Re: Hemicyclium correction - a figure might be needed

[Michael Ossipoff]

I can't find an image on the internet, of a Circumference-Aperture
Cylinder-Equatorial dial, but I'm going to post a drawing of one.

By the way, I use a broad definition of Equatorial Dial. Instead of only
dials with a dial-face parallel to the equator, I include all dials that
directly measure the Sun's apparent movement parallel to the equator.

Well, any dial with a polar style (including the Polar Dial and all the
Polar-Gnomon Flat Dials) measures the Sun's movement about the polar axis
*reasonably* directly. Maybe all such dials almost qualify as Equatorial
then. But I only call a dial Equatorial if it directly measures the Sun's
apparent movement parallel to the equator, on a uniform circular scale that
measures along a line parallel to the equator.  ...even if the dial-face
isn't parallel to the equator.

Michael Ossipoff
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Re: Hemicyclium correction - a figure might be needed

[Michael Ossipoff]

Another typo:

When I said:

"And in north declination, the circumference-aperture would be used."

I mean that in *south* declination the circumference-aperature would be
used.

Michael Ossipoff

On Tue, Oct 24, 2017 at 4:33 AM,  wrote:

> Thank you for your nice considerations.
>
> I think that some kind of visualization would make them more clear to a
> general public. Could you please support your ideas with a figure or a link
> to an external one (if exists)?
>
>
>
> Best regards,
>
> Wojtek
>
>
>
> *From: *Michael Ossipoff 
> *Sent: *Tuesday, October 24, 2017 1:32 AM
> *To: *Brad Thayer 
> *Cc: *sundial list 
> *Subject: *Re: Hemicyclium correction
>
>
>
>
>
> In the Hemicyclium discussion, the OP mentioned having 6-inch copper
> tubing. So, though it was a bit off-topic, I suggested that the tubing
> could be used for an additional, quicker, project, to make a south
> windowsill sundial--a Circumference-Aprerture Cylindrical Equatorial Dial.
>
> But, when I said that the axial dimension of the cylinder has to be at
> least 0.4335 times the diameter, I neglected the fact that there are south
> declinations as well as north declinations. (...funny, because we're in
> south declination now) So, with the circumference aperture in the middle of
> the cylinder, the cylinder's axial dimension has to be at least twice
> 0.4335, which is about 0.867 times the diameter.
>
> But my suggestion for marking points of the declination-lines for each
> hour was correct:
>
> At any hour-line, the axial displacement of a declination-line from the
> equinox-line is equal to the tangent of the declination times the direct
> distance between the circumference aperture and the intersection of that
> hour-line with the equinox-line
>
> That amounts to:
>
>
>
> (Tan dec)(R*2Sin(h) ).
>
> ...where h is the number hours from 12 noon.where R is the cylinderr's
> radius.
>
> Obviously more neatly written:
>
>
> (Tan dec)(DSin(h) ).
>
> ...where D is the diameter of the cylinder.
>
> -
>
>
>
> But a cone would be better than a cylinder, because it opens toward the
> north, the direction from which it would be observed--making it readable
> from a wider-range of directions, and making the inside surface more
> readable in generral. The use of a cone just slightly more complicates the
> declination-lines, but that would take this post even more off-topic.
>
> --
>
> I mentioned that I'd read of a drinking-cup with a hole in it being used
> as a cylindrical sundial. Of course if it were a Cylindrical Equatorial,
> orienting it just by estimation wouldn't give very accurate results. (A
> Cylindrical Equatorial is supposed to be a *mounted* dial, not a portable
> dial).
>
> But actually, maybe they were talking about a Cylindrical *Altitude*
> Dial. But, though that avoids the direction-estimation, the drinking-cup
> would need a way of hanging it in the right orientation, and so it wouldn't
> be much like an ordinary drinking-cup. ...and the line-marking would be
> complicated by the non-cylindrical shape of the cup.
>
>
>
> Michael Ossipoff
>
>
>
> On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer 
> wrote:
>
> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
> metal working class.  What little I can find on them says they are
> inaccurate, without being very clear on the problem.  It appears to me the
> only issue is it needs to be tilted so that the gnomon aligns with the
> Earth’s rotation axis; thus the half-bowl faces south and the gnomon points
> south, but the end of the gnomon that attaches to the bowl points north.
> Am I missing anything?  I am also looking to use an analemma-shaped gnomon
> to cast the shadow on the bowl, and at least month lines for the solar
> elevation.  The bowl will also have a rod and bracket on the bottom to
> allow it to be rotated for daylight-savings time and for local longitude
> corrections.
>
>
>
> Thanks in advance -- Brad
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
---
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Re: Hemicyclium correction - a figure might be needed

