The Science of Slugging

What does it take to hit a home run? Mark McGwire and Sammy Sosa have been showing us all season. Now here's a lesson in the physics of long-distance hitting.

Mark McGwire's Home-Run Swing

When a powerful batter like the Cardinals' Mark McGwire begins his swing, the acceleration actually bends the wooden bat back a tiny bit. A good batter can make the bat snap forward as it hits the ball, for extra power.

For maximum distance, a ball must leave the bat at about a 35-degree angle. To make this, happen, McGwire must swing up on the ball. A pitch comes in at about 8 to 10 degrees. If McGwire connects at a 25-degree angle ...

... he will send the ball into the bleachers. His timing must be perfect, though. His 'uppercut' swing means that if he swings too early or too late, he will ground out or fly out. Players with 'level' swings (8 to 10 degrees, the same angle as the pitched ball) are more likely to intersect the ball even if they swing early or late. They hit safely more often than 'sluggers' do - but they also hit fewer home runs.

Ball Composition

At the center of a baseball is a rubber-coated cork sphere. This is wound with 121 yards of blue-gray wool yarn, 45 yards of white wool yarn, and 150 yards of fine cotton yarn. The cover is two strips of white cowhide stitched with 216 raised red-cotton stitches. It is said that some old-time players used to freeze the baseballs pitched to opposing players. Freezing affects the rubber-coated core, making it less bouncy. A 375-foot shot goes only 350 feet if the ball's core is minus-10 degrees F. To fool the umpire, the balls were taken out of the freezer hours before the game so the outsides would warm up.

How other factors might affect the flight of a 400-foot home run:

ALTITUDE: For every 1,000 feet the playing field is above sea level, the baseball will fly about seven feet farther. At higher altitudes, the air is less dense, so there's less drag on the ball to slow it down. So a 400-foot home run by Mark McGwire at Yankee Stadium, near sea level, would go 407 feet at Turner Field in Atlanta (1,050 feet above sea level). That same blast would go about 430 feet at Coors Field in Denver (5,280 feet). And if Major League Baseball expands to Mexico City (7,800 feet), the ball would carry nearly 450 feet!

AIR TEMPERATURE: For every 10 degrees the temperature rises, the ball will travel four feet farther. Hotter air is less dense. (Warmer baseballs also are more lively, and go farther.)

WIND: Every one mile per hour of tail wind adds three feet of flight.

AIR PRESSURE, HUMIDITY: A high-pressure weather system means the air is more dense, so the ball won't go as far. Humid air may feel thick, but water vapor is actually a bit less dense than air. High humidity adds only a few inches to the flight of a long ball, though.

Ball-Bat Impact

A force approaching 8,000 pounds is required to change the motion of a 5-ounce baseball traveling 90 miles per hour into a 110-mile-per-hour shot over the center-field fence. The bat - swung at nearly 80 m.p.h. - moves only about one inch in the 1,000th of a second that the bat is in contact with the pitched ball. The ball collides with the bat at a combined speed (bat plus ball) of about 140 miles per hour. The impact flattens the ball to about one-half its 3-inch diameter. (The bat is flattened, too, but only by about 1/50th.) The ball compresses like a spring and rebounds off of the bat. Baseballs are not very efficient springs, though: At least two-thirds of the energy applied to the ball is lost as friction - heat.

The Bat

Major-league players must use wooden bats. While most bats today are made of ash, in the past they were exclusively hickory. Old-time players thought big, heavy bats gave them an advantage. Babe Ruth used a 47-ounce hickory model. Mark McGwire's ash bat weighs just 33 ounces.

Today's lighter, ash bats are not as strong as hickory. But a lighter bat is easier to swing, and 'bat speed' is what players desire. One reason: It takes 0.005 seconds longer to swing a 32-ounce bat than it does to swing a 30.5-ounce bat.

A 90-mile-per-hour fastball travels about three feet every 0.025 seconds. That's 8 inches in 0.005 seconds. Only a batter can say if that 8 inches makes a critical difference.

A fast swing also transfers more energy to the baseball. How fast do the pros swing? About 80 miles per hour for a 350-foot drive.

The Pitch

A 90 mile-per-hour fastball takes 0.46 seconds to reach the plate. Because of air resistance, or drag, a fastball slows down about one mile per hour for every seven feet it travels. A baseball that crosses the plate at 92 miles per hour was moving 100 m.p.h. when it left the pitcher's hand.

The Swing

From the time a ball leaves the pitcher's hand, a batter has about 0.15 seconds to decide whether to start his swing. Timing is critical: If a batter is 1/100th of a second too early or too late in swinging at the ball, the ball may go foul. The baseball's impact will bend the bat and make it vibrate. These vibrations are minimized if a batter strikes the ball with the bat's 'sweet spot.' (Technically, the 'sweet spot' is one of two low-vibration 'nodes' on the bat. The other node is near the bat's grip.) You can tell when a batter has hit a ball with the sweet spot by the high-frequency 'crack!' the impact makes. A low-pitched 'thunk!' means the ball missed its ideal mark.

Outfielders are good listeners. They back up when they hear a 'crack!' and move forward for a 'thunk!'

Primary source: 'The Physics of Baseball,' 2nd edition, by Robert Adair (HarperPerennial, 1994)

For animated views of McGwire's home-run swing and the impact of bat and ball, go to:

csmonitor.com/durable/1998/09/22/fp8s1-csm.shtml