Thank you all for the responses.
Gianni, no account needs to be taken for refraction in the design of an
ancient sundial if what they are designing is a way to break up the day into
twelve hours defined as the movement of the sun 1/12 of the way across the sky.
The dial itself will automatically show the hour with refraction included. The
sun and its shadow move in relation to us based on the actual conditions where
we are.
What I am trying to figure out is what that time would be on our clock and
how off the temporal hours would be if the actual phenomena of refraction is
taken into account in the calculations to figure out what the temporal hour
would be on our clock. Since refraction actually exists.
When we think about sundials, we are trying to get the sundial to tell us
what the real time is as defined by our clocks and we try to get them to be as
close as possible. On an ancient sundial with temporal lines there is no need
for the equation of time as what we are looking at, is the percentage of the
sun’s movement across the sky. That is the definition of the temporal hours if
I am not mistaken.
David, I understand that azimuth doesn’t change but I am pretty sure that
the declination changes and therefore the hour angle changes and I am trying to
figure out what the formula is to get the hour angle to include the change in
altitude.
Using Sæmundsson’s formula,
,
I get the the apparent altitude. But how to I translate that change back into
the hour angle.
Here is the code for the formula I thought would work.
newDeclin = Math.sin(lat_Rad) * Math.sin(apparent_altitude_Rad) -
(Math.cos(lat_Rad)*Math.cos(apparent_altitude_Rad)*Math.cos(azimuth_Rad))
newDeclin = Math.asin(newDeclin);
var newHa =
radToDeg(Math.asin(Math.cos(apparent_altitude_Rad)*Math.sin(azimuth_Rad)/Math.cos(newDeclin)));
As I mentioned, the results showed an almost twenty minute difference
between what the temporal hour should be at the eleventh hour with refraction
and without.
Again thanks for all the responses.
Noam Kaplan
From: Gianni Ferrari
Sent: November 14, 2013 9:36 AM
To: LISTA INGLESE
Subject: Re: temporal hour including refraction
No
you're right!
In all the methods
to calculate or draw sundials,
geometric or analytic, the Sun is always
considered punctiform, and reduced
to its center, and no account is
taken of refraction, of the lowering of
the horizon (horizon dip), of other astronomical phenomena such
as parallax, etc..
Sunset
and sunrise (for the calculation of
temporary or italic hours) are always the
instants when the center of the Sun crosses the
theoretical horizon.
Even Islamic
astronomers, who well knew the phenomenon of
refraction, do not take into account of it in
the calculation of sundials and of the
prayers lines.
Best
Gianni Ferrari
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