Re: Shadow Tapering
Hi All, It's nothing to do with latitude, I think. The human eye perceives the edge of a shadow to be where the light has fallen to about 10% to 20%, not 50%. So, where the sun's shadow is cast by an edge (as opposed to a string/wire/rod) we estimate the edge about 12 to 14 minutes of arc from where we should, always in the direction towards the shadow. (The sun's radius being about 16 minutes of arc) Now, 15 minutes of arc is almost exactly how far the sun moves in a minute (it varies a little with the seasons). So, if we're talking of a polar gnomon, use the advice John mentioned: subtract a minute in the morning and add a minute in the afternoon. This works for any sundial whatsoever which has a solid gnomon: vertical or horizontal, any size, anywhere in the world, any time of day, throughout the year. Alternatively, when delineating a dial, pre-distort it as ChiLean did, by a little less than a minute. So, the sides of the noon gap should indeed converge. By the way, the alternative that someone suggested, of making the gnomon thicker towards the top, does not work correctly. It has some effect at noon, but none at 6am/6pm. I suppose you could also make the gnomon slightly steeper, but really you're much better off leaving the gnomon alone but pre-distorting the hour lines. Another alternative is to use a shadow sharpener, which is a pinhole device that allows you much more accurately to estimate the centre of the edge of the shadow. Yet another, and I'm surprised John hasn't mentioned this, is to use John Carmichael's taut wire gnomon, or some other thin form where you estimate the centre of the shadow. Contrary to a recent posting, the gnomon's diameter should be at least 1/105th the maximum distance to the dial, to ensure the centre of the shadow is in the umbra. You can certainly see the shadow further away, but it will be fainter, penumbral shadow with a less well defined centre. So, for instance, a 1cm diameter wire, rod or tube should be used with a dial of around 1 metre radius. This applies equally to equatorial dials. Regards Chris Lusby Taylor - Original Message - From: JOHN DAVIS To: [EMAIL PROTECTED] ; [EMAIL PROTECTED] Cc: Sundial List Sent: Wednesday, February 13, 2008 8:39 AM Subject: Re: Shadow Tapering Hi ChiLian, That's very interesting - I haven't heard before of a dial delineation being "pre-distorted" in this way to allow for the penumbra effect. Perhaps the reason that the 1 minute correction that you adopted was too much is that your latitude (24.79 N) is so much less than the Shetlands at nearly 60 degrees N. Hence the shadow is much closer to the gnomon edge and the penumbra effect is less marked. It is a complicated problem as human eyesight does not respond linearly to varying intensity levels. Regards, John -- Chiu ªô,Chi lian <[EMAIL PROTECTED]> wrote: Hi! >An article by Vicki de Kleer (BSS Bulletin 19(iii), pp.116-117, September 2007) describes an 1890 brass horizontal dial made by the London maker Charles Baker for Sumburgh in the Shetland Islands at latitude 59 degrees 52 minutes N. The dial has a comprehensive Equation of Time table engraved around its periphery and also the two intriguing instructions: "AM Sub.[tract] 1 min" and "PM Add 1 min". < I designed an 8m sundial with solid gnomon for Nat'l Tsing Hua University (Hsinchu, Taiwan, 24.79N, 120.99E) in April, 2006. I noticed the problem of shadow. No one can tell where the shadow starts or where it is perfect. That means no one can really deside by his bare eyes where the middle of the penumbra is. Most people read the dial by the shadow edge and never care about the middle of the penumbra. So I decided to use perfect shadow as time indicater. I took the "one minute off" policy since the full sun angle is about 2 minutes. The policy was "mark the hour lines one minute ahead in the morning hours and one minute behind in the afternoon hours". That is to draw 9:01 line and mark it as 9:00, to draw 2:59 line and mark it as 3:00. So the sundial was done. However, it turns out that "one minute" off is too much. I overlooked the fact that the sun, as a light source, is not square but circular. Regards, ChiLian 2008/2/10, JOHN DAVIS <[EMAIL PROTECTED]>: Hi Patrick, John C and the List, The problem of the shadow not properly filling the noon gap is the same umbra/penumbra related one which affects the reading accuracy of dials with 'solid' gnomons at all times of the day. This is usually ignored by dial makers but I know of one historical example where the maker seems to have offered a possible solution. An article by Vicki de Kleer (BSS Bulletin 19(iii), pp.116-117,
Re: Shadow Tapering
