I have now proved arithmetically (to my own satisfaction at least) that there is no dial shape that works like an analemmatic dial but with the azimuth halved.
I did this by calculating how far the gnomon would have to move at 2pm between the solstices and the equinoxes, and comparing these figures with 4pm (for some arbitrary latitude). The ratios are different, implying that wherever you put a vertical gnomon on these three dates you could not position both a 2pm and a 4pm marker. For a normal analemmatic dial the ratios are all 1, i.e. the distance you move the gnomon from winter to spring = the distance you move it from spring to summer, for all hours of the day. Too bad. But I like the 2:1 gearing idea. Mechanisms to do this are very simple - the top of a pair of compasses is an example. Chris Lusby Taylor 51.4N 1.3W ----- Original Message ----- From: "Chris Lusby Taylor" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]>; <[email protected]> Sent: Wednesday, June 25, 2008 7:01 PM Subject: Re: Advice wanted, on 'Analemmatic' sundial orientation > Very neat John! > > But I don't think it works. Not even if south-facing. > > The problem is that you are halving the angle through which you turn the > dial. That affects the geometry of the elliptical dial. You can't just > renumber the hour marks. The sun's azimuth (measured from south) at 2pm is > not twice the azimuth at 1pm. > So, I'm pretty sure you can't just take an analemmatic ellipse, reverse and > renumber the hours. But maybe there is a shape, perhaps a different ellipse, > that would work. You might well have to change the date scale as well. > > If you can find a shape that works, I have some good news: the hour marks > are unchanged by the realignment of the axis from north-south. Imagine, for > instance, that the path went east-west. The mirror would be at 45 degrees to > the axes of the dial. The rotation of the mirror (and dial) to follow the > sun would be precisely the same as it would for a north-south path, so the > hour marks would still have 12 in the middle and all other angles as before. > > Actually, rather than having the mirror at 45 degrees to the dial's axes and > a north or south pointer to read the time, you could align the dial with the > mirror and turn the pointer 45 degrees. Or, you could have the pointer > mounted with the mirror and the dial on the ground in a fixed orientation > (such as parallel to the infamous path), but able to be slid along its minor > axis according to the date. > The possibilities are almost endless. Or, they would be if we could find a > dial shape that would work! > > But finding a shape that will function as a dial (or even proving that one > exists) will take a little longer than the spare time I have today. Sorry. > If anyone else wants to try it, I suggest tracing the hourly azimuth lines > for the equinoxes overlaid with the same lines for one of the solstices, > assuming the gnomon has moved by some arbitrary distance in the meantime. > Find the dial shape that would work for both dates (there will probably be > one) and see if it will work for all other dates. > > Best wishes > Chris Lusby Taylor > > > ----- Original Message ----- > From: "John Lynes" <[EMAIL PROTECTED]> > To: <[email protected]> > Sent: Wednesday, June 25, 2008 4:46 PM > Subject: Advice wanted, on 'Analemmatic' sundial orientation > > > I'm grateful for the generous reception you gave to my last contribution to > this thread. Here belatedly is another possible solution, less impractical > but more complex than my last effort. > > Imagine a North-South meridian line on flat ground. On this line place a > thin flat vertical mirror - essentially a vertical reflective slit - a few > feet above the ground and pivoted to rotate about a vertical axis through > the mirror and the meridian. When the sun shines, a visitor is asked to > turn the mirrored slit so that the sun's reflection falls along the meridian > line. > > Straight below the slit, locked to the same vertical axis, is a small > horizontal analemmatic sundial, a few inches across, placed so that the axis > of rotation of the assembly coincides with the calendar date-point on the > analemmatic dial, and the major axis of the analemmatic dial's ellipse is > parallel to the plane of the mirror. The direction of the meridian line > indicates the solar time on the (modified, see below) face of the > analemmatic dial. > > The azimuth of the mirror, measured from the meridian, would be only half > the azimuth of the sun, so the hour markings on the analemmatic dial would > need adjusting, e.g. the 1pm mark would be relabelled 2pm (sorry, 10.am). > They would run anti-clockwise, and would of course be reversed from north to > south. > > A groundsman would have to keep the mirror polished, and realign the > date-point with the axis of rotation perhaps once a week. He might fix a > different dial for daylight saving. > > Now comes the nifty bit! Mr Phillips is not forced to accept a North-South > meridian line. He could commission a line parallel to his main driveway, > for aligning the reflection of the sun. A small fixed North-South marker > would still indicate the time on the analemmatic dial. I leave it to the > heavyweights to recalculate the hourly markings on the dial face. > > Alas the gnomon is no longer human, but the device would be interactive, > instructive and, I daresay, unprecedented. > > Apologies for a disgracefully late entry! > > John Lynes > > > -----Original Message-----From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] > > Dear Sundial Experts, > I have recently joined this Mailing List, and hope that any members will be > able to give me some assistance on the following situation. > Our local Stately Home ("Kentwell Hall", Long Melford, Suffolk) is > considering installing an Analemmatic sundial, as a new interactive > attraction for visitors - but we are getting 'conflicting' advice, on > whether this 'Human Sundial' will work in the way we want it to. We have > been in discussion with "Modern Sunclocks" (apparently the acknowledged > 'experts' for these features), who have told us that its central scale of > dates must be aligned North/South - plus that hour markers must be correctly > positioned on an elliptical ring, and which would lie on the Northern side > of that scale of dates. > Photographs on their website ( www.sunclocks.com ) confirm this. > However, our 'Director of Operations' (Mr Phillips) absolutelyINSISTS that > he wants the scale to run exactly parallel with ourmain driveway - on a > compass bearing which is about 162 degreesfrom North, with the hour points > placed on its Southern side.He also wants the hour points to form an exact > semi-circle, andnot be elliptical in shape. Mr Phillips refuses to accept > thathe cannot arbitrarily position the Human Sundial feature as hewishes, > and says that it must be possible to create this so thatit could then align > with the existing layout of buildings/paths. > Can anyone on this Mailing List tell me whether it is possible toinstall a > Human Sundial to fit any existing orientations, (withappropriate > re-calculation of its component parts) - or, if not,just confirm that it > must be as "Modern Sunclocks" have told me. > I can then show the 'weight of evidence' to Mr Phillips. Because"Kentwell > Hall" is a well-known Stately Home (open to the public),we should not want > to become a 'laughing stock' by installing afeature which does not work - > despite Mr Phillips assurance that"all types of sundial can be adjusted to > work, in any location". > Looking forward to all comments (to this List, or sent privately). > Sincerely, Alison Shields. > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
