The pilot reported that they departed Chicago Executive Airport (PWK), Wheeling, Illinois, about 1530 and flew to Burlington Municipal Airport (BUU), Burlington, Wisconsin. They were conducting takeoffs and full stop landings on runway 01 (2,477 feet by 130 feet, turf) at BUU. The pilot stated that on the third takeoff, the engine failed after lift off. The airplane impacted a tree during the forced landing and subsequently came to rest inverted. The pilot informed a Federal Aviation Administration Inspector that the engine began to run rough. He applied carburetor heat and the engine operation smoothed out momentarily, and then quit. The airplane was at an altitude of approximately 250 feet above ground level, in a left turn at the time. A post accident examination of the engine did not reveal any anomalies consistent with a pre impact failure. Engine continuity was confirmed via crankshaft rotation and compression was observed on all cylinders. The magnetos provided a spark when rotated and spark plug appearance was consistent with normal wear. The carburetor was intact. No fluid was observed in the carburetor or in the gascolator. The air filter and intake manifold appeared unobstructed. The fuel selector was set to the right tank and appeared unobstructed. The right fuel tank contained an estimated 4 or 5 gallons at the time of the post accident examination. The left fuel tank was nearly empty at that time. The fuel tank caps were in place and secure. The fuel vents appeared open and functional. The airplane had been inverted for several hours after the accident. The exact amount of fuel on-board at the time of the accident could not be established. The pilot stated that 12 gallons of fuel were on-board at the time of the initial takeoff. The airplane manufacturer reported that the published fuel burn for the airplane was approximately 4.7 ~ 7.0 gallons per hour. Total fuel capacity is 25 gallons, with 21 gallons useable. Each fuel tank is equipped with a single outlet located in the center of the tank, which is the lowest part of the tank in cruise flight. This configuration allows use of approximately 3 additional gallons of fuel in steady level flight. However, for that reason, takeoffs are not permitted with less than 1/4 tank of fuel due to the possibility of unporting a fuel tank outlet at higher pitch attitudes.