Hello Roger, To have an accurate reading for the times of sunset and sunrise on an analemmatic sundial draw arcs through the focus points of the ellipse and a date point. You may see this in the attached picture.
Best wishes, Fer. Fer J. de Vries [EMAIL PROTECTED] http://www.iae.nl/users/ferdv/ Eindhoven, Netherlands lat. 51:30 N long. 5:30 E ----- Original Message ----- From: "Roger Bailey" <[EMAIL PROTECTED]> To: "Sundial Mail List" <[email protected]>; "Steve Lelievre" <[EMAIL PROTECTED]> Cc: "Mike Deamicis-Roberts" <[EMAIL PROTECTED]> Sent: Friday, January 11, 2002 5:35 PM Subject: Seasonal Sunrise Marker > The original copy of this note did not get to/from the sundial mailing list. > I have changed the address on this one and hope for better results. I > apologize if you happen to receive multiple copies. If you do, keep one and > pass the other on to your grandchildren. > > The original note follows. Roger Bailey > > Hi Steve et al, > > You guessed correctly on the sunrise marker. Have a look at the little pdf > file attached showing the seasonal sunrise marker on Mike Deamicis-Roberts' > analemmatic dial. > > The seasonal sunrise marker is a point on the east west axis of the > analemmatic dial that is used in combination with the date line of the > Zodiac table to show when and where the sun rises throughout the year. Stand > on the sunrise marker point and view across date marks on the zodiac to see > where the sun will rise on that date. Or stand on the date mark on the > Zodiac and view past the sunrise marker to see the time of sunrise on that > date. Use a string from the date through the marker to the hour ellipse to > convert the dial into a sunrise calculator. What could be easier? > > The red line on the sketch shows the summer solstice sunrise at 4:49 AM at N > 60.2 East for Mike's latitude of N 36.8. In your mind, rotate the red line > around the marker point to determine the time and direction of other sunrise > dates. For sunsets, use the marker on the east side of the dial. Things are > symmetrical. These two marker points provide an excellent new feature for > analemmatic sundials, the ability to show where and when the sun rises and > sets and how this changes throughout the year. > > This idea started with Mike's "Seasonal Sundial" posting to the sundial > mailing list last fall. He was looking for a sundial design that would show > the cycle of the seasons through the year. I proposed an analemmatic dial > with distant solstice sunrise markers like a "medicine wheel". This did not > suit Mike's topography. He proposed a marker point within the sundial that > could be used with the date table to show sunrise phenomenon. I had not > heard of such a point but did the math to reduce the idea to practice. As > you can see, Mike's brilliant idea works! > > Here are the steps to calculate where to put the seasonal markers on any > analemmatic dial. All you have to do is determine where the red line crosses > the axis. This calculation could be done for any date but the error is least > if you use the solstice, either the summer or winter (they are symmetrical). > > 1. Calculate the azimuth of the solstice sunrise for your latitude. When the > altitude is zero (sunrise), the azimuth (Az) given by Cos (Az) = Sin (Dec) / > Cos (Lat). In Mike's case Cos (Az) = Sin 23.44º /Cos 36.8º = .497 so the > sunrise azimuth, east of north is Az = 60.2º. > > 2. Solve the right angle triangle between the two axes and the red line to > find the marker point on the E/W axis. Start with the zodiac distance on the > N/S axis which is size (or the semimajor axis) x Cos Lat x Tan Dec. In > Mike's case of a 9 meter dial, the semimajor axis is 4.5, so the solstice > zodiac distance is 4.5 x Cos 36.8º x Tan 23.44º = 1.562 meters. From the > triangle geometry, the distance to the marker on the E/W axis is 1.562 x Tan > (Az) or 2.727 meters. > > How accurate is it? The mathematics are not exact as the trig relationships > are not the same, but they are pretty close. Both the zodiac distance are > functions of latitude and declination but not the same functions. The > declination distance relationship of the zodiac is slightly different for > the azimuth derivation. From the layout method, the error is zero at the > solstices. It is also zero at the equinoxes when the sun rises due east. > There is a sinusoidal periodic error for dates in between. This error > increases with latitude. In Mike's case the maximum error is only +/-2.3%. > At my latitude, N51, the maximum error increases to +/-6.5% so the > relationship is only approximately correct. With sundials we are used to > this level of accuracy. Corrections for the equation of time and leap years > are of similar magnitude. > > All these calculations are based on the theoretical sunrise when the > calculated altitude of the sun is zero. Refraction and semidiameter affect > the real view. If you have a perfect horizon (ocean view), allow the sun to > rise one full diameter, from the horizon to the lower limb to correct for > semidiameter and average refraction. For other locations, you will have to > correct for the horizon pollution. In Mike's case there is a devilish range > of mountains affecting his horizon by up about 5 degrees. We are working at > corrections for this. > > My conclusion is that the simple addition of these markers to the design of > analemmatic dials adds a lot to their function of demonstrating the cycles > of the sun with the seasons. > > Roger Bailey > Walking Shadow Designs > N 51 W 115 > > -----Original Message----- > From: Steve Lelievre [mailto:[EMAIL PROTECTED] > Sent: January 8, 2002 7:03 PM > To: Roger Bailey > Subject: Re: Garden/Human Sundial > > > Roger, > > What precisely is the "the sunrise seasonal marker proposed by Mike > Deamicis-Roberts"? I'm guessing it's some sort of mark or curve on the dial, > which gives a line from today's place on the date scale to the a place on > the ellipse showing the corresponding sunrise time, but I've not heard of it > before. > > Thanks, Steve > > > Attachment converted: Macintosh HD:analemdial.gif (GIFf/JVWR) (0003A004)
