Did you know…
Did the NF-104A carry a rocket engine alongside its jet engine?
Short answer
Yes: besides its turbojet, the NF-104A carried a Rocketdyne AR2-3 mounted at the base of the tail fin. It produced 6,000 lbf (27 kN) of thrust and burned JP-4 with a 90% hydrogen peroxide oxidizer solution. It carried enough oxidizer for about 100 seconds of operation.

Three Starfighters for the test pilot school
Three airframes were converted from existing Lockheed F-104A Starfighters and served at the Aerospace Research Pilots School between 1963 and 1971. The aircraft served as a low-cost astronaut training vehicle for the North American X-15 and the planned Boeing X-20 Dyna-Soar. The main modification to those Starfighters consisted of adding a 6,000-pound-thrust rocket engine at the base of the vertical fin.
The engine and its propellant
It was a Rocketdyne AR2-3 mounted at the base of the tail fin. It burned a mixture of JP-4 aviation fuel and a 90% hydrogen peroxide oxidizer solution. Its thrust was 6,000 lbf (27 kN). The aircraft carried enough oxidizer for about 100 seconds of rocket engine operation.
The zoom climb
The NF-104A was capable of zoom-climbing to altitudes above 120 KFT from a ground-level takeoff, combining the power of the turbojet with that of the rocket. The pilot would ignite the rocket engine and raise the nose to begin the steep climb. After two minutes the Starfighter passed through 80,000 feet, the jet engine was shut down, and the rocket ran out of fuel.
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