On August 14, 1996, at 1945 central daylight time, a Piper PA-38, N2538N, registered to Shenandoah Aviation, Inc., nosed over following a loss of control on takeoff from a farm field in Fairbury, Nebraska. The airplane was substantially damaged. The certificated flight instructor (CFI) and the student pilot on board were not injured. The 14 CFR Part 91 flight was operating in visual meteorological conditions without a flight plan. The destination for the flight was Shenandoah, Iowa. The CFI stated that he and the student pilot had flown together from Shenandoah, Iowa, to Omaha, Nebraska, to pick up another airplane. He stated that he was to fly one airplane back to Shenandoah and the student pilot was to fly N2538N back. He stated that the visibility had decreased down to four or five miles with haze at the time of the return flight. Upon his arrival at Shenandoah he noted that the student had not returned. A short time later he received a telephone call from the student who stated that he became disoriented during the return flight and was low on fuel, so he landed the airplane in a farm field in Fairbury. The CFI stated he then flew to Fairbury where he was met by the student pilot. They purchased five gallons of fuel and proceeded to the field where N2538N was located. The CFI stated they added the five gallons of fuel to N2538N and attempted to takeoff from the field. The CFI stated he did not walk the field to check its condition prior to taking off. He stated that the field was rough and there was a ditch at the departure end. The CFI reported, "...when we flew above this ditch, there seemed to be some dead air that pulled us back down and the airplane passed over the ditch and landed hard on the other side of the ditch and then flipped over onto its back." The student pilot's recall of the events surrounding the accident were basically the same as the CFI's.