Re: Is this sundial business 'genuine', or not?
Roger-- I'm not sayings that the vertical projection isn't part of a valid explanation, and I'm not even claiming to set myself up to say that your explanation wasn't. Now that you mention it, I've heard of sundial layout derivations using an orthographic projection. And I never found those derivations to be the ones that showed me anything, though, as I said, I don't presume to say that they aren't valid, or that yours isn't valid. ...only that I myself didn't find them helpful. So, since I perceive those explanations as more difficult, then I don't perceive them as likely to be helpful to gradeschool students. Michael Ossipoff On Tue, Jul 17, 2018 at 7:31 PM, Roger wrote: > Hi Jack and Michael, > > > > I don’t agree. The concept is very simple. Perhaps you have had bad > teachers. One of my presentations at the upcoming conference is a purely > grapghical method of designing an analemmatic sundial. No trig, not even > geometry other than the Greek’s ruler and string or a simple math set with > ruler, protractor and a compass. From this graphical technique comes a > whole new concept by Chris Lusby Taylor for seasonal makers that I will > describe at the conference next month. > > > > To demonstrate the simple concepts for analemmatic sundials, start with > this experiment as a class activity, hands on and interactive. Cut out a > circle of cardboard. Stick a pencil through the center at a right angle to > the disc. Hold it with the pencil vertical. Look straight down on the disc, > a circle true size. Hour angles drawn every 15° would also be true angles. > The pencil is seen as a point. Now physically drop the disc and pencil onto > a horizontal table. Get down to view across the table and turn the disc to > see it on edge. It will be seen as a true length straight line equal to the > diameter of the circle. The pencil will also be seen a true length line. If > you chose the right length of pencil, the pencil will make an angle to the > horizontal equal to your latitude. The disc will make an angle to the > co-latitude. Now get up and look straight down on the disc and pencil on > the table. The disc will be seen as an ellipse and the pencil as a shorter > line as neither disc or pencil are true length. Look at it straight down > from above and mark the point on the desk that is directly under the end of > the hour mark on the disk starting with the disc turned to the starting > point noon being directly under the pencil. These points define. the hour > ellipse for an analemmatic sundial. > > > > Next the enigmatic date line. Consider the sun shining down at noon at any > day of the year onto the pencil through the disc on the table. The sun > shines down on the pencil and there is a unique point on the pencil each > day where the sun at noon shines directly onto the rim of the disc. At the > summer solstice the sun is high in the sky. The angle of the suns ray down > to the disc rim is at an angle of 23.5° to the disc. At the winter solstice > the angle is -23.5 ° On the spring and fall equinox the angle is 0°. Every > day has a different angle, the solar declination for that day. Now you > could switch to ruler and protractor marking on paper right angle > triangles with the base equal to the disc radius. Measure angles from the > base point up at the chosen declination angle and draw a line at that angle > to the line at right angles to the other end of the base line for the > declination points for the chosen dates. Now draw a line for the horizon at > an angle to the disc base line equal the latitude. Draw lines perpendicular > to the horizon line to the chosen declination date points. The points on > the horizon line are the points where you stand on the analemmatic sundial. > > > > In one class activity session all the kids with a good teacher could make > their own analemmatic sundial based on these simple concepts. It involves > simple tools from the standard geometry set and a simple concept of > looking at a circular disc with a rod through the center from different > points of view. > > > > The general problem is that sundials are not on the curriculum for any > school boards. Teachers teach to the curriculum. The few teachers I have > met in NASS are excellent but there are very few others are interested in > such an extracurricular activity. Perhaps that is the value of a > analemmatic sundial installation at a school would be to stimulate interest. > > > > Regards, Roger Bailey > > Walking Shadow Designs > > > > *From: *Jack Aubert > *Sent: *July 17, 2018 6:27 AM > *To: *'Michael Ossipoff' ; 'sundial list' > > *Subject: *RE: Is this sundial business 'genuine', or not? > > > > I very much agree with this. In fact, at the risk of sounding stupid, I > have to confess that I don’t have an intuitive grasp of how an analemmatic > dial works. Yes, I have at various times gone through the explanation, but > it does not stick in any way that I can mentally attach to the
Re: Is this sundial business 'genuine', or not?
