On September 30, 2013, about 1300 central daylight time, a Cessna 172 airplane, N8878B, impacted in a field during takeoff from Lowell Smith Airport (3TX6), Rio Vista, Texas. The airline transport-rated pilot (ATP)/flight instructor, the student pilot, and the passenger on board were not injured and the airplane was substantially damaged. The airplane was owned and operated by the student pilot under the provisions of 14 Code of Federal Regulations Part 91 as a personal flight. Visual meteorological conditions prevailed for the local flight that was not operating on a flight plan. The flight originated from the 3TX6. The student pilot reported that he and the ATP-rated pilot had landed at 3TX6 to pick up the passenger. They then took off from the grass airstrip and the student pilot was flying the airplane. They were about halfway to 3/4 of the way down the runway when the airplane lifted off. They pointed the nose of the airplane forward to increase the airspeed, but they quickly ran out of runway. He raised the nose to climb higher, but the airplane would not climb. At about 70 feet agl, the airplane stalled. The ATP-rated pilot stated he got on the controls when the airplane was not accelerating. The airplane struck a tree at the end of the airstrip before impacting the ground. An examination of the airplane showed substantial damage to the wings, nose wheel, and the firewall. In a subsequent statement the ATP-pilot stated that he did not think the engine was producing sufficient power, however a follow on examination of the airplane showed no anomalies. At 1255, the routine aviation weather report for Cleburne Regional Airport (KCPT), Cleburne, Texas, 8.3 miles north of 3TX6 was wind 170 at 6 kts, clear skies, visibility 10 statute miles, temperature 81 degrees Fahrenheit (F), dew point 52 degrees F, and altimeter 29.92 inches Hg. The Cessna 172 and Skyhawk Take-Off Data table showed that for a 2,300 lb airplane at sea level and 59-degrees F standard temperature, and with a headwind of 10 kts, the takeoff ground run from a hard surface runway would have been 615 ft, and to clear a 50 foot obstacle, 1,170 ft. The table required that the distances must be increased 10 percent for each 25 degrees F above standard temperature, which would have made the takeoff ground run 677 ft and to clear a 50 foot obstacle, 1,287 ft. Runway 17/35 at 3TX6 was 2,600 ft long and 110 ft. wide.