Analemma layout and proportions on a sundial

[1940LaSalle]

TL;DR Summary

Looking for proportions and similar guidance in laying out an analemma: specifically, the abscissa (equation of time) component. Sun declination is fairly easy to get.

I want to lay out an analemmatic sundial, with a true figure 8 analemma for the gnomon position instead of the more common date marks. Everything I read shows that the ordinates of the points on the curve are a function of the sun's declination on a given date. Further, I'm also given to understand that the abscissae are functions of the equation of time on a given date--and the equation of time is fairly easy to get from a source like Meeus' Astronomical Algorithms. What has me baffled is the proportions of the analemma.

I recall that the height of the analemma is some fraction of the major axis of the ellipse on which the hour points are laid out. Let's call that D, since it comes from the sun's declination. I believe that the equation of time varies from about -15 minutes (sun lags behind clock time) to +15 minutes (sun precedes clock time) over the course of a year. Let's call the range of abscissae that cover that ±15 minutes E, for equation of time. What I haven't found and need is the proportion of E to D--or if not a set proportion, a range of values. And a reference for this information would be extremely valuable.

Thanks very much.

 

[phyzguy]

I think your problem is that you have one axis (D) in degrees, and the other axis (E) in minutes. You need to convert E into degrees so you can plot them both in the same units. Since the sun moves 360 degrees in 24*60 = 1440 minutes, E of 15 minutes is an angular deviation E = 15 * 360 / 1440 = 3.75 degrees. Does this help? This link might be useful.