Re: A mis-aligned vertical dial
Diese Nachricht wurde eingewickelt um DMARC-kompatibel zu sein. Die eigentliche Nachricht steht dadurch in einem Anhang. This message was wrapped to be DMARC compliant. The actual message text is therefore in an attachment.--- Begin Message --- Although the original question referred to a vertical dial, for a horizontal dial it works very well 6 months in the year on the pole, fairly well as the latitude moves towards the equator, but does get progressively less and less accurate. Simon Simon On Tuesday, November 9, 2021, 12:08:43 PM MST, Dan-George Uza wrote: Dear all, In his book "Sundials Old and New", A. P. Herbert contends that rotating a vertical dial by 15 degrees towards East (i.e. gnomon pointing 15 deg. West of North) will switch it to Summer Time. Writing that this is against all theory, but works quite well, he calls this "the housewife's trick" (page 80). I find it intriguing. Dan Uza lun., 8 nov. 2021, 23:50 Francesco Caviglia a scris: Dear John, attached you will find a graph calculated at latitude 42 degrees N for a vertical sundial mis-aligned by 1 degree toward West. For 52,5 degrees the values are somewhat larger (by about 10 to 30%). With greater mis-alignement (to some degrees) consider that the values are roughtly proportional to the mis-alignement itself. The original declination of the vertical dial has no influence on the error, just he mis-aligment matters. The graphs show the difference: (value indicated by the mis-aligned sundial) - (true value) They refer to the Time (above) and to the Solar declination (below), the value are expressed as a function of the True Time (Ora reale) of the day, at the equinoxes and at the solstices. In any case, to find the errors it is quite simple: just take the classical graph with the curves showing the elevation of the Sun as a function of the Azimuth for a set of Hours and Solar Declinations. Make a transparent copy of the graph, shift it in Azimuth as the considered sundial and paste it on the original graph. On every point in the plane of the graph you can read the values of the real Time and Declination (on the original graph) and those indicated in the same moment by the misaligned sundial (on the shifted graph). Best wishes Francesco Caviglia > If a vertical dial is relocated and now faces a few degrees east or west of > its designed declination, you might expect it to run a few minutes slow or > fast. Has anyone ever tabulated the greatest error, and at what times and > dates it occurs? And does it make sense to think about the average error? > Clearly the errors depend on the latitude and the design declination, but > for starters they could be tabulated just for a direct south dial at 52.5 > degrees N, and for a location move of 1, 2 and 5 degrees either way. As > the gnomon is no longer polar-pointing I imagine the maths is a bit hairy. > > Best wishes, > > John Foad > > > Francesco CAVIGLIA via SAFFI 21 10138 Torino tel. 011 4333703 mob. 3356121207 francesco.cavig...@tin.it --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- End Message --- --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: A mis-aligned vertical dial
Although the original question referred to a vertical dial, for a horizontal dial it works very well 6 months in the year on the pole, fairly well as the latitude moves towards the equator, but does get progressively less and less accurate. Simon On Tue, Nov 9, 2021 at 12:08 PM Dan-George Uza wrote: > Dear all, > > In his book "Sundials Old and New", A. P. Herbert contends that rotating a > vertical dial by 15 degrees towards East (i.e. gnomon pointing 15 deg. West > of North) will switch it to Summer Time. Writing that this is against all > theory, but works quite well, he calls this "the housewife's trick" (page > 80). I find it intriguing. > > Dan Uza > > lun., 8 nov. 2021, 23:50 Francesco Caviglia a > scris: > >> Dear John, >> attached you will find a graph calculated at latitude 42 degrees N >> for a vertical sundial mis-aligned by 1 degree toward West. >> For 52,5 degrees the values are somewhat larger (by about 10 to 30%). >> With greater mis-alignement (to some degrees) consider >> that the values are roughtly proportional to the mis-alignement itself. >> The original declination of the vertical dial has no influence on the >> error, >> just he mis-aligment matters. >> >> The graphs show the difference:(value indicated by the mis-aligned >> sundial) - (true value) >> They refer to the Time (above) and to the Solar declination (below), >> the value are expressed as a function of the True Time (Ora reale) of the >> day, >> at the equinoxes and at the solstices. >> >> In any case, to find the errors it is quite simple: >> just take the classical graph with the curves >> showing the elevation of the Sun as a function of the Azimuth >> for a set of Hours and Solar Declinations. >> Make a transparent copy of the graph, >> shift it in Azimuth as the considered sundial >> and paste it on the original graph. >> On every point in the plane of the graph you can read >> the values of the real Time and Declination (on the original graph) >> and those indicated in the same moment by the misaligned sundial (on the >> shifted graph). >> >> Best wishes >> Francesco Caviglia >> >> >> > If