The student pilot reported that during a supervised solo training flight, he was instructed to remain within the airport traffic pattern and perform three full stop takeoffs and landings. During the second landing, the airplane porpoised and veered left, so he aborted the landing and initiated a go-around. The student’s flight instructor observed the solo flight and recalled that the wind was light and variable. He reported that during the student’s third landing, the airplane floated for several seconds before the nose dropped and the airplane landed hard. Subsequently, the airplane bounced, a porpoise ensued, and a propeller strike occurred. The airplane remained on the runway and the student pilot taxied to the parking area. The airplane sustained substantial damage to the lower fuselage forward bulkheads and stringers. The student pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.