Re: Hemicyclium correction - a figure might be needed
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 --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Hemicyclium correction
Correction: I'd said: (Tan dec)(R*2Sin(h) ). ...where h is the number hours from 12 noon.where R is the cylinder's radius. Here's the correction: Instead of "hours from 12 noon", It should say: "...where h is 15 degrees times the number of hours from 6 a.m., during the a.m. hours, or the number of hours from 6 p.m., during the p.m. hours." ...which could also be said as: " 15 degrees times (6 minus the number of hours from 12 noon)". ...for the hours from 6 a.m. to 6 p.m. Michael Ossipoff On Mon, Oct 23, 2017 at 7:31 PM, Michael Ossipoff wrote: > > 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
Re: Hemicyclium correction - a figure might be needed
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 > > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Hemicyclium correction - a figure might be needed
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
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
RE: Hemicyclium correction - a figure might be needed
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
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
Re: Hemicyclium correction
I find the video below extremely instructive! https://youtu.be/0hs6QqwJIhs The sundial is marked in old temporary (or seasonal) hours. Changing them to modern hours does not make much sense to me. For it to become a hemicyclium I guess you just have to leave out the unused part of the half-sphere. Dan Uza On Sun, Oct 22, 2017 at 2:40 PM, Patrick Powers < patrick_pow...@compuserve.com> wrote: > Hi Brad > > Further to your interest in an hemicyclium you might like to know of this > link to the former webpages of the late Frans Maes who set out his > instructions for *“Construction of Hemispherium”* some time ago and which > is based on several earlier documents – all referenced. You might find it > useful – or at least interesting! > > http://www.fransmaes.nl/zonnewijzers/downloads/hemisph.htm > > Good luck > > Patrick > > > > *From:* Brad Thayer > *Sent:* Monday, October 16, 2017 1:48 PM > *To:* sundial@uni-koeln.de > *Subject:* Hemicyclium correction > > > 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
Hi Patrick, Thanks for pointing this out. Fortunately, I am still alive and sometimes kicking a bit ... I put the link to Fer de Vries' article temporarily on my own website as it was the quickest and easiest way to answer a query by someone on this list. By now, the (same) article is also available on the website of the Dutch Sundial Society. Best regards, Frans Maes <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> Virusvrij. www.avg.com <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2> On Sun, Oct 22, 2017 at 7:36 PM, Patrick Powers < patrick_pow...@compuserve.com> wrote: > Hi Brad, > > My message re your interest in hemicyclia should have made it clear that > it was Fer De Vries’s original work on the construction of a Hemispherium > that he placed on his website and which was republished after his death by > Frans Maes and then placed on his own website for us to read today. My > sincere apologies to Frans! > > Patrick > > *From:* Patrick Powers > *Sent:* Sunday, October 22, 2017 12:40 PM > *To:* Brad Thayer ; sundial@uni-koeln.de > *Subject:* Re: Hemicyclium correction > > Hi Brad > > Further to your interest in an hemicyclium you might like to know of this > link to the former webpages of the late Frans Maes who set out his > instructions for *“Construction of Hemispherium”* some time ago and which > is based on several earlier documents – all referenced. You might find it > useful – or at least interesting! > > http://www.fransmaes.nl/zonnewijzers/downloads/hemisph.htm > > Good luck > > Patrick > > > > *From:* Brad Thayer > *Sent:* Monday, October 16, 2017 1:48 PM > *To:* sundial@uni-koeln.de > *Subject:* Hemicyclium correction > > > 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
Hi Brad, My message re your interest in hemicyclia should have made it clear that it was Fer De Vries’s original work on the construction of a Hemispherium that he placed on his website and which was republished after his death by Frans Maes and then placed on his own website for us to read today. My sincere apologies to Frans! Patrick From: Patrick Powers Sent: Sunday, October 22, 2017 12:40 PM To: Brad Thayer ; sundial@uni-koeln.de Subject: Re: Hemicyclium correction Hi Brad Further to your interest in an hemicyclium you might like to know of this link to the former webpages of the late Frans Maes who set out his instructions for “Construction of Hemispherium” some time ago and which is based on several earlier documents – all referenced. You might find it useful – or at least interesting! http://www.fransmaes.nl/zonnewijzers/downloads/hemisph.htm Good luck Patrick From: Brad Thayer Sent: Monday, October 16, 2017 1:48 PM To: sundial@uni-koeln.de Subject: Hemicyclium correction 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
Re: Hemicyclium correction
Hi Brad Further to your interest in an hemicyclium you might like to know of this link to the former webpages of the late Frans Maes who set out his instructions for “Construction of Hemispherium” some time ago and which is based on several earlier documents – all referenced. You might find it useful – or at least interesting! http://www.fransmaes.nl/zonnewijzers/downloads/hemisph.htm Good luck Patrick From: Brad Thayer Sent: Monday, October 16, 2017 1:48 PM To: sundial@uni-koeln.de Subject: Hemicyclium correction 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
Re: Hemicyclium correction
Correction: I said that the declination lines would be circles around the cylinder's inside circumference. Actually, because the distance of the light-spot from the circumference-aperature varies, around the dial, the declination lines wouldn't be that simple. The drawing of the declination lines would just be a bit trickier. At a certain hour-line, the axial displacement of the declination-line from the equinox line would be equal to the tangent of the declination, times the straight-line distance between the circumference aperature and the place where the hour-line intersects the equinox line. If a cone (such as a drinking-cup) is used instead of a cylinder, that complicates the declination-lines a bit more, but it's still do-able. I've read that, in ancient times, drinking-cups, perforated with a circumference-aperature nodus, were sometimes used as portable sundials. Presumably, for some particular property-area, a person might know what tree, building or mountain landmark was due north. S/he could point the cup in that direction, with the circumference aperature on top, pointing the cup upward so that its axis points above the horizontal by an amount approximately equal to the local latitude. ...and read the time from the hour-lines marked inside the cup. Obviously the circumference-aperature would limit how high you could fill the cup, when using it for drinking. Michael Ossipoff On Thu, Oct 19, 2017 at 2:31 PM, Michael Ossipoff wrote: > Of course, for the Cylinder Equatorial with circumference aperature, you > could have declination-ilnes, which would be circles around the cylinder's > circumference. > > Michael Ossipoff > > On Wed, Oct 18, 2017 at 10:23 PM, Brad Thayer > wrote: > >> Michael, >> >> >> >> Thank you for the lengthy response. >> >> >> >> This will actually be the fifth sundial I have completed (and the 6th >> that I have started). I’ve already made a band-equatorial (using “Mayan >> digits”), two analemmatic horizonatal sundials, a south-facing vertical >> sundial, and started a cylindrical sundial (aka, shepherds staff). With >> each one, I try something new and challenging. I also use it as a way to >> improve my metal working skills. As I am currently taking a copper >> raising/sinking and chasing metal forming class, I was interested in making >> a bowl with chased lines (aka, repousse) for practice, hence the idea for >> the hemicyclium. >> >> >> >> I lucked into some used 14 gauge copper tubing about 6 inches in >> diameter, which I annealed, cut open and pounded flat as a starting point. >> So I have the basic starting materials. >> >> >> >> If the inside surface is marked with the lines analogous to lines of >> longitude on a globe spaced 15 degrees apart, radiating from the “pole” of >> the hemicyclium, and the entire device is tilted to align with the earth’s >> axis, would it then read out in Local True Solar Time? That is my primary >> sticking point. I’d prefer that than the ancient Temporary hours. It >> would seem it would be mathematically similar to a section of an armillary >> sphere. >> >> >> >> With a proper adjustable mount, I can adjust for the longitude correction >> (I am currently about 4 degrees away from my nearest meridian) and DST >> twice a year as well. >> >> >> >> *From:* Michael Ossipoff [mailto:email9648...