On January 20, 1998, at 1350 eastern standard time, a Piper J-5A, N38645, collided with trees in an orange grove off the departure end of runway 36 at the New Hibiscus Airpark in Vero Beach, Florida. The instructional flight operated under the provisions of Title 14 CFR Part 91 with no flight plan filed. According to the Certified Flight Instructor (CFI) on the flight, visual weather conditions prevailed at the time of the accident. The CFI reported that the airplane had sustained substantial airframe damage. The commercial rated certified flight instructor and his dual student were not injured. The local instructional flight departed Vero Beach, Florida, at 1330. The CFI reported that they had completed a normal training session that included routine air work. They returned to the airport and established a normal approach for a series of touch and go landings. According to the CFI, they used the normal pre-landing check procedures, that included the application of carburetor heat. After a wheel landing was completed, with the carburetor heat in the cold position, the dual student continued the landing roll and applied takeoff power for a climb. According to the CFI, the airplane operated normally until it was 100-150 feet above the ground. At this point, without warning, the engine lost power. The CFI elected to continue the runway heading and selected an orange grove on the departure end of runway 36 for the emergency landing. The airplane collided with trees during the forced landing An examination of the engine assembly disclosed that both magnetos produced ignition sparks for all cylinders. The spark plugs appeared to have been relatively new and showed normal wear. A small quantity of fuel and water was recovered from the carburetor bowl; there was no evidence of water found in the fuel system fuel filters. The CFI did not report a mechanical problem with the engine prior to the sudden lost of power. The CFI reported that the flight departed with 13 gallons of low lead aviation fuel, or a fuel endurance of 2.2 hours. The airplane lost engine power approximately 20 minutes into the planned 1.1 hour flight. A review of recovered weather data from the nearest reporting facility disclosed that, weather conditions were favorable for the formation of carburetor ice at glide and cruise power settings (see attached icing probability curves).