Ok, guys I am on this, but work is getting in my way today.
I have lots of things I can choose from. A polar azimuthal projection comes in lots of flavours.
You guys are interested in triangulation and angles and distances.
I will not therefore be opting for the following ...
Lambert projection because it distorts distances.
Sterographic projection because the map will be stretched to equal a round earth between two latitudes and make false readings of the others
Gnomic was very tempting but Berny's southern hemisphere makes this a no go. Otherwise I'd have nailed you with that one. Only works for 80 degrees or so. We need 180 degrees now.
Zenithal equivelent is great for angles and area but will mess up the distances.
Zenithal equal area is great for area and distance but not angles.
Zenithal equidistant is going to be my weapon of choice. Angles and distances work. Area is distorted, as you calculated in another thread, but that is excepted by FE, so that's the one I'm going to use.
Unfortunately work is getting in the way (I have to earn money too, but am working from home today on some flight data). I'll keep plugging away, but maths for a Polar aspect zenithal equidistant map scalings and angle calcs aren't exactly splattered all over the web so I am having to derive much for myself.
PS - Jackel, remember your scale calcs in another thread? If you had used a Zenithal equal-area map like the one linked below, you would have got the exact same numbers, size of earth, continents etc as an RE earth. Check the link below. I'll report back later with some numbers when I make time around work.
http://www.mapthematics.com/ProjectionsList.php?Projection=169#zenithal equal-area
The point I hope of all this, is that maps don't prove either FE or RE. No map is going to be accurate in everyway for both scenarios, hence killing the OPs statement that maps prove earth round. Which they don't. By selecting the right ones, I can make earth any shape I want, and be able to navigate it purely by manipulating the projection I use. Star shaped flat earth anyone?
http://www.mapthematics.com/ProjectionsList.php?Projection=163#regular star
maybe its a tetrahedron?
http://www.mapthematics.com/ProjectionsList.php?Projection=219#Snyder equal-area tetrahedron
Or shaped like a pair of breasts?
http://www.mapthematics.com/ProjectionsList.php?Projection=207#EisenlohrOr rectangular with 4 poles?
http://www.mapthematics.com/ProjectionsList.php?Projection=212#GuyouOr square with 4 poles?
http://www.mapthematics.com/ProjectionsList.php?Projection=218#Peirce quincuncial
Or shaped like a pill?
http://www.mapthematics.com/ProjectionsList.php?Projection=217#Ortelius oval
Or trapezoidal?
http://www.mapthematics.com/ProjectionsList.php?Projection=113#trapezoidalOr shaped like a giant apple?
http://www.mapthematics.com/ProjectionsList.php?Projection=162#quasiazimuthal equal-area apple
Or a beautiful heart?
http://www.mapthematics.com/ProjectionsList.php?Projection=127#heartOr a shield?
http://www.mapthematics.com/ProjectionsList.php?Projection=133#shieldAnd depending on what version of each I pick, I can prove, distances, angles and areas to suit. Flat earth today. Earth shaped like a giant boner in the sky tomorrow.