Facts (from reality) that we all know:
All places that simultaneously have solar noon lay on the common meridian. It means they have same longitude.
Distances along any single meridian don't depend on Earth model. In reality they are equal to each other between Flat and Globe.
Latitudes also don't depend on shape of the Earth. They are accurate under any model. It means you can perform simple conversion between degrees of latitude and distances along meridians.
Sun relative to Earth travles 15 degrees per hour. It is 1 degree in 4 minutes.
Sun projection (subsolar point) is always between Tropic of Cancer and Tropic of Capricorn.
For Equinox Sun is above Equator, for Summer solstice above Tropic of Cancer, for Winter solstice above Tropic of Capricorn.
Subsolar point has angular ground speed same as angular speed of Sun, which is 15 degrees per hour.
Part of the map, between Tropic of Cancer and Tropic of Capricorn, can be made using known longitudes of places, known distances along meridians, and measured distances along parallels.
Linear ground speed of subsolar point can be derived from angular speed and measured distances between meridians at current parallels.
For example, if in Africa we measure ground speed between two known places, we can be sure on the sea to the east and west that speed was and will be the same during the same day.
Using known degrees from Africa to Australia we can measure distances over Indian Ocean, and using known degrees from Africa to South America we can measure distances over Atlantic Ocean.
When we have accurate segment between two Tropics, we can interpolate places between that and North pole, using known distances and longitudes.
Any suggestions?
Any corrections?
Thanks in advance.