First of all, my thanks to those people who took the time to reply to
my "cry for help" on this - and my apologies for a slight delay in
responding, but I had to 'clarify' a few things with the Muslim group.
The following are (I think!) the criteria that they wish to fulfill:
(1) They are not interested in the East/West DIRECTIONS, but in the
TIMES at which the sun is exactly at those directions - even if
it is obscured, or actually below their horizon at that time.
(2) With regard to 'accuracy', they want the nearest minute (to be
confirmed by direct observation and/or comparison with clocks).
(3) I had originally assumed that they would be more interested in
the 'apparent' (local sun) time, but they insist that it must
be their mean CLOCK time - which introduces added problems of
Longitude, Daylight-Saving, as well as the 'Equation of Time'.
(4) They do not want some form of 'look-up chart', (especially if
it has been produced via a computer) - but instead prefer some
physical 'mechanism', which they can actually observe working.
(I get the impression that an accurate 'orrery' type of thing
would be their ideal, but doubt whether that can be produced).
(5) This group of 'asylum seekers' do not know how these times had
been determined in the past (having lost contact with their
religious leaders) - or it could be that they are confused in
relation to their requirement, or are maybe even some form of
'off-shoot sect' who want to start their own set of rules for
prayer observance times (I did not go into that any further)!
I spoke to a helpful man at "Armagh Planetarium" here in Northern
Ireland, who gave me the following 'formula' for times when the
sun is directly East and West (Hour-angle from South direction).
cosine (Hour-angle) = cotangent (Latitude) x tangent (Declination).
I am not a 'Maths' expert, but this looks reasonable. With a zero
Declination (at Equinoxes), the Hour-angle would be 90 degrees - so
the time will be 6 hours before/after noon, regardless of Latitude).
Could anyone confirm if this formula is OK - but I assume that the
times also need 'corrected' for Longitude, plus Equation of Time?
Would there be any possibility of constructing a simple mechanical
device which could use that formula? Obviously, the Latitude will
be fixed - and, presumably, the sun's Declination could be varied
by means of some scale (like on Analemmatic or Capuchin sundials).
It will require correction for Longitude and Equation of Time, too.
Carl Sabanski had kindly pointed me to his "Dialling Buddy" device,
which seems promising - but it would need to be made in a fairly
large size (in order to have daily and 'nearest minute' accuracy),
as well as having to deal with the points raised in item (3) above.
As Carl had said, the time-keeping accuracy of its mechanical clock
system would also be a 'limiting factor' in using any such device.
At first sight, the suggestion from Tony Moss looked like it had
possibilities too - but although '24-hour' clocks are available,
the Hour-hand still goes round TWICE per day, and we need ONCE.
I suppose some device could be made using a 1-rev-per-day motor,
though there would have to be a way to input the sun's varying
Declination - plus also allowing for the Equation of Time as well,
not forgetting adjustments for Daylight-Saving Time and Longitude.
To be honest, I rather wish that I had not become involved in this
project (more trouble than it is worth!) - but maybe some member
of this list will see it as a 'challenge', since (as confirmed by
Roger Bailey) this is an interesting and non-trivial requirement.
Just to confirm, the direction of Mecca (as such) is not of any
specific interest to this group - only the East/West sun times,
but these must be established in their local mean time (which can
be confirmed by observing a shadow at the clock time indicated, in
order to give 'confidence' in the device when it is not sunny).
Once again, thanks for all your previous (and any future) comments,
but please do not waste a lot of time on this - as I have already
told the Muslim group that it will not be an easy task to fulfill
their criteria, especially if 'modern technology' is not allowed.
Sincerely,
David Lawrence.
--
-
