THE PILOT WAS MANEUVERING HIS AIRPLANE IN RIGHT TURNS FOR APPROXIMATELY 30 MINUTES WHILE HIS PASSENGER PHOTOGRAPHED AN OIL DRILLING PLATFORM IN THE GULF OF MEXICO. THE PILOT BECAME NAUSEOUS AND ELECTED TO LAND HIS AIRPLANE ON A NEARBY ISLAND. THE LANDING WAS MADE TO THE SAND ALONG THE SHORELINE. THE PILOT TOUCHED DOWN ON THE DRY SECTION AND DURING THE LANDING ROLL THE AIRPLANE NOSED OVER. THE PILOT DID NOT REPORT ANY MECHANICAL PROBLEM WITH THE AIRPLANE.