"Let's go!" shouted instructor Mauricio Genore. "Get down! Hands under your glutes!"
The women are clients of Stacy's Boot Camp, one of a growing number of "boot camp" programs that take the workout out of the gym and into parks and other outdoor spaces.
The camps have grown in popularity as people look for a way to enjoy the outdoors while avoiding the hassle of the gym and the cost of a personal trainer. No special machines or equipment are needed - just grass, benches, pavement and gallon water bottles that serve as weights.
"It's an emerging trend," said Cedric Bryant, chief science officer at the American Council on Exercise, which certifies trainers and fitness teachers. "You're able to get a level of supervision but at an affordable cost."
Bryant said that in the early days of fitness boot camps several years ago, the classes really were militaristic, with instructors barking out orders drill sergeant-style.
These days, he said, the workout is still tough but the Marine Corps atmosphere has been relaxed.
John Spencer Ellis, who runs a fitness boot camp in Orange County, Calif., agreed.
"Our model is more about encouragement and camaraderie and personal growth, not demeaning people and making them crawl through barbed wire," he said.
The New York class looked grueling. The women sprinted, did leg lifts and crawled sideways on elbows and knees.
Genore, a 50-year-old whose chiseled physique would be the envy of a man half his age, was more prodding motivator than stern taskmaster, shouting "knees up!" as the women ran in place.
Passersby stopped to gawk, and several teenagers followed along for half the class, either as a joke or to get a free workout.
Other classes in Central Park tend to attract photo-snapping tourists, said Stacy's Boot Camp founder Stacy Berman. "It comes with the territory," she said.
Berman, 31, who started her fitness career as a teenage lifeguard, said people get bored in gyms and don't challenge themselves.
"The workout that we do, there's no way that your body won't change," she said.
The $250 price tag for nine hourlong classes is much cheaper than the $80-an-hour and up that personal trainers charge in many cities.
Berman's classes are open to men and women, but most students are female, perhaps because, as a recent story in The New York Times suggested, men don't take classes for the same reason they don't ask for directions: They hate to appear to need help.
The women who went through their paces with Genore were boot camp believers.
"It's great being outdoors," said Tiffany Wagner, 34, who works in advertising. "I've even done it in the rain and the snow and the sleet."
Graphic designer Susan Fisher, 44, said she had just joined and would now freeze her gym membership.
"There's a sort of built-in competition," she said. "You don't want to be the last person so that keeps you going."
Of the hundreds of fitness boot camps around the country, many are specialized programs targeted at brides shaping up for their weddings or new moms shedding their pregnancy weight.
Kristin Horler started Baby Boot Camp in San Francisco in 2001; there are now classes in 300 locations.
Her clients use their strollers to do walking lunges.
"You don't have to be constrained by the walls of a fitness facility or a gym," Horler said. "They're setting a positive example for their children."