Ice Sundial
Dear Dialists, On this link https://news.artnet.com/style/artist-daniel-arsham-hublots-new-brand-ambassador-just-installed-a-massive-crystal-sundial-high-in-the-swiss-alps-2267460 your see a ’sundial’ made in Switzerland. It’s looks beautful, but it is not really a dial. I would call it a ’timeless’ piece of art … best regards Werner --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Sun elevation tool
Dear John, I know this object as “Horizontoscope". http://www.horizontoscop.com/eng/index_eng.html I bought one recently after reading about it in one of Helmut Sonderegger’s articles, where he gives the math of it. https://www.herzog-forsttechnik.ch/wp-content/uploads/2022/08/Sonnenkompass_Flyer-2022.pdf It’s quite interesting how the hyperbolic surface makes the image independent of the height between the observing eye and the device. There is a german wikipedia entry. https://de.wikipedia.org/wiki/Horizontoskop Maybe someone from the sundial list can produce an english entry with the theory. It’s a nice device ! best regards Werner On 26 Oct 2022, at 02:45, John Pickard mailto:john.pick...@bigpond.com>> wrote: Good morning, Has anyone come across this dial-related device? https://picclick.co.uk/ARCHITECT-TOOL-Window-SUNLIGHT-SUN-ELEVATION-Enraf-144741549298.html Cheers, John. Dr John Pickard. --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: How to turn ecliptic longitude into solar declination?
Dear Steven, The relation of solar declination delta(t) to ecliptic longitude lambda(t) delta(t) = ArcSin[Sin[23.44]*Sin[lambda[t]] You are interested in the relation of solar declination to time since the equinox. Your formula delta(t) = 23.44*Sin(t), with t being the time (in degrees) since the spring equinox, is mathematically the 'first order Taylor expansion in obliquity phi’ of the precise expression for the solar declination. The difference of your formula to the accurate expression is around 0.9 degrees maximum. The 'first order Taylor expansion in eccentricity ecc’ is delta(t) = ArcSin[Sin[phi]*Sin[t]] + ecc * Sin[phi] * Sin[2*t] / Sqrt[1 - Sin[phi]^2*Sin[t]^2] which is accurate to 0.015 degrees. (phi=23.44 degrees) It is a much better approximation because for a Taylor approximation the argument should be much smaller than unity. phi=2*Pi/360*23.44 = 0.41 is not so small, but ecc=0.0167 is very small ... You could still approximate the above expression to delta(t) = ArcSin[Sin[phi]*Sin[t]] + ecc * Sin[phi] * Sin[2*t] which is accurate to 0.03 degrees, and it does take into account the eccentricity of the orbit. Other approximations can quickly become more complicated than using directly the correct formulas. The numbers are still in my head because I recently discussed this point in the NASS293 article on the analemma (Eq. 19, Eq. 20). cheers Werner > On 15 Oct 2022, at 01:56, Steve Lelievre > wrote: > > Hi, > > For a little project I did today, I needed the day's solar declination for > the start, one third gone, and two-thirds gone, of each zodiacal month (i.e. > approximately the 1st, 11th and 21st days of the zodiacal months). > > I treated each of the required dates as a multiple of 10 degrees of ecliptic > longitude, took the sine and multiplied it by 23.44 (for solstitial solar > declination). At first glance, the calculation seems to have produced results > that are adequate for my purposes, but I've got a suspicion that it's not > quite right (because Earth's orbit is an ellipse, velocity varies, etc.) > > My questions: How good or bad was my approximation? Is there a better > approximation/empirical formula, short of doing a complex calculation? > > Cheers, > > Steve > > > > > > --- > https://lists.uni-koeln.de/mailman/listinfo/sundial > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: A new website : Equation-of-Time.info
Dear Kevin, Thanks a lot for putting together this very nice site ! You will also have to write the book. The EOT is such a fundamental ‘cultural and social’ topic that it deserves a proper discussion. In the chapter THE EQUATION OF TIME IN ASTRONOMY & NAVIGATION it could be very nice to add the equation of time table from Kepler’s Tabulae Rudolphinae. It is the first calculation using the correct elliptical orbit (Kepler equation) For the section SHAPED STYLE SUNDIALS There is the original ‘invention’ by John Ryder Oliver https://www.helios-sonnenuhren.de/de/chronos-geschichte On the same site you find a picture of a realization and also one dial by Martin Bernhard that incorporates the idea. I have thought a lot about how eliminate the problem of having to change the Style every 6 months, and I came up with a ‘Double-Style’ http://riegler.home.cern.ch/riegler/sundial/mainpage.htm There are some pictures and details given on this page. What I like particularly is that when looking from the edge of the equatiorial disc to the style it projects the Analemma curve onto the sky. There is a photo under the tab ‘Analemma’. best regards Werner Riegler On 9 Sep 2018, at 01:38, Kevin Karney via sundial mailto:sundial@uni-koeln.de>> wrote: 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. From: Kevin Karney mailto:kar...