Hi Roger, You Wrote: > 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.
True. > The examples given work on the basis of solar azimuth. While this is > related to time angle, the relationship is non-linear and strongly > dependent 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. I had slipped in a parenthesis saying it was true in the equatorial plane, and that would be mostly true as you say, except if the sides of the pie were tall and it acted as a shadow plane dial. As you say, at the equator itself you would have to point it straight up in the air and balance it somehow there, and unless it were some very stiff sort of pie it would all run out. Still at higher latitudes, in the days of the guilds, it may have been done regularly, but I only have clues to this effect, no direct proof. > 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! Now that is very good to know! If you were suddenly transported to some place on the earth at sunset, then you could tell whether you were north or south of the equator by the direction the sun moved at sunset, and then could approximately tell the latitude by how long it took ( If you knew the current declination ). Wow! I've spent some time in the tropics and yes, sunset is quicker, surprisingly so. Thanks for the Info! Edley McKnight [43.126N 123.357W]
