Msg: 7015 *Conference*
03-26-97 18:36:24
From: RON WIESEN
To : COMET _
Subj: REPLY TO MSG #7010 (CYBERLIFE)
Rainbow display is easy because only one angle of solar declination is considered, in contrast to the solar clock which must account for solar declination for every day of the year and combine it with the defference between LOCAL and MEAN time. Because aperature to aperature distance for rainbow display is in inches (4.25 in my case) rather than fractions of an inch as in case of the solar clock gnomon diameter, wider widths of slit are possible. Hence, you don't have to use jewlers saw blades. I do, but you don't have to! If computers are considered as tools, then I used the M102 and an IBM PC. Task is to paint a hyperbolic curve on paper so you can see where to saw to make a slit for one aperature. A small hole, inches away, is the other aperature. In my case the hyperbolic slit is on the sunshine (South) side and the hole is on the shade (North) side. The other way around works but the rainbow (refraction) isn't practical and what is displayed (point of sunlight) will drift across a wide distance. In my case, a fragment of broken glass (crude prism) is just South of the pin hole aperature - so the aperatures do there stuff and on the "day" of alignment sunlight passes out of the pin hole to be refracted into a rainbow which doesn't drift far in the course of hours. It could have been done completely with the M102 and a printer with "pixel dot" graphic capability. At work I have a drawing package (Designer) so I just used BASIC in the M102 to get cartisian X-Y coordinates, typed them into the array generator of the drawing package in the PC, which "threw cross hair targets" to the coordinates. With targets planted, I drew one curve where each target was a high accuracy reference point of the curve. In my case, one point per 15-minutes of time (4 points per hour) sufficiently defined the hyperbolic curve over about a four-hour span centered on "high noon" of midday. Datum for the points can be found in several forms: Right Ascension & Declination or Azimuth & Altitude. The datum varies slightly over decades but not enough for the 20-year life of this object. The sutle point is accomodating Leap-Year as best you can. If the "birth date" of interest is well past February 29 (November 21 in this case), just use datum for the second year of a 4-year leap-year cycle (cycle ends on a leap-year). For a date closely following February 29, you must average the datum over a 4-year cycle to mitigate leap-year effects. For February 29, just treat it as if it were February 28 (best case) and feel sorry for anyone born on such a date! In whatever form of datum you obtain, you still must consider "location" which is Latitude & Longitude. The objective of the software is to prompt you for the "distance" between the aperatures, read each datum point and do the trig math to get a Cartisian X-Y plot of projection onto a flat vertical plane (in my case the front wall of the base box). Of course the folks at Dartmouth who originated BASIC liked angles defined in radians rather than degrees so conversion is needed (datum generally is degrees/minutes/seconds and for Right Ascension its hours/minutes/seconds). Because solar declination changes less than a degree per day, then the hyperbolic curve looks nearly symetrical about its center point. This also means that when you cut the aperature slit, you can maintain a constant angle as you saw and there's no inside/outside surface effects with regard to the "effective width" of the slit due to the thickness of the material. The constant angle can be the same as the "midday angle" or something more or less if you intend the "effective width" to be less than that made by the saw blade. I say make it whatever the saw blade gives you and make the "distance" between aperatures large enough for required accuracy. I say to shoot for an aperature "channel" angle of 0 degrees 25 minutes which I find a good comprimise - the apparent diameter of the Sun averages 0 degrees 32 minutes (- 28 seconds at Aphelion of July 4 and +32 seconds at Perihelion of January 1) and the day-to-day change of solar declination averages 0 degrees 13 minutes 6 seconds. This "channel" angle comprimise envelops the year-to-year variation of solar declination in a 4-year cycle. It guarentees 100% light in the "channel" on the date of interest regardless of year in a 4-year cycle. A day before or day after produces about 50% light in the "channel" at most. Not a bad comprimise. Tools is easy and material isn't critical. Make yourself a test Comet. Get 2 x 4 about a foot long. Go to Radio Shack and get an undrilled piece of printed circuit board material. Saw a shallow slot near opposite ends of one edge of the 2 x 4 so that circuit board material cna be press fit and stand erect. Cut two small pieces of circuit board material, 1 by 1 or so. Drill one small "pin-hole" in each piece - 1/16 inch drill bit is good. Jam each piece (aperature) into a slot. At this point you have "light channel" that's several inches long but a fraction of an inch wide - dang good gun sight! I'll let you do the trig math to find the "angular width" of the channel. If it's around 0 degrees 30 minutes (it will be), then the entire "solar disk" could be seen if one was dumb enough to view the sun through the aperatures. Take it and a white placard (paper etc.) outside. Use bricks, stones, and whatnot to mount the 2 by 4 so that "alignment" occurs. Note the exact time. Leave things undisturbed and the next day a few minutes before the "alignment time" start observing. An image of the solar disk is seen on the "shaded" aperature moving slowly toward the "pin-hole". But the cneter of the solar disk will miss crossing the center of the "pin-hole" due to a 1-day change in solar declination of about 0 degrees 13 minutes. Still, some light from a limb region of the solar disk does pass through at the appointed time. Check it again the following day. It's a cheap experiment that clarifies the idea and gives you some "feel" for a solar calendar. Enjoy.