...whiz:
To sum it up:
1. Put the machine into 'align' mode
2. Sitting motionless on the ramp, the inertial system senses angular motion (and it knows that this motion can only be in a east-west direction). This happens at a certain rate, that's because the earth turns at around 15.04 degress per hour in space (the result of the 24 hour rotation and the annual rotation around the sun). At the equator, you have travel 21600 nm divided by 24 = 900 nm in space every hour by sitting on the ramp. If you go north and follow e.g. the 75 degree latitude around the earth and measure the mileage (or do the math), it falls far short of the 21600 nm at the equator. Therefore the rotational speed is much less until it reduces to practically zero at the poles (neglecting the rotation around the sun). While it may take as little as 2 - 3 minutes to complete the alignment at the equator, it takes an easy ten minutes around the 70 degree north latitude. Further north and the system might not be able to align correctly before it starts to drift and might be unable to enter NAV mode because it doesn't come up with useful numbers to satisfy its criteria for accuracy.
It just gets more difficult to do exact calculations since the starting values are much smaller further towards the poles.
3. Angular rate is determined, the airplane knows where it is. It moves from West to East with the Earth's rotation. Since it knows where East and West are , North has to be in a 90 degree angle to that, that's all there is to finding true north. Knowing true north and where on earth it sits, the inertial system now goes into its data base, pulls up the current world geomagnetic model, checks the stored magnetic variation info for where it is and applies this and, voila, there it is on your nav display: magnetic heading.
Now we can navigate around the globe, while our computer has to constantly compensate for the Earth's rotation and also for the Earth's spherical shape (they call this 'Schuler tuning') since we fly on curved paths in space following the curvature of the surface.