Hi ChiLian, That's very interesting - I haven't heard before of a dial delineation being "pre-distorted" in this way to allow for the penumbra effect. Perhaps the reason that the 1 minute correction that you adopted was too much is that your latitude (24.79 N) is so much less than the Shetlands at nearly 60 degrees N. Hence the shadow is much closer to the gnomon edge and the penumbra effect is less marked. It is a complicated problem as human eyesight does not respond linearly to varying intensity levels. Regards, John -- Chiu ªô,Chi lian <[EMAIL PROTECTED]> wrote: Hi! >An article by Vicki de Kleer (BSS Bulletin 19(iii), pp.116-117, September 2007) describes an 1890 brass horizontal dial made by the London maker Charles Baker for Sumburgh in the Shetland Islands at latitude 59 degrees 52 minutes N. The dial has a comprehensive Equation of Time table engraved around its periphery and also the two intriguing instructions: "AM Sub.[tract] 1 min" and "PM Add 1 min". < I designed an 8m sundial with solid gnomon for Nat'l Tsing Hua University (Hsinchu, Taiwan, 24.79N, 120.99E) in April, 2006. I noticed the problem of shadow. No one can tell where the shadow starts or where it is perfect. That means no one can really deside by his bare eyes where the middle of the penumbra is. Most people read the dial by the shadow edge and never care about the middle of the penumbra. So I decided to use perfect shadow as time indicater. I took the "one minute off" policy since the full sun angle is about 2 minutes. The policy was "mark the hour lines one minute ahead in the morning hours and one minute behind in the afternoon hours". That is to draw 9:01 line and mark it as 9:00, to draw 2:59 line and mark it as 3:00. So the sundial was done. However, it turns out that "one minute" off is too much. I overlooked the fact that the sun, as a light source, is not square but circular. Regards, ChiLian 2008/2/10, JOHN DAVIS <[EMAIL PROTECTED]>: Hi Patrick, John C and the List, The problem of the shadow not properly filling the noon gap is the same umbra/penumbra related one which affects the reading accuracy of dials with 'solid' gnomons at all times of the day. This is usually ignored by dial makers but I know of one historical example where the maker seems to have offered a possible solution. An article by Vicki de Kleer (BSS Bulletin 19(iii), pp.116-117, September 2007) describes an 1890 brass horizontal dial made by the London maker Charles Baker for Sumburgh in the Shetland Islands at latitude 59 degrees 52 minutes N. The dial has a comprehensive Equation of Time table engraved around its periphery and also the two intriguing instructions: "AM Sub.[tract] 1 min" and "PM Add 1 min". It seems to me that these instructions are implying that the true time is being indicated slightly further into the penumbra area of the shadow than the observer might normally expect. With a dial so far north, the effect of 'shadow tapering' will be more prononounced than on most other dials. Does anyone have a different interpretation of these instructions, or know of other dials wich have similar ones? Regards, John Davis Dr J Davis Flowton Dials--- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Shadow Tapering
On Feb 10, 2008, at 6:00 AM, Patrick Powers wrote: > Indeed, if you want a bit of fun, if you have Google Earth and care > to type > in 52 45' 16.28"N, 01 08' 12.33" W then you go directly to the > second of > these dials. Even if you don't have Google Earth you can go to the http:// maps.google.com/ website and type in the coordinates. You'll get to the same place as Google Earth takes you, and if you click the Satellite button you can zoom in on the image just as you would in Google Earth. I have a browser running whenever I'm at the computer (which is way too often) so using Google Maps is much more convenient than launching (and waiting for) Google Earth. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: AW: Shadow tapering thread
Reinhold, That was certainly not the objective of my email. I only wanted to explain why sometimes messages were not included in the discussion. It might be informative for other readers. That 'discussion' you are referring to was already quite some time ago and there may be a number of new addresses to this list that has no knowledge of that discussion. Thibaud At 15:31 10-02-2008, Reinhold Kriegler wrote: O no!!! Are we realy going to start this reply button- discussion again??? RK * ** *** * ** *** Reinhold R. Kriegler Lat. 53° 6' 52,6" Nord; Long. 8° 53' 52,3 Ost; 48 m ü. N.N. www.ta-dip.de <http://de.youtube.com/watch?v=XyCoJHwzzjU>http://de.youtube.com/watch?v=XyCoJHwzzjU -Ursprüngliche Nachricht- Von: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Im Auftrag von Th. Taudin Chabot Gesendet: Sonntag, 10. Februar 2008 14:53 An: Sundial Mailing List Betreff: Re: Shadow tapering thread Mac, You are absolutely right. The problem is that normally I hit the 'reply' button to reply to an email. In