@gmail.com] >> *Sent:* Tuesday, October 17, 2017 8:44 PM >> *To:* Brad Thayer >> *Cc:* sundial list >> *Subject:* Re: Hemicyclium correction >> >> >> >> >> >> >> >> 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. >> >> >> >> But the way, I've seen it spelled "Hemicycleum" as well. I don't know >> which is correct, but "Hemicycleum" looks better, it seems to me. But I'll >> use your spelling. It's probably better-accpeted. >> >> >> >> Whoever said that was mistaken. Hemicyclia are as in principle as >> accurate as any sundial can be. >> >> >> >> In ancient times, Hemicyclia were devised, instead of our modern >> polar-gnomon garden sundial, or our equatorial sundials, because in those >> days, they weren't using our Equal-Hours for civil time (Astronomers used >> it though). They were using "Temporary Hours), that divided each day into >> 12 equal hours,
Re: Hemicyclium correction
Of course, for the Cylinder Equatorial with circumference aperature, you could have declination-ilnes, which would be circles around the cylinder's circumference. Michael Ossipoff On Wed, Oct 18, 2017 at 10:23 PM, Brad Thayer wrote: > Michael, > > > > Thank you for the lengthy response. > > > > This will actually be the fifth sundial I have completed (and the 6th > that I have started). I’ve already made a band-equatorial (using “Mayan > digits”), two analemmatic horizonatal sundials, a south-facing vertical > sundial, and started a cylindrical sundial (aka, shepherds staff). With > each one, I try something new and challenging. I also use it as a way to > improve my metal working skills. As I am currently taking a copper > raising/sinking and chasing metal forming class, I was interested in making > a bowl with chased lines (aka, repousse) for practice, hence the idea for > the hemicyclium. > > > > I lucked into some used 14 gauge copper tubing about 6 inches in diameter, > which I annealed, cut open and pounded flat as a starting point. So I have > the basic starting materials. > > > > If the inside surface is marked with the lines analogous to lines of > longitude on a globe spaced 15 degrees apart, radiating from the “pole” of > the hemicyclium, and the entire device is tilted to align with the earth’s > axis, would it then read out in Local True Solar Time? That is my primary > sticking point. I’d prefer that than the ancient Temporary hours. It > would seem it would be mathematically similar to a section of an armillary > sphere. > > > > With a proper adjustable mount, I can adjust for the longitude correction > (I am currently about 4 degrees away from my nearest meridian) and DST > twice a year as well. > > > > *From:* Michael Ossipoff [mailto:email9648...@gmail.com] > *Sent:* Tuesday, October 17, 2017 8:44 PM > *To:* Brad Thayer > *Cc:* sundial list > *Subject:* Re: Hemicyclium correction > > > > > > > > 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. > > > > But the way, I've seen it spelled "Hemicycleum" as well. I don't know > which is correct, but "Hemicycleum" looks better, it seems to me. But I'll > use your spelling. It's probably better-accpeted. > > > > Whoever said that was mistaken. Hemicyclia are as in principle as accurate > as any sundial can be. > > > > In ancient times, Hemicyclia were devised, instead of our modern > polar-gnomon garden sundial, or our equatorial sundials, because in those > days, they weren't using our Equal-Hours for civil time (Astronomers used > it though). They were using "Temporary Hours), that divided each day into > 12 equal hours, for their civil time. > > > > To achieve that, they used a stick-tip nodus or bead-nodus. to cast a > point-shadow on the hemicyclium surface. As the Sun's declination changes > seasonally, of course the tip-nodus's path on the hemicyclium changes too. > So the hour-lines were curves, drawn so that, for any particular solar > declination, those marks divide the day (sunrise to sunset) into 12 equal > parts. > > > > As you can imagine, that makes the dial more complicated than modern ones. > "Early" doesn't always mean "simpler". > > > > ...and so there was much opportunity for error in the calclulations and > drafting,for those curved hour-lines. > > > > So maybe some hemicyclia *were* inaccurately drafted. For one thing, of > course the exact time of day wasn't as crucial in those days, and of course > the more precisely made, and prestigiously made, a sundial was, the more it > was likely to cost. > > > > But there's no reason why your hemicyclium should be made for Temporary > Hours. Make it for our modern Equal-Hours, also referred to as Local True > Solar Time (LTST). > > > > > > It appears to me the only issue is it needs to be tilted so that the > gnomon aligns with the Earth’s rotation axis; > > > > The equinox circle on the Hemicyclium, the line that the tip-nodus follows > on the day of the equinox, should be a circle parallel to the celestial > equator. > > > > And yes, if you're going to use a polar gnomon instead of a tip-nodus, > then that polar gnomon should be parallel to the Earth's axis, pointed at > the north celestial pole. ...and should go through the center of the sphere > from which the Hemicy
Re: Hemicyclium correction
Brad-- I don't know if this is of interest or not, because I realize that the Hemicyclium is your main project. If you have any of that 6-inch diameter copper tubing left, then why not cut off a section of it, with width equal to half the diameter, for an additional project that can be completed much more quickly, giving you an interesting and accurate south-window-sill dial, while you're working on the main project, the Hemicyclium. This would be a Cylinder-Equatorial Dial, with a circumference-aperature nodus, to cast a light-spot on the inside surface of the cylinder. Such a dial is most easily read from the north, from above the dial. In other words, it would be perfect for a window-sill dial, for a south window For a south windowsill, that kind of dial has major advantages. Unlike a horizontal dial on a south windowsill, it doesn't have a gnomon that's pointing up toward the observer (eye-hazard) Being an Equatorial, its hour-lines are equally-spaced, for the easiest accurate linear-interpolation of the time between hour-lines. (Of course the Hemicyclium, being effectively an Equatorial Dial too, shares that advantage.) And because, over a 12-hour period, the light-spot travels the entire circumference of the cylinder, the lines for the hours will be over an inch and a half apart. ...making it that much easier to read the time. ...especially since that great amount of space between hour-lines allows the convenient reading of quarter hour (or maybe 10-minute) lines. You'd drill the circumference-aperature at the middle of the cylinder's width. If the width is half of the diameter (.4335 times the diameter would be enough), then there will be room for the circumferance-aperature's light-spot to be on the cylinder