The Physics Behind Hitting A Home Run
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?
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 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.
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.
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.
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.
But the effect of air density pales in comparison to that of wind.
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.
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.
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