a vertical dial is relocated and now faces a few degrees east or >> west of >> > its designed declination, you might expect it to run a few minutes slow >> or >> > fast. Has anyone ever tabulated the greatest error, and at what times >> and >> > dates it occurs? And does it make sense to think about the average >> error? >> > Clearly the errors depend on the latitude and the design declination, >> but >> > for starters they could be tabulated just for a direct south dial at >> 52.5 >> > degrees N, and for a location move of 1, 2 and 5 degrees either way. >> As >> > the gnomon is no longer polar-pointing I imagine the maths is a bit >> hairy. >> > >> > Best wishes, >> > >> > John Foad >> > >> > >> > >> >> Francesco CAVIGLIA >> via SAFFI 21 >> 10138 Torino >> tel. 011 4333703 >> mob. 3356121207 >> francesco.cavig...@tin.it >> --- >> https://lists.uni-koeln.de/mailman/listinfo/sundial >> >> --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > -- Simon Wheaton-Smith www.illustratingshadows.com Phoenix, AZ W 112.1, N 33.5 --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: A mis-aligned vertical dial
Dear all, In his book "Sundials Old and New", A. P. Herbert contends that rotating a vertical dial by 15 degrees towards East (i.e. gnomon pointing 15 deg. West of North) will switch it to Summer Time. Writing that this is against all theory, but works quite well, he calls this "the housewife's trick" (page 80). I find it intriguing. Dan Uza lun., 8 nov. 2021, 23:50 Francesco Caviglia a scris: > Dear John, > attached you will find a graph calculated at latitude 42 degrees N > for a vertical sundial mis-aligned by 1 degree toward West. > For 52,5 degrees the values are somewhat larger (by about 10 to 30%). > With greater mis-alignement (to some degrees) consider > that the values are roughtly proportional to the mis-alignement itself. > The original declination of the vertical dial has no influence on the > error, > just he mis-aligment matters. > > The graphs show the difference:(value indicated by the mis-aligned > sundial) - (true value) > They refer to the Time (above) and to the Solar declination (below), > the value are expressed as a function of the True Time (Ora reale) of the > day, > at the equinoxes and at the solstices. > > In any case, to find the errors it is quite simple: > just take the classical graph with the curves > showing the elevation of the Sun as a function of the Azimuth > for a set of Hours and Solar Declinations. > Make a transparent copy of the graph, > shift it in Azimuth as the considered sundial > and paste it on the original graph. > On every point in the plane of the graph you can read > the values of the real Time and Declination (on the original graph) > and those indicated in the same moment by the misaligned sundial (on the > shifted graph). > > Best wishes > Francesco Caviglia > > > > If a vertical dial is relocated and now faces a few degrees east or west > of > > its designed declination, you might expect it to run a few minutes slow > or > > fast. Has anyone ever tabulated the greatest error, and at what times > and > > dates it occurs? And does it make sense to think about the average > error? > > Clearly the errors depend on the latitude and the design declination, but > > for starters they could be tabulated just for a direct south dial at 52.5 > > degrees N, and for a location move of 1, 2 and 5 degrees either way. As > > the gnomon is no longer polar-pointing I imagine the maths is a bit > hairy. > > > > Best wishes, > > > > John Foad > > > > > > > > Francesco CAVIGLIA > via SAFFI 21 > 10138 Torino > tel. 011 4333703 > mob. 3356121207 > francesco.cavig...@tin.it > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: A mis-aligned vertical dial
Dear John, attached you will find a graph calculated at latitude 42 degrees N for a vertical sundial mis-aligned by 1 degree toward West. For 52,5 degrees the values are somewhat larger (by about 10 to 30%). With greater mis-alignement (to some degrees) consider that the values are roughtly proportional to the mis-alignement itself. The original declination of the vertical dial has no influence on the error, just he mis-aligment matters. The graphs show the difference:(value indicated by the mis-aligned sundial) - (true value) They refer to the Time (above) and to the Solar declination (below), the value are expressed as a function of the True Time (Ora reale) of the day, at the equinoxes and at the solstices. In any case, to find the errors it is quite simple: just take the classical graph with the curves showing the elevation of the Sun as a function of the Azimuth for a set of Hours and Solar Declinations. Make a transparent copy of the graph, shift it in Azimuth as the considered sundial and paste it on the original graph. On every point in the plane of the graph you can read the values of the real Time and Declination (on the original graph) and those indicated in the same moment by the misaligned sundial (on the shifted graph). Best wishes Francesco Caviglia > If a vertical dial is relocated and now faces a few degrees east or west of > its designed declination, you might expect it to run a few minutes slow or > fast. Has anyone ever tabulated the greatest error, and at what times and > dates it occurs? And does it make sense to think about the average error? > Clearly the errors depend on the latitude and the design declination, but > for starters they could be tabulated just for a direct south dial at 52.5 > degrees N, and for a location move of 1, 2 and 5 degrees either way. As > the gnomon is no longer polar-pointing I imagine the maths is a bit hairy. > > Best wishes, > > John Foad > > > Francesco CAVIGLIA via SAFFI 21 10138 Torino tel. 011 4333703 mob. 3356121207 francesco.cavig...@tin.it --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: A mis-aligned vertical dial
