You can ignore the simulation in Excel part (unless you want to do it). Please s

Question

You can ignore the simulation in Excel part (unless you want to do it). Please show all work, thanks!

The problem: An aircraft is 40 Miles North and 10 miles West of our launcher. It is flying due east at 600 mph. Our missile maintains a speed of 1200 mph. We want it to ''hit'' the aircraft. We'd like to do so as rapidly as possible, and with the least amount of turning (G stress on the missile) possible. To do that, we need an algorithm that will adjust its direction of flight continuously as the missile flies to the target. The problem is to design an interesting algorithm. Then, use simulation (I've used Excel) to model the intercept problem and see how well it does. Then, test the same algorithm against a ''maneuvering'' aircraft: one that flies a sinusoidal instead of a straight course.

Explanation / Answer

1) As shown in fig, Let us consider our missile is at point O and aircraft is at point P.

OP = 40 miles      .along east OE = 10 miles

2) Let the aircraft is flying horizontally with speed u'. Let missile fired with velocity u and making an angle @ with horizontal to hit the aircraft.

3) Resolving u into two components. u cos@ along X- direction, u sin@ along Y-direction.

4) If t is the time taken by the missile to hit the aircraft ,then horizontal distance travelled by aircraft in time t with velocity u' is equal to the horizontal distance travelled by the missile in time t with velocity u cos@. ie

u'*t = u *cos@*t

cos@ = u' / u

@= cos-1 ( u'/ u)             ( this formula can be used to find the direction of missile)

= cos-1 ( 600/ 1200) = 600 with horizontal

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