The Bloodhound Homing Algorithm

Back in May Peter Wolstenholme kindly reminded the BMPG Group about the Bloodhound homing algorithm.

The method of navigating to the correct interception point is called “proportional navigation” and relies on measurement of sight line spin (sls). That is, if the missile’s dish is pointing in a fixed direction in space, and continues to do that, then the missile will intercept the target. Any need to precess the dish gyros is caused by an error in the navigation path, so the missile needs to change direction so as to servo the sls to zero. The course change is set to a few times the sls.  An interesting control problem, as the computed Miss distance is equal to the sight line spin divided by V t^2.  V is the missile velocity and t^2 is the square of the time to go. So the gain of the servo increases rapidly as one approaches the target. Of course, at interception, if not a direct hit, the s.l.s. becomes larger than the dish servo can track, but by then one is within fuze range.

Peter added, “I spent many hours running end-course simulations for Bloodhound 1 to fix the optimal parameters, around 1957. End-course meant the last 5 seconds. I was very impressed by the agility I observed of twist-and-steer, conferred by the low rotational moment of inertia as compared with  missiles which needed to pitch from rear-mounted control fins”.

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