[Michael Ossipoff]

Typo:

When I said:

"So, in north declination, the south-notch would be used."

...I meant "*north*-notch".

Michael Ossipoff


On Tue, Oct 24, 2017 at 4:33 AM,  wrote:

> Thank you for your nice considerations.
>
> I think that some kind of visualization would make them more clear to a
> general public. Could you please support your ideas with a figure or a link
> to an external one (if exists)?
>
>
>
> Best regards,
>
> Wojtek
>
>
>
> *From: *Michael Ossipoff 
> *Sent: *Tuesday, October 24, 2017 1:32 AM
> *To: *Brad Thayer 
> *Cc: *sundial list 
> *Subject: *Re: Hemicyclium correction
>
>
>
>
>
> In the Hemicyclium discussion, the OP mentioned having 6-inch copper
> tubing. So, though it was a bit off-topic, I suggested that the tubing
> could be used for an additional, quicker, project, to make a south
> windowsill sundial--a Circumference-Aprerture Cylindrical Equatorial Dial.
>
> But, when I said that the axial dimension of the cylinder has to be at
> least 0.4335 times the diameter, I neglected the fact that there are south
> declinations as well as north declinations. (...funny, because we're in
> south declination now) So, with the circumference aperture in the middle of
> the cylinder, the cylinder's axial dimension has to be at least twice
> 0.4335, which is about 0.867 times the diameter.
>
> But my suggestion for marking points of the declination-lines for each
> hour was correct:
>
> At any hour-line, the axial displacement of a declination-line from the
> equinox-line is equal to the tangent of the declination times the direct
> distance between the circumference aperture and the intersection of that
> hour-line with the equinox-line
>
> That amounts to:
>
>
>
> (Tan dec)(R*2Sin(h) ).
>
> ...where h is the number hours from 12 noon.where R is the cylinderr's
> radius.
>
> Obviously more neatly written:
>
>
> (Tan dec)(DSin(h) ).
>
> ...where D is the diameter of the cylinder.
>
> -
>
>
>
> But a cone would be better than a cylinder, because it opens toward the
> north, the direction from which it would be observed--making it readable
> from a wider-range of directions, and making the inside surface more
> readable in generral. The use of a cone just slightly more complicates the
> declination-lines, but that would take this post even more off-topic.
>
> --
>
> I mentioned that I'd read of a drinking-cup with a hole in it being used
> as a cylindrical sundial. Of course if it were a Cylindrical Equatorial,
> orienting it just by estimation wouldn't give very accurate results. (A
> Cylindrical Equatorial is supposed to be a *mounted* dial, not a portable
> dial).
>
> But actually, maybe they were talking about a Cylindrical *Altitude*
> Dial. But, though that avoids the direction-estimation, the drinking-cup
> would need a way of hanging it in the right orientation, and so it wouldn't
> be much like an ordinary drinking-cup. ...and the line-marking would be
> complicated by the non-cylindrical shape of the cup.
>
>
>
> Michael Ossipoff
>
>
>
> On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer 
> wrote:
>
> I am looking to make a hemicyclium-type sundial (half-hemisphere) in a
> metal working class.  What little I can find on them says they are
> inaccurate, without being very clear on the problem.  It appears to me the
> only issue is it needs to be tilted so that the gnomon aligns with the
> Earth’s rotation axis; thus the half-bowl faces south and the gnomon points
> south, but the end of the gnomon that attaches to the bowl points north.
> Am I missing anything?  I am also looking to use an analemma-shaped gnomon
> to cast the shadow on the bowl, and at least month lines for the solar
> elevation.  The bowl will also have a rod and bracket on the bottom to
> allow it to be rotated for daylight-savings time and for local longitude
> corrections.
>
>
>
> Thanks in advance -- Brad
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
>
>
> ---
> https://lists.uni-koeln.de/mailman/listinfo/sundial
>
>
>
---
https://lists.uni-koeln.de/mailman/listinfo/sundial

