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There are a certain type of missiles that roll constantly in flight, so-called rolling airframe missiles. Missiles found in the category range from various MANPADs, to the creatively named RIM-116 Rolling Airframe Missile. Wikipedia explains that by rotating in flight, only one pair of control surfaces are needed. How are the control surfaces directed in order to steer the missile, while constantly rotating?

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It's actually simpler, you simply ignore azimuth error totally and only steer in the alpha direction. If the target is above or below then you nose up or down towards it. Otherwise if the target is on your sides, then you don't do anything but wait for the airframe to rotate.

Imagine how a fighter airplane dog fights: the pilot rolls the airplane towards the enemy then pull the nose up. RIM is very similar but different in two ways: 1) rolling is done by auto-rotation and not initiated by any control surfaces, 2) RIM can handle negative alpha and negative G much better than an airplane so it has two chances to maneuver towards the target, per revolution, instead of just one.

In practice the control low is automatically solved the closed-loop nature of the homing system. From the missile's point of view it nothing but a target that periodically moves up and down. Simply put, auto-rotating airframe turns a 1D homing system into a 2D one.

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