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Thank you for explaining. I can see how sine functions are symmetric around 90
degrees but I still don't see how 90 degrees is an axis of symmetry for
measuring azimuth.
If South is treated as 0 degrees instead of 180 degrees, then, as you describe
it, East could be -90 degrees and West would be +90 degrees. The symmetry
around South would then be Az < 0° or > 0° but still not the Az < 90° or > 90°
that was specified in Morrison's equations.
1. Calculate the sun's altitude when the declination is zero: tan h0 = cos A /
tan phi
2. Calculate an auxiliary angle x from: sin x = (cos h0 sin d) / sin phi
3. Calculate sun's altitude, h, for the azimuth and declination from:
If A < 90, h = x + h0
If A > 90, h = x - h0
NOTE:
h = altitude
A = azimuth
d = solar declination
phi = latitude
> On Jul 12, 2024, at 4:40 AM, Hervé Guillemet <[email protected]> wrote:
>
> Hi John,
>
> If I understand your point, I think that the confusion comes from the fact
> that for gnomonistthe origin of azimuth is South, and not North like it is
> for navigators (salesmen, pilots). In such case East is -90°, West is +90°,
> North is +/- 180°.
> With this origin (South = 0°), there is a symetry in the trigonometric circle
> : sin (pi - A) = sinA. As an example sin 120° = sin 60° = 0,866... For the
> same sine value, you have 2 angles. This is why you need to determine whether
> Az is > 90° or < 90°
>
> I hope that it answers your point.
> Best regards Hervé Guillemet
>
> De: "John Goodman via sundial" <sundial
> <mailto:[email protected]>@uni-koeln.de <mailto:[email protected]>>
> À: "Sundial List" <sundial <mailto:[email protected]>@uni-koeln.de
> <mailto:[email protected]>>
> Envoyé: Jeudi 11 Juillet 2024 20:03:10
> Objet: Azimuth and altitude
>
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