all year. A disadvantage is that this type of dial only tells 12 hours of time. But as I mentioned in an earlier post, that can be remedied by having more than one circumferance-aperature nodus. Of course if your house faces due south, then a south-windowsill dial won't have more than 12 hours of sunlight anyway. But suppose that your house is facing a little left or right of due south. Then you'll be getting some sunlight before 6:00 a.m. or after 6:00 p.m. Say, for example that your house faces a little left of due south. Then you get a little bit of sun on the windowsill before 6:00 a.m. So drill a circumference aperature at the 6:00 p.m. line, at the left (east) side of the cylinder. Of course you'd have to be sure tor read the right light-spot. You could have special early-morning time markings on the cylinder for early mornings. Of course it would be the reverse if your house faces a little to the right of due south. Of course you could cover the early-morning circumference aperature when it isn't in use. A Cylinder-Equatorial is a good choice for a south windowsill, and, if you have any of that 6-inch tubing left over, then it would be a quick project, and you'd have a windowsill dial while working on your main project, the Hemicyclium. Michael Ossipoff On Wed, Oct 18, 2017 at 10:23 PM, Brad Thayer wrote: > Michael, > > > > Thank you for the lengthy response. > > > > This will actually be the fifth sundial I have completed (and the 6th > that I have started). I’ve already made a band-equatorial (using “Mayan > digits”), two analemmatic horizonatal sundials, a south-facing vertical > sundial, and started a cylindrical sundial (aka, shepherds staff). With > each one, I try something new and challenging. I also use it as a way to > improve my metal working skills. As I am currently taking a copper > raising/sinking and chasing metal forming class, I was interested in making > a bowl with chased lines (aka, repousse) for practice, hence the idea for > the hemicyclium. > > > > I lucked into some used 14 gauge copper tubing about 6 inches in diameter, > which I annealed, cut open and pounded flat as a starting point. So I have > the basic starting materials. > > > > If the inside surface is marked with the lines analogous to lines of > longitude on a globe spaced 15 degrees apart, radiating from the “pole” of > the hemicyclium, and the entire device is tilted to align with the earth’s > axis, would it then read out in Local True Solar Time? That is my primary > sticking point. I’d prefer that than the ancient Temporary hours. It > would seem it would be mathematically similar to a section of an armillary > sphere. > > > > With a proper adjustable mount, I can adjust for the longitude correction > (I am currently about 4 degrees away from my nearest meridian) and DST > twice a year as well. > > > > *From:* Michael Ossipoff [mailto:email9648...@gmail.com] > *Sent:* Tuesday, October 17, 2017 8:44 PM > *To:* Brad Thayer > *Cc:* sundial list > *Subject:*
Re: Hemicyclium correction
Just one safety quibble: If you mount the spike sticking up, then it will be an eye-hazard, even with the ball on its end. That's a good reason to mount the spike horizontally, at the rim of the bowl. It could be mounted in a north-south groove at the south side of the bowl. Mounting the spike at the south side of the bowl is likewise probably best for eye-safety, because people will more likely be reading the dial from its south side. ...because the dial-lines are mostly toward the north side. That's probably traditional too. Anyway, that's traditional, it seems to me, and so it's better of ancient realism. Besides, with the spike horizontal, its tip-nodus will still have a shadow that the spike itself doesn't get in the way of at equinox noon. Michael Ossipoff f . On Thu, Oct 19, 2017 at 11:13 AM, Frank King wrote: > Dear Brad, > > I'm delighted that you enjoyued > my "tutorial"... > > > However, its your step 19 I am > > interested in. > > Ah yes. That's where I mention > marking out equal hours. I thought > you would be most interested in > that step :-) > > You add... > > > And if I do tilt the hemispherium > > so that the horizon line is now > > instead parallel to the earth's > > axis, does that solve any of the > > issues? > > This is like taking an aircraft as > your inspiration for designing a > car and not appreciating what the > wings are for. > > The absolutely key feature of the > hemicyclium design is that, at its > top, there is a FLAT HORIZONTAL > surface. > > It isn't like that just so the > Greek user could put his Retsina > glass on it. It is like that in > order to be parallel to the plane > of the horizon and... > > That is important because it > echos the position of the sun at > sunrise and sunset and... > > That is important because the > principal purpose of this dial > was to divide the day into > equal intervals of time starting > at sunrise and ending at sunset. > > These unequal hours may not be > to your taste but this is the > scheme that was in widespread > use for thousands of years! > Why not educate your friends? > Why not educate yourself? > > OK, I'll get round to what you > really want shortly but, meantime, > I am going to stick to the original > purpose... > > In my previous message I was > simplifying matters by saying > that you should cut the sphere > (the orange) into quarters. > > The problem with using a quarter > of a sphere (and this also applies > if you insist on equal hours) is > that you can't represent sunrise > and sunset in the summer months. > > A real hemicyclium was rather more > than a quarter of a sphere. Take > a look at: > > http://www.sundials.co.uk/leicester/fig04.jpg > > You can see the horizontal surface > easily enough and you can also see > a forward-sloping face at the front. > > The slope, relative to the vertical, > matches the local latitude. This is > about 37 degrees off the vertical > in Greece but 50+ in the U.K. > > By leaning forward this allows the > horizontal surface to grow so that > its inside rim is no longer a > semi-circle. It is now much more > of a circle. The tip of the spike > serves as the nodus and this is at > the centre of the rim circle. The > two "wings" are way beyond this > tip. > > If you look at the markings you can see > the three main constant-declination > arcs. The middle one is a great circle > and the tip of the spike is the centre > of this circle too. > > The upper arc is for the winter > solstice and the lower is for the > summer solstice. These are small > circles. If you hold one end of > a piece of string on the tip of > the spike and run the other end > round either of these circles > you would see the string sweeps > out a cone, not a disc. > > OK, once you have this elegant > hollow shape you can make cardboard > templates which exactly fit these > three circular arcs. The template > for the equinoctial arc will be an > exact semi-circle. The other two > have a slightly smaller radius > than the equinoctial circle. > > Clearly, the template for the > summer solstice is more than a > semi-circle and that for the > winter solstice is less than > a semi-circle. If you fit the > two together you should get a > perfect circle. Can you see > why? > > Now all you have to do is to > divide the rims of each of these > three circles into 12 equal parts. > This gives you the unequal hours > of the day exactly as in fig 4. > > Of course, what you really want > are new-fangle
Re: Hemicyclium correction
