-----Original Message----- >From: [EMAIL PROTECTED] >[mailto:[EMAIL PROTECTED] Behalf Of Anselmo PÈrez Serrada >Sent: September 3, 2002 11:17 PM
>Roger is right on this of the double dateline, but (once again) what >about the EoT? I can't see in the pictures any lines like these at Longwood Gardens >approximating (by minimum squares, I believe) the EoT deviation. >Anselmo Hi Anselmo, Fer Mac and all, Let me propose a new idea to correct for the equation of time on analemmatic sundials. Previous methods focused on the date line and the analemma. The analemma pattern often seen on the central axis can be used as an indicator of the EQT error at noon but fails to correct at other times of the day. Complex multiple analemmas as described in Fred Sawyer's Longwood Gardens article can provide a good approximation but such designs have not been frequently used. Let's change the focus of the correction from the date line and analemma to the hour points. Most analemmatic dials have large hour markers of an arbitrary size, scaled to look right and provide a clear if imprecise time indication. The hour markers can be modified to provide a simple correction scale for the EQT. This idea works particularly well when two sets of hour markers are used to correct for daylight savings. Have a look at the sketch "DST Epicycle.pdf" attached to the accompanying email to see the basis for this idea. The sketch is rough and attached to the other email to get it past the size filter. The attachment is under 20 kb so I hope it works. The EQT is caused by two periodic phenomenon: the elliptical orbit of the earth with a once per year frequency and the tilt of the earths axis with a twice per year frequency. These periodic components are superimposed giving us the typical curve shown in the attached sketch. Yes, there are higher order terms but for this simple approximate correction they can be ignored. Lets separate the two curves into the large blue Fall - Winter curve with an amplitude of about +/-15 minutes and the smaller red Spring - Summer curve with an amplitude of about +/- 5 minutes. These are clearly periodic curves that can be approximated with sine curves. These sine curves can be generated with circles with the date plotted around the circumference and the perpendicular to the axis indicating the time correction on that date. Does all of this sound familiar. Yes, we are back to what I have called correction epicycles! How would we apply this concept? First, you should have two hour ellipses of different diameters and appropriately scaled date lines. One ellipse would show spring and summer time when the declination is positive and a daylight savings correction appropriate. The hour markers here could be small, as the correction is only +/- 5 minutes. The other hour Fall Winter standard time ellipse would have larger markers for the +/- 15 minute correction. The correction epicycle would be sized for each hour point as they vary a little due as a function of the time and latitude. A small offset of a minute or so would have to be applied to each hour marker. How would you use it? As usual, place the gnomon on the central axis on the appropriate date point. See where the shadow falls on the hour ellipse appropriate for the date. This gives you the solar zone time (corrected for longitude). For standard and daylight sayings time, correct for the EQT by going to the closest hour marker correction epicycle. From the date around the circumference, drop a perpendicular to the axis of the epicycle to estimate the applicable time correction. Then check your watch, smile and say "Cool! It really works!" How accurate is it? It is not mathematically correct but a good approximation. I would guess it would be within a minute or so +/-. Considering the gnomon width and penumbra shadow fuzziness, you cannot read the dial more precisely that this. In any case the correction scale applies only at the hour points. All times between the hour points would have to be interpolated and this is prone to error. I am putting out this proposal for comment. I recognize that the implementation will require a lot of careful design calculations and accurate construction but I believe it is a good solution to the long perplexing problem of correcting civil time to solar time on analemmatic sundials. Cheers, Roger Bailey Walking Shadow Designs N 51 W 115 -