Diese Nachricht wurde eingewickelt um DMARC-kompatibel zu sein. Die eigentliche Nachricht steht dadurch in einem Anhang. This message was wrapped to be DMARC compliant. The actual message text is therefore in an attachment.--- Begin Message --- It seems as though gnomonicists are like politicians: when asked a question, they’ll always give a reply but generally not an answer to the question that was asked! John’s question relates to declining vertical dials which have been correctly designed but have subsequently been moved to a nearby location but on a wall with a different declination. Regards, John D Dr J Davis Flowton Dials http://www.flowton-dials.co.uk/ BSS Editor http://sundialsoc.org.uk/publications/the-bss-bulletin/ > On 8 Nov 2021, at 18:18, "fabio.sav...@nonvedolora.it" > wrote: > > dear John > > there is a precise theoretical procedure to relocate a sundial so that it > works correctly in a new location (for the hour lines). > > In the most general case, the sundial must be placed with a new orientation > so that the style keeps the polar orientation in the new location (thinking > of the stylus and dial as one whole). > This condition provides for many orientations, all the orientations obtained > by rotating the dial around the polar stylus. > The difference caused by these rotations is the meridian to wich the time > marked will refere, that is, as well as orienting the polar style correctly, > a rotation around the axis may be necessary for the marked time system to be > correct (local sun time, time-zone sun time). > > It seems a little bit complicated, indeed it is, but it can be solved. > > If the new location is very close there are not all these complications, you > have only to keep the same orientation. > If the difference are few degrees in declination of the wall, you can place > the sundial not parallel to the wall (keeping polar the stylus), otherwise, > as you write, you have to accept an error. > The error is not constant at the same time, it also changes with the > declination of the sun, that is, it is seasonal. > The answer to your question is a three-dimensional graph, with time and > declination of the sun on x and y axes and the error on the z axis. > The error doesn't depend on latitude but on the angle between the polar axis > and the non-polar stylus. > > Not last, there is a consideration similar to that of Lewis Carroll about the > stopped clocks that strike the right time twice a day: > a non-polar stylus, whatever its orientation, always shows the correct time > once a day, when the sun is in the hourly plane that contains the non-polar > stylus and the polar axis. This plane relates to two times 12 hours apart. > In the other times the error occurs according to the declination of the sun, > cancelling itself every 12 hours, whit the max error about halfway. > The paradox would therefore be that accepting a little approximation in the > direction of the stylus is not important. This is the reason why even in > front of a wrong sundial there are those who can say that they saw it strike > the right time. > If it were not a paradox it would be the end of gnomonics :-( > > I think that few degrees of error in the direction of the stylus (2-3°) might > be acceptable, but it also depends on the size of the sundial and therefore > on the comparison between the accuracy in the reading and the error due to > the non-polar stylus. > > ciao Fabio > > Il 08/11/2021 14:38, John Foad ha scritto: >> If a vertical dial is relocated and now faces a few degrees east or west of >> its designed declination, you might expect it to run a few minutes slow or >> fast. Has anyone ever tabulated the greatest error, and at what times and >> dates it occurs? And does it make sense to think about the average error? >> Clearly the errors depend on the latitude and the design declination, but >> for starters they could be tabulated just for a direct south dial at 52.5 >> degrees N, and for a location move of 1, 2 and 5 degrees either way. As >> the gnomon is no longer polar-pointing I imagine the maths is a bit hairy. >> >> Best wishes, >> >> John Foad >> >> >> >> >> >> --- >> https://lists.uni-koeln.de/mailman/listinfo/sundial >> > -- > Fabio Savian > fabio.sav...@nonvedolora.it > www.nonvedolora.eu > Paderno Dugnano, Milano, Italy > 45° 34' 9'' N, 9° 9' 54'' E, UTC +1 (DST +2) > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > --- End Message --- --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: A mis-aligned vertical dial
