Hello Fer, hello Roger, your ideas on seasonal sunrise markers are very interesting. After having compared your constructions I have 2 questions: 1. Fer, where can I find the proof, that your construction ist exact? 2. Roger, I think the maximal error in your "linear approximation" would be a bit smaller, if you don't use the summer solstice for fixing the intersection point (you called this point "Sunrise" in your attached pdf-file) on the horizontal axis, but a day with smaller declination, may be half a month later or so. Is that correct? It looks so, when the points of the dates in Fer's construction are conected with the corelating points of sunset. Does anybody know which day would be the best? I suppose it could depend on the latitude. Thanks Helmut
Helmut Sonderegger, A-6800 Feldkirch Email: [EMAIL PROTECTED] URL: http://webland.lion.cc/vorarlberg/280000/sonne.htm ----- Original Message ----- From: "fer j. de vries" <[EMAIL PROTECTED]> To: "Roger Bailey" <[EMAIL PROTECTED]>; "Sundial Mail List" <[email protected]>; "Steve Lelievre" <[EMAIL PROTECTED]> Cc: "Mike Deamicis-Roberts" <[EMAIL PROTECTED]> Sent: Friday, January 11, 2002 10:04 PM Subject: Re: Seasonal Sunrise Marker 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 > > >
