I'm planning a trip this summer to Upper Antelope canyon and I've wondered the question about when the sunbeams at Upper Antelope Canyon are visible. It would be terrible to go all the way there and find out you missed it by half an hour or a couple weeks. What I really need are precise numbers. Data online this is varied at best, with many tour operators saying to come around the summer months and do midday tours. Here is my documented attempt to find out more precisely.
From the air, the canyon is tall and narrow, running primarily in the N-S direction. I don't have exact detailed dimensions of the canyon, but my best guess from internet sources I can approximate it to around 120 feet tall and 8-12 feet wide.
Now in order for direct sunlight to hit the floor of the canyon, the easiest way is for the azimuth of the sun to align with the path or length of the canyon. If it does not, then you must have a clear path to the sun that climbs over the narrow canyon walls. The former doesn't demand the sun to be as high of an altitude, the latter does. In the worst case scenario, the sun's direction is perpendicular to the length of the canyon and therefore the arctan of the height of the canyon over the width of the canyon is the altitude that the sun must be for any of the light to reach the canyon floor. In this case, the arctan of 120/12 or 120/8 is 84-86 degrees. The sun does not reach that high during the summer solstice in Page, AZ. Therefore, we must use the length of the canyon to aid us.
Now if we allow the sun's rays to run along the length of the canyon, then there is more possibility of them striking the ground. If we say have 30 feet of canyon length for the sun's rays to traverse before hitting a 120 foot high canyon wall, then the arctan of that is now 76 degrees which the sun does reach during the solstice. With 60 feet of canyon length, you now only need a 63 degree high sun, creating more possibilities.
Now what is interesting is that many websites claim the sunbeams are visible during a period of time that skews earlier than solar noon (1220pm-1230pm during the summer months) in Page. Another says sunbeams are visible from 10am-1pm from May through early October. One tour website says 11am-130pm and from mid-March through mid-October. If the path of the canyon was perfectly aligned in the in the N-S direction, then for an equal amount of time before and after solar noon should the sunbeams be visible. Instead angle of the canyon being skewed more towards the NW to SE direction which results in more opportunities in the morning hours which agrees with what the websites say.
What is interesting is that the beams can still be visible around mid-October which means the sun is only 44 degrees high during solar noon.
Therefore, it seems the azimuthal direction of the canyon is more important for letting the sun's light in than the altitude of the sun.
I used Photo Pills app to look at the alignment of the canyon, using the object height as 38 meters (approximately the 120 feet of the canyon's walls) and then having the app draw a shadow. Using this diagram, I can see roughly when does the sun's light reach the bottom of the canyon. If the length canyon is at least long enough to encompass the entire shadow, then my belief is that light can reach the floor as it does so at the point just past the shadow.
I set the date in Photo Pills to 6/21 and came up with the following times where the sun hits the floor: 11:58am, 12:21pm, 12:38pm, 12:08pm, 11:48am, 12:07pm.
For the September equinox 9/21, its a bit less rosy. There is maybe only one time when the beams are visible and its 11:31am, and even then I have doubt about it. This is because the canyon isn't long enough to support the much longer shadows that happen as a result of the sun being much lower in the sky.
You can check my work here:Photo Album of Photo Pills Screenshots
I do think that because the sun takes a similar path in the sky when its X days before or after the solstice, that it should be equally visible on those days, so I'm not sure why there seems to be a skew towards the months after the solstice (one of the websites says May through October).
All this really helped me identify which tours to go on. I was initially planning a 230pm tour which I cancelled. I then planned a 12:45pm tour. I think that is going to be too late. I need an 11am. A 10am tour may be too early if it ends before 1130am.
How does all this look?