On June 29, 1996, about 0955 eastern daylight time, a Piper PA-28-161, N8119H, was substantially damaged during landing at Sikorsky Memorial Airport, Bridgeport, Connecticut. The solo student pilot was not injured. The local flight was operated as a instructional flight under 14 CFR Part 91. Visual meteorological conditions prevailed, and no flight plan had been filed. The student had done 4 touch and go landings with an instructor aboard. The instructor deplaned, and the student conducted solo flight, doing touch-and-go landings. He was on his second touch-and-go landing when the accident occurred. The student reported: "After the first touch and go landing, I departed for left closed traffic for my second touch-and-go. While reporting mid-field, downwind as instructed during take-off clearance, I was informed that I was number 2 in sequence to follow traffic on right base for runway 11, and to extend my downwind leg, which I proceeded to do. Final glide path was established, aircraft was trimmed, everything looked good. Final approach was made with the engine at idle. Airspeed was bleeding off, and over the numbers was reading about 65 knots, a little high, but did not seem to be a problem. Everything looked good for the touch and go on the touchdown zone. "When I touched down the aircraft ballooned. I reflared and the plane ballooned again. I felt the plane was down; however, it ballooned again, and on the third attempt to land, the aircraft touched down on the nose wheel. The nose wheel tire blew, causing the propeller to strike the runway. At no time did I feel that the plane was out of control. I was able to maintain directional control and was able to clear the runway at (the taxiway). I brought the aircraft to a stop, secured it using shut-down check-list procedures." The pilot reported no mechanical malfunction. He stated the accident could have been prevented by executing a go-around or "added power to balked landing and reflared."