On March 20, 1994, at 1000 central standard time, a Piper PA-28- 140 airplane, N4373X, sustained substantial damage during a forced landing near Romeo, Michigan. The private pilot sustained no injuries. The personal flight departed the Romeo Airport at 0945 and was conducted under CFR Part 91 in visual meteorological conditions. No flight plan was filed for the local flight. During a telephone interview, the pilot reported he had experienced a rough engine and a loss of engine power shortly after his third touch-and-go landing on runway 36. He said he rapidly cycled the carburetor heat on then off and tried different throttle positions but the engine did not recover to full power. He initiated a slight left turn to "possibly land on runway 27, or turn around 180 degrees". Realizing he had insufficient altitude, he pulled the throttle to idle and made a slight right turn to perform an emergency landing in an open grassy area on the northern edge of the airport boundary. Examination of the aircraft by an FAA Airworthiness Inspector revealed upward crushing on the lower nose section and on the right wing. The propeller, nose gear, and right main landing gear were bent aft. The left fuel tank contained approximately five gallons of fuel and the right tank contained about 12 gallons. The fuel strainer was below the fuselage crush line and was dislodged. Clear, red fuel was leaking from the fuel lines. Further inspection of the aircraft and engine revealed no anomalies. The position of the carburetor heat valve was indeterminate due to crushing. The engine and exhaust system were partially disassembled and inspected by a local aircraft inspector. No discrepancies were noted. According to the icing probability curves published in DOT/FAA/CT-82/44, potential for carburetor icing existed at glide and cruise power settings. A local flight instructor, who was flying in the traffic pattern 30 minutes prior to the accident, reported a loss of engine power which was corrected with the application of carburetor heat.