The pilot reported that he was giving a "discovery flight." After takeoff from the 3400 foot runway, the airplane did not continue to climb or gain altitude. According to the pilot the airplane started to sink and he lowered the airplane's nose. The airplane continued to sink and it sustained substantial damage on impact with terrain. The pilot's accident report listed no mechanical malfunctions with the airplane in reference to the accident flight. The calculated local density altitude was 3,099 feet.