On March 15, 2003, at 0809 mountain standard time, a Piper PA24, N842PS, experienced a partial loss of engine power and inadvertently made hard contact with the runway surface at Memorial Airfield (34AZ), Chandler, Arizona. The flight continued to the Williams Gateway Airport (IAW), Mesa, Arizona, and landed gear up. Arizona Cloud Busters owned and operated the airplane under the provisions of 14 CFR Part 91. The certified flight instructor (CFI), a private pilot under instruction (PUI), and one passenger were not injured. Visual meteorological conditions prevailed for the local area practice flight, and no flight plan had been filed. The flight departed the Stellar Airpark (P19), Chandler, Arizona, at 0710. According to both the CFI and PUI, the purpose of the flight was to practice commercial maneuvers for the PUI's upcoming commercial check ride. The CFI stated that they conducted a preflight, and discussed how to handle an engine failure on takeoff. He stated that after takeoff, about 1,000 feet above ground level (agl), he simulated an engine failure by retarding the throttle. He noted no discrepancies with the recovery of the simulated engine failure. During the flight the CFI and student flew the airplane at various airspeeds and discussed the "best glide speeds for endurance versus range." The plan at 34AZ was to simulate a loss of engine power, make an approach for landing, apply power, and complete a low approach over the field. When the student applied full power, there was no corresponding power increase for "several seconds." The CFI took the flight controls; however, the landing gear contacted the runway surface. At the time the landing gear contacted the surface, the engine "caught and developed full [rpm] in time for me to gain control and the [airplane] to gain altitude." The CFI stated that they believed the landing gear was damaged. They flew to CHD, and tower personnel stated that the landing gear was not fully extended. The CFI and tower personnel discussed landing options. The CFI decided to land gear up at IAW due to the fact that their fire department had more equipment than CHD. After the fire equipment was in place, the CFI landed on runway 12 at IAW with the landing gear retracted, full flaps, and the engine shut down. According to a Federal Aviation Administration (FAA) inspector who visually examined the airplane, there were multiple holes on the fuselage.