Hi Edley, Your idea of interval timers based on the sun is intriguing. I have not seen previous references to this function. The examples that you described will work, but only for location, date and time specific instances.
The examples given work on the basis of solar azimuth. While this is related to time angle, the relationship is non-linear and strongly dependant on the solar altitude determined by latitude, declination and time. (Tan Az = Sin t/(Sin Lat x Cos t - Cos Lat x Tan t) where t is the time angle from noon in degrees). When the altitude is high, the azimuth changes rapidly. The maximum rate of change of azimuth occurs at noon when the declination and latitude are equal. I could prove this mathematically but there isn't enough room in the margin of this note. The consequence is that lunch hours determined by pie sections would be much longer at higher latitudes. Is this fair? One solution would be to tilt the pie from the horizontal plane to the equatorial plane. at an angle from the vertical equal to the latitude. In this orientation the pie will measure the time angle but all the juice will run out! It is better to define lunch as the time interval to consume the pie. Before sundials were invented, stomach time ruled. One time interval that demonstrates the non-linear effect very well is sunset. Let's define sunset as the time taken from the time the lower limb meets the horizon to the last flash as the upper limb disappears. The solar diameter is typically half a degree (or 32 minutes of arc). If this was solely determined by the time angle which changes at 15 degrees per hour, sunset time defined this way would be two minutes of time. That is what it is on the equator on the equinox. Everywhere else the sun sets at an angle approximately equal to the co-latitude ( More precisely Cos Phi = Sin Lat / Cos Dec). The sunset time interval is therefore the solar rate / Sin Phi. Today my theoretical sunset time at latitude 51 and declination -22.73 is 3.7 minutes. This explains why sunsets in the tropics are so short. Time flies when you are having fun! Roger Bailey Walking Shadow Designs N 51 W 115 Further details on "Sunset Phenomenon" are contained in my 1999 NASS presentation, a 394 kb PowerPoint (ppt) file. I would be happy to send a copy as an email attachment to you and others upon request. -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Edley Sent: December 2, 2001 12:11 PM To: [email protected] Subject: Interval Timers? Dear Membership, Sundial interval timers seem to be an area that is not well documented in the documents I have access to. One type of interval timer is a basic triangular wedge of some thickness. When the light is just extinguished on one edge til it just lights up the other ( when in the equatorial plane ) indicates the solar time equal to the angle included. 30 degrees, a 6th of a circle would time two hours, Half that slice or 15 degrees would time an hour. Could it be that pie was invented and in some places eaten last so that, in the sun, it could time out the lunch hour?? An equilateral triangle times out 4 hours. Two of them with a triangular gap between them time out a work day with time off for lunch. Could so many of the triangular markings we see on old sites be interval timers of some kind? What seems to be neat to me is that it doesn't matter whether the sharp end or the blunt end of the triangle faces the sun. When the blunt end faces the sun, a finger held up on the circumference would, when it casts its shadow on the tip of the pie, give an indication of how much lunch hour is left. Long, long ago, I won a bet with my dad by placing a small mirror tile a long way from our house and getting the reflection to sweep from one end of our house to the other in exactly one minute. Later I placed a dowel in a Christmas tree base and with a blob of modeling clay at the top repeated this for several intervals of time. The moon, when it is half full, subtends about a quarter of a degree which movement is about 1 minute. ( unfortunately the width is not in line with it's movement ) A piece of tape, the edge of a building and a fixed viewing point could time a 3 minute egg at midnight?? Write me if you have any documentation regarding this. Especially ancient records of interval timers. Thanks much! Edley McKnight [43.126N 123.357W]
