NavList:

David P., you wrote:
"Can you not produce a form of Mercator chart based on any Great Circle, namely the Oblique Mercator?  Have I not seen this produced for a frequently used route by an organisation, e.g. a pilot’s Enroute Chart for the route between Akrotiri (Cyprus) to Brize Norton (UK)?"

Yes, the Oblique Mercator (OM) is a close cousin of the Transverse Mercator (TM) intended to follow a narrow band of continuous ground track, like a gore on a proper globe. While the TM has a meridian of longitude for its centerline, the OM can use an arbitrary great circle. You can roll right along down the chart. Maybe some of them were distributed on scrolls? :) The common display in ordinary navigation map apps today works much the same way, except, of course, that the "dot" tracks you automatically.

You suggested:
"might such a projection have all of the qualities of the ‘ideal chart’ in this limited application?"

Ideal? Well, how so? What would qualify as an ideal chart? That's a serious question: pick some context, and let's consider what would be an ideal chart for that context. And would an OM chart be better than any number of other locally conformal projections when judged against the "ideal standard"? For the particular problem of following a very specific great circle, there would certainly be production simplifications for printing using the Oblique Mercator. Even if not distributed as a "scroll", the individual panes (pages) of such a chart would fit together seamlessly. When did that advantage become insignificant? Fifty years ago? Twenty-five years ago? I don't think anyone sells (new) Oblique Mercator scrolls today! 

Speaking hypothetically, David, would the RAF, maybe in the 1970s, have provided scroll charts like this, based on Oblique Mercator projection, to its nuclear bomber crews for Sunday sojourns into the Soviet Union?? ...just as a hypothetical.

Frank Reed