The pilot reported that, during takeoff, he rotated around 55 knots and that the gyroplane instantly yawed left about 45°. The pilot reported that he was "behind the power curve" and that the gyroplane could not climb or gain airspeed. The gyroplane began to descend, the pilot turned left, and the gyroplane landed hard and rolled to the right side. The pilot added that he believed that the gyroplane initially yawed left during the climb because of the "P-factor due to [a newly installed] more powerful engine" and that he failed to add right rudder input to correct. He added that it was his first test flight with the new engine. The gyroplane sustained substantial damage to the tailboom. The pilot reported that there were no preaccident mechanical failures or malfunctions with the gyroplane that would have precluded normal operation.