Hi Roger and Mitchael, I'm sure others have thought of and have used these concepts before us. Sundials have been around for a long time. What these concepts achieves are: That all clocks have a energy source to make them work. For sundials it is the rotation of Earth. And that planet Earth rotates (moves) in relation to the sun. It is not the sun that moves. We often say that the sun moves across the sky. But it is planet Earth that rotates and moves. This is important to be able to fully understand how a sundial works. It also shows that sundials are geared to the rotation of planet Earth wherever they are located on Earth. It completes what makes the sundial moves in relation to the sun. Once the concept on how a Equatorial sundial or disk dial works at the South or North pole works. The Equatorial sundial or disk sundial can then be used to draw the hour lines on a horizontal or vertical sundial. There is a complete connection between all concepts. Not just part of it. And it describes it for both hemispheres not just for the Northern hemisphere. Sundial are also located in the Southern hemisphere. It can also be used to show that sundial hours on the dial face runs clockwise in the Northern hemisphere and anticlockwise in the southern hemisphere. I remember reading somewhere that. The reason that clock hours run clockwise is because sundials in the Northern hemisphere had their hours running clockwise. Someone may like to comment as to if this is true. In a classroom a globe or beach ball can be used to show the above concepts. Then the students could then use a Equatorial or disk sundial to draw hour lines on their own sundial. Then go outside in the sun to test their sundial. But 1st make sure they have their hats on and suntan oil on to protect them from the sun. That is what they do in sunny Australia. Have fun, Roderick Wall. --- https://lists.uni-koeln.de/mailman/listinfo/sundial
RE: Is this sundial business 'genuine', or not?
HI Roger, The layout is not the problem. That’s relatively easy. The problem is keeping an image of the relationship between the three dimensional sky and two dimensional earth in your head so that it makes intuitive sense, particularly if you are just a kid. We are dealing with a projection of the equatorial circle of an armillary sphere onto the ground which becomes an ellipse with hour points along it. The projection of the axial gnomon is just a line and doesn’t work for telling time. Instead, we have to locate a point on that line, which could be its end. That point has to move back and forth along the axis throughout the year: your magical pencil, which is able to shorten and lengthen as needed. Why do we have to do that? Well that’s another story we will skip for today. But when we are done, we throw away the circle and the magic pencil and are left with an ellipse on the ground plus a stick (or a person’s head ) that has to move north and south depending on the date according to a secret formula. So first you have to imagine the polar dial as a hoop, translate it to an elliptical projection, and then imagine a magic pencil that projects its tip onto the ellipse. It is not so easy hold all the construction imagery in your head so that you can relate it all back to the celestial sphere with the sun on it. Not only that, but they never told you about the celestial sphere in the first place. They probably told you that the sun is at the center of the solar system and the earth rotates and orbits around it.Good luck imagining how that explains what you see in the sky every day. If I were doing the curriculum I would reintroduce the geocentric view of the solar system to complement the Copernican view. Jack From: Roger Sent: Tuesday, July 17, 2018 7:32 PM To: Jack Aubert ; 'Michael Ossipoff' ; 'sundial list' Subject: RE: Is this sundial business 'genuine', or not? Hi Jack and Michael, I don’t agree. The concept is very simple. Perhaps you have had bad teachers. One of my presentations at the upcoming conference is a purely grapghical method of designing an analemmatic sundial. No trig, not even geometry other than the Greek’s ruler and string or a simple math set with ruler, protractor and a compass. From this graphical technique comes a whole new concept by Chris Lusby Taylor for seasonal makers that I will describe at the conference next month. To demonstrate the simple concepts for analemmatic sundials, start with this experiment as a class activity, hands on and interactive. Cut out a circle of cardboard. Stick a pencil through the center at a right angle to the disc. Hold it with the pencil vertical. Look straight down on the disc, a circle true size. Hour angles drawn every 15° would also be true angles. The pencil is seen as a point. Now physically drop the disc and pencil onto a horizontal table. Get down to view across the table and turn the disc to see it on edge. It will be seen as a true length straight line equal to the diameter of the circle. The pencil will also be seen a true length line. If you chose the right length of pencil, the pencil will make an angle to the horizontal equal to your latitude. The disc will make an angle to the co-latitude. Now get up and look straight down on the disc and pencil on the table. The disc will be seen as an ellipse and the pencil as a shorter line as neither disc or pencil are true length. Look at it straight down from above and mark the point on the desk that is directly under the end of the hour mark on the disk starting with the disc turned to the starting point noon being directly under the pencil. These points define. the hour ellipse for an analemmatic sundial. Next the enigmatic date line. Consider the sun shining down at noon at any day of the year onto the pencil through the disc on the table. The sun shines down on the pencil and there is a unique point on the pencil each day where the sun at noon shines directly onto the rim of the disc. At the summer solstice the sun is high in the sky. The angle of the suns ray down to the disc rim is at an angle of 23.5° to the disc. At the winter solstice the angle is -23.5 ° On the spring and fall equinox the angle is 0°. Every day has a different angle, the solar declination for that day. Now you could switch to ruler and protractor marking on paper right angle triangles with the base equal to the disc radius. Measure angles from the base point up at the chosen declination angle and draw a line at that angle to the line at right angles to the other end of the base line for the declination points for the chosen dates. Now draw a line for the horizon at an angle to the disc base line equal the latitude. Draw lines perpendicular to the horizon line to the chosen declination date points. The points on the horizon line are the points where you
Re: Is this sundial business 'genuine', or not?
