This is a stand for a 1:24 scale model of the Nike-Hercules, a U.S. Army ground-launched anti-aircraft missile. It had a solid-fuel motor, a maximum speed of Mach 3.65, a range of over 87 miles, a ceiling of 150,000 feet, and either a conventional or nuclear warhead. The missile was deployed with the U.S. Army from 1958-1974. The U.S. Army Ballistic Missile Agency built the model and stand and donated them to NASM in 1961.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.