On January 25, 2018, about 1425 eastern standard time, a Piper PA-32R-300, N47863, was substantially damaged during collision with terrain shortly after takeoff from Florida Keys Marathon International Airport (MTH), Marathon, Florida. The private pilot and three passengers sustained serious injuries. Visual meteorological conditions prevailed, and no flight plan was filed for the personal flight conducted under the provisions of Title 14 Code of Federal Regulations Part 91.The accident flight was recorded via airport surveillance video. One video revealed the airplane began its takeoff roll from a complete stop, on runway 07 and travelled about 800 ft before the nose wheel lifted from the runway. At liftoff, the nose pitched up steeply and the airplane rolled left immediately, before it disappeared from the frame. A second video captured the takeoff from a much greater distance. The image in the frame was smaller with poorer resolution. The video revealed a steep pitch and left bank at takeoff. The climb stopped immediately after liftoff, and the airplane maintained approximately the same angle of bank as it departed the runway to its left, entered the trees, and disappeared. Several seconds later, a fireball appeared above the trees about the point where the airplane entered them. The pilot reported to a Federal Aviation Administration (FAA) inspector that the airplane "was performing well and didn't have any issues." The airplane reached approximately 60 knots on the takeoff roll when the nose wheel lifted from the runway and the airplane began an immediate left turn. He attempted to arrest the turn with rudder and aileron, but the turn continued until the airplane entered the trees. A rear seat passenger told the inspector that he was seated in the third row of seats with the other passenger, and that the center row of seats was unoccupied. The pilot held a private pilot certificate with ratings for airplane single engine land and instrument airplane. His most recent FAA third-class medical certificate was issued October 20, 2016. He reported 500 total hours of flight experience on that date. According to FAA airworthiness and maintenance records, the airplane was manufactured in 1977. Its most recent annual inspection was completed October 20, 2017, at 6,156.86 total aircraft hours. The maintenance records reflected a "50-hour" inspection completed January 16, 2018. At 1453, the weather reported at MTH included an overcast ceiling at 4,700 ft, 10 miles visibility, and winds from 050° at 18 knots. The temperature was 22° C, the dew point was 16° C, and the altimeter setting was 30.19 inches of mercury. The wreckage was examined at the accident site by an FAA inspector and all major components were accounted for at the scene. The wings and fuselage were substantially damaged by impact and postcrash fire. According to FAA Advisory Circular AC-61-23C, Pilot's Handbook of Aeronautical Knowledge: "The effect of torque increases in direct proportion to engine power, airspeed, and airplane attitude. If the power setting is high, the airspeed slow, and the angle of attack high, the effect of torque is greater. During takeoffs and climbs, when the effect of torque is most pronounced, the pilot must apply sufficient right rudder pressure to counteract the left-turning tendency and maintain a straight takeoff path."