A line of constant bearing will always be a great circle. A straight line on a mercator projection of the earth does not constitute a great circle (in fact only the equator line is a great circle and each vertical line is half of a great circle).
> A line of constant bearing will always be a great circle.
That's not right. Imagine heading due West, and keeping your compass pointing West every step anywhere not on the equator. That traces out a longitude line, not a great circle.
If you follow a constant compass heading you will spiral toward the poles in a helix, not travel in a circle around the globe. To travel along a great circle, your compass bearing must constantly change as you move.