John, Unfortunately, I can't direct you to an existing tabulation of the alignment errors on a vertical dial. However, I do have a comment regarding your subordinate question about average errors: in my experience of the world of work, it is always a good thing to arrive on time or a little early for meetings, being a minute or two late is accepted, but we are sure to earn a frown when we are more than about 5 minutes late. So back in the era when I would have used a sundial to organize my day, I feel sure that knowing the maximum error would have been as important, if not more so, as knowing the average error. As well, I do not think that the simple average is particularly helpful because sometimes the dial will be early and sometimes late - the result can still be near zero. Instead, I would have wanted to know the average lateness. There have been a few times when I've written software to optimize dial layouts for least error. I usually do it by minimizing the worst case error. But then again, I'm a crank. Steve P.S. As an aside, for a horizontal dial, The Compendium carried a series of detailed articles from 1995 to 1997, under the title 'Error Analysis Of The Horizontal Sundial' / T.J. Lauroesch, J.R. Edinger On 2021-11-08 5:38 a.m., John Foad wrote: If a vertical dial is relocated and now faces a few degrees east or west of its designed declination, you might expect it to run a few minutes slow or fast. Has anyone ever tabulated the greatest error, and at what times and dates it occurs? And does it make sense to think about the average error? Clearly the errors depend on the latitude and the design declination, but for starters they could be tabulated just for a direct south dial at 52.5 degrees N, and for a location move of 1, 2 and 5 degrees either way. As the gnomon is no longer polar-pointing I imagine the maths is a bit hairy. Best wishes, John Foad --- https://lists.uni-koeln.de/mailman/listinfo/sundial ///workers.exist.lookout --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: A mis-aligned vertical dial
dear John there is a precise theoretical procedure to relocate a sundial so that it works correctly in a new location (for the hour lines). In the most general case, the sundial must be placed with a new orientation so that the style keeps the polar orientation in the new location (thinking of the stylus and dial as one whole). This condition provides for many orientations, all the orientations obtained by rotating the dial around the polar stylus. The difference caused by these rotations is the meridian to wich the time marked will refere, that is, as well as orienting the polar style correctly, a rotation around the axis may be necessary for the marked time system to be correct (local sun time, time-zone sun time). It seems a little bit complicated, indeed it is, but it can be solved. If the new location is very close there are not all these complications, you have only to keep the same orientation. If the difference are few degrees in declination of the wall, you can place the sundial not parallel to the wall (keeping polar the stylus), otherwise, as you write, you have to accept an error. The error is not constant at the same time, it also changes with the declination of the sun, that is, it is seasonal. The answer to your question is a three-dimensional graph, with time and declination of the sun on x and y axes and the error on the z axis. The error doesn't depend on latitude but on the angle between the polar axis and the non-polar stylus. Not last, there is a consideration similar to that of Lewis Carroll about the stopped clocks that strike the right time twice a day: a non-polar stylus, whatever its orientation, always shows the correct time once a day, when the sun is in the hourly plane that contains the non-polar stylus and the polar axis. This plane relates to two times 12 hours apart. In the other times the error occurs according to the declination of the sun, cancelling itself every 12 hours, whit the max error about halfway. The paradox would therefore be that accepting a little approximation in the direction of the stylus is not important. This is the reason why even in front of a wrong sundial there are those who can say that they saw it strike the right time. If it were not a paradox it would be the end of gnomonics :-( I think that few degrees of error in the direction of the stylus (2-3°) might be acceptable, but it also depends on the size of the sundial and therefore on the comparison between the accuracy in the reading and the error due to the non-polar stylus. ciao Fabio Il 08/11/2021 14:38, John Foad ha scritto: If a vertical dial is relocated and now faces a few degrees east or west of its designed declination, you might expect it to run a few minutes slow or fast. Has anyone ever tabulated the greatest error, and at what times and dates it occurs? And does it make sense to think about the average error? Clearly the errors depend on the latitude and the design declination, but for starters they could be tabulated just for a direct south dial at 52.5 degrees N, and for a location move of 1, 2 and 5 degrees either way. As the gnomon is no longer polar-pointing I imagine the maths is a bit hairy. Best wishes, John Foad --- https://lists.uni-koeln.de/mailman/listinfo/sundial -- Fabio Savian fabio.sav...@nonvedolora.it www.nonvedolora.eu Paderno Dugnano, Milano, Italy 45° 34' 9'' N, 9° 9' 54'' E, UTC +1 (DST +2) --- https://lists.uni-koeln.de/mailman/listinfo/sundial
