The student pilot and flight instructor were practicing some takeoffs, flight maneuvers, and landings in the student pilot's gyroplane. After landing on the runway with a right crosswind, the student pilot attempted to taxi the gyroplane back to the hangar. During the taxi forward, the gyroplane began to roll to the right and the rotor blades contacted the runway. The student pilot felt the nose wheel and cyclic positions at the time of the forward taxi were the reasons for the roll to the right. The gyroplane sustained substantial damage to the fuselage structure. The student pilot and flight instructor reported no mechanical malfunctions prior to the accident.