Re: Shadow Sharpener Again

[John Carmichael]

Hi Bill and others   I just tested a bead-in-hole shadow sharpener and five pinhole sharpeners ranging in diameter from 2mm to 6mm. I used the shadow edge of my house's roof (which is about one tenth the height of one of Kitt Peak's side styles).  The best image of the half disk was using the smallest pinhole held at a distance of about 1 meter.  The larger holes produced fuzzy images that were larger and less precise.   The bead-in-hole was absolutely useless! In full sun it produced the nice little black spot as it should.  But very strange things happen to the image as you move the sharpener into and out of the umbra. A half disc image is impossible to see using a bead-in-hole no matter where you hold it.   I think my best bet will be to use the 2mm pinhole. But I will take all of them to the mountain because I want to test all the sizes using the telescope's shadow edge.  Maybe the larger holes will work better if the distance to the style is increased? Whadya think?   John   John L. Carmichael Jr. Sundial Sculptures 925 E. Foothills Dr. Tucson Arizona 85718 USA   Tel: 520-696-1709 Email: [EMAIL PROTECTED] Website: <http://www.sundialsculptures.com> ----- Original Message ----- From: [EMAIL PROTECTED] To: sundial@rrz.uni-koeln.de Sent: Thursday, May 30, 2002 6:04 PM Subject: Re: Shadow Sharpener Again In a message dated 05/30/2002 9:25:21 AM Eastern Daylight Time, [EMAIL PROTECTED] writes:    I apologize for my original explanation regarding the perceived edge of a shadow, it was wrong.  The corrected first paragraph should read as follows:    On a bright day with clear skies, the perceived edge of a shadow appears near the inner edge of the penumbra (near the umbra).  With increasing haze or whenever the edge of a cloud passes by, the perceived edge of a shadow moves toward the outer edge of the penumbra (away from the umbra).  This makes it impossible to design an accurate single-edged gnomon (without using a shadow sharpener).  You eliminate this problem with a double-edged gnomon such as a rod, cable, pinhole, slit, etc. Pete,       Thanks for clearing this up.  Amazing how our fingers do not type what we think we have said!  I think your results are in good agreement with mine. Your difference in degrees between the center of the Sun's image and the perceived edge of  the shadow of 0.222 deg corresponds to a difference in time between the passing of the center of the Sun's image and the passing of the shadow of 53 sec.             (0.222 deg)(4 min of time/deg)(60 sec/min) = 53 sec This is in good agreement with my estimate of 40 sec.         I can believe that there is a slight shift of the shadow toward the center of the Sun's image when shadows are formed when the sky is hazy.  However I have not been able to measure this shift.  I would be curious to know how you made your measurements so I could try to repeat them here.       I made a theoretical study of this phenomenon as follows.  I plotted the illumination produced by a circular object as it is progressively uncovered.  This curve, of course, is symmetrical about the center, and, to my surprise, is nearly a linear curve except near the extreme ends.  Because the eye's sensitivity is not linear, but approximately logarithmic, I then plotted the data on a logarithmic scale using EXCEL.  On such a scale you cannot start with zero when the disk of the Sun is covered, but must estimate the illumination in the shadow by the light of the sky alone.  Also the shadow will have more illumination when the sky is hazy.         I took my old SLR camera, along with a Kodak Neutral Test Card (Gray), outside and checked the exposure in the direct sun and in the shadow of my garage.       On a clear day I found the exposure had to be 5 f-stops greater in the shade than in the Sunlight (a ratio of 1 to 128, or  0.0078).  This amount was added to all the calculated values, both sunlight and shade, the resulting values converted to a percentage of the total illumination, and again plotted on a logarithmic scale.       On a hazy day I found the difference to be 4 f-stops or 1 to 32, or 0.031.  In a similar way I plotted a logarithmic curve for the change in illumination from full sun and skylight to shade with skylight only.         These curves are asymmetrical, being very steep just outside the shadow and very gradual near full sunlight. One cannot, from these curves, tell where the eye would perceive the edge of the shadow to be, but can be sure that it would be on the shadow side of the center of the Sun's image, perhaps halfway between the log of the shadow''s illumination and the log of the total illumination.  This would put the edge of the shadow 42 seconds from the middle of the Sun's image on a clear day and 35 seconds on a slightly hazy day.  If I interpret your results correctly, these figures are in rough agreement.         Would like to hear more about your analemmic/equitorial sundial.      Bill Walton      Plymouth,  MA, USA      42 N   71 W