Tuesday, April 3, 2007

Shadows of a Live Man

Back in December, the Sheboygan (WI) newspaper published the photo below, featuring a man in a top hat sitting on a supposedly dead horse, with a man and a dog, plus many buildings, in the background. A full summary of the story, the picture, and the early analysis can be found on Sharon Sergeant's Ancestral Manor site.


Together with Sharon, Colleen Fitzpatrick and Andrew Yeiser have analyzed the photo to try to determine where and when the photo was taken. The first installment of their findings have been written up in a newspaper article in the Sheboygan (WI) Press by Jan Hildebrand. Based on the setting, the buildings in the picture, other features not in the picture, and the shadows cast by the men, they determined that the picture was taken in Sheboygan WI on 24 September 1871.
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Please read the whole article, Sharon's web site and Colleen's web site for more information.
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It seems to me that the shadow lengths can only be determined from the picture above by measuring the shadow of the man in the background with the dog - the shadow appears to extend all the way to the fire hydrant. Measuring the man's height in the picture (which may not be accurate if it's a wide angle lens as Colleen and Andy think) relative to the apparent length of the shadow, the altitude (angle relative to the ground) of the sun is about 30 degrees. The shadows appear to be directly to the east (azimuth angle of about 270 degrees), although it is difficult to tell exactly.
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I found an altitude and azimuth calculator for the sun and the moon at http://aa.usno.navy.mil/data/docs/AltAz.html. Inputting Sheboygan WI and a range of dates, I found that the combination of Altitude = 30 degrees and Azimuth = 270 degrees (east of north, 270 degrees = due west) occurs on about July 21 at 1630 in Sheboygan.
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For Colleen's date of September 24 at 1630 local time, the altitude angle is 12.7 degrees and the azimuth angle is 256.7 degrees. If it were this date, I think the shadow would be much longer than what I see (12.7 degrees means the shadow would be about 4.4 times the length of the object, in this case, the man with the dog).
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If my measurements are off by say 5 degrees in altitude, that would make it either June 21 at 1605 local time (35 degrees altitude) or August 5 at about 1645 local time (25 degrees altitude).
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It's possible that the azimuth angles are not exactly 270 degrees also - they may be off by 5 to 10 degrees - it is very hard to measure that from the photograph.
I'm not saying I'm right and Colleen is wrong - because I cannot be sure what the height of the man is, the length of his shadow or the azimuth angle of the sun. Colleen must have measurements and it would be useful to know what they are and how she calculated the date from them.
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If my measurements are roughly accurate, then the approximate date of the photograph is between June 21 and August 5. I'll leave the year up to Sharon, Colleen and Andy.
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This was an interesting investigation by everyone!
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UPDATE (3 April, 6:30 PM): I've had some emails with Colleen about her calculations, and have tried to explain my comments to her. She provided a marked up photograph with the shadow length of the man sitting on the dead horse, which resulted in a sun altitude angle of about 24 degrees. Based on the calculator at the USNO site, that correlates to August 7 at 1645 for an azimuth angle of 270 degrees.
UPDATE (4 April, 2:30 PM): Colleen has assured me in email that on the large digital image she has of the picture that the shadow of the top hat is visible, and the measurement is fairly exact. She agrees in principle with my methods here and the calculation. She has measured an altitude angle of 23 degrees from the image - that changes the day a bit. In a comment to this post, Steve Danko noted that the same combination of altitude =24 degrees and azimuth angle = 180 degrees also occurs on May 5 at 1636. That is logical, since the sun's path is essentially symmetrical about the solstice in June. Nice catch, Steve.

2 comments:

Steve said...

In addition to August 7 at 16:45 local time, the altitude (24°)and azimuth (270°) also match up on May 5, 1871 at 16:36. I agree with you, though, that if the altitude calculations are off or if the shadows are not exactly east-west, an exact date (or time) cannot be determined. Thanks for the link to the altitude and azimuth calculator, Randy!

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