The private pilot, who held an airplane single engine land rating, had been taking dual instruction in a gyroplane. During the takeoff portion of his first solo flight in the gyroplane, it began drifting toward the edge of the runway. Although the pilot initiated an abort and tried to realign the gyroplane with the runway, his control inputs resulted in the gyroplane rolling onto its side, whereupon it sustained substantial damage. According to the pilot, there was no indication of any mechanical malfunction. Wind conditions were calm.