Re: Expanded Nodi Shadow Experiment - again
I attach the image of a new kind of Nodus made by Roberto Baggio in a Primary School. The nodus is the eye of the Peace Dove 3 mm in diameter . (orthostyle = 40 cm). The eye is on the extension of the polar style Gianni Ferrari <> --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hello Mac, a few minutes ago Roberto Baggio has sent to me two photos of the nodus of his sundial in the square in Varese, taken today 23 m after the true noon. I send them attached to a personal Email. If other are interested to receive them (about 2 Mb), write me. Gianni Ferrari - Original Message - From: "Mac Oglesby" <[EMAIL PROTECTED]> To: "Gianni Ferrari" <[EMAIL PROTECTED]> Cc: Sent: Sunday, August 13, 2006 7:47 PM Subject: Re: Expanded Nodi Shadow Experiment Hello Gianni, Thanks for showing this application, and also for your contributions to this fascinating thread. Are there pictures anywhere on the internet which show the overall installation? It's not completely clear to me just where the nodus is located, relative to the analemma. Best wishes, Mac Oglesby --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hello Mac, I have not found in Internet any image of the Baggio's sundial in Varese . I have written to him asking some photos and I will send them to whom is interested (obviously to you). The photo that I have attached in my last message can appear strange because the meridian line (of the solar noon) doesn't cut the analemma (as we see in the image). This because the Longitude of Varese =8.83° and our TZ = 1h The distance among the two lines changes and its maximum value is = 59 cm. On the day in which the photo was taken the distance is around = 42 cm The pole (diameter 10 cm ) that supports the plate (tilted with an angle = latitude) is put on the prolongation of the meridian line (that of the solar noon) The web-site of Baggio is http://www.meridianevarese.it To note in http://www.meridianevarese.it/realizzazioni.html the photo " Brinzio" where it is visible a spherical nodus star-shaped, suspended to a cable (the analemma is 7-8 m high) Gianni Ferrari P.S. The shape of the Baggio's nodus is indeed equal to that of John Carmichael, but Baggio didn't certainly know it (it is not registered to this list) :-) - Original Message - From: "Mac Oglesby" <[EMAIL PROTECTED]> To: "Gianni Ferrari" <[EMAIL PROTECTED]> Cc: Sent: Sunday, August 13, 2006 7:47 PM Subject: Re: Expanded Nodi Shadow Experiment Hello Gianni, Thanks for showing this application, and also for your contributions to this fascinating thread. Are there pictures anywhere on the internet which show the overall installation? It's not completely clear to me just where the nodus is located, relative to the analemma. Best wishes, Mac Oglesby >After a lots of theory.. a practical object :- ) > > > >I send attached the image of the nodus used by >the Italian dialist Roberto Baggio in a meridian >line built in 2003, in a square of the town of >Varese (northern Italy) > >The nodus is put at a height of 4 m and it is >made with a square plate of brass (side=25 >cm) containing a great hole (diameter 14 cm ) >and a central disk with the diameter = 4.5 cm, > fixed with metallic threads. > >On the 4 points the letters N,E,S,O are cut out (O=Ovest = West). > >The analemma is long 10.6 m and is made with 750 >marble tesserae of 3x3 cm . > >From the summer solstice to the equinoxes the >central disk gives a distinctly visible shadow: >the ratio (distance nodus-image / disk-diameter) >= 410/4 <108 > >From the equinoxes to the winter solstice the >image of the outer circle disappears (fully in >penumbra) because the shadow of the disk widens >and that of the inside ring approaches the >center. In these seasons as nodus the shadow of >the whole plate is used . Its center is easily >located using the symmetry of the structure. > > > >Gianni Ferrari > > >Attachment converted: Macintosh HD:Varese_Nodus.jpg (JPEG/«IC») (00275479) >--- >https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hello Gianni, Thanks for showing this application, and also for your contributions to this fascinating thread. Are there pictures anywhere on the internet which show the overall installation? It's not completely clear to me just where the nodus is located, relative to the analemma. Best wishes, Mac Oglesby After a lots of theory . a practical object :- ) I send attached the image of the nodus used by the Italian dialist Roberto Baggio in a meridian line built in 2003, in a square of the town of Varese (northern Italy) The nodus is put at a height of 4 m and it is made with a square plate of brass (side=25 cm) containing a great hole (diameter 14 cm ) and a central disk with the diameter = 4.5 cm, fixed with metallic threads. On the 4 points the letters N,E,S,O are cut out (O=Ovest = West). The analemma is long 10.6 m and is made with 750 marble tesserae of 3x3 cm . From the summer solstice to the equinoxes the central disk gives a distinctly visible shadow: the ratio (distance nodus-image / disk-diameter) = 410/4 <108 From the equinoxes to the winter solstice the image of the outer circle disappears (fully in penumbra) because the shadow of the disk widens and that of the inside ring approaches the center. In these seasons as nodus the shadow of the whole plate is used . Its center is easily located using the symmetry of the structure. Gianni Ferrari Attachment converted: Macintosh HD:Varese_Nodus.jpg (JPEG/«IC») (00275479) --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
After a lots of theory . a practical object :- ) I send attached the image of the nodus used by the Italian dialist Roberto Baggio in a meridian line built in 2003, in a square of the town of Varese (northern Italy) The nodus is put at a height of 4 m and it is made with a square plate of brass (side=25 cm) containing a great hole (diameter 14 cm ) and a central disk with the diameter = 4.5 cm, fixed with metallic threads. On the 4 points the letters N,E,S,O are cut out (O=Ovest = West). The analemma is long 10.6 m and is made with 750 marble tesserae of 3x3 cm . From the summer solstice to the equinoxes the central disk gives a distinctly visible shadow: the ratio (distance nodus-image / disk-diameter) = 410/4 <108 From the equinoxes to the winter solstice the image of the outer circle disappears (fully in penumbra) because the shadow of the disk widens and that of the inside ring approaches the center. In these seasons as nodus the shadow of the whole plate is used . Its center is easily located using the symmetry of the structure. Gianni Ferrari <> --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hi Gianni, Thank you for your splendid response... > I hope that