Re: Egyptian sundial

[tony moss]

Aleksandr wrote:

In English version of my web-site a have just created a new page. Please, 
visit it and share with me my small success which I have formed in a way 
of picture story. 

A beautiful dial, beautifully crafted.  Don't miss this link SML members.

http://www.sundials.ru/en/egypt_story.html

What do you think about this way of data presentation? 

I wish we could see the development stages of other important dials 
presented in a similar way.

More please Aleksandr!

Tony Moss
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Expanded Nodi Shadow Experiment

[jlcarmichael]

Hello All:

Here is a PDF file (about 600KBs) that shows a new nodi shadow experiment. This is an expanded version of my original experiment and includes 12 different nodi designs. All the nodi are the same height but are different designs.To see photos of the experiment click on this link:

http://advanceassociates.com/WallDial/NodusShadowExperiment.pdf


Purpose: To determine which types of sundial nodi cast the easiest to read shadows and produce the most precise readings. 

Setup: I made twelve common but different sundial nodi. I compared ball nodi of different diameters on posts, truncated rods and pointed rods, thick rods and thin rods, a cone, and a hole-in-disk nodus. All of them were 4” tall and spaced evenly apart in a row attached to one end of a flat board that I marked with parallel measuring lines in inches and as multiples of the height vs. the length of the shadows.

Execution: By tilting the board in the sun, I could lengthen or shorten the shadows and observe the effect that the sun’s angle had on the shadows cast by the different nodi. High sun angles made short shadows and low sun angles made long shadows. I photographed the results (see below)

Conclusions: High sun angles created short shadows and low sun angles produced long shadows. In all cases, the shorter shadows are easier to read than longer shadows because they are darker and there is less fuzziness around the edges. Truncated rods and balls produce the least accurate shadows and the pointed rods and the cone produce the most accurate shadows. Thick rods are easier to see from a distance than thin rods. The hole-in-disk nodus also produces an accurate reading, but only if the shadow is short because the projected image disappears at low sun angles. I my opinion the cone and the thick pointed rod produce the easiest to read and the most precise shadows.

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Re: Expanded Nodi Shadow Experiment

[Frank King]

Dear John,

That is a splendid experiment...

  http://advanceassociates.com/WallDial/NodusShadowExperiment.pdf

It illustrates all kinds of interesting aspects of nodus design
The Purpose, Setup and Execution all earn top marks.  The Conclusion,
though, is subject to a little caveat...

Let's concentrate on just three of your designs: the disc with the
0.25 hole at the top (or leftmost), the cone at the bottom (or
rightmost) and the 1 ball next to the cone.  Now look at the two
sets of shadows:

 1.  When the shadows are short...

 (a) the centre of the anti-shadow of the disc with a hole is
 about 6.1 along your board.

 (b) the centre of the shadow of the ball is just a little
 shorter.  It seems to be almost spot on the 6 mark.  [This
 is possibly because the supporting stick is not quite vertical.
 This is not important.]

 (c) the shadow of the tip of the cone is almost exactly in line
 with the anti-shadow of the disc with a hole, about 6.1 along
 your board.

 2.  When the shadows are long...

 (a) the anti-shadow of the disc with a hole is no longer clear
 (as you say) but because there is an equal amount of fuzz at
 the extremities of the shadow of the disc as a whole you can
 fairly easily estimate the centre.  It seems to be about 23.3.

 (b) the centre of the shadow of the 1 ball is just a little
 less easy to estimate because the supporting stick disturbs
 the fuzz at one of the extremities but one can see that the
 centre is about the 23 mark.  This, as expected, is shorter
 than the shadow to the centre of the disc and is consistent
 with 1(b).  So far everything ties up.

 (c) the shadow of the tip of the cone though has now fallen
 behind the shadow of the centre of the disc.  The shadow may
 be easier to read but IT IS GIVING A FALSE RESULT.

The big big trouble with any asymmetric nodus is that you cannot
cancel out the fuzz.  You have to decide just where in the fuzz
is the point of interest.  This is difficult.  Different people
will estimate different points.

As noted at 2(b), each of your ball nodi is slightly asymmetric
because of the supporting sticks.  If you had mounted the balls
sideways (as you have the disc with the hole) it would be easier
to estimate the centre of the shadow.

To my mind, the disc with the hole gives the most accurate
result even if its shadow isn't the prettiest!

Incidentally, it is worth analysing the hole in your disc in
the long shadow case...

  Diameter of hole   0.25

  Height of hole above the board  4

  Approximate length of shadow   23.3

  Distance of centre of anti-shadow from centre of hole 23.6

  Angle of incidence   arctan(23.3/4)  =  80.3 degrees

  Now consider the hole viewed from the centre of the anti-shadow.
  Given that the disc is parallel to the board, the hole will appear
  as an ellipse whose angular dimensions in radians are:

  Major axis0.25/23.6   approx  1/94.4 radians

  Minor axis  0.25 x cos(80.3) / 23.6   approx 1/558 radians

This last figure should be compared with the angular diameter of the
sun which (by a diallist's rule of thumb) is about 1/107.5 radians.

