On June 10, 2017, about 1050 eastern daylight time, a Cessna 172P, N881AV, was substantially damaged when it was involved in an accident in Tamiami, Florida. The flight instructor and student pilot were not injured. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 instructional flight. The flight was departing from Miami Executive Airport (TMB), Tamiami, Florida. According to the flight instructor, before the accident flight, the airplane was refueled. He observed the student pilot taking fuel samples to test for contaminants; none were present. They also checked the rest of the airplane to complete the preflight inspection. The airplane start was normal with the gauges indicating in the green range. They taxied out from the parking ramp, exited the ramp and then continued taxiing to runway 9L via taxiway "Delta." During the taxi, they did not notice any issues with the airplane. The flight instructor stated that during the engine run-up, they followed the items on the checklist. The flight controls were working correctly, and the engine run-up was completed with no problems noted. He stated that the magnetos had two “good” drops in rpm and that the carburetor heat had a “normal” drop in rpm, both with power on the engine and with the throttle pulled back to idle. The flight instructor asked the student to demonstrate a soft-field takeoff. The student selected 10° of wing flaps, and they received a takeoff clearance and started the takeoff roll. During the takeoff, they had normal engine indications, and airspeed started to climb. The student pilot then kept the airplane in ground effect to build airspeed, as they were simulating takeoff from a grass strip or rough field. At about 80 knots, the student pilot started to climb out from ground effect. He then retracted the wing flaps at 200 ft mean sea level. Up to this point, all indications were normal. At about 350 ft mean sea level, the flight instructor heard a slight decrease in power; he then asked the student pilot if he was guarding the throttle, and he responded that he was. The power then came back. Then, at about 400 ft mean sea level, the engine lost power again. The flight instructor stated that this time it was significant, as it dropped down to 1,900 rpm and was fluctuating. The flight instructor then took the controls of the airplane, after which the power dropped to 1,100 rpm and continued to fluctuate. At this point, there was no available runway remaining and the airplane was losing altitude, so the flight instructor decided to land in a grass field on the airport property. The flight instructor stated that on touchdown, he had very poor braking capability, and even with the use of aerodynamic braking, the airplane felt like it was skidding. The airplane struck a tree with the left wing, then struck the airport fence before coming to a stop. The flight instructor and student pilot then shut off everything, including the fuel, and egressed. Examination of the accident site revealed that the airplane touched down in the grass about 200 ft past the end of runway 9L and then rolled about 1/4 of a mile before impacting the tree and the fence. The grass was wet due to recent heavy rain. Tire marks were visible in the grass at various points from where the airplane touched down to the tree. Examination of the wreckage revealed that the left wing had contacted the tree with the landing and taxi light assembly, which was mounted on the leading edge. Further examination revealed that the right wingtip fairing was broken from impact with the fence, and the upper wing skins were wrinkled from the fuel tank filler caps outward to the wingtips. The spinner and propeller were also damaged from impact with the fence. Engine runs were also performed. Before the engine runs, the cowling was removed, and the engine was completely exposed. The fuel was sampled, and the oil was checked. The fuel and oil showed no signs of contamination and were at appropriate levels. During the first engine run, the engine was started and operated for 8 minutes, 2 minutes of which were at idle, simulating a taxi from the parking ramp to the runway. The engine was then operated for 6 minutes, simulating the run-up and takeoff and was then shut down. During the second engine run, the engine was started and operated for 8 more minutes and then shut down. During both engine runs, the engine ran without hesitation and displayed no evidence of any preimpact mechanical malfunctions or failures that would have prevented normal operation. At 1053, the weather reported at TMB, included a temperature of 30°C and a dew point 26°C. The calculated relative humidity at this temperature and dewpoint was 79%. Review of the carburetor icing probability chart contained within Federal Aviation Administration Special Airworthiness Information Bulletin CE-09-35 revealed the atmospheric conditions at the time of the accident were conducive to the formation if icing at glide [idle] and cruise engine power settings. 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 recommended that when operating in conditions where the relative humidity is greater than 50 percent, "…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."