On August 19, 2004, at 1130 mountain daylight time, a Cessna 172S, N849SP, piloted by a student pilot, was substantially damaged during a hard landing at Cavern City Air Terminal (CNM), Carlsbad, New Mexico. Visual meteorological conditions prevailed at the time of the accident. The solo cross-country instructional flight was being conducted under the provisions of Title 14 CFR Part 91 without a flight plan. The pilot was not injured. The flight to Carlsbad, originated at Hobbs, New Mexico, at approximately 1045. According to the student pilot, the airplane landed hard on runway 14 and bounced. During the second touchdown, the airplane's propeller struck the runway. The student pilot taxied the airplane clear of the runway and shut down the engine. An examination of the airplane revealed that the nose landing gear was displaced aft and the airplane's firewall was buckled. At 1053 and 1153, the reported wind conditions at CNM were, 320 degrees at 11 knots, and 350 degrees at 9 knots, respectively.