our Emails, interesting for us, don't bore > other readers :-) I promise this one will be short!! Oh, and your image arrived first time (a little corrupted but I could read it). This time I agree with EVERYTHING in your reply. > For a declining sundial I think that the direction of the axis > of the hole should coincide with the intersection of the plane > of the equator with the substyle plane (hour plane normal to > the dial and on which the polar style lies) Ah. Now that IS a good rule and, as you say, it works for walls that face east and west too. > In the figure Yes, I agree with your calculations. > CAMERA OBSCURA MERIDIANA I am most grateful to you for your comments here. You are, of course, absolutely right to use sin(h) cubed. I was comparing solid angles. You compare brightness which is definitely better. > sin(45+dec) x sin(45+dec) x sin(45+dec) x sin(45+dec+ang) Yes!! Agreed. > I try to explain this in the note at the end, so the readers not > interested can jump it :-) Yes, your explanation is very eloquent and easy to follow. I see from a very old message that I once omitted a sin term before and you corrected me. I must do better! > Then in my opinion the function to use is > >sa(dec,ang) = sin(h) x sin(h) x sin(h) x sin(h+ang) > or >sa(dec,ang) = sin(45+dec) x sin(45+dec) x sin(45+dec) x sin(45+dec+ang) Yes but we must change the name... I chose sa for Solid Angle. My function is correct for comparing solid angles but solid angles are not (quite) what we want!! Using your function, the King angle is now 108.829 degrees... sa(+23.5,108.829) = 0.038 = sa(-23.5,108.829) = 0.038 This is very academic! The plane of the hole almost aligns with the sun at the summer solstice. The difference is only 2.67 degrees. The hole would have to be in a very thin part of the wall or the summer solstice point would get no light at all. You could make the hole elliptical which would help... If the height of the hole is 20,000mm then the hole could have a major axis of 160mm and a minor axis of 20mm. This would give you an image all year I think. At the summer solstice 1/R would be about 3000 and at the winter solstice 1/R would be about 450 which is acceptable. Unfortunately, at the equinoxes, 1/R would be about 400 which is getting rather low. I don't think Cassini would accept that! I think we can conclude this most interesting exchange. I must find an English church which will let me try some experiments! Thank you again Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
I am sorry but the image is not arrived I try again now Gianni Ferrari <> --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hello Frank, I hope that our Emails, interesting for us, don't bore other readers :-) Your answers put always in evidence some details that we have to consider but that often slip our mind (at least mine !) and remain hidden. I agree completely with your LESS GOOD FEATURES : I have to admit that I had thought only to horizontal sundials, also remembering one made by a friend in a square in Varese, a the town in northern Italy. Obviously a hole with the axis pointing at the position of the equinoctial sun at 12 noon cannot work for a vertical plane facing East or West! For a declining sundial I think that the direction of the axis of the hole should coincide with the intersection of the plane of the equator with the substyle plane (hour plane normal to the dial and on which the polar style lies) This direction is given by the extreme point of the polar style and the point in which the substyle line crosses the equinoctial one; it belongs to the plane of the polar style and makes with the dial plane an angle = (90-style height). If the sundial faces East or West the axis of the hole is normal to the plane, that is the plane of the hole is parallel to the dial . In the figure : Lat.=45° , wall-decl=50° W GG' = 100 ; CG = 220.01 ; SG' = 51.03 ; CS = 247.0 Style height GCS = 27.03° ; SCM = 37.45° ; CSG = 62.97° CAMERAOBSCURA MERIDIANA Note- This is the Latin name but we can call it in different other modes (pin-hole sundial, dark room sundial, etc. ) In an old article (presented in one of our meetings in 2003 ) I made the same considerations (even if using different formulas ) on the uniformity of the brightness, along the meridian line, of the image in a dark room sundial . I had considered different positions of the hole (also a vertical hole) but I had not thought to the King angle and to the possibility to lengthen the hole: this is a good idea . However I have to note that in my formula I have found sin(45+dec) x sin(45+dec) x sin(45+dec) x sin(45+dec+ang) that is sin(h) is cubed . I try to explain this in the note at the end , so the readers not interested can jump it :-) Obviously our considerations are valid only if the "dark room" condition is satisfied, that is if the ratio(distance from the hole to the image) / (least dimension of the hole-as seen by the image) is much greater than 108 (at least 300-500 ) This is not true in the meridian lines that have to work in open air. The brightness of the image in room sundials is too low and cannot be perceived inopen air but only in .. dark rooms :-) Gianni Ferrari NOTE D = hole diameter ; H = hole height from floor ; Fi = sun Diameter (rad) ; J = illumination constant ; h= Sun altitude ; ang = angle of hole to the horizontal If the Sun has altitude = 90° and ang = 0° then : Light through the hole = J x D x D x pi / 4 Image area = (H x Fi) x (H x Fi) x pi / 4 Brightness of the image = (J x D x D) / [ (H x Fi) x(H x Fi) ] = K When the sun has altitude h we have : Light through the hole = J x D x D x sin(h+ang) x pi / 4 Distance hole-image = H / sin(h) Image area = [H x Fi /sin(h)] x [H x Fi /sin(h)] x [1/sin(h)] x pi / 4 = (H x Fi) x (H x Fi) x [1/ sin(h)]^3 Brightness of the image = K x sin(h+ang) x sin(h) x sin(h) x sin(h) Then in my opinion the function to use is sa(dec,ang) = sin(h) x sin(h) x sin(hc) x sin(h+ang) or sa(dec,ang) = sin(45+dec) x sin(45+dec) x sin(45+dec) x sin(45+dec+ang) G.F. clip_image001.gif Description: GIF image --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