all emaillist emails I receive this works fine. Only in this emaillist the replybutton creates only the address of the original sender and not of the list-server. So I have to 'reply to all' and delete the orginal sender by hand. This is not a practical way and I seem to forget it now and then in this mailinglist and I might not be the only one. The reason for this behaviour is I think that in the header there is no 'reply to:' line, only 'Sender: [EMAIL PROTECTED]' to indicate who sent the email and that will be used in case of bouncing the email only. Because of this the hitting 'reply to' button looks at the 'From:' line, which is in your case: 'From: Mac Oglesby <[EMAIL PROTECTED]>'. I have no idea of the reason of the 'X-BeenThere:' line, that is the only place where the address is correct (apart from the 'To:' line) The header of your email looked as follows: To: Sundial Mailing List From: Mac Oglesby <[EMAIL PROTECTED]> Subject: Shadow tapering thread X-BeenThere: sundial@uni-koeln.de X-Mailman-Version: 2.1.9 List-Id: Sundial related list with international audience List-Unsubscribe: < https://lists.uni-koeln.de/mailman/listinfo/sundial>, < mailto:[EMAIL PROTECTED]> List-Archive: < https://lists.uni-koeln.de/mailman/private/sundial> List-Post: < mailto:sundial@uni-koeln.de> List-Help: < mailto:[EMAIL PROTECTED]> List-Subscribe: < https://lists.uni-koeln.de/mailman/listinfo/sundial>, < mailto:[EMAIL PROTECTED]> Sender: [EMAIL PROTECTED] Thibaud At 13:19 10-02-2008, Mac Oglesby wrote: Hello All, Trying to follow this fascinating thread, it seems to me as though some messages are missing -- as though some messages are being replied to without a copy being sent to the entire Sundial Mailing List. Please, unless your reply really needs to be private, include all of us. Best wishes, Mac Oglesby P.S. To John Carmichael -- thanks for initiating this discussion. --- https://lists.uni-koeln.de/mailman/listinfo/sundial -- Th. Taudin Chabot, . [EMAIL PROTECTED] No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.5.516 / Virus Database: 269.20.0/1268 - Release Date: 09.02.2008 11:54 No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.5.516 / Virus Database: 269.20.0/1268 - Release Date: 09.02.2008 11:54 -- Th. Taudin Chabot, . [EMAIL PROTECTED] --- https://lists.uni-koeln.de/mailman/listinfo/sundial
AW: Shadow tapering thread
O no!!! Are we realy going to start this reply button- discussion again??? RK * ** *** * ** *** Reinhold R. Kriegler Lat. 53° 6' 52,6" Nord; Long. 8° 53' 52,3 Ost; 48 m ü. N.N. www.ta-dip.de HYPERLINK "http://de.youtube.com/watch?v=XyCoJHwzzjU"http://de.youtube.com/watch?v=XyC oJHwzzjU -Ursprüngliche Nachricht- Von: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Im Auftrag von Th. Taudin Chabot Gesendet: Sonntag, 10. Februar 2008 14:53 An: Sundial Mailing List Betreff: Re: Shadow tapering thread Mac, You are absolutely right. The problem is that normally I hit the 'reply' button to reply to an email. In all emaillist emails I receive this works fine. Only in this emaillist the replybutton creates only the address of the original sender and not of the list-server. So I have to 'reply to all' and delete the orginal sender by hand. This is not a practical way and I seem to forget it now and then in this mailinglist and I might not be the only one. The reason for this behaviour is I think that in the header there is no 'reply to:' line, only 'Sender: [EMAIL PROTECTED]' to indicate who sent the email and that will be used in case of bouncing the email only. Because of this the hitting 'reply to' button looks at the 'From:' line, which is in your case: 'From: Mac Oglesby <[EMAIL PROTECTED]>'. I have no idea of the reason of the 'X-BeenThere:' line, that is the only place where the address is correct (apart from the 'To:' line) The header of your email looked as follows: To: Sundial Mailing List From: Mac Oglesby <[EMAIL PROTECTED]> Subject: Shadow tapering thread X-BeenThere: sundial@uni-koeln.de X-Mailman-Version: 2.1.9 List-Id: Sundial related list with international audience List-Unsubscribe: https://lists.uni-koeln.de/mailman/listinfo/sundial"; https://lists.uni-koeln.de/mailman/listinfo/sundial>, mailto:[EMAIL PROTECTED]" mailto:[EMAIL PROTECTED]> List-Archive: https://lists.uni-koeln.de/mailman/private/sundial"; https://lists.uni-koeln.de/mailman/private/sundial> List-Post: mailto:sundial@uni-koeln.de"; mailto:sundial@uni-koeln.de> List-Help: mailto:[EMAIL PROTECTED]" mailto:[EMAIL PROTECTED]> List-Subscribe: https://lists.uni-koeln.de/mailman/listinfo/sundial"; https://lists.uni-koeln.de/mailman/listinfo/sundial>, mailto:[EMAIL PROTECTED]" mailto:[EMAIL PROTECTED]> Sender: [EMAIL PROTECTED] Thibaud At 13:19 10-02-2008, Mac Oglesby wrote: Hello All, Trying to follow this fascinating thread, it seems to me as though