Dear Brad, I'm delighted that you enjoyued my "tutorial"... > However, its your step 19 I am > interested in. Ah yes. That's where I mention marking out equal hours. I thought you would be most interested in that step :-) You add... > And if I do tilt the hemispherium > so that the horizon line is now > instead parallel to the earth's > axis, does that solve any of the > issues? This is like taking an aircraft as your inspiration for designing a car and not appreciating what the wings are for. The absolutely key feature of the hemicyclium design is that, at its top, there is a FLAT HORIZONTAL surface. It isn't like that just so the Greek user could put his Retsina glass on it. It is like that in order to be parallel to the plane of the horizon and... That is important because it echos the position of the sun at sunrise and sunset and... That is important because the principal purpose of this dial was to divide the day into equal intervals of time starting at sunrise and ending at sunset. These unequal hours may not be to your taste but this is the scheme that was in widespread use for thousands of years! Why not educate your friends? Why not educate yourself? OK, I'll get round to what you really want shortly but, meantime, I am going to stick to the original purpose... In my previous message I was simplifying matters by saying that you should cut the sphere (the orange) into quarters. The problem with using a quarter of a sphere (and this also applies if you insist on equal hours) is that you can't represent sunrise and sunset in the summer months. A real hemicyclium was rather more than a quarter of a sphere. Take a look at: http://www.sundials.co.uk/leicester/fig04.jpg You can see the horizontal surface easily enough and you can also see a forward-sloping face at the front. The slope, relative to the vertical, matches the local latitude. This is about 37 degrees off the vertical in Greece but 50+ in the U.K. By leaning forward this allows the horizontal surface to grow so that its inside rim is no longer a semi-circle. It is now much more of a circle. The tip of the spike serves as the nodus and this is at the centre of the rim circle. The two "wings" are way beyond this tip. If you look at the markings you can see the three main constant-declination arcs. The middle one is a great circle and the tip of the spike is the centre of this circle too. The upper arc is for the winter solstice and the lower is for the summer solstice. These are small circles. If you hold one end of a piece of string on the tip of the spike and run the other end round either of these circles you would see the string sweeps out a cone, not a disc. OK, once you have this elegant hollow shape you can make cardboard templates which exactly fit these three circular arcs. The template for the equinoctial arc will be an exact semi-circle. The other two have a slightly smaller radius than the equinoctial circle. Clearly, the template for the summer solstice is more than a semi-circle and that for the winter solstice is less than a semi-circle. If you fit the two together you should get a perfect circle. Can you see why? Now all you have to do is to divide the rims of each of these three circles into 12 equal parts. This gives you the unequal hours of the day exactly as in fig 4. Of course, what you really want are new-fangled equal hours... Well, you make the same three templates as before and then, on each, mark the centre point on the rim. This is the noon point. You then mark off at 15-degree intervals either side of this point. This is easy for the equinoctial template. For the other two I suggest you butt them together so you can see the centre of the common circle. It is then a case of joining the dots to get the equal hour lines. You will find that several hour lines run up to the rim and abruptly stop. With the unequal hours ALL the lines run from the winter solstice arc to the summer solstice arc as in fig 4. As a refinement, I don't care for the way the Greeks mounted their spikes! I would allow you to improve on that... I suggest you drill a hole at the point where the noon line and equinoctial arc intersect. You now need a rod whose exposed length matches the radius of your sphere. Fix the hidden part in the hole and fix a small ball at the outer end to serve as the nodus. Make sure it is at the centre of the main horizontal rim. This means that at noon on the day of an equinox, the shadow of the nodus falls at the foot of the support rod. If you REALLY want a polar-oriented gnomon then you drill a hole through the nodus that is at right-angles to the support rod and insert the gnomon into this new hole. Make sure it is oriented towards the north celestial pole. I regard this as serious uglification. Best of luck with your efforts. Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Hemicyclium correction
Brad-- > > If the inside surface is marked with the lines analogous to lines of > longitude on a globe spaced 15 degrees apart, radiating from the “pole” of > the hemicyclium, and the entire device is tilted to align with the earth’s > axis, would it then read out in Local True Solar Time? > Yes, the hour-lines would be exactly like the 15-degree meridian longitude-lines of a globe. (plus whatever intermediate fractional-hour lines). It seems to me that, in the photos and drawings I've seen, both the Hemicyclia and the Hemispheria had a horizontal flat top edge-surface. With that bowl-edge horizontal, and with the stick-tip nodus at the same level as that bowl-edge, the dial wIould tell time whenever the Sun is above the horizon. (So do the Horizontal Dial, the Band-Equatorial, and lots of others) It also seems to me that, in the photos and drawings that I've seen, the stick for the stick-end nodus was horizontal, sticking out so that its tip, the nodus, is at the center of the bowl. If you're sure you want the bigger task of a Hemicyclium instead of a Band-Equatorial, then I'd use the traditional horizontal stick, with its end (nodus) at the bowl's center. ...instead of using a polar-parallel gnomon. Easier, for one thing, and more realistic, for a Hemicyclium or Hemispherium. Though the system of hour-lines should have its poles at the ends of an imaginary line parallel with the Earth's axis (north-south, tipped up at the north-end by an amount equal to your north-latitude), I'd just leave the top-cut, bowl-edge horizontal, like the pictures that i've seen. Anyway, if the surface that includes the bowl edge were tipped from the horizontal, wouldn't that interfere with ensuring that the dial will tell time whenever the Sun is above the horizon? I'd leave the bowl-top edge horizontal. I think that's how Hemicyclia and Hemispheria always were. I'd have declination-lines in the bowl, in addition to the hour-lines. Of course the declination-lines would be exactly like the parallels on a globe. People often mark declination-lines with the date. I'd have the lines marked with declination-degrees as well. In older centuries, they marked declination-lines with zodiac signs instead of month-names. That made sense really, because the zodiac signs coincide with exact solar ecliptic longitudes, corresponding to exact declinations (if you disregard the small change-rate of the obliquity). But of course nowadays the months are much more famiiar. But I'd mark the declination-lines in degrees too. That is my primary sticking point. I’d prefer that than the ancient Temporary hours. It would seem it would be mathematically similar to a section of an armillary sphere. Yes, just maybe a more challenging construction than an Armillary Band-Equatorial. The globe-meridian-like hour-lines would be more work than the straight hour lines on a Band-Equatorial. But, with your metal-working experience, you probably *want* something more challenging. > > > With a proper adjustable mount, I can adjust for the longitude correction > (I am currently about 4 degrees away from my nearest meridian) and DST > twice a year as well. > Ok, but that seems unnecessary extra work, since the longitude-correction could be added to EoT in your conversion-table plaque displayed near the dial. Anyway, it seems more aesthetic for a dial to give Local True Solar Time. Interesting project. I once considered proposing a project of a brass band-equatorial mounted in a concrete structure resembling a Hemicyclium. The copper bowl will have a cool ancient look when it weathers. Michael Ossipoff > > *From:* Michael Ossipoff [mailto:email9648...@gmail.com] > *Sent:* Tuesday, October 17, 2017 8:44 PM > *To:* Brad Thayer > *Cc:* sundial list > *Subject:* Re: Hemicyclium correction > > > > > > > > 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. > > > > But the way, I've seen it spelled "Hemicycleum" as well. I don't know > which is correct, but "Hemicycleum" looks better, it seems to me. But I'll > use your spelling. It's probably better-accpeted. > > > > Whoever said that was mistaken. Hemicyclia are as in principle as accurate > as any sundial can be. > > > > In ancient times, Hemicyclia were devised, instead of our modern > polar-gnomon garden sundial, or our equatorial sundials, because in those > days, they weren't using our Equal-Hours for civil time (Astronomers used > it though). They were using "Temporary Hours), that divided each day into > 12 equal hours, fo
