My first holiday in quite some time has just begun. I don’t have any concrete plans for the fortnight, however I do plan to do as much work on CIC as I can while still relaxing. I haven’t had a lot of time recently to work on CIC, and I’ve spent a lot of my time trying to work out an equation for counter-missile interception. I thought I’d post the problem and see if anyone can come up with a solution. As far as I can see, this is a non-trivial problem, and requires quite a complex equation to calculate. My closest attempt so far has me factoring a polynomial equation, which I’m currently reading up on as I haven’t done it since high-school. The problem is described below.

I have 2 missiles, A and B.
Missile A has a current velocity (Va) and direction (Da), a known constant acceleration (Aa) and a known position (Pa).
Missile B has a current velocity (Vb), a known maximum constant acceleration (Bb) and known position (Pb).

What needs to be calculated is the direction to fire B (Db) so that it can accelerate at it’s maximum acceleration and intercept missile A. It can be assume that the current velocity of B is in the direction that will be calculated, to simplify the problem. This equation must be calculated in 3D with the resultant direction having 3 components, x, y and z. I believe there may be multiple results within a solution, it would be best to have all of these results, however the result that is the shortest distance from B would usually be used.

If anyone has any questions please ask, otherwise please post your answer or email me at [email protected].