On May 8, 2007, about 1222 mountain standard time, a Piper PA-28-140, N5895U, experienced a partial loss of engine power while maneuvering near Tucson, Arizona. The certified flight instructor (CFI) took the airplane controls from the second pilot, who was receiving a check-out, and the CFI proceeded to make a forced landing. The airplane impacted rough, native vegetation-covered, desert terrain about 1/3-mile north of the Ryan Field, Tucson. During the hard landing, the airplane's right main and nose gear were broken off, and the right wing's fuel tank was punctured; the airplane was substantially damaged. Neither the CFI nor the second pilot were injured during the instructional flight. The airplane was operated by the National Pilot Academy, Tucson. Visual meteorological conditions prevailed at the time, and no flight plan had been filed. The flight was performed under the provisions of 14 Code of Federal Regulations Part 91, and it originated from Tucson about 1147. The CFI reported to the National Transportation Safety Board investigator that the accident occurred while he was checking out the private pilot in the airplane. They were maneuvering about 4,000 feet mean sea level (1,600 feet above ground level) when the engine suddenly started running rough and began losing power. In response to the vibration and power loss, the CFI stated that he turned the airplane toward the departure airport. On approach, engine power continued to decrease and he was unable to maintain altitude. Federal Aviation Administration (FAA) personnel examined the airplane under the Safety Board investigator's direction. FAA personnel removed the engine's upper cowling and upper spark plugs. A boroscope inspection of the number 3 cylinder revealed that the top surface of the piston was damaged. Further boroscope inspection of its exhaust valve revealed that the valve was broken and all that remained of the valve was its stem. Cylinders number 1, 2, and 3 showed no evidence of damage. No further inspections were performed.