This appears to be the rocket motor used by U.S. rocket pioneer Robert H. Goddard for his first flight at Roswell, New Mexico, on 30 December 1930. This was Goddard's fifth flight. He had moved to Roswell earlier in 1930. An earlier flight attempt was made with his rocket on 22 December but failed when the rocket came off the launcher rails.
Among the changes made for the next attempt was painting part of the tanks and vanes a bright red instead of black as before, for better tracking. There are red paint spots on part of the motor shown here, perhaps proof that this was the same motor used on the flight of 30 December. On that flight, the rocket reached 2,000 feet. This motor was donated to the Smithsonian in 1959 by Esther C. Goddard.
This object is on display in Rockets & Missiles at the Steven F. Udvar-Hazy Center in Chantilly, VA.