In a previous post, here, I explained how a ballistic missile like Minuteman III knows when to shut off its thrust. How does it know it has enough speed to get the warhead to the target? Asked and answered in that post: We use Pendulous Integrating Gyroscopes, or PIGs.
Then I said: speed is one thing. But direction is also critical. How does the on-board computer know the speed is in the right direction?
That question has two parts. Which way do you aim? How do you know the missile is pointed that way?
The chart above illustrates the pretty simple physics involved in determining the range. Armies have been throwing stuff at their enemies for millennia. With intercontinental ranges there are a few more complicating factors such as varying atmospheric air drag, changing gravitational fields, altitude and stage 3 cut-off and many more. But all of these are small nudges compared to the correct angle at engine cut off.
(To be honest, it is how we deal with the nudges that makes the accuracy so good that I can't talk about it here.)
That's range. There is the azimuth to determine as well. ICBMs fire pretty generally northward to hit their targets. They aim a bit left or right to aim at specific targets. Again, there are nudges to be considered such as Earth rotation.
By the way, while we are talking about gyroscopes and azimuth, one pretty important piece of hardware in the missile is a gyroscope that senses Earth rotation. It does this primarily to make sure the missile knows where North is, so that azimuth calculations can be made from that known direction.
But, to the second part of the question. How does the missile, once in flight, know where it is headed?
Direction is pretty important when hitting a target a half a world away. But if the missile is going to fly with little nudges from the the flight controls to keep the pointy end up and keep it aiming at the target, the computer needs to know what direction it is pointed at any instant in time.
|As the missile pitches, the platform remains in its original orientation|
One solution, the one that Minuteman III uses, is to keep a platform inside the missile "stable", i.e. unmoving, as the missile pitches and yaws and rolls. Mounted to this stable platform are the speed sensing instruments (pendulous integrating gyroscopic accelerometers or PIGAs). The stable platform is always in the same orientation with respect to the Earth no matter what the missile does. The missile knows the orientation of the platform compared to the rest of the missile. Therefore the on-board computer, obsessed with where the missile is and where the Earth is, knows not only its speed, but which direction that speed was measured in relative to the missile and the Earth.
Ah, but how does a platform remain stable? Gyroscopes, of course!
|For more on stable platforms, and their opposite, strap down systems, from Professor Andrisani at Purdue, click here.|
Gyroscopes are placed on the stable platform. When they sense motion, the platform is tweaked back to level.
With all the control circuitry and computer programming it can get quite complicated. But that's what you get when PIGs fly.