On March 5, 2014, about 1930 Pacific standard time, a Zenair CH2T, N285AM, made an off airport forced landing near Woodland, California. Sierra Academy of Aeronautics was operating the airplane under the provisions of 14 Code of Federal Regulations (CFR) Part 91. The flight instructor and the student pilot were not injured. The airplane sustained substantial damage during the accident sequence. The cross-country instructional flight departed Merced (MER), California, with a planned destination of Yolo County Airport (DWA), Woodland. Visual (VMC) meteorological conditions prevailed, and an instrument flight rules (IFR) flight plan had been filed.Postcrash examination determined that both wing spars had been damaged, and the incident was upgraded to an accident on April 2, 2014. The flight instructor reported that the flight was for IFR training. The flight instructor and student completed one leg culminating in an instrument approach to Willows, California. The flight instructor stated that, at 1-2 minute intervals during 10-15 minutes of the flight, the engine rpm dropped about 100 revolutions per minute (rpm) audibly and visually on the tachometer during the flight. The airplane was in level cruise flight at 4,000 feet mean sea level (msl). The drop never exceeded 100 rpm; application of carburetor heat, a magneto check, and adjustment to the mixture and throttle settings had no effect. After 15 minutes, the anomaly ceased to occur. The student completed an approach, executed the missed approach, and proceeded on course to Woodland. The flight instructor reported that he and the student were en route to GHEER intersection on the RNAV 16 approach to Yolo County Airport. Approximately 20 miles from the airport, the student switched fuel tanks as scheduled (every 30 minutes) in accordance with the Sierra Academy checklist. They were cleared to descend to 3,000 feet to cross the GHEER intersection at or above 3,000 feet. With some distance to cover, the flight instructor suggested a descent rate of 200-300 feet per minute (fpm). The student reduced power, and completed the approach checklist, which the flight instructor verified. About 12 miles from GHEER, the airplane entered IFR conditions (a stratus cloud). As the airplane entered the clouds, the flight instructor suggested a higher descent rate to pass through the clouds more quickly. After 1-2 minutes in the clouds, the student pilot reduced power, and pitched slightly down to increase the descent rate. Nearly at the moment of the reduced power, the engine rpm dropped to 800-1,000 rpm, and the propeller sounded as if it were windmilling. The flight instructor asked the student why he cut the power completely, and the student replied that he had not. The flight instructor stated verbally full power, but the rpm did not change. The flight instructor took control of the airplane, and tried to troubleshoot as he completed a mental emergency checklist (carburetor heat, fuel selector-mixture-fuel pump combinations, fuel gauge, throttle pumping, magneto check, starter check, engine instruments crosscheck). The student confirmed all steps using the emergency checklist. The attempts to restore power were unsuccessful, and the airplane exited the cloud layer between 1,500 to 2,500 feet. The flight instructor declared a Mayday with approach control, as he and the student completed the emergency checklist again with no results. The crew resigned themselves to an off airport forced landing. The flight instructor had the student pilot call out airspeed and altitude while focusing on a landing point. During 300 feet of the descent, the airplane began shaking violently; the airspeed indicated 60 knots, and there was no stall horn. The shaking stopped about 300 feet above ground level (agl). About 200 feet agl, the landing lights illuminated a power line, and the flight instructor determined that the airplane would stall if he attempted to climb over it. The flight instructor had the student grab a flight bag as a cushion, and turned the fuel selector off. At this point, the flight instructor flew under the power line, and landed just beyond it. The airplane touched down smoothly, and the flight instructor held the nose wheel off the ground as long as possible. A line of small tress came into view, and the flight instructor began to let the nose drop. The nose drop coincided with the wings hitting the trees. After the airplane came to rest, the flight instructor and student thought that they turned off the rest of the power sources, and exited toward the rear of the airplane. They observed that the fuel tanks appeared undamaged, there was no smell of fuel, and the airplane seemed secure. After waiting a few minutes, they approached the airplane in order to use the radio to call for assistance. They discovered that the avionics master switch was still on. Unable to establish contact with the radio, the flight instructor used his cell phone to contact air traffic control, and provided them with the site's GPS location. About 1.5 hours later, a helicopter spotted them, and directed emergency crews to them. Examination A Federal Aviation Administration (FAA) inspector oversaw an examination of the wreckage at the operator's facility. The left and right fuel tanks contained 5 and 6 gallons of fuel, respectively. The gascolator contained a few ounces. The fuel selector valve was in the OFF position. The oil level was 5.5 quarts. The throttle, mixture, and carburetor heat cables were intact, and operated properly. One propeller blade was bent; the other was undamaged. The engine could not be run; a cold compression check resulted in all cylinders testing at or above 68/80 psi. Carburetor Ice The conditions encountered in this accident (ambient temperature 61 degrees / dew point 55 degrees Fahrenheit, 82 percent relative humidity), were in the area of serious icing at cruise power. The FAA's Handbook of Aeronautical Knowledge Chapter 6 discussed carburetor icing. It stated that whenever the throttle was closed during flight, the engine cooled rapidly, and vaporization of the fuel was less complete than if the engine was warm. In this condition, the engine was more susceptible to carburetor icing. It stated that application of carburetor heat would cause a further reduction in power, and possibly engine roughness as melted ice went through the engine. It stated that these symptoms could last from 30 seconds to several minutes, depending on the severity of the icing. It recommended opening the throttle periodically for a few seconds to keep the engine warm; otherwise, the carburetor heat may not provide enough heat to prevent icing. Airplane Flight Manual The approach (pre landing) checklist in the airplane's flight manual specified that the carburetor heat should be in the ON position. It did not contain any guidance on periodically adjusting power during extended low throttle operation.