The pilot reported that the flight was commenced with minimum fuel. He estimated that the left wing fuel tank had about 2 to 3 gallons of fuel and he was running the right wing fuel tank down. He knew the right tank was about out of fuel, so he had one hand on the fuel tank select valve to switch it to the left tank at the first indication that the engine was being deprived of fuel. The engine sputtered and he switched the fuel select valve to the left tank. The engine caught and ran for about 45 seconds to 1 minute then began to sputter. When it became evident to him that the engine was not going to catch and run, he performed an off airport emergency landing on the tundra which resulted in substantial damage to the airplane. The pilot said that the loss of engine power may have been due to the engine ingesting 'sludge' from the bottom of the right wing fuel tank. The pilot commented that the right wing tank had never been out of the airplane since the plane was built in 1957.