The pilot reported that the purpose of the training flight was to complete multiple simulated, engine failure autorotations without a power recovery (full-down autorotation). After he completed his first right, 180º turn, full-down autorotation, the airspeed was "too slow." He added that the instructor told him to maintain more speed during the right turn of his second attempt, and the pilot focused on maintaining more airspeed, but the descent rate increased "due to the speed." The pilot added that, after he completed the right turn and aligned with the runway centerline, he felt that the airspeed was fast, so he flared to reduce the ground speed and increase the main rotor rpm. However, the helicopter started to sink during the flare, so due to the low altitude, the pilot leveled the helicopter to prevent a tail strike. The helicopter touched down on its skids with "substantial" ground speed and veered slightly right. The pilot applied full left cyclic and pedal input, but the helicopter continued to veer right. The helicopter exited the runway and rolled over on its left side. The fuselage and main rotor blades were substantially damaged. The pilot reported that there were no preaccident mechanical failures or malfunctions with the helicopter that would have precluded normal operation. The flight instructor reported that the 180º right turn aligned the helicopter with the runway centerline but at a lower altitude than was desirable because it prevented the pilot from conducting a normal flare "as the tail would have struck the runway." He added that, a normal flare before touchdown in a full-down autorotation would result in a 30º nose-up attitude, but the pilot was only able to achieve about a 10º nose-up attitude "for fear of damaging the tail."