@me.com>> Subject: A new website : Equation-of-Time.info<http://Equation-of-Time.info> Date: 9 September 2018 at 01:38:22 GMT+2 To: tonylindisun--- via sundial mailto:sundial@uni-koeln.de>> Dear colleagues and friends I have spent a lot of time over the last few years in front of my computer thinking about the Equation of Time. Recently my son asked where all the output of my studies resided. At first, I thought I should write a book. But instead I acquired a new domain and found that Adobe had a simple package that allows one to make a nice looking website with little technical effort. You can find the website at https://Equation-of-Time.info<https://equation-of-time.info/> It contains three main sections, all copiously illustrated... 1. The Equation of Time - 8 pages. Here, see the videos on why the Equation of Time looks as it does (under the page ‘The components of the Equation of Time’). I am particularly proud of these! 2. Sundials that are (or can be) Equation corrected - 8 pages 3. Mechanical Means to Simulate the EoT - 6 pages. I have been harvesting images of EoT related things for many years, often without recording where they came from. So if I have included an image of yours and have not attributed it to you, please let me know. Please do have a look and send comments/additions/corrections/improvements Best wishes Kevin Karney - from Wales --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: 3D analemma
Hi Art, I have put together a few pages that explain the calculation of such a gnomon. http://riegler.home.cern.ch/riegler/sundial/tmpfiles/3Danalemma.pdf The Gnomon of a sundial can be shaped such that the Equation of Time is automatically corrected and the Sundial shows the Civil Time. Because the sun has the same declination twice a year, but the Equation of Time is different at these dates, the gnomon has to be changed twice a year, like it is e.g. the case for the dial of Martin Bernhardt: http://www.praezisions-sonnenuhr.de/ http://www.praezisions-sonnenuhr.de/ In order to avoid changing the gnomon twice a year I developed a 'semi transparent' double gnomon some time ago that incorporates both gnomons so they don't have to be changed: http://riegler.home.cern.ch/riegler/sundial/mainpage.htm The absolute value of the equation of time at a given declination is not very different, so by approximating the analemma with a symmetric curve one can arrive at a single Gnomon that doesn't have to be changed, which is what you want to do. The error introduced by this approximation is at maximum 1.7 minutes, so it is quite good. As Roger points out, this gnomon is infinitely thin in the middle, so there one has to keep some minimum radius to keep it stable. The best way to avoid this problem is to really build the top and bottom piece separately and really have both pieces going to zero radius. Then you drill a hole along the axis and you insert a steel cable that you tention at the two extremities. Like this you don't have to worry about the stability of the thin piece. A steel cable of 2mm diameter is already extremely strong, so this will be a very good approximation to the 'zero' radius. Best regards Werner Riegler From: sundial-boun...@uni-koeln.de [mailto:sundial-boun...@uni-koeln.de] On Behalf Of Art Krenzel Sent: Friday, March 27, 2009 4:56 PM To: sundial@uni-koeln.de Subject: 3D analemma I am seeking some assistance to construct a 3 dimensional analemma to be used on a gnomon of an equatorial sundial. Specifically I am seeking an equation which can be used to plot the analemmic error information in X and Y such that I might enter the data into a CNC machine to cut the curved surfaces. I want to average the time errors from each side of the figure 8 layout to make a symmetrical 3 dimensional object. Does anyone have a formula to plot analemmic timing errors where I can enter a value for X (not days) and get a timing error as Y for graphical purposes? Thank you for any efforts to help me solve my problem. Sincerely, Art Krenzel --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Bernhardt's gnomons
Dear Dialists, Five years ago I built a novel dial that goes a step further that Bernhard's dial. I didn't yet have time to publish it properly because I was extremely busy building the LHC here at CERN in Geneva - and as you might have heard I will continue to be busy ... I have finally put together a WEB page with some pictures and explanations. http://riegler.home.cern.ch/riegler/sundial/mainpage.htm The basic idea is the same as the one from Oliver/Bernhard but I am placing both indicators at the same time and make the 'outer' one semi-transparent. This way one doesn't have to change the indicator. I also like the indication of the calendar on the dial. For calculating the shape of the indicator I use the following 'simple' argument: I start with an equatorial dial with a scale on the edge of the disc. At 12:00 + EoT the sun is exactly in southern direction, i.e. the ray of light indicating the correct time starts at 12:00 + EOT from the edge of the dial and points south with the given solar declination of the day. Drawing one of these light rays for each day of the year produces a surface of sunrays and the indicator of the dial is simply the rotationally symmetric body that is tangential to this surface. This is described in the presentation 24.9.2004 link on the page. Best regards Werner Riegler --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Earth eccentricity
