On November 11, 2001, about 0850 eastern standard time, a Piper PA-28R-200, N3057R, was substantially damaged during a forced landing near Cattaraugus, New York. The certificated flight instructor, private pilot, and a passenger were not injured. Visual meteorological conditions prevailed. No flight plan had been filed for the instructional flight that was conducted under 14 CFR Part 91. According to the pilots, the flight originated November 10, 2001, from Lenawee County Airport, Adrian Michigan, as a dual instructional cross-country flight. The airplane remained overnight at Weedsport, New York. The next morning, the flight departed Weedsport about 0750, for Jamestown, New York. The flight instructor further stated: "...An hour into the flight the aircraft [engine] began running rough. We then turned alternate air on, mixture rich, fuel pump on, and began looking for the nearest airport which was Berdick, a private strip near Otto, NY. Soon after, we heard a bang and could see...[a] hole in the cowling caused by the cylinder. After that, smoke started coming in the vents. We shut the heat and defrost off. For a brief time flames could be seen through the hole. We immediately started turning toward the nearest field. Once the landing was assured...[the private pilot] began shutting the aircraft down - (mixture cut-off, fuel off, master off), and added flaps while I flew the plane to the ground. We had everyone secure themselves and brace for touchdown. Once the aircraft was on the ground...[the private pilot] retracted the flaps and began braking on the rollout. Then in the rollout the right gear sank into the woodchuck hole and broke off as the aircraft slid to a stop; the side load broke the left gear. The gear breaking off caused skin damage to the right wing. Once the aircraft stopped, we evacuated the aircraft. The field was a grass meadow with a rise in the center. According to an inspector from the Federal Aviation Administration (FAA), the number 3 cylinder had pulled away from the engine case. All through bolts and engine case bolts were separated. In addition, the piston and piston wrist pin were fractured. Oil was found in the engine sump. According to logbook records, on March 16, 2001, all of the cylinders were removed, repaired, and reinstalled in accordance with the Lycoming overhaul manual. At the time of the accident, the engine had accumulated 146.7 hours since the cylinder removal and re-installation. Lycoming Service Instruction 1029D, dated August 15, 1986 stated: "All Avco Lycoming aircraft engines incorporate bolts and long thru studs that extend through the crankcase halves primarily for holding them together. The studs also secure the cylinders to their mounting decks on the crankcase...." "To insure uniform loading on the main bearing, it is necessary to tighten these studs and bolts in a sequence beginning at the approximate center of the engine and progressing evenly to both front and rear of the engine as described in detail in the following procedures" The mechanic who performed the cylinder installation was interviewed by another FAA inspector. According to the inspector's statement: "...[the mechanic] was knowledgeable on Lycoming Service Instruction SI 1029D, and knew how to implement it....."