A revenue sight-seeing helicopter flight operating under 14 CFR 91 collided with lava rock while attempting a forced landing on the summit of Muana Loa volcano after a partial loss of power. The pilot stated that while in a shallow downwind turn at approximately 200 ft AGL and an airspeed of about 40 mph, the helicopter began to settle while he continued to add power. The aircraft was too low to increase airspeed. After hitting the lava rock, the helicopter skidded 12 feet, turned to the right, and rolled over to the left. Both the flight controls and the engine functioned to touchdown. Tests disclosed no discrepancies in the fuel system. The height-velocity diagram has only been tested to a density altitude of 10,000 ft. The accident occurred at a density altitude of 15,500 ft. It does not apply above a density altitude of 5,400 ft at a gross weight of 3,600 lbs, the estimated weight of the helicopter at the accident site.