On September 22, 2005, about 1430 Hawaiian standard time, a Robinson R22 Beta, N82001, landed hard on runway 4 at Waimea-Kohala Airport (MUE), Kamuela, Hawaii. Hawaii Pacific Aviation, d.b.a. Mauna Loa Helicopters, Inc., operated the helicopter as an instructional flight under the provisions of 14 CFR Part 91. The helicopter sustained substantial damage when the skid landing gear spread, and the main rotor blades flexed and cutoff the tailboom. The certified flight instructor (CFI) and newly certificated private pilot were not injured. Visual meteorological conditions prevailed for the local area flight that departed Kona International Airport at Keahole (KOA), Kailua-Kona, Hawaii, about 1330. According to the Airport/Facility Directory, Southwest U.S., the altitude at MUE is 2,671 feet mean sea level. The purpose of the flight was to practice autorotations at MUE. According to the CFI he checked Waimea's Automated Weather Observing Station (AWOS), and the National Oceanic and Atmospheric Administration (NOAA) website for satellite imagery. Waimea AWOS was reporting a density altitude of about 4,200 feet; temperature 21 degrees Celsius; visibility greater than 10 statute miles; wind 030 at 11 knots; and altimeter 30.01 inches of mercury. On the initial approach they did a running landing, followed by a straight-in autorotation from about 600 feet above ground level (agl). There were no discrepancies noted with the maneuvers. The next maneuver was a 180-degree autorotation from 1,000 feet agl. Both maneuvers culminated in power recoveries. The CFI noted minor revolution per minute (rpm) fluctuations caused by "too late up collective at the autorotation entry…." However, he also indicted that the student pilot was able to regain control of the rpm situation and completed the maneuver satisfactorily. Due to a low fuel state, both pilots agreed to do one more maneuver, stop to refuel, and then return to KOA. The student set up for a 180-degree full touchdown autorotation from 500 feet agl. The student entered the autorotation abeam runway 4. He started a right turn and "caught the rpm at the right time." The CFI reported that halfway through the turn he noted that the rpm was slightly above the green arc and the indicated airspeed was slightly below 65 knots. He wasn't concerned about the airspeed because he knew that it would increase as the turn continued. He noted the Vertical Speed Indicator (VSI) was approaching the 1,500-foot-per-minute rate. The CFI reported that in order not to be short of the target the student "banked the aircraft harder," with the increased bank, more up collective was required. When the student leveled the helicopter, the CFI noted that the student had not lowered the collective to lower the rpm. The CFI called out to lower the collective, and then initiated the corrective action because he did not feel the student lower the collective. As the helicopter passed through 50 feet agl with an indicated airspeed of about 70 knots, the CFI called out to flare for landing, followed by instruction to "join the needles." He simultaneously realized that the ground was "coming up too fast." The CFI knew they wouldn't be able to arrest their descent rate and forward airspeed before ground impact. He took the flight controls from the student, made sure the helicopter was level, and "pulled in collective to cushion the impact." The helicopter landed hard, the landing gear skids spread, and the main rotor blades flexed and chopped off the tailboom. The helicopter bounced off the runway and started to spin. The helicopter spun several times before the pilots were able to lower the collective and reduce the throttle to stop the spinning. The CFI reported that the combination of the higher descent rate, increased airspeed, and the density altitude led to the accident, and that stored kinetic energy was too high to arrest the descent in the flare. The student reported that there were no discrepancies noted with the first couple of maneuvers at MUE. They were abeam runway 4 when he started the 180-degree autorotation from 500 feet agl, the accident maneuver. He looked outside at this landing spot, started the bank, while raising the collective to stop the rotor rpm from over speeding. When they had turned about 90 degrees, he looked at the ASI (Airspeed Indicator), which read 65 knots, and noted the rotor rpm at 105 percent. The student looked back at the landing area and increased the collective as he continued the turn. The student stated that as he lined up the helicopter with the runway, the CFI instructed him to lower the collective, which the student did, as well as applying aft cyclic to start the flare. He realized at that point that approach was low, and the ground was rushing up at them. The helicopter landed hard, and he recalls bouncing once or twice before the helicopter started to spin. He immediately tried lowering the collective and rolling off the throttle, but was unable too. Once they were able to stop the helicopter from spinning, he pulled the mixture, and saw the CFI shutting off the fuel.