To calculate the time of day (ToD) and day of the year (DoY) that a photo was taken,
you need to know three things:
1. The latitude and longitude of the location of the object whose shadow you are using
for your calculations,
2. The angle the sun is above the horizon (its elevation),
3. The angle the sun is east or west of its position at noon (its azimuth).
The red line shows that the shadows in the picture fall directly to the east across
Griffith St. implying that the sun is directly in the west at an azimuth of 270 degrees.
Having the sun in the west and the camera facing north and aimed directly at the man
on the horse means we don't have to correct the length of the shadows for perspective.
There is a lot of information in this table that you don't need - so I've boxed in the
important items in red. There is no entry that matches our parameters exactly - the
closest we can come is at 16:52:03 (4:52:03 pm) when the son is at 22 deg 52' 58"
elevation (apparent altitude), and 269 deg 29' 43" apparent azimuth. Note that local civil
time is different from local solar time. But this was not important in 1871 when time
had not been standardized into time zones.
As an exercise, see if you can use the calculator to show that the sun is near our
desired position on May 5. The sun occupies the same position two times during a year
- once as it travels higher in the sky during the spring and once when it sinks lower in
the sky during the winter (in the northern hemishpere).
|Calculating the Time of Day and Day of the Year
|An easy example of how to do
this is provided by the
Sheboygan Dead Horse photo.
The man in the photo is sitting at
the intersection of Griffith and
Indiana Sts. The camera is
pointing to the north along
Griffith St. in the direction of
the Sheboygan River.
Sometimes it is easy to figure out the position of the sun from the shadows in a
photograph, and sometimes it is more difficult. It depends on whether the camera was
directly facing the object that was casting the shadow, and whether the object was on
the same level as the camera. In either case, a correction must be done for perspective.
We won't address this here, to keep things simple. If you have a shadow you would
like some help in correcting for perspective, please write to me at
Assuming that either you have a shadow that does not need correction for perspective,
or that has already been corrected, you will need an ephemeris to find the ToD and
DoY based on that shadow. According to Wikipedia
(http://en.wikipedia.org/wiki/Ephemerisn), an ephemeris is a table of values that gives
the positions of astronomical objects in the sky at a given time or times. An easy-to-use
solar ephemeris that is handy for finding the ToD and DoY from shadows is found at
Home page of the Great Circle Studio's solar ephemeris set
up to calculate the ToD and the DoY for the Sheboygan
Dead Horse photo.
Usually, you must supply an ephemeris with the ToD and the DoY for which you
would like to calculate the position of the sun. However, to analyze a photo, you want
to do the reverse - you want to find the ToD and DoY based on the sun's position.
Since the Great Circle Studio Solar Calculator cannot be run backwards, to use it in
reverse, you must enter a guess for ranges for the ToD and DoY and allow the
calculator to produce the position of the sun over this range. If the solar positions that
are output do not match the ones you have calculated from your photograph, you can
adjust the input to the calculator and run it again. You can continue adjusting your input
ToD and DoY until you obtain a solar position that comes close to the one you want.
This will be associated with the ToD and DoY when the photo was taken.
Finding the elevation of the sun is also easy using the triangle outlined in red in this
image. As stated above, the angle of elevation is THETAe = arctan (H/L). We only need
relative measurements of the legs of the triangle, not absolute. Using our high
resolution version (too large to post), and shortening the base of the triangle to account
for the gap caused by the tear in the picture, we obtained THETAe = 22.85 deg.
Going back to the Great Circle Studio Calculator, we input the latitude and longitude of
Sheboygan as Lat = 36 deg 37' 05" N, Long = 121 deg 55' 29" W. We then input
several guesses at the date, and had the calculations done in relatively coarse steps
(indicated as "Data Interval" on the calculator), leaving the rest of the switches
unchanged. We repeated inputting new dates and times based on our previous results
until we pinned down August 10 as a date when the sun came close to our position of
THETAa = 270 deg, and THETAe = 22.85 deg. (It is also close to this position on May
5.) We iterated on the ToD until we produced the chart below. Since the sun traces the
same path every year to within a small error, we don't have to worry about the year.