Sundials & Backyard Astronomy: A Nerd’s Rant
I am a man of obsessions. Over the course of my entire life I have jumped from obsession to obsession for no apparent purpose, and with no clear pattern. Hence why my bookshelves often contain volumes on seemingly random and unrelated topics- codes & ciphers, national flags, oceanography, Elvis, nuclear weapons, boxing, chess. Music and astronomy are the only two obsessions that have stayed with me permanently. But whereas I have owned and played several musical instruments, it was not until recently that I started using astronomical instruments other than my telescope.
A few months ago, I finally made a purchase I’ve waited my life to make- a sundial. And not just any sundial, but an armillary sundial, my absolute favorite kind of sundial, thereby fulfilling yet another long obsession. There is something about being able to use tools like these to derive meaning from the motion of the Sun, or just simply to track it in my own backyard, that I find to be mind-blowingly amazing. Hence, why I have chosen to devote a whole blog article to something which is unrelated to music, but that I am nonetheless very passionate about and cannot help but share. In this post, I’ll give you the skinny on sundials- how they work, and what’s so great about the armillary variety.
A “traditional” sundial, or a horizontal sundial, makes use of a flat plate upon which the hours are marked, and an inclined gnomon (the term for the plane or “stick”) which casts a shadow onto the plate. An armillary, however, is a set of rings welded together which represent different lines on Earth’s surface and the celestial sphere, with a rod going through the center of the circle formed by each ring serving as the gnomon. Don’t worry, I’ll explain, but for now, take a look at the images below.
Horizontal sundial, at the Chapel Hill College of Nursing.
Image credit: John Carmichael, Wikimedia Commons
My armillary sundial.
As you can see, the armillary looks more like a bunch of brass rings randomly welded together, and perhaps could be mistaken for a weird piece of minimalist sculpture. But it is in fact a perfectly functional, and very old, piece of timekeeping equipment. This type of sundial was invented by the ancient Greeks, and was actually designed from the standpoint that the Earth is at the center of the universe. Imagine a miniature Earth suspended in the middle of the sundial, with the brass rod running from pole to pole. This is what the Greeks had in mind when they designed this type of timepiece. Although this way of thinking was of course overturned by Nicolaus Copernicus in the 16th century, the Greeks had nonetheless managed to create a very clever timepiece that, despite its antiquated scientific basis, is still functional and useful.
I promised I would show you how it functions. First of all, I will go over some of the basic principles of how sundials work, then show you what is unique about this particular type, the armillary.
All sundials are constructed with two important principles in mind:
The Sun moves, or traces out, 15 degrees of arc in the sky every hour. This makes sense if you think about the basic truth that it takes the Sun 24 hours to make a 360 degree circle around the Earth, giving us a complete day (of course, Earth is actually taking 24 hours to make a full rotation on its axis, but again, the Greeks thought differently). Dividing 360 by 24, then, yields a rate of 15 degrees per hour. On sundials, the numbers representing each hour are arranged in a circle at intervals of 15 degrees, reflecting the apparent motion of the Sun in the sky.
The gnomon (object which casts the time-telling shadow) must be inclined to an angle equal to the observer’s latitude. This is done to offset the oblique angle your line of latitude forms with the center of the Sun, essentially “equalizing” the sundial with the equator (this will make more sense in a moment). It is then pointed to true north (taking into account magnetic declination, which varies by location), bringing the gnomon parallel to Earth’s axis of rotation.
Here is a diagram of an armillary sundial.
Armillary diagram
1- Gnomon- a straight rod that is inclined to the observer’s latitude, and pointed true north (or directly at Polaris, the North Star). It casts the timekeeping shadow onto the number ring. Huntsville, where I currently live, is at about 34 degrees north latitude, so the gnomon of my sundial is inclined to a 34 degree angle with the ground. I used a protractor and a level to get this precise. The gnomon of an armillary (or any equatorial sundial) is parallel to Earth’s axis of rotation.
2- Equatorial ring (sometimes called the equinoctial)- this ring, the largest on the sundial, is where the numbers are printed. It is parallel to the celestial equator, or Earth’s equator projected into space, hence its name. Imagine again a mini-Earth suspended in the middle of this sundial, with the gnomon serving as Earth’s axis of rotation, running from pole to pole. The equatorial ring would be wrapped around the equator of this miniature Earth.
3- Local meridian- this ring represents your line of longitude. On a solstice, it represents the solstitial colure, a line on the celestial sphere that runs from pole to pole and passes through both solstice points (the points where the Sun is on the summer and winter solstices). Notice in the diagram that there is a larger shadow to the left of the gnomon’s shadow on the number ring; this is produced by the local meridian ring. These two shadows overlap at solar noon, which is when the Sun is at its highest point in the sky during the day, and due south (i.e. directly behind the sundial). This is shown in the bottom photo.
4- Equinoctial colure- not to be confused with the equatorial ring’s alternate name, this ring represents the line on the celestial sphere which runs from pole to pole and passes through both equinox points. It merely serves a representative function and does not cast any useful shadow pattern onto the sundial.