That is all well and good, but by rotating the Camera Obscura (I prefer the term pinhole lens) aperture you can hold angular problems to analemmic degrees, much less problematic when this is the case. This also gives a handy way to make very small angular measurements more visible on a scale attached to the rotating member. Haze, while inconvient, does not make a noticable, or at least consistent, difference in any way that I can discern on a system as described above. There is some discrepancy when the sun becomes oblate near sun rise/set. The measurement of solar radiation falling outside the visible spectrum has always interested me as a way of combating haze, but unfortunatly the results of the few experiments I have tried along these lines were not readily available to me, as they were, by definition, 'invisible'. Cheers! Dave G. http://atensundials.com --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hi Gianni, It is always good to hear from you on this list. Most of what I know about nodus design is a result of reading your papers so your message is of very great interest. You made this comment... > I think that it is advisable that the plane of the hole is a > polar plane with the hole axis on the intersection among the > equator and the meridian planes. Ah. You want the axis of the hole to point at the position of the equinoctial sun at 12 noon. At that instant, the other end of the axis meets the dial where the noon line intersects the equinoctial line. This idea has good features and less good features... GOOD FEATURES The design is very symmetrical. The axis aligns with the sun at a position halfway between the extremes of declination and halfway between sunrise and sunset. Having the hole in a polar plane is particularly good if the dial is also in a polar plane. Of course, the hole is then parallel to the dial. LESS GOOD FEATURES Unfortunately, having the hole in a polar plane does not work well in general. An extreme example is a direct east-facing wall. The hole would then be in a plane perpendicular to the wall. You get no spot of light falling on the dial when the sun is due east. I think you were considering horizontal dials. Your suggestion certainly lets more light fall on the dial at the winter solstice. Let's look at an example... A CAMERA OBSCURA MERIDIANA To make the calculations easy, consider the situation at 12 noon. As an example, I shall consider a camera obscura meridiana at: Latitude 45 degrees Hole diameter 20 mm Height of hole above the pavement 20,000 mm Although millimetres were before their time, Cassini and Bianchini would have been familiar with these dimensions! The brightness of the spot of light falling on the pavement at 12 noon is proportional to the solid angle of the hole as seen from points in the spot. In a really simple case: The hole would be horizontal The altitude of the sun would be 90 degrees In this impossible case, the spot of light would be at the point perpendicularly below the hole. The solid angle is: RSA = (pi x 10 x 10) / (2 x 2) I call this RSA for Reference Solid Angle. This is the area of the hole divided by the square of the hole-to-pavement distance. In reality, the altitude of the sun varies from 45-23.5 degrees (at the winter solstice) to 45+23.5 degrees (at the summer solstice). In general at latitude 45 degrees and at 12 noon: altitude = 45 + dec(where dec = declination) When the altitude is changed from 90 degrees, the hole-to-pavement distance increases by a factor 1/sin(altitude) AND the hole will appear elliptical when you look at it from the spot of light. The semi-minor axis of the hole will be 10 x sin(altitude) if the hole is still horizontal. You suggest that the hole should be 45 degrees to the horizontal. Let's make this angle arbitrary: Let ang = angle of hole to the horizontal The semi-minor axis of the hole is now 10 x sin(altitude+ang) The solid angle is now: SA = RSA x sin(45+dec) x sin(45+dec) x sin(45+dec+ang) In the impossible case where the sun is in the zenith, dec = 45 and, if ang=0, we are back to SA = RSA the reference solid angle. The factor RSA is a constant. It is much more interesting to look at the other terms. Consider the function: sa(dec,ang) = sin(45+dec) x sin(45+dec) x sin(45+dec+ang) If the hole is horizontal ang = 0 and two special cases are: sa(+23.5,0) = 0.805 andsa(-23.5,0) = 0.049 The spot of light is 16 times brighter at the summer solstice than it is at the winter solstice. Now let's try the Ferrari angle. When ang = 45 we have: sa(+23.5,45) = 0.794 andsa(-23.5,45) = 0.123 This give a MUCH better balance. The spot of light is only 6.5 times as bright at the summer solstice as it is at the winter solstice and there is only a slight reduction in brightness at the summer solstice. Your suggestion looks VERY good... We can do even better. Why not align the axis of the hole with the winter solstice point on the noon line? Here ang = 68.5 and: sa(+23.5,68.5) = 0.590 andsa(-23.5,68.5) = 0.134 Now the spot of light is only 4.5 times as bright at the summer solstice as it is at the winter solstice. From the winter solstice point the hole now appears circular. This point is, of course, much further from the hole so it still receives less light. If you really want to achieve balance you can try the King angle. This is over-the-top in at least two senses but it really works. You set ang = 104.267 when: sa(+23.5,104.267) = 0.109 = sa(-23.5,104.267) = 0.109 The hole faces due south and is actually leaning backwards away from the noon line on the pavement. Also, the punto perpendiculare will probably be outside the building but, with modern surveying technology, this should not be a problem! We are severely restricti
RE: Expanded Nodi Shadow Experiment
Hello all, I seem to remember that when I first read about the Bernhardt precision dial, mention was made of the effect of different levels of sunlight and haziness on the edge of the shadow of the thick curved gnomon. Apparently, the gnomon thickness across its height was corrected for the typical variation over the seasons for mid-west Europe. I see no mention of this on the web site, however. Rudolf Hooijenga 52-30N 4-40E -Oorspronkelijk bericht- Van: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Namens Mac Oglesby Verzonden: donderdag 10 augustus 2006 12:27 Aan: Frank King CC: Sundial List Onderwerp: Re: Expanded Nodi Shadow Experiment (...) Isn't it odd that so little has been written, prior to now, about the effects of weak sunshine on gnomon design? -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.405 / Virus Database: 268.10.8/415 - Release Date: 9-8-2006 --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hello Frank, Were Bill still with us he could expand on his reasoning. He would have hugely enjoyed this thread. He did write, "The only thing to watch out for is a case where the thicker post casts its shadow on top of that of one of the cross bars. I suppose it might be good if all three rods were the same diameter, but that would be harder to make." But I don't recall any mention of subdued sunshine (sunlight diminished by haze or thin clouds) as being a complication. Isn't it odd that so little has been written, prior to now, about the effects of weak sunshine on gnomon design. I'm hoping that, once this thread has run its course, you will write a summary, which will clearly state the best nodus design options available. You have a gift for writing clear statements. Best wishes, Mac Oglesby Dear Mac, Thank you for sharing Bill's sketch with the list. I really appreciate his phrase... I'm a bug on symmetry... I think that pretty much describes me too! Moreover, his design satisfies the symmetry goal well. In particular, the fat rod extends beyond the crossing which keeps me happy! The main snag is that the relatively thin rods might disappear into fuzz when the main shadow is long, especially when there is light haze. Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Dear Mac, Thank you for sharing Bill's sketch with the list. I really appreciate his phrase... > I'm a bug on symmetry... I think that pretty much describes me too! Moreover, his design satisfies the symmetry goal well. In particular, the fat rod extends beyond the crossing which keeps me happy! The main snag is that the relatively thin rods might disappear into fuzz when the main shadow is long, especially when there is light haze. Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hi John, Frank and all, As Frank says, it is largely the angular width of the effective sun that causes the major error. On hazy days the brightness versus angle from the center of the sun widens out, sometimes drastically. Using Frank's wall example, as the haziness increases, narrower wire gnomons ( or finger shadows ) begin to disappear and the doubling he mentions occurs with the finger tips further apart. A truncated cone will help somewhat. I've not tried it, but a truncated cone capped by a hemisphere of the same diameter of the truncated end would seem a good compromise, and somewhat safer as well. What have the rest of you folks in hazy climes discovered on this? Let me know what you discover John, and thanks for the neat stuff! P.S. Has anyone built a sundial using longer wavelength radiation from the sun that would penetrate haze and even clouds? Edley McKnight On 9 Aug 2006 at 8:10, John Carmichael wrote: > Hi Edley: > > Well you learn something new every day, especially from the smart people on > this List. > > I had no idea that a hazy day would shorten the shadow cast by a cone's > point! In fact, I still don't quite believe it until I get to see it with > my own eye's. It's our rainy season so we might get a hazy day. I will use > my experiment and will test all the gnomons on the next hazy day. I'm > wondering if the shadow shortening is greater with longer shadows when the > sun at a low angle (I bet it is). And by how much? Is it really > significant? > > Also, does the width of the cone or point make a difference? Wouldn't a fat > cone's shadow be less susceptible to this effect? > > Has anybody else observed this effect? > > very interested in this, > > John > > > - Original Message - > From: <[EMAIL PROTECTED]> > To: "John Carmichael" <[EMAIL PROTECTED]>; "Sundial List" > > Sent: Monday, August 07, 2006 10:26 PM > Subject: Re: Expanded Nodi Shadow Experiment > > --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hello Frank, Thanks to you (and John Carmichael, and others) for the very fascinating discussion on nodus design. You wrote... BALL NODI There is something else your experiments showed up that I hadn't really appreciated before... If you are going to use a ball nodus, then the supporting stick should go RIGHT THROUGH THE BALL so that it sticks out a little bit, perhaps half a ball diameter. This thought struck me when I tried estimating the centres of the shadows in printouts of your photographs. The point on the shadow where the stick meets the ball is not matched by a corresponding point on the far side. Once again, the lack of symmetry makes estimation a little harder. In October, 1999 I received the following private note from William S. Maddux: *** begin quote *** Date: Fri, 15 Oct 1999 14:18:51 -0400 From: "Wm. S. Maddux" <[EMAIL PROTECTED]> Subject: Re: Vertical Wall Declination program Sender: "Wm. S. Maddux" <[EMAIL PROTECTED]> To: Mac Oglesby <[EMAIL PROTECTED]> Mac, Now a question - what treatment of the gnomon's tip would be likely to give a shadow most easily and accurately measured? I'm a bug on symmetry, so I might try something like the attached GIF. The Idea is that the center- lines of all three elements cross at the same point, which is the "virtual tip." You construct that point in the shadow by symmetrical interpolation, which is quite intuitive. The only thing to watch out for is a case where the thicker post casts its shadow on top of that of one of the cross bars. I suppose it might be good if all three rods were the same diameter, but that would be harder to make. The cross bars need not be at perfect right angles, but they might as well be so far as ease of construction is concerned. Bill *** end quote *** He sent a small, rough drawing, which I attach. Bill passed away in December, 2004, but I don't believe he would mind my sharing this with the Sundial Mailing List. Best wishes, Mac Oglesby MASSE-GN.GIF Description: GIF image --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hi Edley: Well you learn something new every day, especially from the smart people on this List. I had no idea that a hazy day would shorten the shadow cast by a cone's point! In fact, I still don't quite believe it until I get to see it with my own eye's. It's our rainy season so we might get a hazy day. I will use my experiment and will test all the gnomons on the next hazy day. I'm wondering if the shadow shortening is greater with longer shadows when the sun at a low angle (I bet it is). And by how much? Is it really significant? Also, does the width of the cone or point make a difference? Wouldn't a fat cone's shadow be less susceptible to this effect? Has anybody else observed this effect? very interested in this, John - Original Message - From: <[EMAIL PROTECTED]> To: "John Carmichael" <[EMAIL PROTECTED]>; "Sundial List" Sent: Monday, August 07, 2006 10:26 PM Subject: Re: Expanded Nodi Shadow Experiment Hi John, Since you are in a very dry climate with clear weather you may not notice that with hazy light the cone image is quite forshortened and points to an incorrect point. Yes, the cone points out a line very clearly and yes, it does look quite like a clock hand, but the very shadow tip position is quite a way off from what it should be. The spherical nodus and other symetrical ones, although not so attractive, give a much more accurate spot. The area of untruth may be mostly in declination rather than hour angle with most dials, such as your neat painted dial. You could try letting the light shine through some thin plastic to simulate haziness, or come visit us on the coast where hazy is very common. Of course, too hazy and nothing works. for an azimuth dial it might work very well, where for a pillar dial, not so well. Thanks for the interesting ideas! Edley. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Expanded Nodi Shadow Experiment