some messages are missing -- as though some messages are being replied to without a copy being sent to the entire Sundial Mailing List. Please, unless your reply really needs to be private, include all of us. Best wishes, Mac Oglesby P.S. To John Carmichael -- thanks for initiating this discussion. --- HYPERLINK "https://lists.uni-koeln.de/mailman/listinfo/sundial"https://lists.uni-koeln .de/mailman/listinfo/sundial _ Th. Taudin Chabot, * [EMAIL PROTECTED] No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.5.516 / Virus Database: 269.20.0/1268 - Release Date: 09.02.2008 11:54 No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.5.516 / Virus Database: 269.20.0/1268 - Release Date: 09.02.2008 11:54 --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Shadow tapering thread
Mac, You are absolutely right. The problem is that normally I hit the 'reply' button to reply to an email. In all emaillist emails I receive this works fine. Only in this emaillist the replybutton creates only the address of the original sender and not of the list-server. So I have to 'reply to all' and delete the orginal sender by hand. This is not a practical way and I seem to forget it now and then in this mailinglist and I might not be the only one. The reason for this behaviour is I think that in the header there is no 'reply to:' line, only 'Sender: [EMAIL PROTECTED]' to indicate who sent the email and that will be used in case of bouncing the email only. Because of this the hitting 'reply to' button looks at the 'From:' line, which is in your case: 'From: Mac Oglesby <[EMAIL PROTECTED]>'. I have no idea of the reason of the 'X-BeenThere:' line, that is the only place where the address is correct (apart from the 'To:' line) The header of your email looked as follows: To: Sundial Mailing List From: Mac Oglesby <[EMAIL PROTECTED]> Subject: Shadow tapering thread X-BeenThere: sundial@uni-koeln.de X-Mailman-Version: 2.1.9 List-Id: Sundial related list with international audience List-Unsubscribe: <https://lists.uni-koeln.de/mailman/listinfo/sundial>, <mailto:[EMAIL PROTECTED]> List-Archive: <https://lists.uni-koeln.de/mailman/private/sundial> List-Post: <mailto:sundial@uni-koeln.de> List-Help: <mailto:[EMAIL PROTECTED]> List-Subscribe: <https://lists.uni-koeln.de/mailman/listinfo/sundial>, <mailto:[EMAIL PROTECTED]> Sender: [EMAIL PROTECTED] Thibaud At 13:19 10-02-2008, Mac Oglesby wrote: Hello All, Trying to follow this fascinating thread, it seems to me as though some messages are missing -- as though some messages are being replied to without a copy being sent to the entire Sundial Mailing List. Please, unless your reply really needs to be private, include all of us. Best wishes, Mac Oglesby P.S. To John Carmichael -- thanks for initiating this discussion. --- https://lists.uni-koeln.de/mailman/listinfo/sundial -- Th. Taudin Chabot, . [EMAIL PROTECTED] --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Shadow tapering thread
Hello All, Trying to follow this fascinating thread, it seems to me as though some messages are missing -- as though some messages are being replied to without a copy being sent to the entire Sundial Mailing List. Please, unless your reply really needs to be private, include all of us. Best wishes, Mac Oglesby P.S. To John Carmichael -- thanks for initiating this discussion. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Shadow Tapering
Hi Patrick, John C and the List, The problem of the shadow not properly filling the noon gap is the same umbra/penumbra related one which affects the reading accuracy of dials with 'solid' gnomons at all times of the day. This is usually ignored by dial makers but I know of one historical example where the maker seems to have offered a possible solution. An article by Vicki de Kleer (BSS Bulletin 19(iii), pp.116-117, September 2007) describes an 1890 brass horizontal dial made by the London maker Charles Baker for Sumburgh in the Shetland Islands at latitude 59 degrees 52 minutes N. The dial has a comprehensive Equation of Time table engraved around its periphery and also the two intriguing instructions: "AM Sub.