On August 31, 2018, about 1400 eastern daylight time, a Luscombe 8E airplane, N2305K, was substantially damaged when it was involved in an accident near New Carlisle, Ohio. The pilot sustained serious injuries. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 personal flight. The pilot reported that his preflight inspection did not reveal any anomalies with the airplane. He visually confirmed that the right wing fuel tank was full and the left fuel tank was about 1/2 full. After starting the engine, he taxied the airplane to the runway and completed an engine runup, which revealed no anomalies. The pilot reported that he verified the proper function of the carburetor heat control and that he did not observe any indication of carburetor ice. The pilot initiated takeoff and the airplane became airborne about one-half to two-thirds down the 2,000-ft-long runway. The pilot reported that airplane had reduced climb performance after liftoff and that the engine began running rough about 150 ft above the ground. The pilot turned the carburetor heat on, but then removed it when he perceived an increase in engine roughness. The engine subsequently lost total power. The pilot entered a right turn toward a nearby nursery, where he completed a forced landing. The airplane landed hard on uneven terrain and the main landing gear collapsed. The airplane came to rest about 1/2 mile west-northwest of the departure end of runway 27. The forward fuselage and the right wing sustained substantial damage during the hard landing. Flight control continuity was confirmed from the cockpit controls to all flight control surfaces. First responders reported a strong fuel smell and observed fuel leaking from the engine compartment, and a mechanic from the airport subsequently turned off the right fuel tank valve to stop the fuel leak. The left fuel tank valve was found turned off. The right and left fuel tanks contained about 5 gallons and 6.75 gallons of fuel, respectively. Samples from the fuel tanks were blue in color, had the odor of 100 low-lead aviation fuel, and exhibited minor particulate contamination. Examination of the vented fuel tank caps did not reveal any anomalies or obstructions. The fuel gascolator bowl shattered during impact. The engine remained attached to the firewall through its mounts, but the carburetor separated from the engine crankcase. Engine control continuity was confirmed from the cockpit to the carburetor. Movement of the throttle arm discharged fuel from the accelerator pump into the carburetor venturi. The carburetor bowl remained intact and contained uncontaminated fuel. The carburetor heat valve position could not be determined due to impact damage. Internal engine and valve train continuity were confirmed as the engine crankshaft was rotated, and compression and suction were noted on all cylinders in conjunction with crankshaft rotation. Compression measurements were above 70 psi for all four cylinders. A borescope inspection of each cylinder did not reveal any evidence of a mechanical failure of the pistons or valves. The spark plugs exhibited features consistent with normal engine operation. Both magnetos produced spark as the engine crankshaft was rotated. The propeller remained attached to the engine crankshaft flange; one propeller blade was bent aft about midspan, and the other blade remained straight with no evidence of rotational damage. Examination of the airplane and engine did not reveal any evidence of mechanical malfunction that would have precluded normal operation. According to a carburetor icing probability chart contained in FAA Special Airworthiness Information Bulletin CE-09-35, entitled "Carburetor Icing Prevention", the recorded temperature and dew point about the time of the accident were conducive to the formation of carburetor icing at a descent engine power setting. The bulletin notes that if ice forms in the carburetor of a fixed-pitch propeller aircraft, the restriction to the induction airflow will result in decreased power output and a drop in engine rpm, which might be accompanied or followed by a rough running engine. The bulletin also notes that a pilot should respond to carburetor icing by applying full carburetor heat immediately and that the engine may run rough initially for a short time while the ice melts.