Background
A flight instructor and an instrument student conducted pre-takeoff checks. The instructor observed that all preflight walk-around, radio, navigational, and engine checks were normal.
Event
During takeoff, engine operation was normal and characterized as "smooth" for initial power application and rotation. At about 200 to 300 feet above ground level, while crossing the departure end of the runway, the engine "burped" and regained power. About the time both pilots decided to return for a landing, the engine quit completely. The instructor took control of the aircraft. They completed the emergency checklist for engine failure on takeoff, including switching the fuel selector to the other (left) tank. Power was not regained, and a landing in the trees was unavoidable.
Post-Event Observations
Both pilots stated that the fuel selector was in the right tank detent at the start of the takeoff roll. At the wreckage site, enough fuel spillage existed that the Chapel Hill Fire Department was called. FAA inspectors did not consider fuel exhaustion. Atmospheric conditions were not conducive to the formation of carburetor ice, based on icing probability charts. Subsequent engine run at an engine repair station with FAA oversight, after adjustments for minor impact damage, revealed a satisfactorily running engine from idle to takeoff power.