continuing to fly straight forward
http://wiki.tfes.org/Circumnavigation
I think this only applies to the unpolar map - not your bipolar thing.
Traveling in a Straight Line
Q. Can't we just circumnavigate the earth by traveling in a straight line without a navigational aid?
A. It is not possible to travel in a perfectly straight line for very long without a navigational aid.
It's not even possible to drive down a long length of highway without turning the steering wheel left or right. Get in a car and see if you can drive down a long stretch of highway without turning the wheel left or right. It's a near impossible thing to do. And when it comes to planes, ships, helicopters, et all., no craft has the ability of traveling in a perfectly straight line without the operator adjusting the craft with regards to visual terrain, compass readings, or what have you.
When one navigates, hands on control is paramount. You wouldn't find a ship captain in New York pointing his vessel in the direction of London, turning on cruise control, and then taking a three week nap in the lower decks. Who knows where he'd end up.
OK - but we're not talking about flying/sailing without control.
We're asking where you go if you:
1) Steer to follow the compass needle.
...AND/OR...
2) Steer to aim towards (or away from) the Pole Star or the Southern Cross.
Please try to concentrate on the question that's actually being asked and not continually try to deflect the difficult bits.
This is a simple enough question Tom.
How can the compass and the pole star/southern cross directions be reconciled on the bipolar map?
Clearly - as both I and CriticalThinker have pointed out, there are SERIOUS anomalies that cannot easily be handwaved away.
Place yourself somewhere "above" the North pole. Which way does the compass needle point? Which way does the pole star appear to be?
Now place yourself on the equator - somewhere off to the right hand side of your map. Same question: Which way does the compass needle point? Which way does the pole star appear to be?
The answer from you has to be either (a) inconsistent or (b) one of your classic "I don't know" answers. Sadly, we DO know. Mariners and early airmen navigated using both the pole star/southern cross *AND* the compass. Those two things had to be consistent over all points on the globe - or long complicated treatises on the subject of these horrible inconsistencies would exist...we'd know about them. They don't exist.
Your maps are screwed up.
In fact, mathematics says (in effect) that no possible FE map can match compass and pole star everywhere on the globe because of the "Hairy Ball Theorem" in topology. (Per Wikipedia: "A consequence of the hairy ball theorem is that any continuous function that maps an even-dimensional sphere into itself has either a fixed point or a point that maps onto its own antipodal point. This can be seen by transforming the function into a tangential vector field as follows.")
It follows that you cannot draw ANY FE map which is devoid of horrible compass/celestial navigation screwups...but it's going to be amusing to watch you try - so have at it!