Prior to the accident, the flight instructor and student practiced "turns around a point," and "S-turns across a road" before returning to the airport to practice landings. They then completed three "touch and goes," in the American Aviation AA-1A without incident. During the downwind leg of the traffic pattern for the fourth "touch and go," the flight instructor demonstrated an "engine out procedure" by bringing the throttle to idle when the airplane was approximately midfield. He did not however, use carburetor heat and kept the throttle at idle all of the way to touchdown. After touchdown, he applied power, then rotated, and the engine "quit." There was not "enough runway left to stop," and the airplane overran the runway. The airplane struck a ditch, the nose gear collapsed and the airplane nosed over, damaging the vertical stabilizer and canopy. The airplane had been filled with automobile gasoline prior to the flight. Both the student and flight instructor stated that there had not been any mechanical problems with the airplane and a post accident examination of the engine revealed no preimpact malfunctions. A review of a carburetor-icing chart revealed that atmospheric conditions at the time of the accident were conducive to "serious icing at glide power."