[El Gato]

Basically, you just set yourself on a heading and go in a straight line in that direction and you arrive at your destination

Not if you measure the heading from a map. In fact a great circle route, which is the shortest distance between two points on a shere, does not maintain a constant heading, relative to true north. Except in the special case of going due north or south.

Get a large shere, a basketball or a large beach ball, and experiment, remembering that north is the direction towards the north pole. Maps show north "up" at both San Diego and Portland Maine, but in 3 dimensions on the surface of the earth, norht is not the same direction at both locations. In fact if you are at the equator and want to go to anther point on the equator on the opposite side of a sphere, you'll find that any of the cardinal directions, (NEWS) will get you there, and at the same distance. This is not true for the earth, because it's not a perfect sphere. GPS uses a system which assumes its an ellipsoid of revolution, like a slighty squashed shere, and that's pretty close, but not exact either, as the earth is actually a bit pear shaped.

[templar]

So, if I under stand you, you're saying that if I set out for Houston from Denver in my automobile, since Houston is not due south of me, I can never actually arrive in Houston unless I figure the curvature of the earth into my directions? Last time I made that trip I just set out and followed the roads just like if they were on a flat world, so how come I managed to get to Houston instead of some other city without using either a GPS or some other means of correcting for the earths curvature, and why do the roads on the roadmap go where they are shown to go instead of somewhere else?

I would thing that travelling with you would be an interesting experience (even if a bit slow) : )