RE: Hemicyclium correction
Michael, Thank you for the lengthy response. This will actually be the fifth sundial I have completed (and the 6th that I have started). I’ve already made a band-equatorial (using “Mayan digits”), two analemmatic horizonatal sundials, a south-facing vertical sundial, and started a cylindrical sundial (aka, shepherds staff). With each one, I try something new and challenging. I also use it as a way to improve my metal working skills. As I am currently taking a copper raising/sinking and chasing metal forming class, I was interested in making a bowl with chased lines (aka, repousse) for practice, hence the idea for the hemicyclium. I lucked into some used 14 gauge copper tubing about 6 inches in diameter, which I annealed, cut open and pounded flat as a starting point. So I have the basic starting materials. If the inside surface is marked with the lines analogous to lines of longitude on a globe spaced 15 degrees apart, radiating from the “pole” of the hemicyclium, and the entire device is tilted to align with the earth’s axis, would it then read out in Local True Solar Time? That is my primary sticking point. I’d prefer that than the ancient Temporary hours. It would seem it would be mathematically similar to a section of an armillary sphere. With a proper adjustable mount, I can adjust for the longitude correction (I am currently about 4 degrees away from my nearest meridian) and DST twice a year as well. From: Michael Ossipoff [mailto:email9648...@gmail.com] Sent: Tuesday, October 17, 2017 8:44 PM To: Brad Thayer Cc: sundial list Subject: Re: Hemicyclium correction On Mon, Oct 16, 2017 at 8:48 AM, Brad Thayer mailto:wissenschaft...@verizon.net> > 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. But the way, I've seen it spelled "Hemicycleum" as well. I don't know which is correct, but "Hemicycleum" looks better, it seems to me. But I'll use your spelling. It's probably better-accpeted. Whoever said that was mistaken. Hemicyclia are as in principle as accurate as any sundial can be. In ancient times, Hemicyclia were devised, instead of our modern polar-gnomon garden sundial, or our equatorial sundials, because in those days, they weren't using our Equal-Hours for civil time (Astronomers used it though). They were using "Temporary Hours), that divided each day into 12 equal hours, for their civil time. To achieve that, they used a stick-tip nodus or bead-nodus. to cast a point-shadow on the hemicyclium surface. As the Sun's declination changes seasonally, of course the tip-nodus's path on the hemicyclium changes too. So the hour-lines were curves, drawn so that, for any particular solar declination, those marks divide the day (sunrise to sunset) into 12 equal parts. As you can imagine, that makes the dial more complicated than modern ones. "Early" doesn't always mean "simpler". ...and so there was much opportunity for error in the calclulations and drafting,for those curved hour-lines. So maybe some hemicyclia were inaccurately drafted. For one thing, of course the exact time of day wasn't as crucial in those days, and of course the more precisely made, and prestigiously made, a sundial was, the more it was likely to cost. But there's no reason why your hemicyclium should be made for Temporary Hours. Make it for our modern Equal-Hours, also referred to as Local True Solar Time (LTST). It appears to me the only issue is it needs to be tilted so that the gnomon aligns with the Earth’s rotation axis; The equinox circle on the Hemicyclium, the line that the tip-nodus follows on the day of the equinox, should be a circle parallel to the celestial equator. And yes, if you're going to use a polar gnomon instead of a tip-nodus, then that polar gnomon should be parallel to the Earth's axis, pointed at the north celestial pole. ...and should go through the center of the sphere from which the Hemicyclium is cut. But, if you're going to do that, then why make it a Hemicyclium? Why not just a Band-Equatorial dial? You could mount a cylindrical brass band, parallel to the equator, with a polar-parallel rod-gnomon mounted to go through the central axis of that band. You could mount that brass Band-Equatorial on a mount of whatever kind. For extra durability, you could mount it inside a concrete structure resembling a Hemicyclium. The durability of a Hemicyclium, with the simplicity and modernity of a Band-Equatorial. So then the hour-lines would just be polar-parallel lines equidistantly drawn along the inside of the band, dividing the lower half of the band into 12 equal parts. Of course you'd want
RE: Hemicyclium correction
Frank, Thank you for the tutorial. I believe I followed all the logic and steps. However, its your step 19 I am interested in. Any suggestions as to how to mark the inner surface with equal duration hours throughout the year? And if I do tilt the hemispherium so that the horizon line is now instead parallel to the earth's axis, does that solve any of the issues? -Original Message- From: Frank King [mailto:f...@cl.cam.ac.uk] Sent: Monday, October 16, 2017 11:12 AM To: Brad Thayer Cc: sundial@uni-koeln.de; Frank King Subject: Re: Hemicyclium correction Dear Brad, You say: > I am looking to make a > hemicyclium-type sundial > (half-hemisphere) in a > metal working class. > Am I missing anything? Er, yes. Rather a lot alas... Before you start bashing metal it may be worth spending rather less effort on a prototype. > ...they are inaccurate... I am not sure where you got that from. There is no reason why they shouldn't be accurate provided you know what you can expect of one. > ...without being very clear > on the problem. I suspect the writer of your quote either didn't know what a hemicyclium was or had looked at one and noted that it didn't indicate the same time as his watch so it must be wrong. > It appears to me the only > issue is it needs to be > tilted so that the gnomon > aligns with the Earth's > rotation axis... Er, no. The polar-oriented gnomon wasn't invented for nearly 1500 years after the hemicyclium was in common use. What looks like a gnomon and may well be CALLED a gnomon is not what you think of as a gnomon. It is actually a "nodus support". Only the shadow of the tip is of interest. > I am also looking to use > an analemma-shaped gnomon > to cast the shadow on the > bowl... First, build a prototype. You can think about fancy upgrades later. Imagine the following... 1. Take an orange. 2. Cut it in half. Throw one half away. [OK, maybe eat it first.] 3. Then cut the half in half and throw one of these quarters away. 4. What you are left with is your half hemisphere. 5. This has one curved surface and two plane surfaces. 6. Arrange for one of the planes to be horizontal and the other to be vertical and facing due south (assuming you are in the northern hemisphere). 7. Now place a bead in the middle of the edge that is common to the two flat faces. THIS is the nodus. 8. Now imagine that all the space between the bead and the skin is replaced by a transparent medium. 