Hi Roger, Thank you for sending the sketch "DST Epicycle.pdf".
Your concept is interesting and applicable when using a movable gnomon. When, however, I act myself as gnomon - the attractive property of the analemmatic dial - the distance between my position and the time correction indicator will be too great to read the correction I suppose. Willy Leenders Hasselt, Flanders in Belgium. Roger Bailey wrote: > -----Original Message----- > >From: [EMAIL PROTECTED] > >[mailto:[EMAIL PROTECTED] Behalf Of Anselmo Pérez 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 > > - -