The Greenwich Dolphin Sundial has two tips, the tails of two Dolphins, coming together in the manner suggested by Frank King. See http://www.sundials.co.uk/~thames.htm or http://www.sundials.co.uk/~thames.htm for pictures. Roger Bailey -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Frank King Sent: August 8, 2006 1:17 AM To: John Carmichael Cc: Sundial List Subject: Re: Expanded Nodi Shadow Experiment Dear John (and Edley), .. One thing that hasn't been suggested is to use TWO cones arranged so that they meet tip to tip. Approximations to this arrangement are not uncommon. I am thinking of statue sundials where perhaps two fingers meet almost tip to tip. .. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
I thank John Carmichael for his interesting experiment on the different types of nodi since I am very interested in this subject ; I agree completely with the analysis made by Frank King in his Email (August 6) I think however that the experiment with the disk with the hole can give distorted results since the plane of the hole has been taken orthogonal to the style and parallel to the plane. In this way the image of the hole, when it is visible, is perfectly circular , but its brightness decreases very quickly when the angle between the hole axis and the rays from the sun increases. In the second Johns experiment this angle is around 80.1° and causes, as clearly Frank has shown, the disappearance of the image of the hole itself. I would like to point out however that in a horizontal sundial, for a place with latitude = 45°, the rays of the sun have this inclination only around 1h before the sunset or after the dawn and therefore only in extreme points of the dial. As King has already written the ratio R=( Distance hole-shadow / Diameter of the hole) = 558 : the spot of light decreases in brightness when this ratio R gets over the value 107.5 and disappears when it becomes greater than 200-300 ( around ). When the ratio R becomes very great, in practice higher than 400-500 (pin-hole or stenopeic hole), the spot of light has no more the shape of the hole but it is the image of the sun , whatever is the shape of the hole itself. --- I think that it is advisable that the plane of the hole is a polar plane with the hole axis on the intersection among the equator and the meridian planes. Obviously the image of the hole now appears elliptic and no more circular. In this way, at noon, the angle between the rays from the sun and the hole axis is always less than 23.5° and also on the winter solstice the ratio R = 48 and the spot of light is clearly visible. Also in the extreme points of the dial the things improve. A hour before sunset we have: - on summer solstice the angle between Suns rays and hole axis = 41.3°; the observer sees the hole (that appears elliptic) under the angles 26 x 36 '. The ratio R =99.4 - on the equinoxes the angle between rays and hole axis = 35°; the observer sees the hole with axis of 32x39'. The ratio R=106. -on winter solstice the angle = 53.7° and the observer sees the hole with axis of 18x 30 '. The ratio R =190 Therefore only under these extreme conditions (1h before the sunset in winter) the spot of light if greatly attenuated. Best wishes Gianni Ferrari P.S. - In Cassini sundial in S. Petronio (Bologna) the ratio R = ( Distance hole-spot / Diameter of the hole) changes from 1070 to 2670 during the year P.P.S. Here the weather is very hot , and I hope that mine calculations are correct :-) --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Dear John (and Edley), Your experiment continues to fascinate me and I have some fresh comments which include an experiment that everyone can carry our very easily and which amplify Edley's remarks. First, many thanks for your dimensions: > the cardboard thickness: 3/32" > the hole diameter: 1/4" > the disk diameter: 2") I got the external diameter wrong but that's not too important. My guess at 0.1" for the internal diameter was almost exactly right! Accordingly, my figures don't really need amending. THICK VERSUS THIN I have some comments on your practical points... > ...if I were to make one for a real sundial, I'd use strong, thin > metal instead of cardboard! Interestingly, you don't have to use thin material for a disc nodus. You could use quite thick material PROVIDED you taper the internal and external rims to knife edges. Even a thick disc then works as though it were paper thin! CONES AND CLOCK HANDS > On the practical and artistic level, I love the cone gnomons' > shadows because they look like clock hands. Yes, I very much accept this. The shape of the long shadow of your cone is very elegant. It is such a shame that such a shadow gets foreshortened when the shadows are long. One thing that hasn't been suggested is to use TWO cones arranged so that they meet tip to tip. Approximations to this arrangement are not uncommon. I am thinking of statue sundials where perhaps two fingers meet almost tip to tip. AN EXPERIMENT ALL CAN TRY This isn't what you have in mind when you seek a shape that looks like a clock hand but it prompts me to suggest a simple experiment that anyone can do anytime the sun is shining without any equipment at all. Here's what you do... 1. Stand with your back to the sun about 6 to 10 feet from a plane surface which is approximately facing the sun and look hard at this surface. [The experiment doesn't work well if the sun is shining through glass, especially double-glazing, so do this outside or, at least, open the window!] 2. Point your two forefingers at each other so that there is about a 1" gap between them and arrange that the shadows of the fingers fall on the plane surface. 