Bad model. Good solution.

Sometimes a false model is more useful than a true model - i.e. a true model might be too complex to provide practical solutions in a timely manner.  Like Jack Nicholson says in "A Few Good Men" - "You can't handle the truth!".

Case in point:  In general, a great circle track changes course.  This has nothing to do with variation (the difference between true north and magnetic north), or deviation (the difference between your actual compass and a perfect magnetic compass).  Instead, the course change along a great circle track is due to the coordinate system of the Earth.

There are special cases where the great circle course is constant - If your course is true north or true south, you are flying along a longitude line and your course doesn't change until you cross over the pole, when it flips 180 degrees. And then there is the case when you are at the Equator - you can go all the way around the Earth on a course of east or west while staying on a great circle.

In the general case, however, the great circle course is variable.  The rate of course change is given by a fairly complex equation involving latitude and current course.  The combination of high latitude (north or south), and easterly or westerly heading, causes the great circle track to change - the course change always being towards the Equator, and sometimes quite rapid.

So why is this of any practical concern to anyone?  Modern aircraft navigation systems calculate and fly great circle tracks. (The shortest distance between two points on a sphere.)  When pre-flighting the Flight Management Computer in preparation for an oceanic flight, the pilot must compare the programmed FMC courses for each leg to the courses printed on his flight plan.

Here's the rub - they are not the same!  In the FMC the course displayed between two way-points is the initial outbound - the course that the aircraft will turn to immediately after passing ("eating up") a way-point.  On the flight plan the course is the average course for the entire great circle leg.

There can be a significant difference between these two courses.  Imagine a great circle route between Chicago and Hong Kong.  The great circle track goes very close to the North Pole; meaning it starts out going north and ends up going south.  What's the average between north and south? Certainly something quite different from the FMC's displayed northerly course out of Chicago.

Because of the variability of this comparison, the only guidance given the pilot is to check for "reasonability".

Here is an example of a totally false physical model which, while having nothing to do with reality, gives the pilot a tool for rapidly determining the reasonability of the above comparison which he is responsible for.

Imagine that the poles of the Earth push on the nose of the aircraft.  The closer you are to a pole, the harder it pushes.  If you are at the Equator, both poles are pushing with the same force and you can go east or west without these forces changing your course.  If you are going true north or true south, you are heading straight towards a pole - it doesn't matter how close you are to the pole, there is no moment arm, so even an extreme force imbalance doesn't change your course.  If, however, you are close to a pole and going east or west, the pole that you are closest to will push the nose towards the Equator.

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