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.
Ready?
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.
Dr. Adair does not speculate about what will happen when major-league ball reaches Colorado's own Leadville (the highest U.S. city: 10,152 feet) or Wenzhuan, a town on a lonely stretch of road between Qinghai and Tibet, north of the Tangla Range. But we can imagine. Wenzhuan, the Guinness Book of Records assures us, is the world's highest inhabited place, at 16,732 feet above sea level. Don't you think if Mr. Fielder played a couple of seasons there (for the Wenzhuan Wasps, perhaps?), Roger Maris and Henry Aaron would be marked men, even if Cecil found himself hitting the ball off the end of the bat (the "anti-node" to you)?
On the other hand, the John Burkes and Bill Swifts and Bruce Ruffins of the world probably wish they were pitching for Ein Bokek. This settlement on the shore of the Dead Sea is the world's lowest human habitation, at 1,291 feet below sea level, and there the Navier-Stokes Equation would do for pitchers what it does for sluggers in Tibet. In his chapter on pitching, Dr. Adair points out that a fastball thrown in Denver takes less time to cross the plate--gaining about six inches. But pitchers who rely on the deuce, the yakker, Uncle Charlie--call it what you will--are in big trouble.
"[In Denver] the curve will break about 25 percent less," Adair writes. "A curve that will break left-right about 8 inches and drop an extra 8 inches [due to the overspin component] at sea level will break about 1 5/8 inches less and drop about 4 inches less in Denver. The ball breaks less because it crosses the plate faster and thus has a little less time to break."
Knuckleballers are no better off. Their stuff, Dr. Adair assures us, loses 25 percent of its dancing ability en route to the plate.
Even those with no faith in science cannot argue with facts. In 1996 the Colorado Rockies were the best-hitting team in the league, with a .287 batting average (seventeen points higher than second-place Atlanta's), 24 more home runs and 174 more runs batted in than anybody else. The 961 runs they scored was 183 better than second-place Cincinnati, and they had 92 more hits than runner-up New York.
Meanwhile, the Colorado pitching staff's balloon-like 5.59 earned-run average was the worst in the league (San Francisco was next, with a mere 4.71), and the 964 runs they gave up was 102 more than the Giants, who finished thirteenth. Rox hurlers yielded 198 home runs, and opposing batters hit .285--22 points higher than the league average.
Now, if you want a detailed explanation of what Adair calls the Magnus Force (no, it's not a Clint Eastwood movie) or his mysterious Reynolds Numbers (nope--not Harold's batting average), you'll just have to wait until Professor Berra comes in from the pool. Suffice it to say, as another lopsided pitching/hitting season (and another third-place finish) looms for the Colorado Rockies, the club could do worse than to trade for a couple of starting pitchers named Navier and Stokes. They might not win, but at least they'd already know all about stress-strain cycles.
A three-year-old racehorse is half a ton of raw power and desire, perched on spindles that appear too delicate to support a card table. Humans aspiring to win the Kentucky Derby come to the fray full of hope and care, but their young equine partners are subject to all manner of mystery--from cruel injury to bewildering failure of heart.
With these cautions in mind, here's a word in support of Pulpit, the spirited Frankie Brothers-trained bay colt that electrified all witnesses Saturday afternoon at Gulfstream Park. After just two races (and two brilliant wins) as a three-year-old--he did not race at all at two--this inexperienced son of A.P. Indy and Preach took on stakes company for the first time Saturday in the Fountain of Youth. After tracking a scorching pace set by Arthur L and Confide, who had previously run in five graded stakes between them, jockey Shane Sellers asked Pulpit to run in the turn for home; he cruised past the leaders, won the mile and a sixteenth in 1:41 4/5 and firmly established himself as the early favorite for the May 3 Run for the Roses.
"I roughed him up a little bit in the stretch," Sellers reported afterward. Sellers also kissed his mount on the neck en route to the winner's circle. It was one of those moments racing fans remember.
Much can go wrong in the testing prep races between now and May, and it probably will. But here's hoping only good luck visits Pulpit. He'll need it. No horse unraced at two has won the Derby in 111 years. The only time legendary Claiborne Farm, from which he hails, won the Derby was in 1984, with the ill-fated Swale.
Can Pulpit buck the odds? Let us now pray.
