FEATURE ARTICLE
Predicting a Baseball's Path
A batter watches the pitcher's motion plus the spin on the ball to calculate when and where it will cross the plate
A. Terry Bahill, David Baldwin, Jayendran Venkateswaran
The Physics of a Pitch
Before you have to figure out the World Series–winning or
–losing pitch, let's learn more about the entire process. A
pitcher stands on the mound and throws a baseball—a bit under
three inches in diameter and covered in leather—toward home
plate, which is 60.5 feet away from the pitcher's rubber on the
mound. A strike must cross the plate, which is just 17 inches wide,
at a height that is roughly between a batter's knees and armpits. An
extremely fast pitcher can throw a baseball that reaches 95 miles
per hour, maybe a little faster. At that speed, a ball reaches home
plate in less than half a second. On the way from pitcher to home
plate, though, several forces determine a baseball's trajectory.
As soon as a pitcher releases a ball, it's in gravitational free
fall, whether it's a blistering fastball or a gentle change-up. A
95-mile-per-hour fastball drops 1.7 feet between the pitcher's
release point and the point of a bat-ball collision. Slower pitches
fall more. A 75-mile-per-hour curveball, for instance, drops 5.7
feet. Clearly, a ball's pathway to the plate also depends on other forces.
A pitcher cannot control gravity, but he can put spin on a pitch.
During the nearly two centuries that baseball has been played,
pitchers have invented more than a dozen pitches, and each is
characterized by its specific spin rate, spin direction and forward
velocity. A pitcher controls these characteristics by assuming a
grip and wrist movement devised to provide a given trajectory.
Spin on a ball creates a so-called Magnus force. In the
mid-1850s, German physicist and chemist Gustav Magnus was one of the
first scientists to study this effect. Imagine watching any ball
moving right to left with topspin—meaning that the top of the
ball rotates in the direction of flight. Air flows smoothly around
the ball until it gets to about one o'clock on the top and four
o'clock on the bottom. At those positions, called separation
points, the airflow changes into a turbulent wake that deflects
upward with this spin. The physics behind this force can be
explained in a couple ways. The first invokes Bernoulli's
principle, postulated by 18th-century Swiss mathematician,
Daniel Bernoulli. When a ball with topspin is placed in moving air,
the movement of the ball and its seams slows down the air flowing
over the top of the ball and speeds up the air flowing underneath
it. According to Bernoulli's equation, the point with lower
speed—the top—has higher pressure and the point with
higher speed—the bottom—has lower pressure. This
difference in pressure produces the Magnus force, which pushes the
ball downward. This model has not been validated experimentally.
The second—and probably better—model of the Magnus force
has been validated by wind-tunnel tests. It involves the principle
of conservation of momentum. With topspin, the wake of
turbulent air behind the ball is deflected upward. Anyone can prove
that a body moving in air goes the opposite direction of the
deflected air, which conserves momentum. With a driver aware of your
plan, put your hand out the window of a moving car, and tilt it so
that air is deflected downward; your hand will be pushed upward.
Now, let's relate that to a baseball with topspin moving
horizontally in air. Before the ball interacts with the air, all the
momentum is horizontal. Afterward, the air in the wake has upward
momentum. The principle of conservation of momentum requires that
the ball have downward momentum, which makes it go down.
Of course, a pitcher can put a wide variety of spins on a ball. A
couple of easy "hand" rules reveal which way a spinning
ball will travel. The so-called angular right-hand rule reveals the
spin axis of a pitch. If you curl the fingers of your right hand in
the spin direction, your extended thumb will point in the direction
of the spin axis. For instance, if a ball is spinning in a
counterclockwise direction when viewed from above—as in a
right-handed pitcher's curveball or a left-handed pitcher's
screwball—the thumb will be pointing upward.
Once you know the spin axis, you can find the spin-induced
deflection with the coordinate right-hand rule. Point the thumb of
your right hand in the direction of the spin axis, and point your
index finger in the direction of forward motion of the pitch. Bend
your middle finger so that it is perpendicular to your index finger.
Your middle finger will be pointing in the direction of the
spin-induced deflection. In our example of a pitch with a
counterclockwise spin when viewed from above, your middle finger
will be pointing toward first base.
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