One important feature of sundials is that they show you local solar time, which is not always the same as clock time; in fact, it usually isn’t. For sundials, sunrise is at exactly 6 am, solar noon is 12 pm, and sunset is 6 pm. As noted above, solar noon happens when the Sun reaches its highest point in the sky during the day, and then begins to set. Clock time, however, is not dependent on the apparent motion of the Sun. This is because sunrise, solar noon, and sunset do not happen at the same time for everyone. For example, when the Sun peaks in the sky on a particular day for me in Huntsville, it has not yet peaked for those living to the west of me. It is still “traveling” from east to west,* so anyone to the west of me sees the Sun still moving towards its highest point in their own local skies. When it does finally peak for them, the Sun is already setting for me (meaning, beginning to move downwards in the sky, not actually already at sunset). Clock time, as I mentioned, is a standardized average that eliminates the need for all of us to rely on any fixed moment in the Sun’s apparent motion, giving us a time we can all agree on (time zone differences notwithstanding).
This leads me to the first important factor in explaining why your sundial doesn’t always reflect your clock time. Where time zones are concerned, the discrepancy between solar and clock time is also affected by how far away you live from the median longitude of your time zone. In plain English, time zones are formed around every 15 degrees of longitude (remember, the Sun moves 15 degrees per hour, hence the hour difference between zones). The median of your time zone is whichever of these lines of longitude happens to be in your time zone- for me, it is 90 degrees west, the median of the Central time zone. Noon for everyone in your time zone is when the Sun reaches its highest point in the sky over the median. If you live east of the median, solar noon will be earlier than clock noon; if you live to the west of it, solar noon will be later. This happens for the same reasons I listed in the previous paragraph- the Sun’s east-to-west motion across the sky. I live east of the Central time zone’s median, so my solar noon is earlier than clock noon.
The difference between solar time and clock time can be large, and confusing. In fact, the photo showing solar noon on my sundial above was taken on 11 July 2020, at 12:52 p.m. Why the large difference? Didn’t I just say my solar noon is earlier than clock noon? In the first place, Daylight Savings was active when the photo was taken, making it an hour later than normal. So, it was technically taken at 11:52 a.m. Sundials do not take Daylight Savings into account unless specifically designed to do so.
It doesn’t end here, however. There is one other important factor that needs to be taken into account to explain the difference- the equation of time (EoT). This tool, which applies to all sundials across the world, measures a few important factors that can further throw off sundial time relative to clock time by several minutes- namely, the eccentricity of Earth’s orbit (it is slightly elliptical instead of a perfect circle), and its axial tilt. So even for observers living on the median of a time zone, clocks and sundials will only exactly agree four times a year, and can disagree by as many as fifteen minutes depending on the time of year.
10:30 solar time, taken on 21 June 2020 at 11:19 a.m. Notice the dots on the number ring, underneath the numbers and midway between them. These are placed at 30 minute, or 7.5 degree, intervals.
The equation of time. The day of year is plotted on the horizontal x-axis, and the discrepancy between sundial and clock time is plotted in minutes on the vertical y-axis. For positive values on the y-axis, the sundial will run faster than clock time; for negative values, it will run slower.
Image credit: user:Drini, Wikimedia Commons, licensed under Creative Commons ShareAlike 2.5 Generic
Your head is probably spinning right now; I certainly understand if it is, because this concept still zaps my brain into mush sometimes. I will do my best to explain. Let me summarize the important points.
The Earth’s orbit is slightly eccentric, i.e. not a perfect circle, and its axial tilt is about 23.5 degrees relative to the ecliptic (i.e. the plane of the solar system). Don’t worry too much about what these mean- just understand that they throw off the time sundials would measure if Earth’s orbit was a perfect circle, and its axial tilt was zero. In that case, the equation of time graph would look like a straight line (and would run right along the x-axis since the time difference would always be zero).
The equation of time measures the discrepancy between the time sundials would show if Earth had no axial tilt and its orbit had no eccentricity. This hypothetical time is called mean solar time. (for clarification, sundials show local solar time.)
There are only four times during the year in which the equation of time yields a time difference of zero, meaning that local and mean solar time agree. The eccentricity of Earth’s orbit and its axial tilt have been compensated for. You can see these four times in the graph as the four points (to the right of the vertical axis) where the curve crosses the horizontal axis (y=0).
On these dates, an observer living on the median of a time zone will see the Sun reach its highest point in the sky at both local solar noon AND mean solar noon, AND clock noon. In other words, solar time and clock time agree precisely. (Again, all of this would happen every day if Earth’s orbital eccentricity and axial tilt were both zero.)
Most people do not live on a time zone median, however, so observers to the east and west of the median will observe agreement between local solar time and mean solar time, but still not clock time. This is because, once again, the Sun peaks later or earlier depending on your location relative to the time zone median.
