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I am considering small "artsy" project. I would like to create sundial by placing gnomon on the window and painting hour lines on the window facing wall.

Since this is to be placed in bedroom I am constrained by my geographic location, wall, window placement and orientation. The esthetic and size (I have one wall only) of the project is gating factor (otherwise known as "the wife" factor).

Due to above I am perfectly OK with the fact that this sundial will "work" by limited time of the day and even limited time of the year. However whenever it will work (that is the shadow of the gnomon will be cast on the "said" wall) I would like it to be as accurate as possible.

Also all of the above make the calculations for creating hour lines quite challenging (at least for me) and to be honest I do not know where to start.

Could you point me the resources that would help in calculating hour lines (software, tutorials, books, math equations)?
Could you describe how would you approach the task of calculating hour lines?

(Resources that are little heavy on math side are OK for me. I am also capable of wring software on my own.)

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The empirical method is likely to be the most practical (and probably the most fun). If you want a good reference, I suggest Sundials: Their Theory and Construction by Albert Waugh. –  EHN Aug 9 '11 at 0:19
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2 Answers 2

up vote 11 down vote accepted

I believe the easiest way to do this would be empirical, rather than theoretical- Just mark out each hour, all day. It would be especially fascinating if you did this, say, every Saturday, starting with the upcoming Summer Solstice. The artistic possibilities are endless as well... different symbols, colors, outlines, etc., for different times of the year, day, ambient temperature, etc.

But if you really wanted to do a theoretical prediction, here are the steps.

  1. The Sun is at 0 RA, 0 DEC on the Vernal Equinox. Its DEC increases nearly linearly at 360 degrees/365.25 days. The RA is sinusoidal with an amplitude of 23.5 degrees. 1b. OR just get the Sun's sky position from a table or chart.

  2. Use spherical trigonometry to transform the RA and DEC chart you made in step 1 into its ALT and AZ coordinates for your geographic location and particular times of day. 2b. OR skip all previous steps and just get the ALT-AZ coordinates from some planetarium software (Starry Night, with which I taught an astronomy course for six or seven years, will do this, but it's commercial software. There are other, free packages out there.)

  3. Use regular trigonometry to figure out where the line from the Sun's predicted positions to the tip of the gnomon will intersect the plane of your wall. This will depend on your room's geometry, of course. Basically, if the Sun were at 29 degrees ALT, you would project a line downwards from the tip at 29 degrees. If its AZ were 1 degree East of the meridian (line from North to South), you would run the projecting line at a heading of 1 degree W of North. Hopefully your projection wall runs due East and West, or this will get really ugly. Definitely need a spreadsheet or algorithm to do this for you, if you had any interest in doing a large number of hour lines.

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+1 on the empirical method. If you're going to actually try to calulate it, use a chart of solar positions as the Sun does not move the same amount each day since the earth's orbit is elliptical and not spherical. –  dagorym Jun 12 '11 at 15:37
    
Of course, but I thought the difference would be negligible for a sundial. I really only included all the theory to show what a good idea the empirical method was. PS On the draft, my comment is nicely spaced and logically numbered, but the website has enabled some kind of auto-formatting script makes it all screwy and I don't have any control over that. It's supposed to be "3. Use regular trig..." –  Andrew Jun 12 '11 at 18:38
    
I fixed the list for you. You were using 1a. and 2a. which aren't recognized as list numbers by the formatter. When you used 3., it recognized that as a list number and started a list. Since you had no other numbers before that as far as the formatter was concerned, it just started it at 1 for you. –  Carson Myers Jun 14 '11 at 2:10
    
The error due to the eccentricity of the earth's orbit is sufficient (up to 15 minutes each way) to need taking into account for any serious sundial - see mb-soft.com/public3/equatime.html for a detailed treatment and calculation. ) –  Floris Jul 8 at 19:42
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Look at this web page, it makes something similar to what you are looking for, http://sundial.damia.net

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