The pilot stated that the take-off was normal until he was about 50 feet in the air, at which time the engine lost power after he closed the carburetor heat. The airplane’s landing gear then contacted top of a security fence beyond the end of the runway and bounced into a plowed field in a nose-down attitude. The pilot further stated that before he exited the airplane, he checked the fuel valve and found that it was not locked in the full forward position but was midway between the ON and OFF positions. The pilot said that in retrospect, he was not positive that he had placed the fuel valve in the full forward position during his pre-flight inspection, and that this was the reason for the engine losing power on take-off.