3. Now, very slowly, bring the fingers close together. You will find that, sometime before they actually touch, a mysterious blob appears between the shadow fingers. The result is that the shadow fingers appear to touch before the real fingers do. This effect is, of course, because the sun is not a point source of light. The critical moment comes when the angular separation of the fingers becomes less than the angular diameter of the sun. The gap between the shadows stops receiving full sunlight and becomes penumbra instead. You will get something of the same effect if you bring two of your cones together tip to tip. I mention all this to demonstrate that curious effects occur in the vicinity of the shadows of tips. If you have a PAIR of tips this doesn't matter too much. You can look at the symmetry and estimate fairly accurately where the mid-point is. If you have just ONE tip, estimating gets much harder. Edley's message alludes to this difficulty. BALL NODI There is something else your experiments showed up that I hadn't really appreciated before... If you are going to use a ball nodus, then the supporting stick should go RIGHT THROUGH THE BALL so that it sticks out a little bit, perhaps half a ball diameter. This thought struck me when I tried estimating the centres of the shadows in printouts of your photographs. The point on the shadow where the stick meets the ball is not matched by a corresponding point on the far side. Once again, the lack of symmetry makes estimation a little harder. Often a ball nodus is mounted on a regular gnomon, perhaps half-way along, so you get the symmetry for free. Amazingly, I have somehow missed out analysing the shadows of balls at the ends of sticks (rather than in the middle) so I am most grateful to you for thrusting these images my way. I have also become very impressed by the quality of PDF format. I found I could enlarge your images many times without serious degradation of quality. All the best Frank --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hi John, Since you are in a very dry climate with clear weather you may not notice that with hazy light the cone image is quite forshortened and points to an incorrect point. Yes, the cone points out a line very clearly and yes, it does look quite like a clock hand, but the very shadow tip position is quite a way off from what it should be. The spherical nodus and other symetrical ones, although not so attractive, give a much more accurate spot. The area of untruth may be mostly in declination rather than hour angle with most dials, such as your neat painted dial. You could try letting the light shine through some thin plastic to simulate haziness, or come visit us on the coast where hazy is very common. Of course, too hazy and nothing works. for an azimuth dial it might work very well, where for a pillar dial, not so well. Thanks for the interesting ideas! Edley. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hi Frank (cc. SML) Glad to be of help. (For your calculations, here are the dimensions of the hole-in-disk nodus. the cardboard thickness: 3/32" , the hole diameter: 1/4", the disk diameter: 2"). Of course, if I were to make one for a real sundial, I'd use strong, thin metal instead of cardboard! On the practical and artistic level, I love the cone gnomons' shadows because they look like clock hands. Look at a traditional clock hand. It's basically shaped like a long skinny triangle, wide at the center of rotation and pointing to the time. A cone's shadow has the same shape does the same thing. In fact, you could even make the cone a pointed teardrop or spindle shape or with indentations that would produce more interesting shadow shapes that look like differently shaped clock hands. - Original Message - From: "Frank King" <[EMAIL PROTECTED]> To: "John Carmichael" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Monday, August 07, 2006 2:30 AM Subject: Re: Expanded Nodi Shadow Experiment Dear John Many thanks for your response. I'm still pondering all of the information you gleaned from my experiment. Well, I am still pondering the experiment! I have often thought of setting up almost exactly that experiment but never quite got round to it! You have certainly done it very elegantly. What is amazing serendipity is that I have recently been doodling with a dial design which requires a nodus about 4" from the dial plane so you saved me a whole lot of work! I need to point out something important about the light projection (or antishadow) cast by the hole-in-disk nodus: As you can clearly see in the long shadow photo, the spot of light (the antishadow) is not there at all. This is true. As you will see in a moment, the place where the spot of light should be is getting no sun at all through the hole but it IS getting some sun from round the edge of the nodus disc! This I think was due to the thickness of the cardboard that I used to make the disk. Indeed it is. For completeness, there are three factors which determine whether a hole-in-a-disc nodus will project a spot of light: 1. The diameter of the hole 2. The thickness of the material (you are right here) 3. The diameter of the surrounding disc (if this is too small it won't block out all the sun which is one factor in your long-shadow case) As a designer, you have to chose both the internal and external diameters of the disc-with-a-hole carefully. You can easily sketch what's going on. Just draw a right-angled triangle 4" high and 23.3" long and sketch in the cross-section of your nodus at the top of the 4" side. You will soon see why no light is getting through! The golden rule in the analysis is to consider how the nodus appears when viewed from the centre of the shadow (or anti-shadow). You don't give the diameter of your disc or its thickness so I cannot give a precise analysis. If you could let me have these dimensions I could easily explain more! Here is a first stab... Let's guess that the disc diameter is 1.25" We CAN assume the hole diameter is 0.25" Let's assume that the thickness is zero (just for the moment) Using my previous analysis, the appearance of the NODUS to an insect sitting at the centre of the anti-shadow will be an elliptical disc with an elliptical hole. In your LONG shadow experiment, when the shadow is 23.3" from the foot of the nodus support and 23.6" from the centre of the nodus, we get the following angular dimensions: 1. Apparent major axis of disc 1/19radians 2. Apparent minor axis of disc 1/112 radians 3. Apparent major axis of hole 1/94radians 4. Apparent minor axis of hole 1/558 radians 5. Diameter of circular solar disc 1/107.5 radians If you draw a scaled picture so that the solar disc is (say) 1" in diameter, you will find that the minor axis of the nodus disc isn't quite big enough to hide the sun (1/112 is smaller than 1/107.5). Every point in your shadow can actually see a little bit of the sun. Nowhere is in full shadow. In short, the disc isn't big enough to hide the sun completely and the hole isn't big enough to expose the whole sun. In fact the hole exposes less than one-fifth of the sun even in the zero-thickness case. If the disc is made of thick material the insect sees even less of the sun through the hole. Instead of appearing as an ellipse, the hole appears as a lens shape. [Try holding a tube up to your eye and angling it slightly so you don't look straight through it.] The angular dimension of the minor axis is now given by the formula: d cos(i) - t sin(i) nodus-to-shadow distance d is the d