Now imagine an insect (wearing eye protection) at the point where
the centre of the anti-shadow should be.  As seen by the insect,
the minor-axis of the hole appears to be less than one-fifth the
diameter of the sun.  The anti-shadow is entirely penumbra and
impossible to detect.

In my opinion this is NOT a design error.  My eccentric view is
that a disc with a hole IS the best form of nodus, especially for
big sundials (well ALMOST the best) because...

  when the angle of incidence is small (short shadows) you
  observe the centre of the anti-shadow and...

  when the angle of incidence is high (long shadows) you
  observe the centre of the shadow of the disc as a whole.

I say ALMOST the best because there is a special case of a disc
with a hole, and that is the great camera obscura sundials which
one comes across in Europe.  There the angular diameters of the
holes are even smaller than yours.  [According to Gianni Ferrari,
Cassini took the view that the hole should be 1/1000th of its
distance to the floor, half the size of your hole at 23.6.].

The disc though is effectively of infinite diameter because
the entire building surrounds the hole and you DO see a
splodge of light.  This is not anti-shadow though; it is
actually an image of the sun and you can estimate its centre
VERY precisely.

Try making your disc of infinite size and you will see how
this works :-)

MORAL: Sticks and cones are seductive but should be resisted!

I hope this hasn't been too tiresome a message for this list!

Frank H. King
Cambridge, U.K.



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RE: Egyptian sundial

[Carl Barbara Sabanski]

Sunny Day,

I don't know how important it is, but I have a site showing the development
of a monumental sundial located in my community that I was the project
leader for.  It was a millennium project.  There are many photos that show
the construction of all the various parts of the sundial; gnomon, dial
plate, hour lines, hour markers, etc.  For example, one very interesting
task was the placement of the 1200+ pound granite blocks that border the
dial plate.  I made dozens of ice discs using ice cream pails.  Each granite
block was placed on 3 of these ice discs.  This allowed the machine operator
to set the block down, remove the forks or straps and adjust the position of
the granite as the ice melted.  This technique worked very well.

Prior to the construction of this sundial I knew nothing about the design
and operation of a real sundial.  Our library brought in a few books for me
and I did a lot of searching on the internet.  I had many volunteers help
with construction and fundraising efforts.  The sundial is now a focal point
and tourist attraction for our town.

I invite you to come and visit the Pinawa Heritage Sundial.  I am very proud
to have had the opportunity to be involved in this project.  You can get
there via:

www.mysundial.ca

Happy Dialling!

Carl Sabanski

-Original Message-
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] Behalf Of tony moss
Sent: Sunday, August 06, 2006 4:06 AM
To: Sundial Mail List
Subject: Re: Egyptian sundial


Aleksandr wrote:

In English version of my web-site a have just created a new page. Please,
visit it and share with me my small success which I have formed in a way
of picture story.

A beautiful dial, beautifully crafted.  Don't miss this link SML members.

http://www.sundials.ru/en/egypt_story.html

What do you think about this way of data presentation?

I wish we could see the development stages of other important dials
presented in a similar way.

More please Aleksandr!

Tony Moss
---
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Re: Expanded Nodi Shadow Experiment

[John Carmichael]

Hi Frank:

I'm still pondering all of the information you gleaned from my experiment. 
You have given your comments a lot of thought and I don't want to quickly 
dismiss anything you said as being inaccurate without being sure first.


But I need to point out something important about the light projection (or 
antishadow) cast by the hole-in-disk nodus:


As you can clearly see in the long shadow photo, the spot of light (the 
antishadow) is not there at all.  When tilting the board, the antishadow 
became smaller and smaller as the shadow lengthened.  In fact, when I was 
tiltling the board, it disappeared when the shadow was 3 times longer than 
the gnomon.  This I think was due to the thickness of the cardboard that I 
used to make the disk.  The cardboard of the disk, in fact, was what shaded 
the hole.  If I had used a paper thin metal to make the disk, then I think 
the antishadow would not have disappeared so quickly.


My conclusion about this is that the hole-in-disk works fine and is 
extremely precise at high solar angles when you can see the anti-shadow, but 
is completely useless at low solar angles when the antishadow disappears.


Do you agree?

John

p.s. I love your term antishadow  to describe the projected sunlight 
through an aperture nodus.  Do you invent this term?
pps.  I will try to bring the experiment to Vancouver if it will fit in my 
suitcase.



- Original Message - 
From: Frank King [EMAIL PROTECTED]

To: [EMAIL PROTECTED]
Cc: sundial@uni-koeln.de; [EMAIL PROTECTED]
Sent: Sunday, August 06, 2006 11:45 AM
Subject: Re: Expanded Nodi Shadow Experiment


Dear John,

That is a splendid experiment...


http://advanceassociates.com/WallDial/NodusShadowExperiment.pdf


It illustrates all kinds of interesting aspects of nodus design
The Purpose, Setup and Execution all earn top marks.  The Conclusion,
though, is subject to a little caveat...

