On May 26, 2006, about 0800 mountain standard time, a Piper PA-28-140, N6309W, made a forced landing in rocky terrain at Eagar, Arizona. Kestrel Aviation, Inc., operated the airplane under the provisions of 14 CFR Part 91 as an instructional flight. The airplane sustained substantial damage. The certified flight instructor (CFI) was not injured, and the student pilot sustained minor injuries. Visual meteorological conditions prevailed for the local area flight, and no flight plan had been filed. The National Transportation Safety Board investigator-in-charge interviewed the CFI. He and the student had been doing pattern work at the municipal airport in the town of Springerville, Arizona. They had completed one flight around the pattern prior to the accident. On the accident takeoff from runway 21, they had been doing a high-speed taxi on the 8,000-foot runway. He reported that he was on the controls (throttle and ailerons), and the student was on the rudders. The CFI was adding and reducing power to get the student used to the directional control of the airplane (left turning tendency). As the CFI added power to takeoff, he noted 2,300 revolutions per minute (rpm). After liftoff, he said that the airplane was not climbing, and the engine sounded normal, but was still only producing 2,300 rpm; not the 2,500 rpm that was normal. The engine was not stuttering or missing, and the airplane was not climbing. The CFI indicated there were houses and rising terrain in the area. There were also power lines. He knew that he would have to give up airspeed in order to get over the power lines. He lowered the nose to get the best angle of climb airspeed, and noted a 50 fpm rate of climb. After clearing the power lines, he made the forced landing. When the CFI noted that the airplane was not climbing, he checked the magnetos and mixture, but did not apply the carburetor heat. He said that it was dry and warm outside, and he did not believe that carburetor ice was an issue. He had the airplane configured for takeoff; the mixture was at a lean setting, and one notch of flaps. He attempted to readjust the mixture during the event, but that did not work. He also indicated that he did not raise the flaps, because the airplane would have settled. He noted the weather as calm winds, clear, and about 65 to 70 degrees. They used the calm wind runway 21. The CFI stated that he normally flies early in the morning with his students for density altitude considerations. The airplane had plenty of fuel onboard. A deputy from the Apache County Sheriff's Office reported that the accident site was 3 miles west of the Springerville airport in the neighboring town of Eagar. He noted landing gear skid marks in the rocky terrain. The airplane struck a small tree, and came to rest upright facing towards the west. The deputy further noted that the landing gear wheels had separated from the airplane. The deputy interviewed the student pilot, who indicated that after takeoff they were "not able to gain their normal airspeed." He noted their airspeed at 65 miles per hour (mph), with 2,000 rpm. A Federal Aviation Administration inspector interviewed the CFI. The CFI indicated that after applying power to takeoff, he noted they had no more available runway left in which to make the forced landing.