9. You now have an embryonic hemicyclium. Let's think about some of its properties 10. At sunrise (and sunset) the sun is in the plane of the horizontal flat surface, and the shadow of the bead (in the winter half of the year) will fall on the inside rim of the horizontal element of skin. This rim is the "horizon line". 11. At an equinox the shadow of the bead during the course of a day will follow a great (half) circle on the inside surface of the skin. 12. At the winter solstice it will follow a small (less than half) circle on the inside surface and this will be above the equinoctial circle. 13. At the summer solstice you hit a minor snag. At sunrise the sun is north of due east and the shadow of the bead will not fall on the rim. Don't worry about this yet. [The Greeks DID cope with this but that's for later.] 14. Instead, pick up the path of the shadow starting from when the sun is due east and, by then, some way above the horizon. 15. You will again get a small (less than half) circle. 16. Now add lots of intermediate small circles for other times of year. 17. At this point you have a choice as to how you chop up each circle into hours... 18. The ancients chopped each part circle in the winter half into 12 parts, thus dividing the daylight period into unequal hours. You could label the spaces 1 to 12 if you like. The Greeks didn't have digits or even Roman Numerals and labelled the hours alpha, beta, gamma etc. 19. That's the way I would do it but if you insist on using iconoclastic new fangled equal hours then you can. You will find it rather harder! 20. That completes your prototype. Now have a long think about what you really want to do. Very best wishes Frank Frank H. King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Hemicyclium correction
When I have a clock and not a sundial, clock time has to be converted into sundial time (Local True Solar Time) to make it day-relevant. So, if you make a sundial, shouldn't it just show sundial time? Isn't that really what a sundial for--showing Local True Solar Time? You could make a correction-table to convert sundial-time to clock-time--consisting of the EoT, with the longitude-correction added to it for converting from sundial time to clock time. ...and display it beside the sundial. By the way, when I said that a Disk Equatorial is incomparably easier to make than a Band or Cylinder Equatorial, of course should have added "...unless you already have a cylinder or a band, and a means to make a hole in it, to make a circumference hole-nodus. Of course such a dial can only show 12 hours of time, but that can be remedied by having more than one circumference-hole nodus. I don't know the right terminology for what I call a Band-Equatorial or a Cylinder-Equatorial. If the band is wide enough for a circumference hole-nodus to cast it light-spot on the band all year, so that the band has a width equal to D*2tan(obliquity), giving it a width nearly equal to half its diameter, maybe that's the practical-difference-point at which a Band-Equatorial becomes a Cyllinder-Equatorial. As I understand it, "Equatorial Dial" usually refers to a Disk-Equatorial. I call it the Cylinder and Band versions Equatorials because they measure time in the same direct way that a Disk-Equatorial does. ...but their dial-surface is parallel to the Earth's polar-axis so someone could argue that they should be called Polar Band or Cylinder dials. So what are they correctly called? Michael Ossipoff .. On Wed, Oct 18, 2017 at 3:29 AM, Nathaniel Shippen wrote: > Well, my first attempt at a sundial is about the simplest you could > imagine. However, I did follow Albert Waugh's suggestion in "Sundials: > Their Theory And Construction" and offset the time marks to Hawaii Standard > Time, so I only have to keep the daily Equation of Time value in mind. Note > that the 12:30 mark is almost vertically below the gnomon. At my location > near Honolulu mean solar time is 32 minutes behind HST (GMT - 10). In fact > until after World War 2 clocks in Hawaii were set to GMT - 10:30, much > closer to mean solar time throughout the state. In 1947 Hawaii was > shoehorned into the GMT - 10 timezone also used in the Aleutian Islands. > > https://en.wikipedia.org/wiki/Hawaii%E2%80%93Aleutian_Time_Zone > > Nathaniel Shippen > > On Wed, Oct 18, 2017 at 3:53 AM, Michael Ossipoff > wrote: > >> But, if you're willing to give up the Horizontal-Dial's advantages, then >> an Equatorial-Dial has the following advantages: >> >> 1. Its equally-spaced hour-lines allow perfectly accurate linear >> interpolation of the time, when the shadow is between hour-lines. >> >> (But, when usiing pocket horizontal tablet-dials, linear interpolation >> gave results accurate with 3 minutes, when only the hours and half-hours >> were marked. So interpolation with unequally-spaced hour-lines doesn't seem >> a problem.) >> >> 2. Its principle is obvious. The Horizontal-Dial's construction-principle >> isn't difficult to explain, but the Equatorial's construction-principle is >> obvious at a glance. It would make perfect sense to anyone, without any >> explanation. >> >> (By the way, it's true that a Bifilar Dial shares the advantage of >> equally-spaced hour-lines. But it only tells time for part of the day, >> because, when the Sun is low, the shadow of interest won't be on the >> dial-plate.) >> >> Of course a two-sided Disk-Equatorial is incomparably easier to construct >> than a Band-Equatorial or Cylinder-Equatorial. ...if you don't mind the >> fact that a Disk-Equatorial can only be read from the north in the summer, >> and from the south in the winter. >> >> 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
Re: Hemicyclium correction
But, if you're willing to give up the Horizontal-Dial's advantages, then an Equatorial-Dial has the following advantages: 1. Its equally-spaced hour-lines allow perfectly accurate linear interpolation of the time, when the shadow is between hour-lines. (But, when usiing pocket horizontal tablet-dials, linear interpolation gave results accurate with 3 minutes, when only the hours and half-hours were marked. So interpolation with unequally-spaced hour-lines doesn't seem a problem.) 2. Its principle is obvious. The Horizontal-Dial's construction-principle isn't difficult to explain, but the Equatorial's construction-principle is obvious at a glance. It would make perfect sense to anyone, without any explanation. (By the way, it's true that a Bifilar Dial shares the advantage of equally-spaced hour-lines. But it only tells time for part of the day, because, when the Sun is low, the shadow of interest won't be on the dial-plate.) Of course a two-sided Disk-Equatorial is incomparably easier to construct than a Band-Equatorial or Cylinder-Equatorial. ...if you don't mind the fact that a Disk-Equatorial can only be read from the north in the summer, and from the south in the winter. 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
Re: Hemicyclium correction