Hello Jos, As you know the equation of time (EOT), which you measure, is a unique function of three parameters: 1) The tilt of the earth's axis towards the ecliptic 2) The distance (or time) between the perihelion passage of the earth (around Jan. 4th) and the spring equinox (around March 21st) 3) The earth's eccentricity Assuming that you measure the EOT and you know 1) and 2) you can find the eccentricity by finding the best fit to your data. Theoretically you need only 2 points on the EOT, but in practice you need of course a large part of the EOT to get a good fit. Don't forget that you have to correct you sundial time for the longitude of you dial before comparing it to you watch. In case the earth would orbit in a circle, the EoT would only be due to the tilt of the earth's axis and the analemma would be a symmetric 8 curve. The middle point of the 8 would be at the equinoxes. For me, the 'symbolic', effect of the earth's eccentricity is therefore the displacement of the middle point of the analemma towards positive declination. Regards Werner From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Jos Kint Sent: Thursday, August 21, 2008 10:12 AM To: sundial@uni-koeln.de Subject: Earth eccentricity Hello all, I am looking for some help in observing the earth's orbital eccentricity, just by using my sun dial. Who gives me some hint? With my vertical 2,5 meter by 1,5 meter sun dial I can measure the local solar time with an accuracy of less than 60 seconds. Jos Kint, Belgium --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: simultaneous sunset
Dear Frank, It is not really possible to tidy up your efforts, because I think they are as clean as they can possibly be - but I can try to mess up your efforts by another concept: CONCEPT Sunset in Paris means that the rays of sunlight are in a plane tangential to the earth in Paris. Sunset in London means that the rays of sunlight are in a plane tangential to the earth in London. Sunset at the same time in London and Paris means that both of the above conditions have to be fulfilled, which means that I have to find the intersection of the two tangential planes, which gives a straight line. The angle between this straight line and the earth's axis is equal to 90-declination of the sun. MATH la1 = latitude of place 1 la2 = latitude of place 2 d = their difference in longitude The equations for the two tangential planes are (assuming the earth's radius to be 1): 1) x.cos(la1)+z.sin(la1)=1 2) x.cos(la2).cos(d)+y.cos(la2).sin(d)+z.sin(la2)=1 If I find the intersection of these two planes and calculate the angle between earth's axis and this line I find the result sin(dec)=-sin(d)/sqrt(t1^2 - 2.t1.t2.cos(d) + t2^2 + sin^2(d)) Expressing tan(dec)=sin(dec)/sqrt(1-sin^2(dec)) I find exactly your formula ! So I guess this is proof that you haven't goofed. Best Wishes Werner Riegler -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Frank King Sent: Monday, June 18, 2007 7:20 PM To: Frank Evans Cc: Sundial Subject: Re: simultaneous sunset Dear Frank, I do enjoy your puzzles!! ... a question appeared of the form: Find a day on which the sun sets (altitude 0 deg.) at the same moment in London and Paris (positions given). Conceptually this is trivial. Mathematically it gets a little messy but I think I can get a closed form of the solution. CONCEPT I assume that at any instant half the Earth is in sunlight and half is in darkness. A great circle separates the two halves. Any place on this great circle is experiencing the moment of (mathematical) sunset or sunrise. The solution to your problem is to draw a great circle from London to Paris and extend it until it reaches the Equator. The angle this great circle makes to the plane of the Equator is the complement of the solar declination (subject to a minus sign). MATHEMATICS Let t1 = tangent of the latitude of place 1 Let t2 = tangent of the latitude of place 2 Let d = their difference in longitude We then have: tan(dec) = -sin(d)/sqrt(t1^2 - 2.t1.t2.cos(d) + t2^2) Where dec is the required solar declination. EXAMPLE You cite London and Paris. I take the latitudes as being 51 deg 30' and 48 deg 52' and the difference in longitude as being 2 deg 23'. This gives the solar declination as -18.7 degrees. I expect I have goofed. Some bright youngster can now tidy up my efforts!!! Best wishes Frank King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Relativistic sundial
