HISTORY OF FLIGHTOn June 21, 2019, about 1900 eastern daylight time, a Piper PA-28-180 airplane, N2360R, was substantially damaged when it was involved in an accident near Cottrellville Township, Michigan. 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 he refueled (topped off) both fuel tanks before flying from Marine City Airport (76G), Marine City, Michigan, to Oakland County International Airport (PTK), Waterford Township, Michigan, to deliver some paperwork to his son. The pilot estimated that the airplane had used 4 to 6 gallons of fuel during the flight from 76G to PTK and that about 45 gallons of fuel remained for the return flight to 76G. He selected the right fuel tank shortly before takeoff from runway 27 at PTK. After takeoff, the pilot flew a direct route to 76G, which took about 20 to 25 minutes. As the airplane approached 76G, the pilot entered the traffic pattern for a full-stop landing on runway 4. He decided to go around when the airplane got too low during the base leg. The pilot attempted to increase engine power by moving the throttle forward, but the throttle control remained stuck near an idle power setting regardless of how hard he pushed the throttle. The engine continued to run smoothly, but it did not produce enough power to maintain altitude. The pilot reported that the flaps were extended for landing, the fuel mixture control lever was set to full rich, the electric fuel pump was off, and the carburetor heat control was off. He did not recall the final moments of the flight. The airplane crashed into a field about 0.3 miles southeast of runway 4 at 76G. WRECKAGE AND IMPACT INFORMATIONThe main wreckage was in a field consisting of tall grass and trees. The wreckage debris path was oriented on a west bearing. The nose landing gear separated from the fuselage about 80 ft east of the main wreckage. Both wings separated from the fuselage during impact. All airframe structural components and flight control surfaces were located along the wreckage debris path or with the main wreckage. The ignition switch was on both, the carburetor heat control was off, the flap control was retracted, and the electric fuel boost pump was off. The throttle control cable was continuous from the cockpit lever to the carburetor throttle arm. The throttle control was found halfway between the idle stop and maximum power, and the friction lock for the engine controls was found fully engaged. The throttle lever could initially not be moved through its full travel due to impact-related damage; the throttle control and its associated control cable moved freely after the engine exhaust was removed, the intake airbox was bent into a normal position, and the throttle control cable was disconnected from the carburetor throttle arm. A fuel sample drained from the right tank was blue in color with no evidence of contamination. The fuel selector valve was in the right tank position. A functional test of the fuel selector valve did not reveal any anomalies. Fuel was present in the fuel selector valve, fuel lines in the engine compartment, and the carburetor. The engine remained attached to the fuselage mounts, which exhibited impact-related damage. Internal engine and valve train continuity were confirmed as the crankshaft was rotated through the propeller. Compression and suction were noted on all four cylinders in conjunction with crankshaft rotation. The upper spark plugs were removed and exhibited features consistent with normal engine operation. The lower spark plug for the No. 4 cylinder exhibited black soot or oil deposits. The remaining lower spark plugs exhibited features consistent with normal engine operation. Both magnetos remained firmly attached to the crankcase. Both magnetos functioned normally when removed from the engine and bench tested. The carburetor discharged fuel when the throttle arm was cycled. The carburetor heat control cable separated from the heat valve and exhibited impact-related damage. The engine crankshaft flange was bent during impact, which prevented a comprehensive test run during the investigation. The engine examination did not reveal any preimpact anomalies that would have precluded normal operation during the flight. ADDITIONAL INFORMATIONAccording to a carburetor icing probability chart contained in Federal Aviation Administration Special Airworthiness Information Bulletin CE-09-35, Carburetor Icing Prevention, the recorded temperature and dew point at the time of the accident were in the range of susceptibility for the formation of serious carburetor icing at glide (descent) engine power. According to the bulletin, a pilot should use carburetor heat when operating the engine at low power settings or while in weather conditions in which carburetor icing is probable.