Hello John,
I routinely use Napier's Analogue as suggested by Fred Sawyer when I asked
this question several years ago. This involves an intermediate step
involving an angle B. Here are the formulae.
Napier's Analogues: Knowing Latitude, Declination and Azimuth, Solve for
Altitude and TimeFindangle B : Sin B =Sin Az Cos Lat/ Cos Dec.
Then Tan .5(90-Alt)=Tan .5(Lat-Dec)Cos.5(B-Az)/Cos .5(B+Az),
Then the Sine Rule for t: Sin Az=CosDec Sint/CosAlt or
Sint=SinAzCosAlt/CosDec
These are fairly easy to program into a spreadsheet.
Regards, Roger Bailey
--------------------------------------------------
From: "John Goodman" <johngood...@mac.com>
Sent: Saturday, January 31, 2015 7:05 AM
To: "Sundial List" <sundial@uni-koeln.de>
Subject: A question for the mathematically inclined
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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