Hi Rod,
The equations you are looking for are: Alt = Arcsin(Sin Lat * Sin Dec + Cos Lat * Cos Dec * Cos t) Azimuth = Arcsin( Cos Dec * Sin t / Cos Alt) These are the equations from spherical trig that astronomers, navigators and dialists commonly use to solve for altitude and azimuth. With scientific calculators and computers that are much easier to solve than they appear. The answers to your other specific questions are included below. >Other questions: > >1. Is elevation the same thing as altitude, i.e. the >angle between the sun and the horizon? Yes, this is how altitude is defined. > >2. Is the calculation for azimuth the same one I've >been using for drawing hour lines on horizontal dials, >i.e. D = arctan( tan HA * sin LAT ) ? No. Azimuth is the direction of the sun in the horizontal plane, and not the hour angle which is the shadow on the plane of a polar oriented gnomon. > >3. Have I used the term "hour angle" correctly? A >negative hour angle would mean it's morning, a >positive HA would mean afternoon, and HA=0 means the >sun lies in the observer's meridian. > Note that I have used the time angle t in the equations and not hour angle. For sundial design the time angle t is 15 degrees per hour, measured from noon = 0 with AM- and PM+. Hour angle for sundial design is as defined above. Confusion arises because astronomers and navigators use the term local hour angle LHA as the time angle. This local hour angle involves longitude, time and the suns position at that time as defined by right ascension or siderial hour angle. Dialists have it easier by ignoring this and just defining the time angle t as the time (15 degrees per hour) from the noon zenith position. Welcome to the warped world of spherical trigonometry when parallel lines meet, triangles contain more than 180 degrees and the sides of triangles are also angles. If you are seeking the altitude of the sun at noon when the azimuth is zero, you do not have to use these equations. In this special case, the altitude is the Co-Latitude + Declination or (90-Lat+Dec). Roger Bailey Walking Shadow Designs N 51 W 115
