Careful - don't get Bishop Tom started on the analemma - last time he tried explaining it he said it was evidence that the sun traces a figure-8 in the sky because it switches directions and goes backwards over the south pole in winter.
https://forum.tfes.org/index.php?topic=6072.msg114202#msg114202And I wouldn't hold your breath for any mathematically coherent model.
Once again, the tools needed to express the Flat argument for the movements of the sun in terms used by most debaters are these:
The height of the Sun
The size of the Sun
The luminosity of the Sun
The composition of the Sun
The orbital characteristics of the Sun
- width of ellipse
- speed in various seasons
The refractive index of the atmosphere
The speed of light
The rate at which light loses energy in the atmosphere (since it fades rapidly with distance)
The dimensions of the light cone (in the spotlight sun model)
All in an easily workable list. Should be no problem at all for a coherent cosmological model used to explain the realities witnessed every day by billions of people!
And if the answer is "I don't know" then so be it! We understand.
But it does mean you'll have to find some alternative explanation quick smart if you want to make your theory worth anything.
I suggest going from top to bottom, being
very careful how each is answered. The wrong numbers could mean something fascinatingly disastrous for your model.
Have fun.