Did you know…
How was the NF-104A controlled once the rudders stopped working?
Short answer
With a reaction control system, because in the thin air of the high stratosphere the normal control surfaces had little or no effect. It consisted of eight pitch/yaw thrusters, four per axis, and four roll thrusters, located in the nose and at each wingtip. The pilot fired them with a side-stick controller.

Where air no longer holds you up
In the thin air of the high stratosphere, the aircraft's conventional control surfaces had little or no effect. During the parabolic arc the pilot experienced "weightlessness" for about a minute and used a side-stick controller to fire the reaction-control rockets and manage the aircraft's pitch, roll, and yaw.
Eight pitch and yaw thrusters
The reaction control system consisted of eight pitch/yaw thrusters, four for each axis, and four roll thrusters. Those thrusters were located in the nose and at each wingtip. They used the same type of hydrogen peroxide fuel as the main rocket engine, fed from a dedicated 155 lb (70 kg) tank.
The control in the cockpit
The pilot operated those thrusters using a grip mounted on the instrument panel. The cockpit thus had a manual control for operating the reaction-control thrusters. The side-stick controller handled pitch, roll, and yaw.
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