When I mentioned (at least hypothetically) a mechanical method and an empirical method for constructing a Reclining-Declining Dial, they were intended as ways to assure someone that s/he knows of a way that such a dial can be constructed. (I feel that it's unsatisfying to own, use, or visit a sundial (or use a map-projection) whose construction-explanation you haven't heard. ...though of course the empirical method that I described is perfectly do-able without difficulty. But there's another empirical method that's a lot easier to build than the mechanical method, and a lot faster than the empirical method that I described. It combines attributes of both of them: On a flat plywood base, on the ground, build and fassten a Disk-Equatorial or a Band-Equatorial dial. Under that dial's gnomon, make and fasten a block or plate having a surface that's oriented to the base, and to the gnomon-north of the Equatorial, in the same manner that you want your Reclining-Declining Dial to have with the horizontal and north. Directly under the Equatorial's gnomon (as determined by a plumb-line or T-Square) contact a stick with the base. By Plumb-line or T-square, ensure that the entire stick is directly under the Equatorial's gnomon. By measuring the stick's length and it's high-end's height, you can make its angle to the base equal to that of the Equtorial's gnomon. So, when the stick is fastened in that orientation, it's parallel to the gnomon of the Equatorial. (...further checkable by vertical ruler-measurements between both ends of the stick and the Equatorial.) Now, out in the sunlight, rotate the base until the equatorial's gnomon-shadow point to one of its hour (or half-hour) lines. Then mark a line on the block or plate representing the Reclining-Declining surface. That's the same hour-line, for for the Reclining-Declining Dial. Do that for every one of the Equatorial's hour-lines. If necessary, of course, the base could be tipped upward at one end, with that end resting on a boulder, tree-stump, box, etc. ...or leaned on a house, or laid on an inclined-surface. The orientation of the base doesn't matter, as long as it's in the sunlight, and it's oriented so that the Equatorial Dial's gnomon-shadow is on an hour-line. Then, of course copy the hour-lines on your Reclining-Declining model to the actual Reclining-Declining Dial that you want to build. Michael Ossipoff On Wed, Jul 18, 2018 at 2:10 PM, Michael Ossipoff wrote: > Yes, the central-gnomon Equatorial dials, with their gnomon parallel to > the Earth's axis, and their circular measuring-scale parallel to plane of > the equator is educational, because its measurement of Solar Time is > completely direct. > > And yes, you're quite right: The construction of the Horizontal Dial is > easily described in terms of a central-gnomon equatorial (...say, a > Disk-Equatorial). Stand a disk-equatorial with its disk resting on the > ground and its gnomon (by choosing the right length for it) parallel to the > Earth's axis. Draw an east-west line through the point where the disk > contacts the ground. > > Extend the Disk-Equatorial's radial hour-lines (as "rays") to where they > meet that east-west line on the ground. > > Obviously, when the gnomon's shadow is along a radial hour-line of the > Disk-Equatorial, it will also go to the point where that ray meets the > ground. So draw a line from the ground-contacting end of the gnomon to that > point on the east-west line. > > And then you've constructed a Horizontal Dial. > > There's a widely-distributed graphical construction instruction that > models that construction. > > The formula: > > tan A = sin lat tan h > > ...comes directly from that construction. > > And yes, as I said in one of my recent posts here, any Vertical or > Reclining (but not Declining) flat dial can easily be shown to be a > horizontal dial for a different latitudedemonstrable with a globe. > > Of course the broad category that I described in the paragraph before this > one includes the Horizontal Dial, Disk Equatorial, and the Polar Dial as > special cases. > > So yes, all of what you said is true, but it's all surely been out there > for a long time. Dialing or dyalling has been studied and described for a > long time. > > I outlined a 5-day set of discussions to explain the construction of the > Reclining-Declining Dial. > > I'll just add that of course it's obvious that there are ways in which a > 3D working model of the 3 relevant co-ordinate-systems (Horizontal, > Equatorial, and Dial-Plate) could be made and used to construct a > Reclining-Declining Dial. I mention that to show that it's possible to > truly tell someone that they know of a way that such a dial could be made, > even if they haven't heard the 5-day explanation that I suggested. > > Or, as someone (but probably more than one person) else has suggested one > could also start with a Relining-Declining surface, and experimentally, > with a plumb-line, and
Re: Is this sundial business 'genuine', or not?
