Nantucket is getting a new hospital to replace the old and cramped Cottage Hospital. Dr. Margot Hartmann, Cottage’s chief executive, said the facility is 57 years old, energy inefficient, and lacks adequate parking. It has just one operating room and the emergency department is too small, especially when summer residents descend on the island. She said the 19-bed wood-shingled hospital was built at a time when ‘‘medicine was delivered in a very different way.’’ She told the Cape Cod Times that a new facility on a 20-acre campus in the middle of the island is expected to cost about $75 million. There is no timetable for the new facility to open.