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. > But the way, I've seen it spelled "Hemicycleum" as well. I don't know which is correct, but "Hemicycleum" looks better, it seems to me. But I'll use your spelling. It's probably better-accpeted. Whoever said that was mistaken. Hemicyclia are as in principle as accurate as any sundial can be. In ancient times, Hemicyclia were devised, instead of our modern polar-gnomon garden sundial, or our equatorial sundials, because in those days, they weren't using our Equal-Hours for civil time (Astronomers used it though). They were using "Temporary Hours), that divided each day into 12 equal hours, for their civil time. To achieve that, they used a stick-tip nodus or bead-nodus. to cast a point-shadow on the hemicyclium surface. As the Sun's declination changes seasonally, of course the tip-nodus's path on the hemicyclium changes too. So the hour-lines were curves, drawn so that, for any particular solar declination, those marks divide the day (sunrise to sunset) into 12 equal parts. As you can imagine, that makes the dial more complicated than modern ones. "Early" doesn't always mean "simpler". ...and so there was much opportunity for error in the calclulations and drafting,for those curved hour-lines. So maybe some hemicyclia *were* inaccurately drafted. For one thing, of course the exact time of day wasn't as crucial in those days, and of course the more precisely made, and prestigiously made, a sundial was, the more it was likely to cost. But there's no reason why your hemicyclium should be made for Temporary Hours. Make it for our modern Equal-Hours, also referred to as Local True Solar Time (LTST). > It appears to me the only issue is it needs to be tilted so that the > gnomon aligns with the Earth’s rotation axis; > The equinox circle on the Hemicyclium, the line that the tip-nodus follows on the day of the equinox, should be a circle parallel to the celestial equator. And yes, if you're going to use a polar gnomon instead of a tip-nodus, then that polar gnomon should be parallel to the Earth's axis, pointed at the north celestial pole. ...and should go through the center of the sphere from which the Hemicyclium is cut. But, if you're going to do that, then why make it a Hemicyclium? Why not just a Band-Equatorial dial? You could mount a cylindrical brass band, parallel to the equator, with a polar-parallel rod-gnomon mounted to go through the central axis of that band. You could mount that brass Band-Equatorial on a mount of whatever kind. For extra durability, you could mount it inside a concrete structure resembling a Hemicyclium. The durability of a Hemicyclium, with the simplicity and modernity of a Band-Equatorial. So then the hour-lines would just be polar-parallel lines equidistantly drawn along the inside of the band, dividing the lower half of the band into 12 equal parts. Of course you'd want half-hour lines too. Maybe, if you want it to be fancier and more accurate, you could divide each hour, instead, into 3, 4, or even 6 parts. ...depending on how much precision and work you want. But that's a lot of work. There's a good reason why the garden-style Horizontal-Dial is the most popular design for a stationary dial-- 1. It's easy to construct. 2. It tells the time whenever the sun is up (a Hemicyclium can do that too). 3. Unlike a Hemicyclium, a Horizontal-Dial is readable from all directions, provided that you're close enough to look at it from above. I'd say, forget about the analemic-edge gnomon. For one thing, that of course hugely complicates the design and construction. For another thing, if someone wants clock time, they can look at a clock or watch. A sundial should give sundial time, Local True Solar Time. You can have a nearby plaque-chart that tells the corrections, what to add to the sundial's time, to give the Standard-Time for your time-zone at various times of year.. ...and a reminder to add an hour for DaylightSavingTime, between the specified dates. I'd make the sundial for Local True Solar Time, equal-hours, instead of for Temporary Hours, because, not only is that easier, but it's also the basis Standard-Time (when adjusted for Equation-of-Time and for your longitude). I'd suggest changing your project to a garden-style Horizontal-Dial. Michael Ossipoff > > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Hemicyclium correction
Dear Brad, You say: > I am looking to make a > hemicyclium-type sundial > (half-hemisphere) in a > metal working class. > Am I missing anything? Er, yes. Rather a lot alas... Before you start bashing metal it may be worth spending rather less effort on a prototype. > ...they are inaccurate... I am not sure where you got that from. There is no reason why they shouldn't be accurate provided you know what you can expect of one. > ...without being very clear > on the problem. I suspect the writer of your quote either didn't know what a hemicyclium was or had looked at one and noted that it didn't indicate the same time as his watch so it must be wrong. > It appears to me the only > issue is it needs to be > tilted so that the gnomon > aligns with the Earth's > rotation axis... Er, no. The polar-oriented gnomon wasn't invented for nearly 1500 years after the hemicyclium was in common use. What looks like a gnomon and may well be CALLED a gnomon is not what you think of as a gnomon. It is actually a "nodus support". Only the shadow of the tip is of interest. > I am also looking to use > an analemma-shaped gnomon > to cast the shadow on the > bowl... First, build a prototype. You can think about fancy upgrades later. Imagine the following... 1. Take an orange. 2. Cut it in half. Throw one half away. [OK, maybe eat it first.] 3. Then cut the half in half and throw one of these quarters away. 4. What you are left with is your half hemisphere. 5. This has one curved surface and two plane surfaces. 6. Arrange for one of the planes to be horizontal and the other to be vertical and facing due south (assuming you are in the northern hemisphere). 7. Now place a bead in the middle of the edge that is common to the two flat faces. THIS is the nodus. 8. Now imagine that all the space between the bead and the skin is replaced by a transparent medium. 9. You now have an embryonic hemicyclium. Let's think about some of its properties 10. At sunrise (and sunset) the sun is in the plane of the horizontal flat surface, and the shadow of the bead (in the winter half of the year) will fall on the inside rim of the horizontal element of skin. This rim is the "horizon line". 11. At an equinox the shadow of the bead during the course of a day will follow a great (half) circle on the inside surface of the skin. 12. At the winter solstice it will follow a small (less than half) circle on the inside surface and this will be above the equinoctial circle. 13. At the summer solstice you hit a minor snag. At sunrise the sun is north of due east and the shadow of the bead will not fall on the rim. Don't worry about this yet. [The Greeks DID cope with this but that's for later.] 14. Instead, pick up the path of the shadow starting from when the sun is due east and, by then, some way above the horizon. 15. You will again get a small (less than half) circle. 16. Now add lots of intermediate small circles for other times of year. 17. At this point you have a choice as to how you chop up each circle into hours... 18. The ancients chopped each part circle in the winter half into 12 parts, thus dividing the daylight period into unequal hours. You could label the spaces 1 to 12 if you like. The Greeks didn't have digits or even Roman Numerals and labelled the hours alpha, beta, gamma etc. 19. That's the way I would do it but if you insist on using iconoclastic new fangled equal hours then you can. You will find it rather harder! 20. That completes your prototype. Now have a long think about what you really want to do. Very best wishes Frank Frank H. King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Hemicyclium correction
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
Re: Hemicyclium dials
I built this hemisherium from a clear 4" plastic Christmas ornament. The location of the center, the radius and the circles draw was an experience greater than one can have from looking at a model or viewing pictures. Thank you Fer for providing the directions. Warren Thom On Tue, 26 Oct 2010 14:01:59 -0500, fer de vries wrote: Phil, On this address http://www.dse.nl/~zonnewijzer/hemisph.htm you find a pocedure I once wrote to construct a hemisherium. Best wishes, Fer. Fer J. de Vries De Zonnewijzerkring http://www.de-zonnewijzerkring.nl Molens http://www.collsemolen.dse.nl Eindhoven, Netherlands lat. 51:30 N long. 5:30 E - Original Message - From: Phil Walker To: sund...@rrz.uni-koeln.de Sent: Tuesday, October 26, 2010 6:48 PM Subject: Hemicyclium dials Hi diallers, I am considering a model cube dial with E. S and W faces, each with a concave hemisphere on it. It would have a pin gnomon with a ball nodus at the end, at the centre of the hemisphere. I understand that this is based in the Greek" hemicyclium" but there.are a few 16th century cube dials of this type in England and Scotland. I've two questions, What are the dial equations for the hour- and day-curves for a hemicyclium-based dial? Do they require some spherical trigonometry? How' in practice, could I draw/paint/scribe etc the said curves onto the concave shapes? Your help would be appreciated, Phil Walker 52N2W (ish) http://www.sundial.pwp.blueyonder.co.uk/ -- --- https://lists.uni-koeln.de/mailman/listinfo/sundial -- Using Opera's revolutionary e-mail client: http://www.opera.com/mail/ --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Hemicyclium dials
