I'm trying to relate the VOR radial "rule of 60" to magnetic compass headings.
I *think* the thing about the operation of the compass, is though the Earth has a magnetic "north pole", the magnetic field is obviously not just concentrated on that spot. (Like a theoretical VERY long range VOR would be).
There seems to be some confusion about the "rule of sixty". That rule states that for each 1 degree of error in your heading, you will accumulate (about) 1 mile of error in your position for each 60 miles flown. This is entirely a geometric problem totally unrelated to magnetic vs true north. Further, because a nautical mile is about 6000 feet, the 60:1 rule also applies. Thus, each one degree error in heading will result in 100 feet error in position for each NM flown. Keep in mind these are only approximations and only valid for
small angles.
This also works great for flight path vertical angles. Each degree of climb (or descent) gradient will result in 100 feet increase (or decrease) in altitude for each NM flown.
Or did I misunderstand the question?
BTW, there is an error in the following statement: "
Since the field is all over the world, I think the north attraction just gets stronger right at the pole." Actually, no. The magnetic poles generate lines of magnetic field. A magnetic compass aligns with the magnetic lines and point to the magnetic poles. But near the poles, the magnetic lines are vertical or near vertical, so a magnetic compass is very erratic near the poles. At the magnetic poles this is like the "cone of confusion" right above a VOR beacon.