On October 9, 2007, about 1630 eastern daylight time, N71HP, a Eurocopter AS 350 B2 Ecureuil helicopter, operated by the State of Ohio, sustained substantial damage during an autorotation at the Ohio State University Airport (OSU), near Columbus, Ohio. Visual meteorological conditions prevailed at the time of the accident. The public-use training flight was being conducted under 14 Code of Federal Regulations Part 91. No flight plan was on file. The certified flight instructor (CFI) and private pilot receiving instruction reported no injuries. The local flight originated from OSU about 1530. The CFI reported that he flew with three students that day. During the first flight of the day, a hard landing occurred while practicing an autorotation. The emergency locator transmitter (ELT) was set off and post flight inspection revealed no damage. The second flight of the day was conducted and a post flight inspection revealed no damage. The CFI said that the preflight inspection of the helicopter revealed no damage and that: During hovering autorotations we hit the ground hard due to an early and rapid pull of the collective. During all three of these training periods I thoroughly brief the students of how I am going to use a count down method prior to reducing the FFCL (Fuel Flow Control Lever). I announced Engine failure in 3-2-1, at the time I would retard the FFCL. On the first attempt, there was a rapid and early pull of the collective along with excessive right pedal and we hit the ground and bounced. I explained to the student how to correctly execute the maneuver and we continued training. On the second maneuver, the heading control was correct but we hit hard due to an early collective pull and the ELT did go off, I am not sure if I reset it or [the student pilot] did. I felt it wasn't a very hard impact and we continued training. The maneuvers continued to improve, so we moved on to the Hover Taxi Autorotations. During the first two hover taxi autos, again was an early application of the collective to cushion the landing resulting in a hard landing. The last maneuver was perfect. After completing those maneuvers we transitioned in to Standard Autorotations and then to 180 degree turn Autorotations. On the second auto with the rotor rpm was high I instructed [the student pilot] to shallow out his decel ... to maintain the rotor rpm within limits. We cushioned the touch down but due to the lack of time and high rotor rpm I could not make a power recovery and made the decision to continue to the ground. Upon touch down we touched down with minimal impact but slid for approximately 40 feet on uneven terrain rocking side to side and fore and aft until we stopped. I debriefed the maneuver and continued training completing two more 180 autos with turn and then went back to parking to debrief the flight. I failed to complete a post flight and then completed a thorough debrief. The next morning the damage was found during a preflight inspection. At 1653, the recorded weather at OSU was: Wind 280 degrees at 15 knots gusting to 21 knots; visibility 10 statute miles; sky condition clear; temperature 24 degrees C; dew point 7 degrees C; altimeter 29.90 inches of mercury. The CFI's safety recommendation was to conduct "Autorotational Training to a Runway or improved surface."