Yes, the central-gnomon Equatorial dials, with their gnomon parallel to the Earth's axis, and their circular measuring-scale parallel to plane of the equator is educational, because its measurement of Solar Time is completely direct. And yes, you're quite right: The construction of the Horizontal Dial is easily described in terms of a central-gnomon equatorial (...say, a Disk-Equatorial). Stand a disk-equatorial with its disk resting on the ground and its gnomon (by choosing the right length for it) parallel to the Earth's axis. Draw an east-west line through the point where the disk contacts the ground. Extend the Disk-Equatorial's radial hour-lines (as "rays") to where they meet that east-west line on the ground. Obviously, when the gnomon's shadow is along a radial hour-line of the Disk-Equatorial, it will also go to the point where that ray meets the ground. So draw a line from the ground-contacting end of the gnomon to that point on the east-west line. And then you've constructed a Horizontal Dial. There's a widely-distributed graphical construction instruction that models that construction. The formula: tan A = sin lat tan h ...comes directly from that construction. And yes, as I said in one of my recent posts here, any Vertical or Reclining (but not Declining) flat dial can easily be shown to be a horizontal dial for a different latitudedemonstrable with a globe. Of course the broad category that I described in the paragraph before this one includes the Horizontal Dial, Disk Equatorial, and the Polar Dial as special cases. So yes, all of what you said is true, but it's all surely been out there for a long time. Dialing or dyalling has been studied and described for a long time. I outlined a 5-day set of discussions to explain the construction of the Reclining-Declining Dial. I'll just add that of course it's obvious that there are ways in which a 3D working model of the 3 relevant co-ordinate-systems (Horizontal, Equatorial, and Dial-Plate) could be made and used to construct a Reclining-Declining Dial. I mention that to show that it's possible to truly tell someone that they know of a way that such a dial could be made, even if they haven't heard the 5-day explanation that I suggested. Or, as someone (but probably more than one person) else has suggested one could also start with a Relining-Declining surface, and experimentally, with a plumb-line, and a compass, north-star or pre-made landmark, align a stick (in contact with the surface) so that it's 1) pointing northward, and 2) elevated above the horizontal by an angle equal to your latitude. ...and, from that, build the gnomon. ...and then, using, as reference-dial, any one of the Horizontal, Reclining or Vertical (or Equatorial or Polar) dials described above, hour lines could be drawn on the reclining declining surface where the style-shadow is, when the reference dial says that it's a certain time. That might sound like cheating, but it's a legitimate way that such a dial could be constructed, and for anyone who doesn't want to hear the 5-day explanation, it's way that you could remind someone that they could make such a dial. Michael Ossipoff On Tue, Jul 17, 2018 at 7:13 PM, rodwall1...@gmail.com < rodwall1...@gmail.com> wrote: > Hi all, > > The following is what I think is the best way to describe how sundials > work to kids or anyone. > > > 1st start with the largest sundial in the world. Planet Earth the Master > sundial clock. Stick a vertical stick into the ground at the South pole or > North pole. And describe how the shadow shows the time throughout the day. > Draw the 24 hour lines every 15 deg and that 15 deg x 24 hours = 360 deg > one day. > > Then show how the Equatorial sundial relates to our stick sundial at the > poles. Place it at the South or North pole. And show that the Equatorial > sundial style edge is parallel with the stick and the axis of the Earth. > And that the hour lines are the same every 15 deg. And that it will keep > the same time. > > Then place the Equatorial sundial anywhere on earth. And show that the > sundial is geared to Earth the largest sundial in the world (the Master > sundial clock). Therefore it will keep the same time. Show how the sundial > time markings relate to your local time. And that the style edge of the > sundial must be parallel with the axis of the earth and parallel with the > vertical stick at the poles. And that at night time the sundial is in the > shadow of Earth. > > Then place a horizontal sundial at the same location. And describe that > the style edge is also placed parallel with the stick and the axis of the > Earth. And how the hour lines are projected every 15 deg from the > horizontal sundial style. That is to place the style edge of the equatorial > sundial onto the horizontal sundial style edge and use it to project the > hour points onto the horizontal base of the horizontal sundial. Then draw > the hour lines on the horizontal sundial. Then