This sounds very interesting. However -- the formula quoted below is completely wrong in this context and has nothing to do with relativity. Does it say that it has to do with relativity ? To me it looks more like a formula for the effect of Abberation. Could you send me the picture of the dial ? Thanks Werner -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Roger Bailey Sent: Monday, May 30, 2005 7:15 PM To: anselmo; sundial@rrz.uni-koeln.de Subject: RE: Relativistic sundial I was surprised recently to see a sundial that has a relativistic time dilation correction. There is a dial by Atelier Tournesol in the hamlet of Les Vigneaux, Vallouise, Haut Alpes. It is a triangular North east facing vertical declining on the old presbytery across from the church clock tower with a pair of corner VD dials. Above the dial is the equation delta tau = square root(delta t -((V(t)/c))). Text does not render it very well but in looks like relativity to me. The dial, dated MCMLXXXIX, has both classical and republican hour markings (decimal hours) so someone has had fun with this dial design. Picture available on request. SaF catalogue # 0518002. Regards, Roger Bailey -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of anselmo Sent: May 30, 2005 1:02 AM To: sundial@rrz.uni-koeln.de Subject: Relativistic sundial Dear all, Everybody knows the story of a salesman that, after having been travelling at a very high speed, discovers that his wrist-watch is delayed respect the rest of the world's, isn't it? But what if his wrist-watch were a sundial? Obviusly it can't be delayed so... what has happened? Anselmo - - -
RE: Relativistic sundial
Hi Dave, The formula you quote is the correct one. The one quoted from the sundial delta tau = square root(delta t -((V(t)/c))) is not correct since there is no square and the t is inside the root ... The correction for Aberration of the starlight is delta t = v/c. See e.g. http://www.phy6.org/stargaze/Saberr.htm The traditional analogy to explain the effect is the umbrella rain: If it is raining and you stand under the umbrella you stay dry. If you walk in the rain with a velocity v and the rain comes down with velocity c, then the apparent angle of the raindrops is given by tan(alpha) = v/c, so your feet get wet when you walk quickly. The same is true when the earth is moving around the sun, so it should have an effect on the sundial time ... Werner -Original Message- From: Dave Bell [mailto:[EMAIL PROTECTED] Sent: Tuesday, May 31, 2005 4:31 PM To: Werner Riegler; sundial@rrz.uni-koeln.de Subject: Re: Relativistic sundial What do you mean by Aberration, Werner? The formula looks close to right for the time dilation effect, as if quoted from memory. I think it was supposed to be delta Tau = delta t times the square root of (one minus v squared over c squared). Dave Werner Riegler wrote: This sounds very interesting. However -- the formula quoted below is completely wrong in this context and has nothing to do with relativity. Does it say that it has to do with relativity ? To me it looks more like a formula for the effect of Abberation. Could you send me the picture of the dial ? Thanks Werner -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Roger Bailey Sent: Monday, May 30, 2005 7:15 PM To: anselmo; sundial@rrz.uni-koeln.de Subject: RE: Relativistic sundial I was surprised recently to see a sundial that has a relativistic time dilation correction. There is a dial by Atelier Tournesol in the hamlet of Les Vigneaux, Vallouise, Haut Alpes. It is a triangular North east facing vertical declining on the old presbytery across from the church clock tower with a pair of corner VD dials. Above the dial is the equation delta tau = square root(delta t -((V(t)/c))). Text does not render it very well but in looks like relativity to me. The dial, dated MCMLXXXIX, has both classical and republican hour markings (decimal hours) so someone has had fun with this dial design. Picture available on request. SaF catalogue # 0518002. Regards, Roger Bailey -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of anselmo Sent: May 30, 2005 1:02 AM To: sundial@rrz.uni-koeln.de Subject: Relativistic sundial Dear all, Everybody knows the story of a salesman that, after having been travelling at a very high speed, discovers that his wrist-watch is delayed respect the rest of the world's, isn't it? But what if his wrist-watch were a sundial? Obviusly it can't be delayed so... what has happened? Anselmo - - - -
RE: Relativistic sundial
Indeed -- this is of course the correct formula for the time dilatation. It would still be interesting to figure our whether the effect from Aberration or the effect of time dilatation is larger Werner -Original Message- From: Roger Bailey [mailto:[EMAIL PROTECTED] Sent: Tuesday, May 31, 2005 6:21 PM To: Dave Bell; Werner Riegler; sundial@rrz.uni-koeln.de Subject: RE: Relativistic sundial A small picture of the formula is attached. I hope it gets through the size filter. Roger -
RE: Relativistic sundial
Well -- the salesman's watch is traveling together with him at very high speed, so it measures 'his' personal time. If the salesman looks at his sundial -- then goes on his fast trip and returns to look again at his sundial -- is the same thing as leaving a watch in the place and taking a trip without it. Taking the sundial with him would mean to pack the earth and the sun in his suitcase and bring it on the trip ... Werner Riegler -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of anselmo Sent: Monday, May 30, 2005 10:02 AM To: sundial@rrz.uni-koeln.de Subject: Relativistic sundial Dear all, Everybody knows the story of a salesman that, after having been travelling at a very high speed, discovers that his wrist-watch is delayed respect the rest of the world's, isn't it? But what if his wrist-watch were a sundial? Obviusly it can't be delayed so... what has happened? Anselmo - -
