the care and feeding of analemmas

[Aten Heliochronometers]

Hello group, I am new here, but have been reading the posts for a few days. I have a question for the group, I am designing a new heliochronometer (afterwards to be referred as a "helio" for brevity) and I am striving for a bit more accuracy.  Roughly, I intend to try and cast a point of light on a surface that contains an analemma. Should I create the analemma on a flat or bowl shaped surface?  In other words would it be more accurate to project the analemma onto a plane or a section of a concave sphere? I am mainly concerned with the 47deg. motion of the sun over the course of the year.   TIA for any thoughts Dave G.   PS sorry if this is a double post having trouble getting the list to work