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The physics behind hitting a home run

Baltimore Orioles first baseman Chris Davis competes in the home run derby at the All Star game on July 15, 2013, in New York City. (Jonathan Newton/The Washington Post)

On Monday night, some of Major League Baseball’s best sluggers will square off in the sport’s biggest annual display of brute strength: the home run derby. Each batter has seven “outs” to hit as many balls as possible out of San Diego’s Petco Park.

To most fans, it’s just a fun spectacle. But to Alan Nathan, home-run hitting is a physics problem. Given the distance between home plate and the outfield wall, what combination of ball speed, bat angle and external factors will send the ball out of the park?

“It's driven by a need to understand,” he said. “It’s the same reason I did experimental nuclear physics for many years.”

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By day, Nathan is a professor emeritus at the University of Illinois at Urbana-Champaign, working to elucidate the structure and interactions of subatomic particles. But the rest of the time, he’s watching baseball with an eye for the underlying physics of the sport. He’s even written several peer-reviewed papers on the subject, which are all available on his website.

At the most basic level, he said, there are just two elements to a well-hit home run: exit speed (the speed at which the ball leaves the bat) and launch angle. If you were a freshman physics student calculating the path of a projectile, these two numbers would be all you needed to know to predict how far the ball would travel.

According to ESPN’s hit tracker, the fastest-hit home run of the season so far was a solo shot slugged by the Angels’ Mike Trout in April. That ball was traveling 120.5 mph when it left Trout’s bat. The optimum launch angle, Nathan said, is between 25 and 30 degrees. A ball hit at a lower angle will become a line drive or a grounder; a higher angle gives you a pop-up.

These factors can balance one another. A slower ball may make it out of the park if it’s hit at the right angle; a batter can make up for a bad trajectory by hitting the ball super fast.

But astute students of baseball science should take other factors into account. As Nathan points out, “Life is more complicated than a Physics 101 class.” Unless they’re hit in a vacuum, home-run balls’ flights will be affected by a host of external factors: elevation, air temperature, air pressure, humidity and wind speed.

Those first four all boil down to the same thing: air density. The less dense the air is, the less resistance the ball will encounter as it soars through the stadium.

The thin air at high elevations helps balls travel farther — that’s part of how Denver’s Coors Field, which sits at an MLB-high of 5,200 feet above sea level, got its reputation as a pitcher’s nightmare. The park was called “Coors Canaveral” and “the mile high mistake” until the Rockies began using a humidor in 2002 to add moisture to the balls. The humidor lowers balls’ “coefficient of restitution” — the technical term for bounciness — and makes them fly off the bat with less power.

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In the late 1980s, Robert Adair, a physicist at Yale and author of “The Physics of Baseball,” conducted a study on humidors for then-National League President A. Bartlett Giamatti, and he found that storing balls at 100 percent humidity made them travel only 90 percent as far. Adair told the New York Times in 2006 that he thought the Rockies’ humidor was making “a slight difference.” (An alternative explanation for the decline in home runs hit at Coors? The Rockies got better pitching.)

On the other hand, humidity in the stadium can help a home-run ball — if only ever so slightly — by making the air less dense.

“People think of more humid air as being heavy and more dense, but humid air is less dense than dry air for the very simple reason that a water molecule weighs less than an air molecule,” Nathan said, though he cautioned that this effect is negligible. 

Air temperature also plays a part, Nathan said. A 1995 study found that fly balls travel a few feet farther for every 10 degree increase in temperature. The average fly ball distance in above-90-degree heat was 320 feet; on sub-50-degree days, that distance fell to 304 feet. And a 2013 review in the journal Weather, Climate, and Society found that away batters in the American League slammed an average of 46 percent more home runs in warmer-than-average temperatures; National League batters hit 29 percent more.

But the effect of air density pales in comparison to that of wind.

“A small little breeze can play amazing games with the trajectory of a ball,” Nathan said. He has calculated that a 5 mph breeze blowing out of the ballpark can carry a ball an extra 18 to 19 feet. “That’s enormous.”

How far a ball flies also depends on the ball itself. The stitches on a baseball help it travel farther by reducing drag, but only to a degree — high, loose seams, like those of the repeatedly reused baseballs of the “dead ball” era, will slow it down again.

“There seems to be some optimum height for the seams,” Nathan said. 

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Then there’s how you hit the ball. Side spin — which happens when the batter is out in front of the ball or just a little bit late — can cause a line drive to curve foul. But a small amount of back spin gives the ball lift, allowing it to seemingly defy gravity for slightly longer than it otherwise would. Like high seams, this effect has diminishing returns: Too much backspin can increase air drag.

As a spectator, this kind of stuff is fun for Nathan to think about (unless his favorite team, the Red Sox, is playing — then he’s too emotionally invested in the outcome of the game to bother with things like air drag and wind speed). But he doesn’t think ballplayers should be signing up for a physics class before they head to the home run derby.

“You can’t think and hit at the same time,” he said, paraphrasing the late, great sage of baseball, Yogi Berra.

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Likewise, he’s willing to take ballplayers’ word for it when they question whether the derby is such a good idea in the first place. Popular myth has it that trying to hit so many home runs in a row can mess up a player’s swing; after slugging a record 41 homers in the derby in 2005, Philadelphia Phillies outfielder Bobby Abreu hit only six home runs in the rest of the season.

There’s no reason why that should be the case, Nathan noted — the derby is not much different from batting practice, and analysts at the Society for American Baseball Research have concluded that there’s no data to back up the myth. But many players still choose to sit the competition out.

“I don’t want to go out there and swing and swing and swing,” the Nationals’ Bryce Harper told The Post this year. (Harper says he won’t participate until the All Star game comes to Washington in 2018, and maybe not even then.) Trout also opted out of the competition this year.

That’s their prerogative, Nathan said. He may understand physics, but they’re the professionals.

“The hitters have had years of experience playing the game,” he said. “They know what to do.”

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