On a flat map, point A might be to point B at, say, heading 060. [...] Is there a formula to determine the optimum heading at the outset (even though it may not 'seem' correct), thereby, reaching the desired point B on the globe at the end of the cruise?
As written in the other answer, this is not how large distanced are flown, as aircrafts follow great circles for a minimal distance. But if you want to fly a constant heading from your outset, this can be done:
Imagine, you have one of these illuminated globes and put it into a paper cylinder, such that the cylinder touches the equator everywhere. All contours of the earth are projected against the cylinder, and you can retrace them with a pen. Unfold the cylinder, and you get a mercator projection:
Mathematically, this can be calculated by this conversion of earth coordinates:
and drawing this into a coordinate system where unit length is equal for x and y. (the labels on the y-axis are not y-coordinates, they denote the latitude.)
As you see, the face of the earth is vertically warped, and the size of continents is not preserved. For example, Greenland seems to be of the same size as Africa, though it's actually only 7%. Also, distances are not preserved.
BUT: Angles are preserved!
Draw a straight line from your location to any destination, and read the angle between this line and the vertical lines. Follow this heading, and you will reach your destination. Mathematically, you can determine the course by the following formula, but keep in mind that the arctan function does not always give you the correct formula. You need to know if you have to fly NE, SE, SW or NW and apply this do the value. (Can be done automatically with more math, too.)
As said above, distances are not preserved. This straight lines are by far not the shortest routes and your passengers will complain about the long flight, as well as your airline about all the burned fuel...
To answer the question in the comment:
In a standard mercator projection as above, only pure north-south tracks as well as tracks on the equator lie on great circles and so are the shortest route.
Of course, you can put that paper cylinder around your globe in an other orientation, for example touching the 0-meridian instead of the equator. This way, you get the transversal mercator projection, which looks like this:
(by Lars H. Rohwedder, http://commons.wikimedia.org/wiki/File:Transversal_Mercator_0.jpg)
In this map, straight horizontal lines will lie on great circles, but the heading (angle to meridians) will change during flight.
You can also use other arbitrary orientations for the cylinder, like this 45° projection, looking even more weired.
However, if you are searching for a constant heading and don't care about distance, the standard mercator projection gives the answer.