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Anallematic horizontal sundial in parking lot

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klugesmith

Mon Mar 20 2017, 07:55AM

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

This stuff will have to be dribbled in, bit by bit. And some day consolidated.

The other day I finally made a plane-of-the-sky chart of sun position errors. My shadow modeling is all done in MS Excel spreadsheets. The foundation is a .xls file downloadable from NOAA, with self-contained formulas for solar ephemeris calculations. It's accurate within a few seconds of time over many years. It includes columns for computing apparent solar zenith angle and azimuth angle at any designated place on Earth surface.
NOAA_Solar_Calculations_year.xls from

[edit] The equations and coefficients are credited to Astronomical Algorithms, by Jean Meeus. [\edit]

For projects needing more accuracy, in pre-Internet days we would open a paper book full of tables, called the Astronomical Almanac, for the current year. Nowadays it's much easier. From the U.S. Naval Observatory data services page, we can generate tables with user-selected time periods and resolution. For the sundial application, go to

and select Geocentric Positions of Major Solar System Objects and Bright Stars:

Example output:

Sun                                   
                            Apparent Geocentric Positions                      
                     True Equator and Equinox of Date                     
     
   Date        Time          Right       Declination     Distance     Equation
        (UT1)              Ascension                                   of Time
             h  m   s     h  m   s         Â°  '   "         AU          m   s
2017 Mar 17 00:00:00.0   23 47 27.361   -  1 21 30.02   0.994963120   - 8 25.1
2017 Mar 18 00:00:00.0   23 51 06.547   -  0 57 47.01   0.995244208   - 8 07.7
2017 Mar 19 00:00:00.0   23 54 45.578   -  0 34 03.85   0.995527233   - 7 50.2
2017 Mar 20 00:00:00.0   23 58 24.473   -  0 10 20.87   0.995811896   - 7 32.5
2017 Mar 21 00:00:00.0    0 02 03.255   +  0 13 21.54   0.996097887   - 7 14.8

Dates must all be in the current calendar year, last year, or next year. 2015 is no longer accessible, but I saved a sun table for every day of that year at 20h UT (clock noon in my time zone). Year 2018 has been accessible for 2 1/2 months now, and I just appended its sun table to my comparison spreadsheet. Here is a chart of the discrepancy between the online USNO ephemeris and the self-contained formulas in spreadsheet from NOAA:

For a more intuitive view of the Declination and Equation of Time errors, we can chart them with respect to each other over the whole four-year data set. Red circle shows the average extent of the solar disk. At the same scale, black markers show the position error from using the NOAA formula. Other thin lines show the error, magnified by ten, year by year.

1489995446 2099 FT177676 Noaa Usno Diff Xy

Before finding the self-contained formulas, set up in spreadsheet cells by somebody else, I used tabular data from USNO and trivial interpolation formulas. A bit more accurate for matching field observations

. But for drawing sundials good for more than one year, those real irregularities interfere.

Those tables downloaded from USNO site are not the best in the world. I think a good way to get fancier would be to start with the Solar System Dynamics group at JPL.

Their work has been fundamental to deep-space-probe navigation for many decades.

Sulaiman

Mon Mar 20 2017, 04:48PM

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

I like the last figure, the error plots.

You may need a callibration device

klugesmith

Mon Feb 26 2018, 08:36AM

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

Hey, I'm finally striping some pavement, starting a couple weeks ago. The project has evolved from observation & modeling, to progressively more efficient ways to make stencils.

The two sides of each stencil are connected with bridges, one per day, with a wide one for day numbers that end in 1 or 6, and a whole-day gap between months.
Soon it will be time to add words like JANUARY and FEBRUARY. At the hardware store they sell sets of individual letters, die-cut in heavy paper. It would take at least two sets; a lot more if I want to assemble all 12 months at the same time. Anyone know an easier way? Want a laser-cutting project?

Also just took the opportunity to correct my misspelling of analemma in a couple of posts more than a year old. Please excuse a mnemonic which may be hard to unread or unremember: Anal Emma.

klugesmith

Thu Mar 08 2018, 07:09AM

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

The eastern arc runs close to the parking lot drain, and Tuesday morning I checked the ground slope with due diligence. Had marked approximate Y location of that curve, every 2 feet in X, based on known profile along the meridian. Then moved a laser level to each of those spots, and projected it to a fixed target set where meridian meets curb.

Marked each spot's height on paper, graphically recording a profile which could be measured later, and re-measured in case of a blunder with the numbers.

In the same session, re-measured part the meridian profile using different symbols, to fix the new east-arc profile with respect to a familiar reference.