Phil, On this address http://www.dse.nl/~zonnewijzer/hemisph.htm you find a pocedure I once wrote to construct a hemisherium. Best wishes, Fer. Fer J. de Vries De Zonnewijzerkring http://www.de-zonnewijzerkring.nl Molens http://www.collsemolen.dse.nl Eindhoven, Netherlands lat. 51:30 N long. 5:30 E - Original Message - From: Phil Walker To: sund...@rrz.uni-koeln.de Sent: Tuesday, October 26, 2010 6:48 PM Subject: Hemicyclium dials Hi diallers, I am considering a model cube dial with E. S and W faces, each with a concave hemisphere on it. It would have a pin gnomon with a ball nodus at the end, at the centre of the hemisphere. I understand that this is based in the Greek" hemicyclium" but there.are a few 16th century cube dials of this type in England and Scotland. I've two questions, What are the dial equations for the hour- and day-curves for a hemicyclium-based dial? Do they require some spherical trigonometry? How' in practice, could I draw/paint/scribe etc the said curves onto the concave shapes? Your help would be appreciated, Phil Walker 52N2W (ish) http://www.sundial.pwp.blueyonder.co.uk/ -- --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Hemicyclium dials
Dear Phil, You don't need any spherical trig or formulae. Here's how to do it for the south dial. First make two semicircular templates from stiff card or thin stiff plastic with radius equal to that of your hemisphere, so that each one fits into the recess across a diameter and with a flange at each end of the semicircle that can rest on the flat surface of the cube. On one, (A), that will sit in the vertical plane, mark lines on it from the semicircle centre to the perimeter that correspond (i) to the equator at (90 - lat) to the horizontal, and two others (ii) and (iii) that correspond to the tropics (+/- 23.5 deg). Place this semicircle vertically in the recess (in the meridian plane) and mark the positions of the equator and two tropics on the meridian (12 noon) line (also marked). On the other semicircle,(B) mark radii at 15 degree intervals, or divide the perimeter (if your recess is truly hemispherical) into 12 equal parts. Then hold B in the recess so that the flat-surface flanges are on the horizontal diameter and the perimeter is on the previously-marked equator position. Draw the whole equator line, and mark the 15 degree (hour) divisions. You're part way there, but the story is not complete. Is it clear so far, or do you want some drawings/sketches? David Brown Somerton, Somerset UK (51N3W-very ish!) Phil Walker > Hi diallers, > I am considering a model cube dial with E. S and W faces, each with a concave hemisphere on it. It would have a pin gnomon with a ball nodus at > the end, at the centre of the hemisphere. I understand that this is based > in the Greek" hemicyclium" but there.are a few 16th century cube dials of > this type in England and Scotland. > I've two questions, > What are the dial equations for the hour- and day-curves for a > hemicyclium-based dial? Do they require some spherical trigonometry? How' in practice, could I draw/paint/scribe etc the said curves onto the concave shapes? > Your help would be appreciated, > Phil Walker > 52N2W (ish) > http://www.sundial.pwp.blueyonder.co.uk/ > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Hemicyclium dials
Hi diallers, I am considering a model cube dial with E. S and W faces, each with a concave hemisphere on it. It would have a pin gnomon with a ball nodus at the end, at the centre of the hemisphere. I understand that this is based in the Greek" hemicyclium" but there.are a few 16th century cube dials of this type in England and Scotland. I've two questions, What are the dial equations for the hour- and day-curves for a hemicyclium-based dial? Do they require some spherical trigonometry? How' in practice, could I draw/paint/scribe etc the said curves onto the concave shapes? Your help would be appreciated, Phil Walker 52N2W (ish) http://www.sundial.pwp.blueyonder.co.uk/ --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Hemicyclium
It's http://www.sundialsoc.org.uk/ actually. Thanks - I now understand ;) Descriptions of both can be found in the BSS Glossary, under "Dial (types of") at www.britishsundialsociety.org.uk.
Hemicyclium
Hi Alexei et al, You asked: > on another topic, what is the difference between a hemispherium and a > hemicyclium? Descriptions of both can be found in the BSS Glossary, under "Dial (types of") at www.britishsundialsociety.org.uk. Regards, John - Dr J R Davis Flowton Dials N52d 08m: E1d 05m -
hemicyclium at cleopatra's needle
>Dear list members, IN the article The History of the Sundial : The Beginning of Recorded Time found at http://www.americanantiquities.com/articles/article14.html, I quote:' Almost 1500 years later, the emperor of Rome, Augustus (63 B.C. - 14 A.D.) moved Cleopatra's Needle to Alexandria, founded by Alexander the Great some three hundred years before. The hemicyclium in question was unearthed at the base of Cleopatra's Needle there; the numeral style indicates it was there after Alexander (about 332 B.C.). This artifact now resides in the British Museum.' In short, I am interested in learning more about this particular hemicyclium. Sincerely, Ronit Maoz Hi Ronit, Strictly speaking a conical dial, it has the reference 3086G in Sharon Gibbs 'Greek and Roman Sundials' Yale UniversityThesis which is published by Yale University Press, 1976. It has the British Museum ref 1936 3-9 1. Details are given by Gibbs as: H=404mm W=429mm (There are other measurements given there too.) The gnomon hole has a semicircular vertical section 50mm wide and 51mm deep. Eleven hour lines extend from winter to summer solstice. The three 'day' curves have been engraved always equidistant from each other and from the lower edge of the conical surface. Dots are visible at the junctions of hour lines and winter solstice line. Six shallow steps decorate the base. Seven greek letters have been engaved in the spaces below the equinox close to the right hour line. It was found in 1852 at the base of the needle in Alexandria. Gibbs says that it is a unique example of a conical dial with hours marked in Greek letters. The lettering is probably Byzantine but the museum has charaacterised the dial as Ptolemaic. Ref: A Guide to the Eguptian Collections in the British Museum, London 1909, p72 and p273. Also Mrs Gatty's Sundials pp42-43 There is a B&W photo (Plate 48) of the dial in Gibbs book. Hope this helps Patrick - E-Mail: [EMAIL PROTECTED] Web: http://ourworld.compuserve.com/homepages/Patrick_Powers/ Lat: N 51d. 49m. 09s: Long: W 00d. 21m. 53s -
hemicyclium at cleopatra's needle
Dear list members, IN the article The History of the Sundial : The Beginning of Recorded Time found at http://www.americanantiquities.com/articles/article14.html, I quote:' Almost 1500 years later, the emperor of Rome, Augustus (63 B.C. ñ 14 A.D.) moved Cleopatraís Needle to Alexandria, founded by Alexander the Great some three hundred years before. The hemicyclium in question was unearthed at the base of Cleopatraís Needle there; the numeral style indicates it was there after Alexander (about 332 B.C.). This artifact now resides in the British Museum.' In short, I am interested in learning more about this particular hemicyclium. Sincerely, Ronit Maoz