On April 29, 2019, about 1305 eastern daylight time, a Piper PA-28-161, N3031W, was substantially damaged when it was involved in an accident near Melbourne, Florida. The student pilot and flight instructor were not injured. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 instructional flight. The flight instructor stated that he and the student pilot departed to a nearby practice area to train emergency procedures. At 2,500 ft, they performed a simulated loss of engine power. The student pilot established best glide speed, identified a landing spot, and completed the checklist. At 500 ft, when the student added power to recover from the maneuver, the engine did not respond. The instructor took control of the airplane and verified the correct fuel selector position. The airplane continued to descend, and he landed on a brush-covered island surrounded by swamp. A Federal Aviation Administration (FAA) inspector traveled to the site and examined the airplane. The right wing was partially separated from the fuselage and there was leading edge damage to the right wing. The inspector noted fuel in both wing tanks. The flight instructor later reported to the FAA that he had overlooked the carburetor heat and did not apply it during the simulated loss of engine power or attempted recovery. Review of the icing probability chart contained within Federal Aviation Administration Special Airworthiness Information Bulletin CE-09-35 revealed that the atmospheric conditions at the time of the accident were "conducive to serious icing at glide [idle] power."