On May 1, 2004, about 0945 central daylight time, a Cessna 172K, N7448G, piloted by a flight instructor and a dual student, was substantially damaged when it departed runway 35 (4,000 feet by 75 feet, asphalt) during landing at the Lawrence Smith Memorial Airport (LRY), Harrisonville, Missouri. The aircraft subsequently encountered a ditch and nosed over. The instructional flight was operating under 14 CFR Part 91 without a flight plan. Visual meteorological conditions prevailed at the time of the accident. The flight instructor reported minor injuries and the dual student reported no injuries. The local flight departed LRY approximately 0900. In his written statement, the flight instructor reported that the dual student had completed three landings with his assistance and that he had made one landing as a demonstration. The CFI stated that on the next approach he requested that the student hold the aircraft in the landing flare "longer so that he could get a proper feel and visual picture." The CFI noted that during the flare the aircraft began to drift to the right. He requested that the student correct back toward the centerline, at which point the student banked to the left and applied left rudder. The CFI stated "My flight controls" to the student and applied right rudder. However, the dual student apparently did not hear him because the student maintained left rudder input, overpowering the CFI. The CFI recalled that the aircraft contacted the runway with the left main wheel and "veered" to the left. The aircraft subsequently departed the runway pavement, struck a ditch adjacent to the runway and nosed over. The dual student reported that during the landing flare, the aircraft drifted to the right. He reportedly applied left rudder and the aircraft corrected. He stated that as the aircraft approached the runway centerline, he applied right rudder. However, the aircraft did not respond but continued toward the left side of the runway. He recalled that he applied right brake in an attempt to remain on the runway. The student stated that these efforts were not successful and the aircraft departed the left side of the runway and nosed over after encountering the ditch adjacent to the runway. The student stated that the CFI was "always good about saying 'My flight controls' and likely stated this. However, I believe I . . . did not relinquish [the] controls to [the] instructor." He recalled: "I applied rudder(s), I applied brake and I recall my hand(s) on [the] yoke towards impact point." He commented that he was "much bigger" than the CFI. The CFI reported that there were no failures or malfunctions associated with the aircraft prior to the accident. The LRY Automated Weather Observing System recorded the following wind conditions: At 0755, winds from 350 degrees at 9 knots; At 0855, winds from 030 degrees at 7 knots; At 0955, winds from 350 degrees at 6 knots; At 1055, winds from 010 degrees at 9 knots; At 1155, winds from 020 degrees at 7 knots.