On June 20, 2013, about 2100 central daylight time, a Piper PA-28-140, N589FL, sustained substantial damage to the firewall during a forced landing following a loss of engine power during cruise flight near De Smet, South Dakota. The pilot and pilot rated passenger were not injured. The airplane was registered to a private individual and operated by the pilot under the provisions of 14 Code of Federal Regulations Part 91. The two pilots were competing in a cross country air race when the accident occurred. Visual meteorological conditions prevailed for the flight, which was not on a flight plan. The flight originated from the Rawlins Municipal Airport (RWL), Rawlins, Wyoming, at an unconfirmed time. The Brookings Regional Airport (BKX), Brookings, South Dakota, was the intended destination. The pilot reported that prior to the accident flight, she and another pilot had completed a flight that originated from the Grant County Regional Airport (GCD), John Day, Oregon, and ended at RWL. She reported that the flight lasted 5.7 hours and that 41 gallons of fuel were consumed during the flight. After filling the airplane's fuel tanks, the two pilots departed RWL and proceeded to Spearfish, South Dakota, where they performed a fly-by, and then continued on toward BKX. The pilot reported that when the airplane was about 50 miles from BKX at 7,500 feet altitude, they started a slow descent. She reported that as the airplane descended through 5,500 feet altitude, the engine speed dropped to 1,000 rpm and then spiked to 2,750 rpm. The pilot reported that the engine again dropped to 1,000 rpm and then spiked to 2,750 rpm. She stated that she performed the emergency checklist procedures, including switching fuel tanks, insuring the primer was in and locked, cycling the magnetos, applying carburetor heat, opening the throttle, and applying full rich mixture. She reported that these efforts were unsuccessful and the engine continued to surge. At this point the pilot realized that they were not within gliding range of an airport and selected a field in which to make an off-airport landing. She stated that the landing was successful but during the landing roll the airplane went through a ditch and hit a rock. The pilot reported that the accident flight was 4.8 hours in duration when the engine problems occurred. Postaccident examination of the airplane did not reveal any preimpact anomalies with regard to the engine or fuel system. A subsequent engine test run was performed by the aircraft salvage operator on the request of the National Transportation Safety Board's (NTSB) investigator in-charge. The salvage operator reported that the engine started and idled normally for several minutes. A full power run was not accomplished due to safety concerns. During the engine test run, the fuel selector was positioned on the left tank and the electric fuel pump was tested with no anomalies detected.