[tract] 1 min" and "PM Add 1 min". It seems to me that these instructions are implying that the true time is being indicated slightly further into the penumbra area of the shadow than the observer might normally expect. With a dial so far north, the effect of 'shadow tapering' will be more prononounced than on most other dials. Does anyone have a different interpretation of these instructions, or know of other dials wich have similar ones? Regards, John Davis Patrick Powers <[EMAIL PROTECTED]> wrote: > If you make the dial with a tublular gnomon, and you design the face so that the time is read from the center of the shadow instead of the edges of the gnomon's shadow, then you eliminate the Noon Gap. Do you think this is the best solution? < >From the point of view of an accurate dial, one that can be calculated and one that members of the public can read easily, I am certain that it is. I have designed two 12m (or so) diameter dials this way and, by a proper choice of gnomon diameter the shadow is very easy to read. Indeed, if you want a bit of fun, if you have Google Earth and care to type in 52 45' 16.28"N, 01 08' 12.33" W then you go directly to the second of these dials. It's in Barrow-on-Soar in Leicestershire, UK. The time can even be read from space (well, with good magnifcation it can ). Google Earth's imaging is so good that I have even thought of trying to calculate what day that photo was taken - though I haven't done so yet. (If anyone wants to try, the gnomon length was such that the shadow on the summer solstice just touches the outer diameter of the chapter ring which is just inside the 'mini-stonehenge' like stone circle). Regards Patrick --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Shadow Tapering
> If you make the dial with a tublular gnomon, and you design the face so that the time is read from the center of the shadow instead of the edges of the gnomon's shadow, then you eliminate the Noon Gap. Do you think this is the best solution? < >From the point of view of an accurate dial, one that can be calculated and one that members of the public can read easily, I am certain that it is. I have designed two 12m (or so) diameter dials this way and, by a proper choice of gnomon diameter the shadow is very easy to read. Indeed, if you want a bit of fun, if you have Google Earth and care to type in 52 45' 16.28"N, 01 08' 12.33" W then you go directly to the second of these dials. It's in Barrow-on-Soar in Leicestershire, UK. The time can even be read from space (well, with good magnifcation it can ). Google Earth's imaging is so good that I have even thought of trying to calculate what day that photo was taken - though I haven't done so yet. (If anyone wants to try, the gnomon length was such that the shadow on the summer solstice just touches the outer diameter of the chapter ring which is just inside the 'mini-stonehenge' like stone circle). Regards Patrick --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Shadow Tapering
Dear Patrick: I completely agree with you Patrick! Tubular gnomons are good. And I think your comment directly pertains to the shadow tapering problem. In fact, using tublar gnomons could be the best solution to the shadow tapering problem. If you make the dial with a tublular gnomon, and you design the face so that the time is read from the center of the shadow instead of the edges of the gnomon's shadow, then you eliminate the Noon Gap. Do you think this is the best solution? At least it doesn't violate gnomonic rules as the other solutions do. Thanks for your comments! They are valuable to this discussion. John -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Patrick Powers Sent: Saturday, February 09, 2008 10:40 AM To: Sundial List Subject: FW: Shadow Tapering >When I did this with the big dial I first set out a parallel noon gap near the plate edge expecting the shadow to fill this at noon!! It was only when I came to observe this in sunlight that I found the apparent shadow was less than 10" wide because of the umbra/penumbra effect. The shadow was *tapered* of course and so should the noon gap lines be too. < Hi John, This is not really a comment on Tony's very important observation about large dials with solid triangular gnomons but just a note to say that if the gnomon is instead made tubular then, because time assessment is then made from the centre of the resulting shadow and not from an edge, the observed umbra-penumbra does not affect time measurement in the same way - unless of course the dial is too large for the gnomon's diameter - by which point there is no umbra at all at the point of the chapter ring. Large dials designed with tubular gnomons can in fact be remarkably accurate and their timescales can be predictably calculated too. Regards Patrick --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Shadow Tapering
