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Anallematic horizontal sundial in parking lot

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klugesmith

Mon Aug 22 2016, 05:57AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

I'm almost ready to paint some anallemas on a parking lot at work, so people can tell time (or even set their watches) by the shadow of a lamp-post about 26 feet (8 meters) tall.

Have been marking the shadow end at various dates and times, and fitting a spreadsheet model to it.

It's popular to annotate anallemas with the associated months and, sometimes, days. I want to have marks about every 10 days, probably days 1, 11, and 21 of each month. Most equation-of-time references use the average over some number of ordinary years and leap years. Here's a chart showing the sun's position along the ecliptic, and shadow's position on a painted anallema, around the February/March transition for several years.

Unless someone has a better idea, I will use the average of 2017, 2018, 2019, and 2020 -- shown with green line. I think an Excel charting bug makes the marker average for Feb.29 not exactly line up with that for Feb.29, 2020.

Sulaiman

Mon Aug 22 2016, 07:15AM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

based on similar thoughts;

. cars park on and drive over the paint daily

. try to determine how long the lamp post will be as-is,

it would be annoying if the lamp post was made taller or shorter just after your masterpiece is finished

(e.g. last year, where I work, entire lamp posts were swapped-out for LED lamps )

. how will you get your computer generated precision drawing onto the car park with watch-setting accuracy ?

as a start, each day you could put one or more marks on the car park at key times (e.g. noon, go home ...) which should over the year form nicee lines.

klugesmith

Thu Aug 25 2016, 06:47AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Thanks for the cautionary words, Sulaiman. The lot was re-sealed early this year, for the first time since 2008, so the surface ought to be around for a while.
Here's the venue:

My field methods, during brief outings a few times each week, have been evolving since April.

Initially: wait for some exact hour, such as 13:00, and make a chalk mark where the pole shadow ends. If wristwatch is known to be 6 seconds behind, then make the mark when 12:59:54 is indicated. The watch-error hassle went away when I got a portable radio-controlled clock. About the same time as I found out how my analog-dial watch could be losing 5 to 10 seconds per day. On occasion, a wrist motion would unintentionally press the watch stem, thus turn on the EL backlight. Battery was so low that motor didn't step when backlight was on.

Marks made with crayon or colored pencil withstand rain better than ones made with chalk.

Exact location of the shadow (center of umbra) is still rather subjective. For more accuracy, I started marking the shadow location at a few arbitrary times shortly before and after the target time. For interpolation, mark the predicted spacing of actual and target times on a strip of paper, and fit it by eye to the chalk marks.

Instead of trying to read the clock and mark the shadow at the same time, one can make the mark 10 or 20 seconds ahead of the shadow, then note the time when shadow is centered on mark.

Finally, as of Monday this week, I started taking a photograph that shows clock time, shadow, and reference marks all at the same time. Duh! Here getting a data point for the exact ground location of lamp-post-top meridian.

Image-processing tools like posterizing, and/or magic wand selector, can take much of the guesswork out of pinpointing the shadow tip. When the shadow is substantially oblique to the square post, I've been marking the shadow of post's corner instead of the middle of its north edge.

WaveRider

Thu Aug 25 2016, 01:17PM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

Interesting fun field project! If you want watch setting accuracy, you might be inspired by this "sundial" found here in Belgium!

Sulaiman

Thu Aug 25 2016, 03:31PM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

I see minor divisions of 5 minutes,
even with interpolation hardly watch-setting accuracy.

The car park / lamp post will have much greater precision due to the length of the shadow path.

klugesmith

Thu Aug 25 2016, 11:44PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Phase 1 is to mark a single analemma, for noon on the clock ( 1 pm when Daylight Savings Time is in effect).

Please review this preliminary (and incomplete) rendering of a plan to segment and color the curve. I finally got a thumbnail image to appear inline, by uploading a snip which is much less elongated than the whole picture.

]anotherv.jpg[/file]
]visio-analem_breaks.pdf[/file]

The horizontal line represents the local meridian just north of the lamp post. It's marked in units of post height. Vertical dashed line is where equatorial plane of post top intersects the ground. Each month is drawn in 3 segments, connecting days 1-10, 11-20, and 21-final.
Two June segments are drawn "curved" using three sub-segments. Entry would be much less tedious if I knew how to draw stuff in Visio from a command file instead of manually entering numbers in GUI size-and-position window.

klugesmith

Tue Nov 29 2016, 03:55AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Glad to report my first paint on pavement. Last Friday was dry but cloudy, and was a company holiday. I marked the meridian line with white spray paint. A movable stencil was two strips of sheet metal placed 1/4 inch apart. The line is surprisingly obvious even from far away.

Actually it's the "working meridian" line established with colored pencil and crayon marks, months ago. Part of a grid used to measure the locations of actual shadow marks. Grid errors can go into my spreadsheet model to reconcile measured shadow coordinates with theoretical ones.

Two much bigger corrections need to go into the spreadsheet: the non-level ground and the finite apparent solar diameter. It was evident in spring and summer that the most repeatable, least subjective "end" of lamp-post shadow is where the umbra meets penumbra.

Trouble is, now that shadows are long and sundial play time is short, I think the umbra tapers to nothing. From the more distant vantage point, angular width of the square post top might be less than angular width of the sun (which is approaching the big end of its 3.3% seasonal variation).

klugesmith

Wed Nov 30 2016, 03:43AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Today I tested a new and very precise way to track a fuzzy shadow, while shadow moves eastward at a slow snail's pace (2.5 inches per minute).

Here's a simulated azimuth-altitude view, looking toward the sun at the moment it crossed the celestial meridian today, from the shadow-end at ground level.
Model includes the top 10 inches of the 5-inch square lamp post, and includes today's angular width of the sun.
The precise viewpoint is on the ground meridian, at the distance where upper limb of sun is tangent to the shadow-casting edge.

Materials:
1. thin, flat glass mirror about 3/4" square.
2. Shade 10 welder's glass, appropriate for looking at the solar disk.

Put mirror on the ground, with one edge propped up so it tilts toward the sun.
Look down at the mirror, through the welder's glass.
Move head until reflection of solar disk is centered in the mirror.
Wait for post-top and solar disk to align as shown, note the time and mark the mirror location.
Repeat, moving mirror eastward each time. Adjust the north-south position if sun passed too high or too low last time.

Sulaiman

Wed Nov 30 2016, 08:59AM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

would it be better to mount either a sphere or a rod gnomon parallel to Earth's axis on top of the lamp post ?

klugesmith

Fri Mar 17 2017, 09:02PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Yes, it'd be simpler if we looked at the shadow of a ball. But I'm not equipped to climb the pole!

The project is still alive, after a winter hiatus while the shadow extended into planted area north of the pavement.
Before that, the scope had been narrowed to a single analemma for clock noon, Standard time.

It came back, fancier and more precise than ever before, beginning with observations on January 13.
The methodology using small mirror at ground level, and welders' glass, has evolved substantially.
Brief little eclipses (annular or total) were tracked from positions measured to the millimeter,
in a vague shadow zone with no umbra. Even through thin clouds, if disk of sun was visible.
It was immediately clear that the model needed to include a correction for cross-slope (east to west).

No time today for a full write-up, so I'll post a composite picture showing a Google aircraft image, a new reference grid with semi-permanent corner marks on the pavement, and the proposed analemmas. The venue is close to ideal.

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