This is a stand for a 1:40 scale model of the Redstone, a U.S. Army surface-to-surface missile based on mobile launchers. Developed in the 1950s by Werner von Braun and his collegues at Redstone Arsenal, it carried a nuclear warhead and had a range of approximately 250 miles. First deployed in the 1950s in Western Europe, it was replaced completely by the Pershing I by the end of 1963. A modified version of the Redstone formed the basis of the Mercury-Redstone, which launched America's first suborbital manned spaceflights in Project Mercury. The 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.