Hi All,
It's nothing to do with latitude, I think. The human eye perceives the edge of
a shadow to be where the light has fallen to about 10% to 20%, not 50%. So,
where the sun's shadow is cast by an edge (as opposed to a string/wire/rod) we
estimate the edge about 12 to 14 minutes of arc from where we should, always in
the direction towards the shadow. (The sun's radius being about 16 minutes of
arc)
Now, 15 minutes of arc is almost exactly how far the sun moves in a minute (it
varies a little with the seasons). So, if we're talking of a polar gnomon, use
the advice John mentioned: subtract a minute in the morning and add a minute in
the afternoon. This works for any sundial whatsoever which has a solid gnomon:
vertical or horizontal, any size, anywhere in the world, any time of day,
throughout the year.
Alternatively, when delineating a dial, pre-distort it as ChiLean did, by a
little less than a minute. So, the sides of the noon gap should indeed converge.
By the way, the alternative that someone suggested, of making the gnomon
thicker towards the top, does not work correctly. It has some effect at noon,
but none at 6am/6pm. I suppose you could also make the gnomon slightly steeper,
but really you're much better off leaving the gnomon alone but pre-distorting
the hour lines.
Another alternative is to use a shadow sharpener, which is a pinhole device
that allows you much more accurately to estimate the centre of the edge of the
shadow.
Yet another, and I'm surprised John hasn't mentioned this, is to use John
Carmichael's taut wire gnomon, or some other thin form where you estimate the
centre of the shadow. Contrary to a recent posting, the gnomon's diameter
should be at least 1/105th the maximum distance to the dial, to ensure the
centre of the shadow is in the umbra. You can certainly see the shadow further
away, but it will be fainter, penumbral shadow with a less well defined centre.
So, for instance, a 1cm diameter wire, rod or tube should be used with a dial
of around 1 metre radius. This applies equally to equatorial dials.
Regards
Chris Lusby Taylor
----- Original Message -----
From: JOHN DAVIS
To: [EMAIL PROTECTED] ; [EMAIL PROTECTED]
Cc: Sundial List
Sent: Wednesday, February 13, 2008 8:39 AM
Subject: Re: Shadow Tapering
Hi ChiLian,
That's very interesting - I haven't heard before of a dial delineation being
"pre-distorted" in this way to allow for the penumbra effect.
Perhaps the reason that the 1 minute correction that you adopted was too much
is that your latitude (24.79 N) is so much less than the Shetlands at nearly 60
degrees N. Hence the shadow is much closer to the gnomon edge and the penumbra
effect is less marked. It is a complicated problem as human eyesight does not
respond linearly to varying intensity levels.
Regards,
John
--------------------------
Chiu ªô,Chi lian <[EMAIL PROTECTED]> wrote:
Hi!
>An article by Vicki de Kleer (BSS Bulletin 19(iii), pp.116-117, September
2007) describes an 1890 brass horizontal dial made by the London maker Charles
Baker for Sumburgh in the Shetland Islands at latitude 59 degrees 52 minutes N.
The dial has a comprehensive Equation of Time table engraved around its
periphery and also the two intriguing instructions:
"AM Sub.[tract] 1 min"
and
"PM Add 1 min". <
I designed an 8m sundial with solid gnomon for Nat'l Tsing Hua University
(Hsinchu, Taiwan, 24.79N, 120.99E) in April, 2006. I noticed the problem of
shadow. No one can tell where the shadow starts or where it is perfect. That
means no one can really deside by his bare eyes where the middle of the
penumbra is. Most people read the dial by the shadow edge and never care about
the middle of the penumbra. So I decided to use perfect shadow as time
indicater. I took the "one minute off" policy since the full sun angle is about
2 minutes. The policy was "mark the hour lines one minute ahead in the morning
hours and one minute behind in the afternoon hours". That is to draw 9:01 line
and mark it as 9:00, to draw 2:59 line and mark it as 3:00. So the sundial was
done.
However, it turns out that "one minute" off is too much. I overlooked the
fact that the sun, as a light source, is not square but circular.
Regards,
ChiLian
2008/2/10, JOHN DAVIS <[EMAIL PROTECTED]>:
Hi Patrick, John C and the List,
The problem of the shadow not properly filling the noon gap is the same
umbra/penumbra related one which affects the reading accuracy of dials with
'solid' gnomons at all times of the day. This is usually ignored by dial
makers but I know of one historical example where the maker seems to have
offered a possible solution.
An article by Vicki de Kleer (BSS Bulletin 19(iii), pp.116-117, September
2007) describes an 1890 brass horizontal dial made by the London maker Charles
Baker for Sumburgh in the Shetland Islands at latitude 59 degrees 52 minutes N.
The dial has a comprehensive Equation of Time table engraved around its
periphery and also the two intriguing instructions:
"AM Sub.[tract] 1 min"
and
"PM Add 1 min".
It seems to me that these instructions are implying that the true time is
being indicated slightly further into the penumbra area of the shadow than the
observer might normally expect. With a dial so far north, the effect of 'shadow
tapering' will be more prononounced than on most other dials.
Does anyone have a different interpretation of these instructions, or
know of other dials wich have similar ones?
Regards,
John Davis
--------------------------------
Dr J Davis
Flowton Dials
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