Re: Expanded Nodi Shadow Experiment
Hi Mac: Yes, on a perpendicular cone or pointed rod gnomon, the slope of the point or cone could cause a self-shading problem if the cone or point is too wide at the bottom (a fat cone). But you can easily determine the maximum allowable width of the cone or point and avoid that design problem if you look at the nearest solstice line to the nodus. The base of the cone must be smaller than that distance to avoid self-shading. For my wall dial, the largest cone possible that would not cause shading would have been just under 5 inches wide, so the cone had to be skinnier so that it would cast a shadow on the face at noon on the winter solstice. I made it just two inches wide at its base, much smaller than the allowable width. I think fatter cones and points produce easier to read shadows than than the skinny ones, especially when the shadows are long. So the idea would be to have the fattest cone or point possible that does not shade itself. (You may even want to make the cone even skinnier to accomodate artwork around it. That's why I made my cone much thinner than the allowable so that I could put the points of a star around its base). Does this make sense? - Original Message - From: "Mac Oglesby" <[EMAIL PROTECTED]> To: "Sundial Mailing List" Sent: Sunday, August 06, 2006 2:28 PM Subject: Re: Expanded Nodi Shadow Experiment One problem I've personally encountered with a pointed post gnomon is that if the post's shadow falls too close to the foot of the post, the shadow of the tip may be lost in the shadow of the post's shoulder. This was on a vertical decliner. Mac Oglesby http://www.sover.net/~oglesby/Gnomon%20Notes/GnomonShadows3.jpg --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
One problem I've personally encountered with a pointed post gnomon is that if the post's shadow falls too close to the foot of the post, the shadow of the tip may be lost in the shadow of the post's shoulder. This was on a vertical decliner. Mac Oglesby http://www.sover.net/~oglesby/Gnomon%20Notes/GnomonShadows3.jpg --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Expanded Nodi Shadow Experiment
Hi Frank: I'm still pondering all of the information you gleaned from my experiment. You have given your comments a lot of thought and I don't want to quickly dismiss anything you said as being inaccurate without being sure first. But I need to point out something important about the light projection (or antishadow) cast by the hole-in-disk nodus: As you can clearly see in the long shadow photo, the spot of light (the antishadow) is not there at all. When tilting the board, the antishadow became smaller and smaller as the shadow lengthened. In fact, when I was tiltling the board, it disappeared when the shadow was 3 times longer than the gnomon. This I think was due to the thickness of the cardboard that I used to make the disk. The cardboard of the disk, in fact, was what shaded the hole. If I had used a paper thin metal to make the disk, then I think the antishadow would not have disappeared so quickly. My conclusion about this is that the hole-in-disk works fine and is extremely precise at high solar angles when you can see the anti-shadow, but is completely useless at low solar angles when the antishadow disappears. Do you agree? John p.s. I love your term "antishadow" to describe the projected sunlight through an aperture nodus. Do you invent this term? pps. I will try to bring the experiment to Vancouver if it will fit in my suitcase. - Original Message - From: "Frank King" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Cc: ; <[EMAIL PROTECTED]> Sent: Sunday, August 06, 2006 11:45 AM Subject: Re: Expanded Nodi Shadow Experiment Dear John, That is a splendid experiment... http://advanceassociates.com/WallDial/NodusShadowExperiment.pdf It illustrates all kinds of interesting aspects of nodus design The Purpose, Setup and Execution all earn top marks. The Conclusion, though, is subject to a little caveat... Let's concentrate on just three of your designs: the disc with the 0.25" hole at the top (or leftmost), the cone at the bottom (or rightmost) and the 1" ball next to the cone. Now look at the two sets of shadows: 1. When the shadows are short... (a) the centre of the anti-shadow of the disc with a hole is about 6.1" along your board. (b) the centre of the shadow of the ball is just a little shorter. It seems to be almost spot on the 6" mark. [This is possibly because the supporting stick is not quite vertical. This is not important.] (c) the shadow of the tip of the cone is almost exactly in line with the anti-shadow of the disc with a hole, about 6.1" along your board. 2. When the shadows are long... (a) the anti-shadow of the disc with a hole is no longer clear (as you say) but because there is an equal amount of fuzz at the extremities of the shadow of the disc as a whole you can fairly easily estimate the centre. It seems to be about 23.3". (b) the centre of the shadow of the 1" ball is just a little less easy to estimate because the supporting stick disturbs the fuzz at one of the extremities but one can see that the centre is about the 23" mark. This, as expected, is shorter than the shadow to the centre of the disc and is consistent with 1(b). So far everything ties up. (c) the shadow of the tip of the cone though has now fallen behind the shadow of the centre of the disc. The shadow may be easier to read but IT IS GIVING A FALSE RESULT. The big big trouble with any asymmetric nodus is that you cannot cancel out the fuzz. You have to decide just where in the fuzz is the point of interest. This is difficult. Different people will estimate different points. As noted at 2(b), each of your ball nodi is slightly asymmetric because of the supporting sticks. If you had mounted the balls sideways (as you have the disc with the hole) it would be easier to estimate the centre of the shadow. To my mind, the disc with the hole gives the most accurate result even if its shadow isn't the prettiest! Incidentally, it is worth analysing the hole in your disc in the long shadow case... Diameter of hole 0.25" Height of hole above the board 4" Approximate length of shadow 23.3" Distance of centre of anti-shadow from centre of hole 23.6" Angle of incidence arctan(23.3/4) = 80.3 degrees Now consider the hole viewed from the centre of the anti-shadow. Given that the disc is parallel to the board, the hole will appear as an ellipse whose angular dimensions in radians are: Major axis0.25/23.6 approx 1/94.4 radians Minor axis 0.25 x cos(80.3) / 23.6 approx 1/558 radians This last figure should be compared with the angular diameter of the sun which (by a diallist's rule of thumb) is about 1/107.5 radians. Now imagine an insect (wearing eye protection) at the point where the centre of the anti-sha
