RE: Temporal Hours and Refraction

[Roger Bailey]

Hello Noam,   This is an appropriate question for this list. You would be amazed by the range of questions we consider in the name of sundials. Ask and you will receive a variety of answers from diverse and knowledgeable respondents. I can only offer opinions as I could not open your _javascript_. At least I was courageous enough to download the executable file from an "unknown" source.   Here are my opinions based more on concepts than calculations. For normal sundials and uniform hours, refraction is minor effect. At most refraction is  about 34' or half a degree as the sun sets. As one degree of time angle is 4 minutes of time. this may cause an error of a couple of minutes, no big deal for sundials. This is based on the the normal case when the gnomon is parallel to the polar axis and time is uniform. In your case of temporal (unequal or antique hours) and a vertical gnomon, the refraction error can be significantly greater. Increasing latitude and declination amplify the problem. This is because the angle of the setting sun (Phi) varies with latitude and declination. The math is Cos Phi = Sin Lat / Cos Dec. This explains why sunsets at fast in the tropics and go on forever at higher latitudes in the summer. The saying that time passes when you are having fun is a reality during tropical vacations. I gave a presentation on "Sunset Phenomenon" at the NASS conference in Hartford in 1999 and would be happy to provide the slides as a 425 kb pdf file. The presentation covers the equations for the time, location, path and rate of sunset. It does not specifically cover refraction but does discuss the "Green Flash".   Temporal hours are unequal. The time from sunrise to sunset is always divided into 12 hours, no matter how long the day is. At higher latitudes and declinations the length of a temporal hour in the summer can be twice that of the winter. I am used to less than 8 equal hours in the summer and over 16 equal hours in the winter. We will not even consider the endless days and nights above the polar circles. The small difference for refraction has much more of an effect on unequal or temporal hours as the sun is just skimming the horizon at higher latitudes and declinations.   Try some sample calculations using Fer De Vries ZW 2000 program* for local time and antique hours for different latitudes. The non linear nature of temporal hours is quite apparent.   Regards,   Roger Bailey Walking Shadow Designs N 48.6  W 123.4   *http://www.de-zonnewijzerkring.nl/eng/index-links.htm and click on downloads for ZW 200 -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]On Behalf Of Noam Kaplan Sent: September 23, 2004 3:30 PM To: sundial@rrz.uni-koeln.de Subject: Can anyone answer this? If this is the wrong forum, I apologize. I have a calculation to figure out the atmospheric refraction from Fred Sawyer's article in the NASS Compendium. It is based on calculations that Meeus brings in his book. Refraction changes the apparent altitude of the sun, thereby changing both the apparent declination and apparent hour angle of the sun.   Am I making a mistake when I use the apparent declination and apparent hour angle for the temporal hour calculation? The effect of a few seconds difference for atmospheric refraction on the hour angle seems to have a much bigger effect on the temporal hours.   Thanks for any help you can offer, Noam   My calculations can be seen on the web at http://www.riets.edu/stuff/suncalc/zman.js in the function temporal(localTime)