On August 3, 2004, at 1455 eastern daylight time, N7957U, a Cessna 172F, was substantially damaged when it impacted the runway, during takeoff from the Cooperstown-Westville Airport (K23), Cooperstown, New York. The certificated commercial pilot was seriously injured. Visual meteorological conditions prevailed and no flight plan was filed for the local personal flight conducted under 14 CFR Part 91. According to the pilot, she initiated the takeoff from runway 20 (a 2,600-foot long, 125-ft. wide turf runway), and during the takeoff roll, the airplane veered sharply to the left. She applied right rudder to realign the airplane on the centerline, and when "nothing changed," she "responded instinctively" and pulled back on the controls to lift the airplane off the runway. Because the airplane "lacked adequate airspeed," immediately after rotation, it descended, and impacted the ground. The pilot additionally stated that the correct action, to "pull the power back" and abort the takeoff, did not occur to her until it was too late. Examination of the airplane by the FAA inspector revealed substantial damage to the empennage of the airplane. No mechanical deficiencies were observed. The winds reported at an airport approximately 38 miles to the northwest, at 1456, were from 260 degrees at 3 knots.