Richard: You wrote:
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. [endquote] Once, in an unfamiliar town, I wanted to find when the sun's direction is south, east, west, southeast, and southwest--for orientation in the new town. At first, I used the successive substitutions method that you describe above. As you suggest there, that method doesn't always work, but, when it does, it's convenient. But then I noticed that the equation can be solved as an equation quadratic in sin h. Just write cos h in terms of sin h, and put that term by itself on the left side of the equation. Square both sides. You get an equation quadratic in sin h. When dec is positive, then, to choose from the quadratic formula's 2 answers for sin h, it might be necessary to consider the requirement that the azimuth be north (or south) of the east-west line, as determined in the denominator of the azimuth formula. John: I'll soon post the resulting formula for h, given Lat, Az, and dec. Most likely someone else will post it before I do, though. I'm quite conscious of the fact that there are some people at is list, and in dialing, who are a lot more qualified than I am. Of course a frequent need to find h, given Lat, Az, and dec, is when it's necessary to find when a sundial won't be shaded by a building. Michael Ossipoff -- 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. *
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