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My homeschoolers are studying the sun & time. We have set up a fence post to create a shadow and we are using it with experiments I found on the web to track the sun.

What we cannot find is information on how to reference points on a sundial other than solar noon. What are the other points of time on the sundial called? We purchased the sundial below. Roman numerals aside, the sundial has clear markings on it for various times. However, it does not appear to match a clock face as it has 17 reference points, not the expected 12.

Not being able to read the sundial face is proving frustrating. For instance, my little experimenters want see the difference a tracked shadow makes taken at the same watch-time vs. the same solar time.

So I am looking for how to properly read and reference the points of time on a sundial face. For example, let us say the shadow is pointing to the position I have drawn. What "sundial" time is that.

![enter image description here

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    $\begingroup$ Did you get any instructions with this sundial? Do you have a link for the website of the place you bought it, or the manufacturer? It's hard to tell from the angle of the photo, but it looks like the hour angles are spaced equally, which implies it's a kind of equatorial sundial, and you need to set the angle of the dial plate appropriate for your latitude. OTOH, the gnomon of that dial isn't correct for an equatorial dial, it's more appropriate for a horizontal dial. So it's a bit confusing... $\endgroup$
    – PM 2Ring
    Nov 17 '20 at 2:09
  • $\begingroup$ FWIW, that Wikipedia article on sundials is quite good. There's a section that explains how to convert from sundial time (local apparent solar time) to standard time. You need to compensate for the difference between your longitude and the standard longitude of your time zone. You also need to adjust for the Equation of Time. Eg, at this time of year you need to add ~15 minutes to the sundial time to get local mean time. $\endgroup$
    – PM 2Ring
    Nov 17 '20 at 2:33
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    $\begingroup$ My favourite piece of whimsical sundial terminology is that coined by Lewis Carroll: A "wabe" is the grassy area that surrounds a sundial. (because it goes a long wabefore it and a long wabehind it) $\endgroup$
    – James K
    Nov 17 '20 at 19:17
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In principle this sundial is designed be used this way:

  1. Use the built-in compass to align the XII hour mark with geographic north. Look up the magnetic declination for your area to see how this differs from magnetic north.

  2. Use the hinge below the XII mark to tilt the dial for your latitude as indicated on the vertical protractor. The gnomon's angle above horizontal should equal your latitude.

annotated picture of hinged brass compass-sundial

  1. The hour marks nearest the shadow of the gnomon indicate apparent solar time. For example, the IX in the northwest quarter of the dial is 9 AM; the III in the northeast quarter is 3 PM. Apply the equation of time to convert this to mean solar time, e.g. in mid November subtract 15 minutes from apparent solar time.

  2. Civil time usually corresponds to mean solar time for a nearby multiple of 15° longitude; local mean solar time differs by 4 minutes per degree. For example, if you are in the US Eastern time zone (based on 75° W) and your longitude is 80° W, add 20 minutes to your mean solar time to get EST. Add 1 hour for daylight/summer time if applicable.

In practice the maker of this sundial seems to have prioritized aesthetics over accuracy. Hour marks should radiate from the base of the gnomon, but these radiate from the center of the dial. If your students are sufficiently motivated, they could make a more accurate sundial themselves as a follow-up project. An equatorial dial would not require any trigonometry, only a protractor.

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    $\begingroup$ There are various graphical construction techniques that don't require much trigonometry. Although if you want to understand how those constructions work, trig is certainly helpful. ;) $\endgroup$
    – PM 2Ring
    Nov 17 '20 at 15:57
  • $\begingroup$ Wouldn't you know I would buy the 1 sundial on the planet whose markings made no sense. Off to buy another one. This time I will make sure the markings make sense as we actually want to use it. $\endgroup$
    – Bookaholic
    Nov 19 '20 at 1:50
  • $\begingroup$ @Bookaholic Other sundials won't necessarily make more sense. Items 3 and 4 in this answer apply to any sundial. $\endgroup$
    – Mike G
    Nov 19 '20 at 2:02
  • $\begingroup$ @Bookaholic sundials.org has a good sundial pattern, just print the page for your latitude and follow the instructions. $\endgroup$
    – Mike G
    Nov 19 '20 at 14:42
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The "stick" that casts a shadow is called a "gnomon"

The gnomon should point at the celestial North pole (and so is angled at about 45 degrees for most people in temperate climates, or more precisely it is angled by your local Latitude. So if you are Scotland at 55 degrees North, you should angle the gnomon at 55 degrees to the horizontal.)

If your dial is perpendicular to the gnomon then you mark the hours at equal angles, since the sun moves at about 15 degrees per hour around the Pole star, you mark one hour every 15 degrees. This forms an equatorial sundial. That is simple but now, since your dial is parallel to the equator, you won't get any shadow when the sun is south of the equator.

So usually the dial is laid horizontally with the angles projected from a perpendicular dial to a horizontal one. The angles between the hours are now variable,according to trigonometry $$\tan H_H = \sin L \tan(15^{\circ} \times t)$$ where $L$ is the sundial's geographical latitude (and the angle the gnomon makes with the dial plate), $H_H$ is the angle between a given hour-line and the noon hour-line (which always points towards true North) on the plane, and $t$ is the number of hours before or after noon.

The sun moves once around the pole star every day, so you would expect 24 divisions of time. However it is rather pointless to mark the position of the shadow after sunset, so most sundials don't mark all 24 hours. Since the dial is not in the same plane as the equator, the angles between the hours are not all equal, due to the projection.

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