Tony & all: One more comment on shadow tapering solutions. Your solution Tony is to decrease the size of the Noon Gap to compensate for the decreased observed shadow width. My two different proposed solutions that I described in my last letter involved changing the width of the gnomon instead of the width of the Noon Gap. But all of these solutions violate traditional gnomonic rules. My guess is that our proposed solutions would work at noon, but what about other times of the day when the sun is at different angles? Isn't is possible or probable that our solutions will cause time reading errors at other times of the day? John -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of John Carmichael Sent: Saturday, February 09, 2008 10:17 AM To: sundial@uni-koeln.de Subject: FW: Shadow Tapering -Original Message- From: John Carmichael [mailto:[EMAIL PROTECTED] Sent: Saturday, February 09, 2008 10:07 AM To: 'Tony Moss' Subject: Shadow Tapering Dear Tony (I'm ccing The List on your letter because it is a great new observation that The List has never discussed before. Your observation concerning the decreased shadow width at the Noon Gap of thick polar axis gnomons on giant sundials will surely be interesting to everybody. I'd be most interested in hearing other dialists' opinions about this interesting shadow phenomenon and possible solutions to combat it. Everybody should read Tony's letter below.) How interesting! Yes, now that you mention this effect seems inevitable knowning what we know about umbras, penumbras and fuzz zones.! I had not thought of this phenomenon and have never personally observed it because I have never seen a dial like this at Noon. To minimize the shadow tapering on giant polar axis thick gnomon sundials, your idea of using the equinox's taper as a design guide seems reasonable. The amount of shadow tapering would be greater with gnomons that have a steep slope (gnomons at high latitudes). Since this one is at 28 degrees, the shadow taper would be less. According to your theory, one might be able to decrease the effect of shadow tapering by constructing the thick polar axis gnomon so that it get slightly wider towards the top. Of course this would violate all the gnomonic laws we hold so dear! The two shadow casting edges of the angled gnomon would not be precisely parallel and would not face precisely north! I don't think I'm ready to make this unorthodox design change without doing some rigorous experiments first. But I could maybe try an alternative less radical solution to the shadow tapering problem. But this would also require experiments, because it also violates traditional sundial design rules. One might make the gnomon slightly wider than is called for by traditional gnomonics, so that the shadow completely fills the Noon Gap on the Equinox. How does this solution sound to you and everybody else? It's a radical idea that makes me cringe a little but it just might work. I wonder how one could mathematically calculate how much wider to make the gnomon to counter the thinning of the observed shadow. It'd probably be easier and more correct to conduct an experiment using a full-size model. John p.s. the dial we are discussing is horizontal, but the tapered shadow effect would also be visible on any large sundial with a thick polar axis gnomon. -Original Message- From: Tony Moss [mailto:[EMAIL PROTECTED] Sent: Saturday, February 09, 2008 9:04 AM To: John Carmichael Subject: Re: Sundial for an odd timezone Hi John, > You got that right! Frank's comment about the locals changing the Time Zone > system is just as scary because it would ruin the dial. > > This is a typical horizontal dial with a thick polar axis gnomon with two > shadow casting edges. > > My Silverlink dial was/is 20 metres in diameter with a polar axis gnomon 6 metres high and 12" wide with two parallel style edges. Up to that point I had only made small-ish dials so my habit had been to set a pair of *parallel* noon lines from the dial origins and then set of the calculated angles from the noon lines. When I did this with the big dial I first set out a parallel noon gap near the plate edge expecting the shadow to fill this at noon!! It was only when I came to observe this in sunlight that I found the apparent shadow was less than 10" wide because of the umbra/penumbra effect. The shadow was *tapered* of course and so should the noon gap lines be too. Once you have the noon line correctly placed you can then set out the hour lines at their calculated angles. At that point I resolved that big sundials can only be set out initially by actual marking of the shadow at solar noon. Exactly the same problem occurs with small dials of course but the amount of shadow taper is insignificant. The problem doesn't end t
FW: Shadow Tapering
>When I did this with the big dial I first set out a parallel noon gap near the plate edge expecting the shadow to fill this at noon!! It was only when I came to observe this in sunlight that I found the apparent shadow was less than 10" wide because of the umbra/penumbra effect. The shadow was *tapered* of course and so should the noon gap lines be too. < Hi John, This is not really a comment on Tony's very important observation about large dials with solid triangular gnomons but just a note to say that if the gnomon is instead made tubular then, because time assessment is then made from the centre of the resulting shadow and not from an edge, the observed umbra-penumbra does not affect time measurement in the same way - unless of course the dial is too large for the gnomon's diameter - by which point there is no umbra at all at the point of the chapter ring. Large dials designed with tubular gnomons can in fact be remarkably accurate and their timescales can be predictably calculated too. Regards Patrick --- https://lists.uni-koeln.de/mailman/listinfo/sundial
