Solar Analemma Fundamentals

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This page is intended to address the mathematics of analemma calculation used in drawing shadow analemmas in our Solar Position program.  (Without supporting diagrams so far).

For the "shadow analemma"  for a given altitude, the shadow tip will lie somewhere on a circle centered on the base of our vertical stake and with radius = height/tangent(altitude).  If we switch our viewpoint to look straight down with south away from us, the azimuth will produce a shadow extending from the base of the stake at angle azimuth+180 (or azimuth-180, same thing).  Since the tip of the line is at R, we can draw the right triangle and see that sin(azimuth-180)=X/R and cos(azimuth)=Y/R.  So, substituting, X= sin (azimuth - 180) * (Height / Tan(Altitude)) and  Y=cos(azimuth-180) * (Height/ Tan(Altitude).  Clearly  the height of our stake affects only the size not the shape of the analemma.   I choose Height=1000 just to ensure reasonable accuracy for X,Y values. 

Still no good diagrams here but there is good information and some image links available at    

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