TERRE HAUTE, Ind. — John Shipman, standing on an elevated platform beside a small dusty track, wiped the sweat from his eyes and tucked away a checkered racing flag. For the past 10 minutes, nine small cars had circled in front of him during a qualifying race, bolting along at speeds approaching 40 miles per hour.

The catch: Not one of the nine racers had a driver’s license. The eldest, in fact, was still in middle school.

“Some people call us bad parents,” Mr. Shipman said.

The Terre Haute Quarter Midget Association, where Mr. Shipman is a volunteer flagman, is one of more than 70 racing clubs — many of whose members are drawn from the rural parts of the country — designed for the thousands of children, ages 5 to 17, who race quarter-midget cars.