No "expert", but as one who designs such things, perhaps I can offer an explanation.
When designing the North Atlantic Tracks there are numerous factors which must be taken into consideration, but we basically start off with Company Preferred Routes. These take the form of Minimum Time Paths between destinations in North America paired with European departure aerodromes. These are drawn up by airlines, using forecast Met data to calculate the route that provides the minimum flying time for each pairing. The MTPs are then forwarded to us in Oceanic ATC where they often appear on our system looking not a whole lot different from great circle routes.
Once we have a sufficient number of MTPs from the operators we can establish where the bulk of the traffic wishes to route and then design a set of tracks to maximise airspace utilisation. Factors we must also take into account include ensuring separation standards are maintained, (obviously), complying with requirements from adjacent ATC centres, avoiding areas of military activity, etc. For numerous reasons the Organised Track Structure typically routes via whole degrees of Latitude at intervals of 10 degrees of Longitude, therefore the final design will conform
approximately to the MTPs.
The routes flown are from waypoint to waypoint, rather than along a fixed track. Therefore due to the curvature of the earth if, for example, an aircraft routes from 55N020W to 55N030W, it will cross 25W at approximately 55º05'N. It would not, in this case, follow the 55th parallel along its' entire length between 20W and 30W. To put it another way, the tracks are a series of great circle routes between consecutive waypoints, typically at intervals of ten degrees of Longitude.
Therefore to say that "the routes are flown in a series of straight lines over the earth's curvature with an alteration of heading now and then" pretty well sums it up. Although when you say "alteration of heading now and then", a great circle route involves a constantly changing heading, as opposed to a rhumb line, but before I get way out
my depth, perhaps I can point you in the direction of:
http://en.wikipedia.org/wiki/Great_circle
http://en.wikipedia.org/wiki/Great-circle_navigation
http://en.wikipedia.org/wiki/Great-circle_distance
http://en.wikipedia.org/wiki/North_Atlantic_Tracks
Hope that clarifies rather than confuses.
