These are steamlined, retractable jet deflector vanes mounted on a tail section of a rocket of the American rocket pioneer Dr. Robert H. Goddard. Designed to achieve better stability in flight, the moveable vanes worked by deflecting the rocket's exhaust gases away from the axis of the rocket.
The rockets using the vane system, known as the L-series of rockets, were produced and tested from May 1936 to August 1938 at Roswell, New Mexico. Goddard found that the vanes provided "much improved stabilization." This object was found in the Smithsonian collections.