Re: Expanded Nodi Shadow Experiment
Dear John, That is a splendid experiment... > http://advanceassociates.com/WallDial/NodusShadowExperiment.pdf It illustrates all kinds of interesting aspects of nodus design The Purpose, Setup and Execution all earn top marks. The Conclusion, though, is subject to a little caveat... Let's concentrate on just three of your designs: the disc with the 0.25" hole at the top (or leftmost), the cone at the bottom (or rightmost) and the 1" ball next to the cone. Now look at the two sets of shadows: 1. When the shadows are short... (a) the centre of the anti-shadow of the disc with a hole is about 6.1" along your board. (b) the centre of the shadow of the ball is just a little shorter. It seems to be almost spot on the 6" mark. [This is possibly because the supporting stick is not quite vertical. This is not important.] (c) the shadow of the tip of the cone is almost exactly in line with the anti-shadow of the disc with a hole, about 6.1" along your board. 2. When the shadows are long... (a) the anti-shadow of the disc with a hole is no longer clear (as you say) but because there is an equal amount of fuzz at the extremities of the shadow of the disc as a whole you can fairly easily estimate the centre. It seems to be about 23.3". (b) the centre of the shadow of the 1" ball is just a little less easy to estimate because the supporting stick disturbs the fuzz at one of the extremities but one can see that the centre is about the 23" mark. This, as expected, is shorter than the shadow to the centre of the disc and is consistent with 1(b). So far everything ties up. (c) the shadow of the tip of the cone though has now fallen behind the shadow of the centre of the disc. The shadow may be easier to read but IT IS GIVING A FALSE RESULT. The big big trouble with any asymmetric nodus is that you cannot cancel out the fuzz. You have to decide just where in the fuzz is the point of interest. This is difficult. Different people will estimate different points. As noted at 2(b), each of your ball nodi is slightly asymmetric because of the supporting sticks. If you had mounted the balls sideways (as you have the disc with the hole) it would be easier to estimate the centre of the shadow. To my mind, the disc with the hole gives the most accurate result even if its shadow isn't the prettiest! Incidentally, it is worth analysing the hole in your disc in the long shadow case... Diameter of hole 0.25" Height of hole above the board 4" Approximate length of shadow 23.3" Distance of centre of anti-shadow from centre of hole 23.6" Angle of incidence arctan(23.3/4) = 80.3 degrees Now consider the hole viewed from the centre of the anti-shadow. Given that the disc is parallel to the board, the hole will appear as an ellipse whose angular dimensions in radians are: Major axis0.25/23.6 approx 1/94.4 radians Minor axis 0.25 x cos(80.3) / 23.6 approx 1/558 radians This last figure should be compared with the angular diameter of the sun which (by a diallist's rule of thumb) is about 1/107.5 radians. Now imagine an insect (wearing eye protection) at the point where the centre of the anti-shadow should be. As seen by the insect, the minor-axis of the hole appears to be less than one-fifth the diameter of the sun. The anti-shadow is entirely penumbra and impossible to detect. In my opinion this is NOT a design error. My eccentric view is that a disc with a hole IS the best form of nodus, especially for big sundials (well ALMOST the best) because... when the angle of incidence is small (short shadows) you observe the centre of the anti-shadow and... when the angle of incidence is high (long shadows) you observe the centre of the shadow of the disc as a whole. I say ALMOST the best because there is a special case of a disc with a hole, and that is the great camera obscura sundials which one comes across in Europe. There the angular diameters of the holes are even smaller than yours. [According to Gianni Ferrari, Cassini took the view that the hole should be 1/1000th of its distance to the floor, half the size of your hole at 23.6".]. The disc though is effectively of infinite diameter because the entire building surrounds the hole and you DO see a splodge of light. This is not anti-shadow though; it is actually an image of the sun and you can estimate its centre VERY precisely. Try making your disc of infinite size and you will see how this works :-) MORAL: Sticks and cones are seductive but should be resisted! I hope this hasn't been too tiresome a message for this list! Frank H. King Cambridge, U.K. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Expanded Nodi Shadow Experiment
Hello All: Here is a PDF file (about 600KBs) that shows a new nodi shadow experiment. This is an expanded version of my original experiment and includes 12 different nodi designs. All the nodi are the same height but are different designs. To see photos of the experiment click on this link: http://advanceassociates.com/WallDial/NodusShadowExperiment.pdf Purpose: To determine which types of sundial nodi cast the easiest to read shadows and produce the most precise readings. Setup: I made twelve common but different sundial nodi. I compared ball nodi of different diameters on posts, truncated rods and pointed rods, thick rods and thin rods, a cone, and a hole-in-disk nodus. All of them were 4 tall and spaced evenly apart in a row attached to one end of a flat board that I marked with parallel measuring lines in inches and as multiples of the height vs. the length of the shadows. Execution: By tilting the board in the sun, I could lengthen or shorten the shadows and observe the effect that the suns angle had on the shadows cast by the different nodi. High sun angles made short shadows and low sun angles made long shadows. I photographed the results (see below) Conclusions: High sun angles created short shadows and low sun angles produced long shadows. In all cases, the shorter shadows are easier to read than longer shadows because they are darker and there is less fuzziness around the edges. Truncated rods and balls produce the least accurate shadows and the pointed rods and the cone produce the most accurate shadows. Thick rods are easier to see from a distance than thin rods. The hole-in-disk nodus also produces an accurate reading, but only if the shadow is short because the projected image disappears at low sun angles. I my opinion the cone and the thick pointed rod produce the easiest to read and the most precise shadows. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
