If you know the zenith distance, z, of the sun (90° - elevation angle) as well as the azimuth (A) then you could use:
sin(h) = -sin(z)*sin(A)/cos(delta) where delta is the sun's declination. The latitude of the site, phi, is not needed. Computing the hour angle when the zenith distance is not known is a little trickier. In principle, this equation could be used: sin(h) = tan(A)*(sin(phi)*cos(h) - cos(phi)*tan(delta)) but you'll notice that h appears on both sides of the equation. Possibly this can be solved in an iterative fashion by selecting an approximate trial value for h and using it on the r.h.s. to compute a new value of h. You would then use this new value on the r.h.s. and continue the iterative procedure until the new value does not change significantly from the previous value. I've not actually tried this myself so proceed with caution. -- Richard Langley On Saturday, January 31, 2015, 31, at 11:05 AM, John Goodman wrote: > Dear dialists, > > Does anyone know a formula for calculating the hour angle given the azimuth, > declination, and latitude? > > I’d like to know the time of day, throughout the year, when the sun will be > positioned at a particular angle. This will allow me to determine when > sunshine will stream squarely through a window on any (sunny) day. > > I’ve seen several formulae for calculating azimuth. I suspect that one of > them could be rewritten to solve for the hour angle given the azimuth instead > of the finding the azimuth using the hour angle (plus the declination and > latitude). Unfortunately, I don’t have the math skills for this conversion. > > Thanks for any suggestions. > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > ----------------------------------------------------------------------------- | Richard B. Langley E-mail: [email protected] | | Geodetic Research Laboratory Web: http://gge.unb.ca/ | | Dept. of Geodesy and Geomatics Engineering Phone: +1 506 453-5142 | | University of New Brunswick Fax: +1 506 453-4943 | | Fredericton, N.B., Canada E3B 5A3 | | Fredericton? Where's that? See: http://www.fredericton.ca/ | ----------------------------------------------------------------------------- --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
