Hi Geoff, Your most interesting ‘penumbral’ comment also raises another possibility that this could be a tad more interesting if we can believe a ‘throw away’, and not fully explained, comment about the monument which suggests a question that there might be still more to the design than we thought.
“The ellipses of the Anthem Veterans Memorial will form a circle of light once a year, but we can only experience the eleventh year once in a hundred years.” Maybe this might also be connected with the odd proliferation of the number 11 in the engineer’s explanation? It occurs in this link: http://www.isisinform.com/category/memorials/anthem-veterans-memorial/ Regards Patrick From: Frank King Sent: Saturday, January 21, 2017 2:59 PM To: Geoff Thurston Cc: John Goodman ; Sundial List Subject: Re: Unusual bi-annual sundial Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii -------- Dear Geoff, As so often, you cause me to reflect a little and to refine my analysis... > I wonder if the errors might be masked > by the 32 arc minute solar penumbra. In pondering this "instrument" I made the naive assumption that we had an ordinary aperture nodus. It IS an aperture nodus but it is hardly ordinary... Imagine a bug sitting at the centre of the Great Seal and looking up the array of elliptical openings. We can think of the bug looking along a tube which has a uniform elliptical cross-section along its length. Of course, to the bug, the far end of the tube appears smaller than the near end. From photographs, I estimate that the angular separation of the top and bottom of the far end of the tube is about 4 degrees or about 8 times the diameter of the solar disc. The angular width is about 11 solar discs. Although we are referring to the far end of the tube, it is still many times larger than the apparent diameter of the solar disc. The tube is therefore much too big to be regarded as a shadow-sharpener and, when investigating the patch of light on the ground in the vicinity of the Great Seal, we can deem the relevant aperture to be the hole in the nearest face of the shortest column. This is the hole closest to the Great Seal. The only effect of the long tube is to limit the range of declinations and the range of hour-angles for which the relevant aperture can give rise to a full patch of light. Clearly this is several days either side of 11 November and several minutes either side of 11:11. When the patch of light is anywhere near the Great Seal we can ignore every aspect of the tube except the nearest hole. It is a great pity that the time lapse video doesn't start early enough to see just when the patch starts to appear "full". Otherwise I could determine the dimensions with more precision. I did say at the outset that this is a whole can of worms! OK, that's a preliminary. Now to your pertinent observation... I am sure you are right. At 11:11 the extreme altitudes over the 10 year period are +/- 5.5 arc minutes either side of the mean. The fuzz at the top and bottom of the patch of lighe illuminating the Great Seal will always be around +/- 16 arc minutes (half the solar diameter) which is definitely a greater range. That said, the many photographs of the spot of light at the critical instant seem to show the top edge of the Great Seal not quite fully illuminated. It is a very small effect but it does make me wonder whether the Great Seal has been put in the correct place. It would be most interesting to see photographs on 12 November when the declination and hence altitude are slightly lower and the patch would be further out. I think there would be a slight over-correction and we would conclude that the design date of 11 November is better. My concluding thought is that there should be a removable Great Seal printed on some high-quality material and treated with due respect. Each year, Anthem's official astronomer would oversee the placing of the Great Seal in the exact position for the declination this time round! Very best wishes Frank --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
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