Updating the Z profile in my spreadsheet moved the predicted day-mark locations slightly. Some as much as 1 or 2 cm, mostly in X (roughly parallel to the curve).
Then I cut my first stencil made from paper in a continuous roll. Did the section from x=34' to X-40', representing noon shadows between November 3 and November 19. The longest so far, and the first with paint in the color chosen for autumn months.

Sulaiman

Thu Mar 08 2018, 12:21PM

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

I'm glad to see that you are progressing,

I'd not considered the flatness of the car park,
mainly because the car park at my factory is concrete,
but thinking about it, even the concrete has a slight gradient for drainage.
annoying details.

just to put you on the spot;
How accurate do you now guesstimate your sundial will be ?

klugesmith

Tue Mar 20 2018, 05:25AM

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

Got a chance to check accuracy today, with only thin clouds in the sky after a solid week of rain. The Sun's ascent toward the equator has almost caught up with the extent of my green stripe. The view is from the north. Shadow, moving right to left, is supposed to cross the line an hour after noon (Pacific Daylight Time).

Also took the opportunity to extend the orange line by six feet, tying my previous record for longest stencil.

This part covers October 20 to November 2. Not sure why my pencil marks from 2 weeks ago are 4 mm east of today's measurements (and stencil placement).

Uspring

Tue Mar 20 2018, 11:47AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
Location:
Posts: 711

That's impressively accurate considering the suns size worth more than 10 min. Perhaps a gust of wind bent the lamp pole.

Possible is also uneven thermal expansion of the pole. An 8m iron pole of 10cm diameter will bend 3mm per degree temperature difference across it.

klugesmith

Wed May 09 2018, 06:03AM

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

Uspring: that unexplained discrepancy was between new and old pencil marks drawn _from_ spreadsheeted coordinates. Probably due to operator error.

Making stencils by hand was getting tedious, and the sun got a month ahead of my spray paint while I looked into laser-cut stencils. Need to get drawing in an appropriate file format, with vector coordinates automatically imported from spreadsheet.

Then, last week, electricians started replacing all the sodium vapor luminaires with LED units. I hope they have not accidentally moved my pole.

The new lights are smaller, but their arms bolted to the pole are thicker and extend higher than before. I think it will still be easy to identify the pole top in noon shadows, but maybe not so well in the oblique shadows that would touch sundial lines for 10h or 14h.

The work on "my" pole was finished an hour before shadow-on-meridian time, and I took a now-very-routine observation. Haven't yet compared it with the prediction. Three photographs, at least 30 s apart, with clock and shadow on a paper grid. A few minutes late in this case.

Then each image is viewed on computer screen, zoomed to actual size. Locating "top center" is facilitated by image editing tools like "magic wand" selection or posterizing, which are essential with faint and fuzzy winter shadows.

klugesmith

Sat Mar 30 2019, 10:45PM

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

This year I'm staying ahead of the sun. Let's see if inline image is too big.

Got custom-cut stencils for the names of the months, and numbers 6, 11, 16, 21, and 26.

February and March sections are already numbered at the 11th and 21st.

Hand-cutting the line stencils is measurably tedious. Yesterday I made one to extend line for 17 days, and it took about 1 hour: selecting day-marker shapes in Visio, typing XY coordinates and angles from Excel, printing, joining two 11 x 17 inch sheets, and cutting with x-acto knife and straight edge. Then it was too dark to place it and use it outdoors.

Looking for suggestions about practical ways to make vector graphic files, so I can finish the project using custom laser-cut stencils. It looks like generating .svg or .dxf files from scratch is manageable. General requirement: insert dozens of polygons (trapezoids) with computer-generated vertex locations. Not using much pointing, dragging, or clicking with mouse. That's why inkscape seems unpromising.

Is there any free drawing program that lets you 1) draw a polygon using nothing but keystrokes, and 2) execute drawing commands from a text file? Decades ago I would do that in Autocad.

klugesmith

Sun Mar 31 2019, 08:35PM

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

Yay! Just downloaded Draftsight Free (which is going to stop at the end of December 2019).
Very much like Autocad, and you can draw anything with command line entries.
Within an hour I had exported .svg and .dxf files from an initially blank drawing with these figures added:

POLYLINE
2,2
2,3
2.5,3.1
2.5,1.9
CLOSE
POLYLINE
1,2
1,3
1.5,3.1
1.5,1.9
CLOSE

Only complaint is against Microsoft. The draftsight/autocad script file had extension .scr.
Windows has a different use for that extension. When you browse to the file and want to open it with a text editor, Windows doesn't provide the right-click,Open-With option.

A whole generation has now grown up with the silly concept that a file's name extension dictates the program for that file. Guess that's OK, since Windows is for dummies.

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