At 1200 Central time, the rental airplane was substantially damaged during a forced landing near Lees Summit Municipal Airport (LXT). Visual conditions prevailed; there were no injuries. The local flight originated from LXT at 1030. The pilots preflight inspection included checking the fuel gauges and the fuel level in each tank, which was just under the tabs. After a touch-and-go landing at a nearby airport, 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 the nearby airport, landed and performed a runup. He then shut down the engine and checked the fuel sumps again. He restarted the engine and performed another runup and then flew to a third airport and performed another touch-and-go. He then departed and was en route back to LXT when the engine began to run rough. He then performed a forced landing. An FAA inspector reported that no usable fuel was aboard.