Re: Hemicyclium correction - a figure might be needed

[Michael Ossipoff]

Hi--

I'll look for some images of Circumference-Aperture
Cylinder-Equatorials.and Cone-Equatorials.

It can be shown that the light-spot projected by the circumference-aperture
moves around the inside of the cylinder at a uniform rate that's twice the
rate at which an axial-gnomon's shadow would move.

So, during the 12 hours from 6:00 a.m. to 6:00 p.m, the light-spot moves
all the way around the inside of the cylinder, while the shadow of an axial
gnomon would only move halfway around the cylinder.

(But, as I was saying, if the south-window isn't facing due-south, and so
the early sunrise or late sunset illuminates the dial, then an additional
circumference aperture could be added at the 6:00 p.m. line, on the east
side of the cylinder, or at the 6:00 a.m. line, on the west side of the
cylinder. In that way, the dial would have more than 12-hour coverage.)

So, with the hour-lines twice as far apart, the dial is that much easier to
read accurately. The spacing between hour-lines is .2618 times the diameter
of the cylinder.
-
Of course, with a Cylinder-Equatorial dial, with the circumference-aperture
at the middle of the cylinder, with the declination-line-area having an
axial dimension of 0.867*D, the mid-summer position of the light-spot will
be far down the cylinder, where it could be more difficult to read. That
could be a reason to prefer a Cone-Equatorial.

But, with a Cylinder-Equatorial, the situation could be remedied by adding
another circumference-aperture barely south of the top of the north edge of
the cylinder.  ...or a notch in the north edge of the cylinder. So, in
north declination, the south-notch would be used. And in north declination,
the circumference-aperture would be used.

But then you'd need two separate sets of declination-lines, one for north
declination, and another for south declination. Maybe one set of lines
could be dotted.

Or maybe one set of declination-lines, labeled on the east side of the
cylinder could be solid lines on that side, and dotted on the other side.
And likewise for the other set of declination-lines, labeled on the west
side, solid on that side and dotted on the other side.
--
Of course, instead of a circumference-aperture and an edge-notch, one could
instead use two edge-notches, one north and one south.  But then the
cylinder would best be cut to an axial-dimension of 0.867*D. That would
increase the work of making the dial, and the force involved in sawing or
cutting could deform the cylinder.. The appeal of the combination of a
circumference-aperature in the top- middle, and an edge-notch at the top of
the north-edge  (or just using the aperture and no notch), is that the
cylinder wouldn't have to be sawed or cut.

With the cylinder or cone supported at its north end by a support with a
semicircular hole in which the north end of the cylinder rests, and with
the south-end of the cylinder resting on the window-sill, of course the
cylinder's inclination above the horizontal is easily adjusted by sliding
the cylinder (or cone) northward or southward   ...to incline the cylinder
or cone with its axis parallel to the Earth's axis.

Michael Ossipoff







On Tue, Oct 24, 2017 at 4:33 AM,  wrote:

