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# Rockies Will Play Ball With an Altitude

## Knuckle balls with less dig, curve balls with less break, 9 percent more on flies - a letter from Denver

WHILE the rest of the country scratches its head over the base-running strategy of Atlanta Braves left fielder Lonnie Smith, some Denverites are scratching their pencils over a different question:How far will a baseball travel in a mile-high stadium? Home of the new National League expansion team, the Colorado Rockies, Denver is five times higher than any other major-league city. At 5,280 feet elevation, the air is 17 percent thinner than it is at sea level. Less resistance means increased propulsion. A batted ball should therefore travel 9 percent farther. According to University of Denver physicist Thomas Stephens, who calculated the odd-ball behavior, not only will a ball batted or thrown cross more turf, it will behave in other bizarre ways. The first third of the ball's trajectory (during which out-fielders usually judge the distance the ball will travel) will be the same as it would be at sea level. But during the second third of its flight, the ball will follow a different arc. It will actually land a good 30 to 35 feet farther out than it would at sea level, Dr. Stephens says. So ballplayers used to judging fly balls in the flatlands will have to relearn how to judge a pop-up when they play here. An outfielder will be able to throw about 9 percent farther, as well, so he who fails to compensate for lighter air density may overthrow his mark. If that isn't bad enough, knuckle balls and curve balls will have less "dig" in Denver. A 14-inch curve ball at sea level will curve only 11 inches in Denver. Since fast balls will be faster, batters will have slightly less time (.003 second) to hit what would be a 100 m.p.h. pitch at sea level. Should the playing field be extended by 9 percent to avoid Denver becoming home-run alley? "Should they design a high-altitude baseball?" asks Stephens. "They sell high-altitude tennis balls because they are pressurized. Up here you don't have as much pressure on the outside of the ball. But it seems to me they are not going to change the game, they are not going to change the ball for high altitude. The altitude is going to affect the outfielders more than anyone else." But moving the fence back, Stephens adds, would give the outfielders that much more ground to cover. Stephens's work started when he and some colleagues were wondering one day how a baseball would behave at high altitude, so he decided to run some calculations in his spare time. "The National League rules say a baseball has to be 9- to 9-and-1/4 inches in circumference. It has to have a weight about 5 ounces, smooth cow-hide cover, it has to be stitched. You cannot change it because even roughing up the surface affects the drag coefficient. The physics of sports is well understood and I built my research on what is already known," he explains. The research on the physics of baseball "is not dissimilar to the tables and tables of calculations the military has done on projectiles," says Stephens. "The calculations themselves in physical terms are almost trivial - they are well understood." Not so well understood is why Denver taxpayers are getting stuck with almost the entire bill for their new stadium. The cost for Coors Field was supposed to have been divided up between the taxpayers and the private sector. All but \$9.5 million of the total \$156 million bill for the real estate and construction of the stadium will be handed to the taxpayers. The assets that would have generated revenues to reimburse investors - the name of the stadium, seat rights, luxury seating, advertising, parking, and concession rights - have been given to the Rockies' owners - the Colorado Baseball Partnership - for 17 years, plus a five-year option. The owners sold only the right to name the stadium. There's no provision for capital improvements or for the revenue sharing taxpayers were promised.

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