Hello all: As I was calculating the height and width of my vertical nodus and the position of the lines of declination, I noticed that the tapering of the nodus's pointed tip must be very sharp so that the shadow of the body of the gnomon does not shade and overlap the shadow of the tip at apparent noon on the summer solstice. As the sun's altitude is maximum at this time, it is critical that the taper angle of the vertical gnomon be sharp enough to not block the shadow of the tip.
In another words, the taper angle is the angle formed from the nodus tip down to the northern foot of the gnomon against the vertical which is equal to the sun's angular distance from the zenith at apparent noon on the summer solstice. I came up with this simple little formula to calculate the taper angle: Taper Angle = latitude - 23.5. This means that vertical gnomons at lower latitudes must have more taper. Here in Tucson the sun is almost directly overhead at noon on the summer solstice, just nine degrees from the zenith. (32.5 - 23.5 = 9). I am using a 1/4 " thick rod, 8" (20 cm.) tall, so it is going to have to taper 9 degrees at the tip. I'll have to taper the upper 3/4" of the rod to avoid gnomon shadow blockage. This makes a very sharp little point indeed. I hope nobody gets inpaled on it! There is some doubt as to whether the egyptian obelisks were used as vertical gnomons. I wonder if anyone has bothered to check their taper angles? Since Cairo Egypt is at about 30 degrees latitude, the taper angle of an egyptial obelisk should be less than or equal to 30 - 23.5 = 6.5 degrees, or else they would not be suitable gnomons in the egyptian summertime. I'm pretty sure that my thinking is correct on gnomon taper angles, but if I am wrong, please let me know. John Carmichael http://www.azstarnet.com/~pappas
