As I mentioned at my implementation approach I eventually did not take the parameters I got from maps or measurements by a ruler – I took the least square error approach by finally parameter adjustment and e.g. got to the news that the wall is horizontally 0.7° out of angle with respect to remote imaging/mapping.
Kurt Von: Perit Alexei Pace [mailto:[email protected]] Gesendet: Dienstag, 30. Juli 2019 21:30 An: Patrick Vyvyan <[email protected]> Cc: [email protected]; Sundial List <[email protected]> Betreff: Re: What accuracy to aim for with a carefully made sundial? Another source of error apart from those mentioned in the original post is how accurate can a wall's declination be measured, say to half a degree. And what error would half a degree make depends on the size of your sundial. We are also assuming the wall is planar and built perfectly plumb! Alexei On Tue, 30 Jul 2019 at 21:16, Patrick Vyvyan <[email protected] <mailto:[email protected]> > wrote: A basic problem with the accuracy of sundials is the Analemma. Due to the tilt of the Earth, the position of the shadow for a given time moves in a "figure-of-eight" shape over the course of the year. Therefore, even if the sundial is very accurately marked and positioned, the shadow will only fall exactly on the hour line twice a year - the winter and summer solstices. The figure-of eight Analemma is quite often marked for midday (and can serve to give the date as well). On large sundials, the Analemma may also be marked for every hour - but on a smaller dial, this can be visually very confusing! Another solution, used on heliochronometers, is to allow the dial to rotate against a scale marked with the appropriate Analemma offsets according to the date. Best wishes, Patrick On Tue, 30 Jul 2019 at 14:40, <[email protected] <mailto:[email protected]> > wrote: Hi Steve, as I built a large one (https://Kepleruhr.eu with 240m²) and thought some about getting as accurate as possible here are my readings so far: 1) If you go for a sharp edge you will find out that the penumbra is all the times about 2 min in width which is the wandering time of all of the sun diameter: The sun diameter is roughly 0.5° in the sky and it takes roughly 2 min for the sun to move this angle. The penumbra in angle does not depend on the distance from the gnomon to the face. So I would suggest that the reading would be +/-2 min for untrained and about +/-1 min for trained observers. This is valid for sundials using the bypassing shadow of the Gnomon or the moving flare of any rectangle or circular iris. 2) I estimate a reading accuracy of the Kepleruhr by +/-15 sec (at high noon only): There is a wandering flare of 2 cm (+/- penumbra) with two side edges on a line of 2 cm which increases the reading accuracy. This wandering flare is produced by a spherical Nodus with this 2 cm gap southwards. There are some movies at the concerning YouTube-channel (links given at the website). 3) In my case I made the calibration of the sundial by a) calculate the hour and day line positioning by given parameters (declination, geometry of gnomon, Nodus, wall) b) erect the gnomon to the wall firstly without the painting c) observe the shadow at one of the next fully sunny days - taking series of photos, calibrate them with respect to lens distortions, positioning, etc d) find the hourly shadow positions by machine vision techniques e) adjust the above given parameter set as long as the total error of deviations between the calculated and measured positions got a minimum f) calculate the lines with the latest parameter set and do the painting. g) BINGO - it turned out (observing the sundial since years) that the lines correctly follow the shadow on time. 4) I am on to build a sundial with a second reading of high noon - and did do the concerning presentations (theory, fulfilled and planned implementation steps) at sundial conferences in Austria. Good luck! Kurt -----Ursprüngliche Nachricht----- Von: sundial [mailto:[email protected] <mailto:[email protected]> ] Im Auftrag von Steve Lelievre Gesendet: Dienstag, 30. Juli 2019 19:38 An: Sundial List <[email protected] <mailto:[email protected]> > Betreff: What accuracy to aim for with a carefully made sundial? Hello everyone, I'm planning to make a small vertical west dial, about 1m for the width of the dial face, at my latitude of 49N. It will not use a nodus. The angular width of the sun makes it hard to get a really accurate time reading, but there will also be small errors from mis-positioning of the dial plate when installing (declination and inclination), imprecise positioning of the gnomon or the hour lines, and perhaps other causes too. First, questions directed at those of you who have practical experience of creating vertical sundials: If I'm careful and have a well-machined gnomon, what level of accuracy might be achievable in practice? I assume +/- 5 minutes throughout the day and year is fairly easy to achieve, but what about +/- 2 minutes, or even +/- 1 minute? How well did you do? How did you measure your wall's declination? Second, have there been any studies of how well dial users compensate for a penumbra - by which I mean gathering data from volunteers, studying the spread of errors in time readings taken from a dial versus a reference time source? (without employing a shadow sharpener) Thanks, Steve --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
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