On October 3, 2018, about 1730 central daylight time, a Piper PA-24-180, N8371P, was substantially damaged during a forced landing after takeoff from Smithville Municipal Airport (0A3), Smithville, Tennessee. The private pilot was seriously injured. The airplane was privately owned and operated under the provisions of Title 14 Code of Federal Regulations Part 91 as a personal flight. Visual meteorological conditions prevailed and no flight plan was filed for the local flight. According to the pilot, there was no taxiway at 0A3 so he was delayed about 10 minutes by traffic before he could back-taxi to the run-up area prior to takeoff from runway 24. The pilot completed the engine run-up and takeoff roll with no anomalies noted. After liftoff, the pilot retracted the landing gear and during the initial climb, about 300 feet above the runway, the engine stopped producing power, but the propeller continued to "windmill." The pilot stated that there was no time to perform remedial actions to restore power, so he lowered the landing gear and touched down on the remaining runway. The airplane overran the departure end of the runway, traveled down an embankment, crossed a road, and came to rest upright in low brush. The pilot held a private pilot certificate with ratings for airplane single-engine land and instrument airplane. His most recent Federal Aviation Administration (FAA) third-class medical certificate was issued April 25, 2012, and his most recent FAA Basic Medical was issued on May 1, 2017. A review of the pilot's logbook revealed 834 total hours of flight experience, of which 431 hours were in the accident airplane make and model. The four-seat, single-engine, low-wing, retractable landing gear airplane was manufactured in 1964 and powered by a Lycoming O-360 engine, rated to produce 180 horsepower. Its most recent annual inspection was completed on October 1, 2018, at 2,840 aircraft hours. The engine had also accrued 2,840 total hours of operation; of which, 1,200 hours were since its last major overhaul. The accident flight was the first flight following the annual inspection. The FAA inspector who responded to the accident location reported the airplane came to rest in an upright position, 384 ft beyond the departure end of runway 24. The airplane remained intact, but the aft portion of the fuselage was fractured and twisted, and the left aileron was bent. Examination of the engine revealed that all three propeller blades exhibited twisting, tip curl and chordwise scratching. The inspector noted fuel in both wing tanks and the fuel appeared absent of water and debris. The engine and its accessories were examined under the supervision of an FAA inspector. All of the spark plugs were removed and visually examined with no anomalies noted. Rotation of the engine's crankshaft produced compression on all four cylinders, and normal valvetrain movement was observed when the crankshaft was rotated. Examination of the engine's cylinders with a lighted borescope revealed no damage to the cylinders or pistons. Fuel was present throughout the fuel system ,carburetor, and fuel filters, and it the fuel was absent of water and debris. Fuel was also present in the carburetor and no water and no debris was found within the carburetor float bowl. The engine-driven fuel pump was actuated by hand and functioned normally. The engine oil, engine oil filter, and engine oil pickup screen were all absent of debris. Both magenetos were removed and when their input drives were rotated with a drill, produced spark at all towers. At 1735, the weather reported at Upper Cumberland Regional Airport (SRB), about 14 miles east of the accident site, included wind from 200° at 4 knots, visibility of 5 miles with haze, few clouds at 4,400 ft, temperature 28° C, dew point 21° C, and an altimeter setting of 30.06 inches of mercury. The calculated relative humidity at this temperature and dewpoint was 65%. According to an FAA Icing Probability Chart, the atmospheric conditions at the time of the accident were "conducive to serious icing at glide [idle] power." According to FAA Advisory Circular 20-113, "To prevent accident due to induction system icing, the pilot should regularly use [carburetor] heat under conditions known to be conducive to atmospheric icing and be alert at all times for indications of icing in the fuel system." The circular recommend that when operating in conditions where the relative humidity is greater than 50%, "…apply carburetor heat briefly immediately before takeoff, particularly with float type carburetors, to remove any ice which may have been accumulated during taxi and runup." It also stated, "Remain alert for indications of induction system icing during takeoff and climb-out, especially when the relative humidity is above 50 percent, or when visible moisture is present in the atmosphere."