This is one of Robert H. Goddard's P-series rockets, probably the one he used for a test in October 1941 during which the rocket jammed in the launch tower and failed to lift. Goddard's P-series was so designated because they contained his propellant pumps. The series was also his largest and last liquid-fuel flight rockets and were tested at Roswell, New Mexico, during 1938-1941.
However, only two P-series rockets achieved flight. But the tests were discontinued because Goddard moved in 1942 to Annapolis, Maryland to undertake wartime work for the Navy on non-flight rocket motors. This rocket was donated to the Smithsonian by the Daniel and Florence Guggenheim Foundation for the Promotion of Aeronautics in 1985.
Gift of Daniel and Florence Guggenheim Foundation