A MIDAIR COLLISION OCCURRED BETWEEN A PIPER PA-28, N473FT, & AN AMERICAN AA-1A, N9486L, AS THE 2 ACFT WERE ON FINAL APCH TO LAND ON RWY 13 AT AN UNCTLD ARPT. BOTH ACFT THEN CRASHED TO THE GROUND. THE PLT OF THE AA-1A SURVIVED THE ACDNT, BUT DUE TO INJURIES, HE COULD NOT RECALL DETAILS OF THE OCCURRENCE. THE AA-1A WAS INITIALLY IN LEFT TRAFFIC BEHIND THE PA-28. A CFI (IN TRAFFIC AHEAD OF BOTH ACFT) HEARD THE PA-28 PLT RPRT ON A 1-3/4 MI FINAL APCH. HE THEN HEARD THE AA-1A PLT RPRT ON BASE LEG. THEREAFTER, THE CFI HEARD THE AA-1A PLT RPRT TURNING ON A SHORT FINAL APCH & BECAME AWARE OF A POTENTIAL TRAFFIC CONFLICT. THE CFI THEN SAW THE AA-1A IN A LEFT TURN ON THE RGT SIDE OF THE FINAL APCH PATH, AS IF THE PLT HAD OVERSHOT THE TURN TO FINAL. ALSO, HE SAW THE PA-28 ON FINAL APCH. SUBSEQUENTLY, THE 2 ACFT CONVERGED & COLLIDED. DURING IMPACT, THE PROP & NOSEWHEEL OF THE AA-1A HIT THE EMPENNAGE OF THE PA-28.