By Alan Prendergast
By Michael Roberts
By Michael Roberts
By Amber Taufen
By Patricia Calhoun
By William Breathes
By Michael Roberts
By Melanie Asmar
That hint of springtime you feel in the air can mean only one thing. The attention of red-blooded sports fans in these parts will soon turn to the fluid dynamics of air flow, plausible stress-strain cycles at fixed impact velocities and (everybody's favorite up in the Rockpile) the Navier-Stokes Equation.
Why, just the other night at Jackson's Hole, two fans were engaged in spirited debate about the upcoming season:
"Listen, you. The magnitude of the induced vibration is proportional to the natural amplitude of vibration at the point of impact," the first fan said with some heat. "Hence, no vibrations are set up when the ball strikes the bat at a node, and maximal vibrations are set up if the point of impact is near an anti-node, a point of maximum vibration amplitude."
The second fan's face reddened. "Not in your lifetime," he said, taking a belt of Budweiser. "The amplitude of the vibration induced by the collision must be proportional to the impulse--the force applied to the bat multiplied by the time over which the force is applied--inversely proportional to the weight of the bat, and inversely proportional to the frequency of vibration. Put that in your pipe and smoke it."
"Ridiculous!" the first fan shouted. "You're not even considering the dynamics of spin frequency. Much less the Bernoulli Effect."
Where, oh, where was Yogi Berra when these two needed him? Surely he could have settled their argument in a New York second. But Professor Berra was likely curled up by the swimming pool in Florida, reading a good book on drag co-efficients and ballistic pendulums. This time of year, after all, what baseball fan in his right mind shouldn't be?
In seasons past, late February was the time when Little Leaguers took their ball gloves out of the toy box and started rubbing them down with neat's-foot oil, a pale yellow elixir derived from the shinbones of cattle. In the sun-drenched camps of Arizona and Florida, larger, stronger players would start cantering across damp swells of emerald outfield, dreaming lazily of crucial doubles struck in the shadowy late afternoons of September. Of scorched liners chased and retrieved in the nick of time scarcely three feet from the looming green wall. Of the World Series.
These days, ballplayers of all ages, shapes and sizes--not to mention Colorado Rockies fans--would instead do well to brush up on their vibrational anti-nodes and plausible stress-strain cycles, along with the basic tenets of the Navier-Stokes. When facing the Astros in late August, such knowledge could become very important indeed.
To this end, I have recently taken down from the shelf my copy of Robert Kemp Adair's The Physics of Baseball (Second Edition, Revised, Updated and Enlarged 1994)--a volume that will prove interesting to any serious student of the game and absolutely essential to anyone who plays or watches baseball in Coors Field. Dr. Adair, the Sterling Professor of Physics at Yale University, was once a teaching colleague of the late Bart Giamatti, former president of the National League and later commissioner of baseball. In 1987 Giamatti appointed him "Physicist to the National League." After all, here was a guy who knew the difference between a Magnus Co-efficient and a resistive drag force--as well as exactly what he wanted on his hot dog. He published his book a year later.
But it wasn't until the Second Edition that Dr. Adair turned his attentions to altitude and--without indulging in myth, speculation or folklore--told us why Dante Bichette and Andres Galarraga hit the stuffing out of the ball in their home park, while Kevin Ritz should probably be doing his job in a suit of body armor.
In Chapter 2, "The Flight of the Baseball" (the very title should strike fear into the hearts of the game's most battered pitching staff), Dr. Adair explains the intricacies of the Navier-Stokes Equation, which governs fluid dynamics and gives pitchers a pain in the ass whenever they take the mound at Coors Field. It's about the density of air and retardant forces, and that's probably all that Jamey Wright or Curtis Leskanic care to know about it. But here's a translation: A ball struck on the bat's sweet spot (that would be your "node," physics rookies) by, say, Cecil Fielder, that travels 400 feet in sea-level Yankee Stadium on a windless summer day would be a 407-foot drive in Atlanta, which is 1,050 feet high in the Georgia Piedmont. Here in mile-high Denver, the good doctor points out, Fielder's blast goes 430 feet--and should expansion come to Mexico City, 7,800 feet above sea level, ol' Cecil's selfsame clout will travel 450 feet.
That's not all. Because of less air drag, hit balls also get to fielders faster: Our physicist points out that a gapped liner to, say, left-center gets to a 300-foot landing point three-tenths of a second faster in Denver than it does in Boston, cutting the outfielders' range by an amazing eight to nine feet. "Even the range of a shortstop covering a line-drive or a one-hopper," he points out, "will be cut by nearly a foot in Denver." Baseball, as we know, is a game of inches.