Sunset Down the Channel

Sunset Down the Channel 2023

David Roseman


David Roseman 2002


Will Wright 2016

In 2002 the Pentwater Yacht Club began celebrating the evenings when the sun sets down the center of the channel. This, of course, happens twice a year, in May and August. The date is predicted by using 293.6 as the true bearing of the channel, and by using the US Naval Observatory data for altitude and azimuth. The chosen date is the one when the altitude of the sun approximates 0 and the azimuth is closest to 293.6.

I use latitude = 43.779 and longitude = -86.434. In the past, I've used 0.0 degrees as the target altitude. However, because of refraction by the earth's atmosphere, the apparent sunset occurs when the sun is below the horizon. This varies slightly by such factors as temperature, but -0.833 degrees seems best. [This is included in the NOAA formulas.]

The correct viewing location is important--the center of the channel projects to about the Chesney boathouse. A discussion of parallax is here.

NOAA has a nice application, with the advantage that it projects the sunset (and sunrise) on an ESRI map.

For example,



Here are the tabular data:

Date Time Azimuth Day
May 4, 2023 20:50 293.23 Thursday
May 5,2023 20:51 293.62 Friday
May 6,2023 20:52 293.9 Saturday
August 4, 2023 20:50 293.2 Friday
August 5, 2023> 20:51 293.6 Saturday
August 6, 2023 20:52 293.9 Sunday


The closest dates this year are May 4 and August 7. The official dates will be determined by the Commodore. [This is a bit like the Church determining the date for Easter.

Easter is the Sunday after the Paschal full moon, which is approximately the first full moon after the Vernal Equinox. The Paschal full moon is determined by the Church, however, and may not coincide with the actual full moon. See this for more detail.].

The first time I went through all of this (2002), I attended 10 AM coffee at the Pointe Wine and Deli. The subject came up, and Murph Schader said "Of course it's August 6. The sun always sets down the middle of the channel on that date."

Note that the May date and the August date are the same number of days from the Summer solstice. This seems pretty reasonable.

Another source of sunset/sunrise info was provided by Mike LaHaye.

I had hoped to write a Tcl/Tk application to automate these calculatons for the future. I still may do this, but it isn't getting any easier. One problem is that I don't have a background in spherical trigonometry. Karl Dahlke is an old friend who has a MS in math from the U of California. He is a superb programmer, so I asked for help. Karl has been blind since childhood, which makes his visualization even more humbling. Here is the program that he wrote, with his explanations. The PERL version is here.
When Dick Ouweneel checked the data in 2002, he found that the sun set at 19:51 on May 5, and 20:00 on August 6. Why the difference in time? This led to an interchange between Dick Ouweneel and his friend Bill Brandenburg. Here is the exchange.

Dave,

It's relax and enjoy time.

A few days ago I finally got around to sending the "sun observation timing dilemma" to the friend who can and did get in to this. The following are his words from a just-received email. I do remember that in the analemma's figure-eight pattern, the lower portion is larger than the top portion. Hold that image.

May I introduce Bill Brandenburg. Dave, Bill, Bill, Dave.

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The Earth's orbit around the Sun is an ellipse (not a circle) and the earth's axis-of-rotation is tilted approx 23.5 degrees to the plane of that orbit. (The Earth is nearest the Sun in Jan and farthest away in Jul). And a "year" is just a bit more than 365.24 days. All of these lead to the Sun being slow, compared with the time on your accurate wrist-watch, from late Dec thru mid-Apr and mid-Jun thru late Aug, and fast from mid-Apr thru mid-Jun and late-Aug thru late-Dec. (Remember the figure 8 -- the analemma -- on world maps and globes). Although your 5/5 observation was about 46 days before the Summer Solstice, and your 8/6 one will be about 46 days after, 5/5 was when your watch was behind the Sun and 8/6 will be when the Sun is behind your watch. (Let's ignore the atmospheric refraction that causes the "apparent" time of sunset to differ slightly from the "actual" time). I haven't (probably can't anymore) "done the calculation", but interpolating an analemma (see, what else, www.analemma.com), it looks to me like the Sun was about 3 minutes ahead of your watch on 5/5, and will be maybe 5 minutes behind on 8/6; so, considering only the analemma, I'd guess that the 8/6 event might be 8 minutes later than that on 5/5. If the difference is actually only 3 minutes, there's probably something significant that I'm not considering (relativity?). Like hops in a Bell, we probably ought to nail down the projected vs actual and the reasons for the differences.

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I should add that the "Bell" which Bill referred to is Bell's beer of Kalamazoo, such as the Oberon served at the PYC. Bill and I had a recent exchange on this subject and he is responding in the above context. As I find new beers, I send Bill a geometric figure which describes the beer to Bill. It is a language that has taken many years and other units of research to develop, but the effort has been rewarding to date and will definitely be funded in the future.

Regards,

Dick Ouweneel
Bill Brandenberg also pointed to an interesting discussion of Flatland. It makes it nice that we live in a 3 dimensional (or is it 11 dimensional) world. .

There is an interesting and educational applet here.
Parallax. It all depends on your viewpoint. Some people have complained that the sun didn't really set down the center of the channel when, for example, they were standing near the door from the dining room to the docks. The "problem" is that the sun is so far away that, for practical purposes, its distance is infinite. This means that if 2 observers simultaneously sight down the north and south channel piers, both will get the same bearing to the sun. The center of the channel projects to a location on the South docks, near Chesney's boat house.

This explanation may help.

Past information.