On December 1, 2004, at 1200 central standard time, a Piper PA-28-181, N3575X, operated by Wing Flying Club Inc. as a rental airplane, received substantial damage on impact with terrain during a forced landing near Lee's Summit Municipal Airport (LXT), Lee's Summit, Missouri. Visual meteorological conditions prevailed at the time of the accident. The 14 CFR Part 91 personal flight was not operating on a flight plan. The private pilot reported no injuries. The local flight originated from LXT at 1030. The pilot stated that he performed a preflight inspection of the airplane in a hanger equipped with fluorescent lighting. During the inspection, he checked the fuel gauges and visually checked the fuel level in each tank and stated that the fuel level in each fuel tank was "just under the tabs." The pilot stated that the runup was normal and after departing from LXT, he flew to a point 5 miles west of Butler Memorial Airport (BUM), Butler, Missouri, and then entered the traffic pattern there to perform a touch and go. After the touch and go, he climbed and headed to the east. A few minutes later the engine sputtered "just a little." He applied carburetor heat, and the engine "smoothed out." He returned to and landed at BUM where he performed a runup. He then shut the engine down and checked the fuel sumps again. He restarted the engine and performed another runup and then flew to Lawrence Smith Memorial Airport (LRY), Harrisonville, Missouri, where he performed a touch and go. He then departed and was en route to LXT when the engine began to run "rough" about 5 miles from LXT. He then performed a forced landing on a muddy field where the airplane's left wing contacted weed resulting in the airplane skidding sideways in the mud. Inspection of the airplane by a Federal Aviation Administration inspector revealed that the fuel selector was positioned to the left fuel tank and no usable fuel was noted in that tank. Inspection of the right fuel tank did not note usable fuel.