Let's concentrate on just three of your designs: the disc with the
0.25 hole at the top (or leftmost), the cone at the bottom (or
rightmost) and the 1 ball next to the cone.  Now look at the two
sets of shadows:

1.  When the shadows are short...

(a) the centre of the anti-shadow of the disc with a hole is
about 6.1 along your board.

(b) the centre of the shadow of the ball is just a little
shorter.  It seems to be almost spot on the 6 mark.  [This
is possibly because the supporting stick is not quite vertical.
This is not important.]

(c) the shadow of the tip of the cone is almost exactly in line
with the anti-shadow of the disc with a hole, about 6.1 along
your board.

2.  When the shadows are long...

(a) the anti-shadow of the disc with a hole is no longer clear
(as you say) but because there is an equal amount of fuzz at
the extremities of the shadow of the disc as a whole you can
fairly easily estimate the centre.  It seems to be about 23.3.

(b) the centre of the shadow of the 1 ball is just a little
less easy to estimate because the supporting stick disturbs
the fuzz at one of the extremities but one can see that the
centre is about the 23 mark.  This, as expected, is shorter
than the shadow to the centre of the disc and is consistent
with 1(b).  So far everything ties up.

(c) the shadow of the tip of the cone though has now fallen
behind the shadow of the centre of the disc.  The shadow may
be easier to read but IT IS GIVING A FALSE RESULT.

The big big trouble with any asymmetric nodus is that you cannot
cancel out the fuzz.  You have to decide just where in the fuzz
is the point of interest.  This is difficult.  Different people
will estimate different points.

As noted at 2(b), each of your ball nodi is slightly asymmetric
because of the supporting sticks.  If you had mounted the balls
sideways (as you have the disc with the hole) it would be easier
to estimate the centre of the shadow.

To my mind, the disc with the hole gives the most accurate
result even if its shadow isn't the prettiest!

Incidentally, it is worth analysing the hole in your disc in
the long shadow case...

 Diameter of hole   0.25

 Height of hole above the board  4

 Approximate length of shadow   23.3

 Distance of centre of anti-shadow from centre of hole 23.6

 Angle of incidence   arctan(23.3/4)  =  80.3 degrees

 Now consider the hole viewed from the centre of the anti-shadow.
 Given that the disc is parallel to the board, the hole will appear
 as an ellipse whose angular dimensions in radians are:

 Major axis0.25/23.6   approx  1/94.4 radians

 Minor axis  0.25 x cos(80.3) / 23.6   approx 1/558 radians

This last figure should be compared with the angular diameter of the
sun which (by a diallist's rule of thumb) is about 1/107.5 radians.

Now imagine an insect (wearing eye protection) at the point where
the centre of the anti-shadow should be.  As seen by the insect,
the minor-axis of the hole appears to be less than one-fifth the
diameter of the sun.  

Re: Expanded Nodi Shadow Experiment

[Mac Oglesby]

One problem I've personally encountered with a pointed post gnomon is 
that if the post's shadow falls too close to the foot of the post, 
the shadow of the tip may be lost in the shadow of the post's 
shoulder. This was on a vertical decliner.


Mac Oglesby

http://www.sover.net/~oglesby/Gnomon%20Notes/GnomonShadows3.jpg



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Re: Expanded Nodi Shadow Experiment

[John Carmichael]

Hi Mac:

Yes, on a perpendicular cone or pointed rod gnomon, the slope of the point 
or cone could cause a self-shading problem if the cone or point is too wide 
at the bottom (a fat cone).  But you can easily determine the maximum 
allowable width of the cone or point and avoid that design problem if you 
look at the nearest solstice line to the nodus.  The base of the cone must 
be smaller than that distance to avoid self-shading.  For my wall dial, the 
largest cone possible that would not cause shading would have been just 
under 5 inches wide, so the cone had to be skinnier so that it would cast a 
shadow on the face at noon on the winter solstice.  I made it just two 
inches wide at its base, much smaller than the allowable width.


I think fatter cones and points produce easier to read shadows than than the 
skinny ones, especially when the shadows are long.  So the idea would be to 
have the fattest cone or point possible that does not shade itself. (You may 
even want to make the cone even skinnier to accomodate artwork around it. 
That's why I made my cone much thinner than the allowable so that I could 
put the points of a star around its base).


Does this make sense?


- Original Message - 
From: Mac Oglesby [EMAIL PROTECTED]

To: Sundial Mailing List sundial@uni-koeln.de
Sent: Sunday, August 06, 2006 2:28 PM
Subject: Re: Expanded Nodi Shadow Experiment




One problem I've personally encountered with a pointed post gnomon is that 
if the post's shadow falls too close to the foot of the post, the shadow 
of the tip may be lost in the shadow of the post's shoulder. This was on a 
vertical decliner.


Mac Oglesby

http://www.sover.net/~oglesby/Gnomon%20Notes/GnomonShadows3.jpg



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