> Thank you for your nice considerations.
>
> I think that some kind of visualization would make them more clear to a
> general public. Could you please support your ideas with a figure or a link
> to an external one (if exists)?
>
>
>
> Best regards,
>
> Wojtek
>
>
>
> *From: *Michael Ossipoff 
> *Sent: *Tuesday, October 24, 2017 1:32 AM
> *To: *Brad Thayer 
> *Cc: *sundial list 
> *Subject: *Re: Hemicyclium correction
>
>
>
>
>
> In the Hemicyclium discussion, the OP mentioned having 6-inch copper
> tubing. So, though it was a bit off-topic, I suggested that the tubing
> could be used for an additional, quicker, project, to make a south
> windowsill sundial--a Circumference-Aprerture Cylindrical Equatorial Dial.
>
> But, when I said that the axial dimension of the cylinder has to be at
> least 0.4335 times the diameter, I neglected the fact that there are south
> declinations as well as north declinations. (...funny, because we're in
> south declination now) So, with the circumference aperture in the middle of
> the cylinder, the cylinder's axial dimension has to be at least twice
> 0.4335, which is about 0.867 times the diameter.
>
> But my suggestion for marking points of the declination-lines for each
> hour was correct:
>
> At any hour-line, the axial displacement of a declination-line from the
> equinox-line is equal to the tangent of the declination times the direct
> distance between the circumference aperture and the intersection of that
> hour-line with the equinox-line
>
> That amounts to:
>
>
>
> (Tan dec)(R*2Sin(h) ).
>
> ...where h is the number hours from 12 

RE: Hemicyclium correction - a figure might be needed

[wsgalinski]

Thank you for your nice considerations. 
I think that some kind of visualization would make them more clear to a general 
public. Could you please support your ideas with a figure or a link to an 
external one (if exists)?

Best regards,

Wojtek

From: Michael Ossipoff
Sent: Tuesday, October 24, 2017 1:32 AM
To: Brad Thayer
Cc: sundial list
Subject: Re: Hemicyclium correction


In the Hemicyclium discussion, the OP mentioned having 6-inch copper tubing. 
So, though it was a bit off-topic, I suggested that the tubing could be used 
for an additional, quicker, project, to make a south windowsill sundial--a 
Circumference-Aprerture Cylindrical Equatorial Dial.
But, when I said that the axial dimension of the cylinder has to be at least 
0.4335 times the diameter, I neglected the fact that there are south 
declinations as well as north declinations. (...funny, because we're in south 
declination now) So, with the circumference aperture in the middle of the 
cylinder, the cylinder's axial dimension has to be at least twice 0.4335, which 
is about 0.867 times the diameter.
But my suggestion for marking points of the declination-lines for each hour was 
correct:
At any hour-line, the axial displacement of a declination-line from the 
equinox-line is equal to the tangent of the declination times the direct 
distance between the circumference aperture and the intersection of that 
hour-line with the equinox-line
That amounts to:

(Tan dec)(R*2Sin(h) ). 
...where h is the number hours from 12 noon.where R is the cylinderr's radius.
Obviously more neatly written:

(Tan dec)(DSin(h) ).
...where D is the diameter of the cylinder.
-

But a cone would be better than a cylinder, because it opens toward the north, 
the direction from which it would be observed--making it readable from a 
wider-range of directions, and making the inside surface more readable in 
generral. The use of a cone just slightly more complicates the 
declination-lines, but that would take this post even more off-topic.
--
I mentioned that I'd read of a drinking-cup with a hole in it being used as a 
cylindrical sundial. Of course if it were a Cylindrical Equatorial, orienting 
it just by estimation wouldn't give very accurate results. (A Cylindrical 
Equatorial is supposed to be a mounted dial, not a portable dial). 

But actually, maybe they were talking about a Cylindrical Altitude Dial. But, 
though that avoids the direction-estimation, the drinking-cup would need a way 
of hanging it in the right orientation, and so it wouldn't be much like an 
ordinary drinking-cup. ...and the line-marking would be complicated by the 
non-cylindrical shape of the cup.

Michael Ossipoff

On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer  
wrote:
I am looking to make a hemicyclium-type sundial (half-hemisphere) in a metal 
working class.  What little I can find on them says they are inaccurate, 
without being very clear on the problem.  It appears to me the only issue is it 
needs to be tilted so that the gnomon aligns with the Earth’s rotation axis; 
thus the half-bowl faces south and the gnomon points south, but the end of the 
gnomon that attaches to the bowl points north.  Am I missing anything?  I am 
also looking to use an analemma-shaped gnomon to cast the shadow on the bowl, 
and at least month lines for the solar elevation.  The bowl will also have a 
rod and bracket on the bottom to allow it to be rotated for daylight-savings 
time and for local longitude corrections.
 
Thanks in advance -- Brad

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