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I'm doing some work with sports statistics where I need to evaluate at what times part of the field is covered by shade. I already know that shadows cover the portion I'm interested in from roughly 4:33 EDT to 5:00 EDT on 4/28/22 and from roughly 4:51 EDT to 5:26 EDT on 5/22/22. Is there a mathematical way of estimating the time/length for other days based on the known values? Any help would be greatly appreciated.

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  • $\begingroup$ Short answer: no. Without knowing the orientation of the objects involved there is no way to know if that part of the field would be in the sun or deeper in shadow as the Sun moves. $\endgroup$
    – Greg Miller
    Jun 3, 2022 at 4:14
  • $\begingroup$ We can do something, by assuming the shadow is created when the sun is at a certain angle above the horizon (simple model, but might work) It would help to know your exact location. $\endgroup$
    – James K
    Jun 3, 2022 at 5:18
  • $\begingroup$ Would the website Find My Shadow help? $\endgroup$
    – Fred
    Jun 6, 2022 at 4:09

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Not certainly, but some fiddling with Suncalc.org suggest that your shadow starts when the sun reaches an altitude (angle above the horizon) of 36 degrees in New York, and leaves when it reaches an altitude of 30 degrees.

Here's what I did. I set the location to 40.78, -73.87. I then set the times in your question, and noted that the azimuth (bearing) of the sun was very different at those times, but the altitude was very similar (36 degrees). This might be the case if the shadow is caused by a some horizontal stands. You can use Suncalc to find when the sun reaches 36 degrees and that will predict the time when the shadow will start.

For example, this model predicts that the shadow will start at 3:00 EDT on October 1st, and continue until 3:44.

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  • $\begingroup$ This explanation is very helpful thank you so much! Just to add a bit more clarity, the location is New York City (40.78,-73.87) and the shadows are generated by seating stands. I also probably slightly misrepresented my end goal as I just need to know when the shadows "pass" a certain location on the field. Since my background knowledge of this subject is extremely limited I had only toyed with a code that returns the azimuth for given time and lat/long but fortunately that code can also return the altitude so I'm going to try that out. Thanks again! $\endgroup$
    – Nick
    Jun 3, 2022 at 16:51

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