When a baseball is
thrown
or
hit,
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 baseball in flight.
The forces are the weight, drag, and lift.
Lift and drag are actually two
components
of a single
aerodynamic force
acting on the ball.
Drag acts in a direction opposite to the
motion, and 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 baseball is 5 ounces.
A baseball is made with a solid core, a string wrapping around the core,
and a stitched covering, so the weight is
distributed throughout 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 baseball 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.
The physics describing the rotation, translation, weight and center of gravity
of a baseball is the same for any ball. A softball is larger and slightly heavier
(6.25 ounces) than a baseball. So the trajectory of a batted softball will be similar, but
not the same as a batted baseball. In the software described below, the student can
vary the type of ball to see the difference that weight produces in the flight of a ball.
Strictly speaking, the weight of the ball should not be specified in ounces.
The ounce(oz.) is a measure of mass and not of weight.
Weight is a force, mass times acceleration, and is not equal to the mass of an
object. The pound is a measure of force.
Unfortunately, people often use the units for weight and mass interchangeably;
the assumption being that we are talking about the weight at the surface of the Earth
where the acceleration is a constant (32.2 ft/sec^2 or 9.8 m/sec^2).
So when the rule states that the ball weighs 5 oz,
it should more correctly specify that the weight is 5/16 lb.
At NASA, we have to be very careful of the distinction between mass and weight.
On Mars, the mass of a baseball is the same as on Earth. But since the
gravitational acceleration on Mars is 1/3 that of the Earth,
the weight of a baseball on Mars is only 5/48 lb.
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 baseball, this is particularly difficult
because the stitches used to hold the ball together are not
uniformly or symmetrically distributed around the ball.
Depending on the orientation of the ball in flight, the drag
changes as the flow is disturbed by the stitches.
To determine the magnitude of the drag, aerodynamicists normally use a
wind tunnel to
measure
the drag on a model. For a baseball, the
drag
can be determined experimentally by throwing the ball and accurately
measuring the change in velocity as the ball passes between two points
of known distance.
A softball is slightly larger than a baseball, so the magnitude of the drag force will
be different for a softball. Students can use the software mentioned below
to study these differences.
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 and the direction of the force
is perpendicular to the axis of rotation.
The orientation of the axis of rotation can be varied by the pitcher when the ball is
thrown. If the axis is vertical, the lift force is horizontal and the ball can be made to
curve to one side.
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 stitches on a baseball introduce some additional complexity in the
generation 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 baseball in flight is neither smooth nor symmetric because of the stitches.
So the center of pressure for a baseball moves slightly about the center of the
ball with time, depending on the orientation of the stitches.
The timevarying aerodynamic force causes the ball to move erratically.
This motion is the source of the "dancing" knuckleball 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
baseball
was determined by high speed photography of the flight of a pitched ball.
The motion of the ball through the air depends on the relative
strength and direction of the forces shown above.
We have built two simulation packages that look at the
physical problem of pitching a
curve ball,
and of the flight of a baseball that is
hit
from home plate.
The curve ball problem involves all three forces with the lift force
producing the
side force
that causes the ball to curve. The simulation calculates the magnitude of
the lift force and it can be shown that even big league pitchers can not generate
enough lift force to overcome the weight of the ball. There are no rising fast balls.
The hit baseball problem considers only the forces of drag and weight. the
simulator demonstrates the important role that atmospheric conditions
play on the flight of a baseball. The
flight trajectory
is very different from the idealized
ballistic flight
that occurs when drag is neglected.
The figure on this web page was created by Elizabeth Morton, of Magnificat
High School, during a "shadowing" experience at NASA Glenn during May of 2007.
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