On January 3, 2012, approximately 1730 central standard time, a Piper PA-28-160 airplane, N5768W, was substantially damaged during a forced landing near San Angelo, Texas. Visual meteorological conditions prevailed at the time of the accident. The instructional flight was being conducted under the provisions of 14 Code of Federal Regulations Part 91 without a flight plan. The certified flight instructor and student pilot were not injured. The local flight departed the San Angelo Regional Airport (KSJT), San Angelo, Texas, approximately 1705. The flight instructor reported that they were performing touch-and-go landings in the traffic pattern. While on the downwind leg, the flight instructor asked the student to switch fuel tanks in order to balance the remaining fuel. Shortly thereafter, the student added power to adjust his approach path to the runway and the engine did not respond. The student switched back to the previous tank; however, engine power was not restored. During the forced landing, the right wing struck a tree and separated from the airplane. The flight instructor stated that during the previous flight, the student had mentioned that the fuel selector valve did not have a noticeable detent position and asked if it was normal for the selector to rotate 360 degrees. The flight instructor was not familiar with the accident airplane and had not flown it prior to the day of the accident. He stated that he was not familiar with the various nuances of the accident airplane. An on scene examination of the engine, conducted by the Federal Aviation Administration (FAA), revealed no anomalies. On February 29, 2012, the fuel selector valve and fuel assembly were examined by investigators with the National Transportation Safety Board and Piper Aircraft. The examination revealed that the fuel selector valve was firm to rotate with notable detents at the prescribed positions. The fuel lines, filters, and fuel pump were free of blockage. The reason for the loss of engine power was not determined. The temperature and dew point at the time of the accident were 15 degrees and minus 7 degrees Celsius respectively. A review of the carburetor icing probability chart, located in the FAA's Special Airworthiness Information Bulletin CE-09-35, dated 6/30/2009, revealed that the airplane was not operating in an area favorable for the formation of carburetor icing.