On August 24, 2004, at approximately 1350 mountain daylight time, a Robinson R22, N7530D, operated by Cross Country Aviation Inc., was substantially damaged during a hard landing at Logan-Cache Airport (LGU), Logan, Utah. Visual meteorological conditions prevailed at the time of the accident. The local instructional flight was being conducted under the provisions of Title 14 CFR Part 91 without a flight plan. The commercial certificated instructor and private pilot receiving instruction were not injured. The flight originated at approximately 1330. According to the instructor, after demonstrating some ground maneuvers, he entered the pattern to demonstrate a "practice autorotation with a power recovery." The instructor stated that, at approximately 850 feet above the ground, on approach to runway 35, he entered the autorotation. In the glide, the airspeed "was 65 to 70 knots, [rotor] rpm was in the green, and the descent was around 1500 feet per minute. Everything was good." The instructor stated that at approximately 40 feet above the ground, "we" started the flare. At the end of the flare, I announced "recover." The student was "very tight on the throttle." Then I announced, "I have the controls." The instructor said he was unable to recover the [engine] rpm. The instructor leveled the helicopter and landed hard on the runway. The impact with the runway crushed the landing gear skids upward, and buckled the fuselage and tail boom. At 1351, the recorded weather conditions at Logan (4,454 feet msl) were, wind, 000 degrees at 0 knots; visibility, 10 statute miles; sky condition, overcast at 085; temperature, 19 degrees C.; dew point, 08 degrees C.; altimeter setting, 29.96. The calculated density altitude was 5,939 feet msl.