Weight is a force that is always directed
toward the center of the earth. In general, the
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
center of gravity. Newton's laws of motion
of the center of gravity.
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
that affect the magnitude
of the drag force including the
of the object,
the square of the
velocity of the object,
and conditions of the air; particularly, the
viscosity of the air.
Determining the magnitude of the drag force is difficult
because it depends on the
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
the drag on a model. For a soccer ball, the
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 is the component of the
aerodynamic force that is perpendicular to the flight direction.
Airplane wings generate
to overcome the weight of the airplane and allow the airplane to fly. A
also generate aerodynamic lift.
Like the drag, the magnitude of the lift depends on several
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
If the axis is vertical, the lift force is horizontal and the ball can be made to
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
using theory, and then correct the prediction using experimental data.
lift coefficient - Cl
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
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