There has been a lot of discussion about setting sundials by establishing the north south axis at solar noon. See the previous notes on www.solar-noon.com . Personally I have been frustrated by trying to use solar noon for laying out and setting sundials. The first problem is weather. Whenever I am on site at around solar noon, a big cloud rolls in and the sun disappears until well after noon. The second problem is altitude. Even if the sun is out, the sun is so high these days as we approach the solstice that the shadow is very short and it is difficult to get an accurate fix on the shadow of a plumb line. A lens as a shadow sharpener helps some but the vertical distance is still so much greater than horizontal that the accuracy is poor. It may work for small dials but not for the layout of a typical analemmatic dial. I have two modest proposals to work around this problem.
1. Set the east west axis: For the good half of the year, spring and summer, when the solar declination is positive, the sun is due east in the early morning and west in the late afternoon, at times when you can get good long shadows for setting the east west axis. The complicated looking trig functions simplify to a relatively simple formula solvable with a pocket scientific calculator. If you found solar noon, which you need to do anyways, you can solve for the time when the sun's azimuth is due east and west. Cos (t) = Tan (Dec) / Tan (Lat) You needed to know declination and latitude so just plug these angles in this formula and solve for t. This is time from solar noon as an angle. This you will have to divide by 15 to convert to hours and then convert the decimal part to minutes and seconds in the usual way. For example, here is the calculation that I did recently for Elliston Park in Calgary where I am laying out an analemmatic dial. The site is at Latitude 51.03632 and Longitude 113.9438. Local solar noon on 5 June was at 13:34:20 MDST when you make the usual longitude and EQT corrections. The solar declination was 22.61739. All this information was calculated from the date and site data using the NASS Dialists Companion. Plugging the dec and lat into the above formula gave me a time angle t of 70.31 degrees which converts to 4:41:14. Adding this to local noon gives me 18:15:34. At a quarter after six that evening the sun was due west. Subtracting from solar noon tells me that the sun was due east at 8:53:06. This gave me two more shots at specific times, before and after normal business hours, to get the dial axis set. For the record, it rained all day on 5 June in Calgary and I missed the opportunity to set the dial. Oh well, we need the rain. There has been a drought in Alberta. 2. Use Offsets: The above method is fairly simple but the clouds can still roll in at the wrong time. What we really need is a way to calculate the offset from the north south axis for any convenient time. One formula for azimuth adapted from the one in the BSS Glossary is: Tan Az = Sin t / (Sin Lat x Cos t - Cos Lat x Tan Dec) This looks pretty bad but the declination and latitude can be stored as constants in your calculator leaving only one variable to be dealt with, the time angle t. A simple program in a pocket calculator will allow you to input the current time, as an angle from solar noon, and solve for Tan Az. This is all you need as the tangent is the offset. From 1 meter down the shadow line from your centre point, measure out at a right angle the offset (Tan Az) to establish a point on the north south axis. This formula is now programmed into my Radio Shack / Sharp calculator so I am all set for the next sunny day when I am in Calgary. Anyone who stayed with this note this far will see that the first equation is simply derived from the second for case of the east or west azimuth of 90 degrees. Tan Az is infinite at 90 degrees so the denominator must be zero. Then Sin Lat x Cos t must equal Cos Lat x Tan Dec. QED I hope this will help us get past our solar noon fixation. Roger Bailey Walking Shadow Designs N 51.0842 W 115.3775