FW: Shadow Tapering
-Original Message- From: John Carmichael [mailto:[EMAIL PROTECTED] Sent: Saturday, February 09, 2008 10:07 AM To: 'Tony Moss' Subject: Shadow Tapering Dear Tony (I'm ccing The List on your letter because it is a great new observation that The List has never discussed before. Your observation concerning the decreased shadow width at the Noon Gap of thick polar axis gnomons on giant sundials will surely be interesting to everybody. I'd be most interested in hearing other dialists' opinions about this interesting shadow phenomenon and possible solutions to combat it. Everybody should read Tony's letter below.) How interesting! Yes, now that you mention this effect seems inevitable knowning what we know about umbras, penumbras and fuzz zones.! I had not thought of this phenomenon and have never personally observed it because I have never seen a dial like this at Noon. To minimize the shadow tapering on giant polar axis thick gnomon sundials, your idea of using the equinox's taper as a design guide seems reasonable. The amount of shadow tapering would be greater with gnomons that have a steep slope (gnomons at high latitudes). Since this one is at 28 degrees, the shadow taper would be less. According to your theory, one might be able to decrease the effect of shadow tapering by constructing the thick polar axis gnomon so that it get slightly wider towards the top. Of course this would violate all the gnomonic laws we hold so dear! The two shadow casting edges of the angled gnomon would not be precisely parallel and would not face precisely north! I don't think I'm ready to make this unorthodox design change without doing some rigorous experiments first. But I could maybe try an alternative less radical solution to the shadow tapering problem. But this would also require experiments, because it also violates traditional sundial design rules. One might make the gnomon slightly wider than is called for by traditional gnomonics, so that the shadow completely fills the Noon Gap on the Equinox. How does this solution sound to you and everybody else? It's a radical idea that makes me cringe a little but it just might work. I wonder how one could mathematically calculate how much wider to make the gnomon to counter the thinning of the observed shadow. It'd probably be easier and more correct to conduct an experiment using a full-size model. John p.s. the dial we are discussing is horizontal, but the tapered shadow effect would also be visible on any large sundial with a thick polar axis gnomon. -Original Message- From: Tony Moss [mailto:[EMAIL PROTECTED] Sent: Saturday, February 09, 2008 9:04 AM To: John Carmichael Subject: Re: Sundial for an odd timezone Hi John, > You got that right! Frank's comment about the locals changing the Time Zone > system is just as scary because it would ruin the dial. > > This is a typical horizontal dial with a thick polar axis gnomon with two > shadow casting edges. > > My Silverlink dial was/is 20 metres in diameter with a polar axis gnomon 6 metres high and 12" wide with two parallel style edges. Up to that point I had only made small-ish dials so my habit had been to set a pair of *parallel* noon lines from the dial origins and then set of the calculated angles from the noon lines. When I did this with the big dial I first set out a parallel noon gap near the plate edge expecting the shadow to fill this at noon!! It was only when I came to observe this in sunlight that I found the apparent shadow was less than 10" wide because of the umbra/penumbra effect. The shadow was *tapered* of course and so should the noon gap lines be too. Once you have the noon line correctly placed you can then set out the hour lines at their calculated angles. At that point I resolved that big sundials can only be set out initially by actual marking of the shadow at solar noon. Exactly the same problem occurs with small dials of course but the amount of shadow taper is insignificant. The problem doesn't end there because at the solstices the shadows are longer or shorter with different amounts of taper. Perhaps the best compromise is to mark out the noon gap at an equinox. On the BSS tour of Italy I saw two large and VERY expensive horizontal dials with parallel noon gaps. Obviously set out at the CALCULATED angles so I wonder how accurate the a.m. and p.m. hourlines are?? Hope this makes sense. Tony --- https://lists.uni-koeln.de/mailman/listinfo/sundial
