The pilot reported that he departed with about 47 gallons of fuel onboard for a 551-nautical mile cross-country flight. About 3-hours and 15-minutes into the flight, the pilot said he was concerned the way the right fuel tank gauge was moving down faster than he’d seen before. He added that, he told Air Traffic Control (ATC) that he needed to change his destination for fuel. Shortly thereafter, he stated that the left tank was out of fuel, so he switched back to the right fuel tank and looked for a place to conduct an emergency landing. During the approach for a forced landing, the engine changed from idle to full power for 10 to 15 seconds, before a complete loss of engine power. The airplane’s nose dropped sharply and the airplane impacted the roof of an unoccupied barn near vertically. During recovery of the airplane, no fuel was found on site or in the airplane’s fuel tanks.