On May 10, 1997, about 1303 eastern daylight time, an American AA-1, N5734L, was destroyed as it impacted the ground and collided with a fence during a forced landing south of the Greenbrier Valley Airport (LWB), Lewisburg, West Virginia. The certificated airline transport pilot/owner was not injured. Visual meteorological conditions existed and no flight plan was filed for the personal cross country flight conducted under 14 CFR Part 91. The flight originated from the Summit Airpark, Middletown, Delaware, about 1005. The pilot was en route to San Antonio, Texas, with a planned stop at the Raleigh County Memorial Airport (BKW), Beckley, West Virginia. He reported that due to the weather conditions, he changed his stop from BKW to LWB. Thirty three miles from LWB, when the pilot contacted the tower controller for the weather, he stated that he checked the right wing tank and it was 1/2 full. He reported that 23 miles from LWB, he checked the right tank again, and the fuel sight gauge indicated zero fuel. The pilot stated that because of the weather and surrounding mountainous terrain, he requested a frequency for Washington Center to obtain an Instrument Flight Rules flight plan. Upon contacting the Center, the pilot stated that he was not sure of the amount fuel onboard, and was fuel critical. Shortly after notifying Center, the engine lost power and the pilot switched to the left tank. The engine restarted, and he climbed to 5,000 feet. Encountering weather, the pilot requested a lower altitude. The engine lost power once again, and the pilot switched back to the right tank. The engine operated for a few minutes, and then lost power again. Unable to restart the engine, the pilot descended through instrument meteorological conditions to about 1,000 feet agl. The pilot stated that he circled above a small pasture, and executed a forced landing. On May 12, 1997, a Federal Aviation Administration Inspector conducted an examination of the wreckage and the impact area. The Inspector reported that the airplane impacted on an upward sloping pasture, at an elevation of 2,410 feet mean sea level. The airplane was heading about 050 degrees magnetic, when it impacted the terrain collapsing the left main and nose gears. After traveling about 175 feet, the airplane struck a wooden post supporting a wire fence. The airplane continued 200 feet further, coming to rest upright, on a reciprocal heading. Inspection of the engine spark plugs, magnetos, timing gear section, throttle and mixture linkage, and electric fuel pump failed to uncover any anomalies. No useable fuel was found in left fuel tank. The right wing fuel cap was off, and not found in the wreckage area. The Inspector reported that a small amount of fuel and about a quart of water was found in the right fuel tank. He stated that it had rained between the time of the accident and his examination. A photograph taken by the West Virginia State police within 2 hours of the accident, showed the right tank fuel cap missing. The fuel cap had not been connected to a chain, and the owner stated that it attached by turning the cap a quarter of a turn. The Inspector did not find any scarring or damage to the right fuel tank lip area. The Airplane Owner's Manual indicated that the airplane's total fuel capacity was 24 gallons, with 22 gallons useable. The Performance Charts indicated that between 2,500 feet and 4,500 feet, utilizing between 67 and 70 percent power, the endurance was 3.5 to 3.7 hours. At the same altitudes and utilizing 75 and 77 percent power, the endurance was 3.1 to 3.3 hours. The pilot stated that he checked the fuel caps during preflight and sighted them en route, but could not remember seeing the fuel cap after the fuel sight gauge indicated zero fuel.