Here’s how this applies to me, and how I can use it. Look on the graph and locate the point where the curve crosses with the x-axis just to the left of the number 180. This corresponds to about 12 June, the 164th day of the year in 2020 (not 163 since this is a leap year). On that day, according to the graph, the equation of time yields a difference of zero from mean solar time. If I lived on the median of my time zone, my sundial and my clocks would agree exactly, and solar noon would have happened at 12:00 local solar time, 12:00 mean solar time, and 12:00 clock time. For me, it happened at 11:46 a.m. clock time, fourteen minutes shy of perfect agreement. This reveals that 11:46 a.m. is my “zero point” for the equation of time. If Earth had no axial tilt and its orbit was a perfect circle, solar noon would be at 11:46 a.m. clock time every day. The equation of time, then, shows me how fast or slow my sundial will be relative to 11:46 a.m. throughout the year.
You can determine the EoT zero point for your own longitude without having to wait for solar noon on a day when EoT=0. Let’s say I did not know what my own zero point was. Here’s what I do know. First, the Sun moves across the sky at 15 degrees per hour, which comes out to 0.25 degrees per minute (15 divided by 60). Second, I know that at 12:00 clock time, the Sun will be directly overhead my time zone’s median, which is at 90 degrees west longitude. Huntsville is at about 86.5 degrees west longitude, meaning that there are 3.5 degrees on Earth’s surface between me and the Central median, and 3.5 degrees in the sky that the Sun must travel on its way to the median after it peaks for me. Since we determined that the Sun moves at 0.25 degrees per minute, all we have to do is some division- 3.5 degrees divided by 0.25 degrees per minute equals 14 minutes. This is the time difference between my solar noon and the median’s solar noon, and how long it will take the Sun to get from me to the median. Since I am to the east of the median, this means my solar noon will happen earlier than that of someone on the median, so I just subtract 14 minutes from 12:00 p.m. to get 11:46 a.m.
So, here is what I must do in order to convert what I see on my sundial to what time it actually is on my clocks. Let’s pick a random date- say, 10 August. I go outside to look at my sundial, and it shows 1:00 p.m. First, I will check the equation of time. Since 10 August is the 222nd day of the year (223rd in leap years), this means that my sundial, according to the graph, is running about 5 minutes slow, so we must add five minutes to our observed time. This brings our time to 1:05 p.m. Then, I must remember that, due to my longitude, I am fourteen minutes behind the time zone median, so I must subtract this from our current value of 1:05 p.m., yielding 12:51 p.m. Only one last step remains: I must add an hour since Daylight Savings is active in August (this step is of course unnecessary in the winter months). This means that the current clock time is 1:51 p.m.
I am sure you are thinking: good grief John, what possible fun are sundials if I have to go through all of that Mickey Mouse hocus-pocus just to tell what time it is?
Well, that’s part of the reason I like armillary sundials- they’re not only useful for telling time, but they can also mark the passing of the seasons. Let me show you something really cool.
Just a few days ago, it was the autumnal equinox, or first day of fall (for us in the northern hemisphere, of course). In case you don’t know exactly what happens on an equinox, let me explain.
As you probably know already, seasonal change happens because of Earth’s tilt relative to the Sun. On the first day of summer, the northern hemisphere is tilted to its maximum degree towards the Sun, and is receiving the most direct sunlight. When this happens, the Sun is directly above the Tropic of Cancer. On the first day of winter, the opposite happens- the northern hemisphere is tilted at its maximum degree away from the Sun, which is directly above the Tropic of Capricorn. In between these two events are the spring and fall equinoxes- Earth is tilted so that both hemispheres receive the same amount of sunlight, and the Sun is directly above the equator.
For you and me, we see the Sun at its highest point in the sky all year on the summer solstice, at solar noon. Then, it gets lower and lower in the sky and the days get shorter as it approaches its lowest point on the winter solstice. On an equinox, day and night are of (roughly) equal length; at least, as close to equal as they get all year. If you have an armillary sundial, and you’ve set it up correctly, you’ll see something amazing on it if you check it on an equinox.
Remember when I said that the equatorial ring of an armillary sundial is parallel to Earth’s equator and the celestial equator? That’s very important here. Remember also the fact I just mentioned- that on an equinox, the Sun is directly above the equator. This means that on an equinox, the Sun’s path in the sky is directly above the equatorial ring of the sundial. And when that happens, it casts a shadow that covers up the whole number ring. Check out the photo below.
The 2020 autumnal equinox, on 22 September, as shown on my armillary sundial. The inside of the equatorial ring, including the numbers, are in complete shadow, because the Sun is directly overhead Earth’s equator and hence directly behind the sundial’s equatorial ring. When I took this photo, I was evidently too excited to notice the result of one particular bird’s contempt towards my quest for scientific erudition. I suspect the bird was a flat-earther, because this sundial would not work on a flat Earth.
Imagine once more that miniature Earth suspended inside the sundial rings, the equatorial ring wrapped around its equator and the gnomon running from pole to pole. This mini-Earth is positioned exactly as the real Earth is in space. On the real Earth, if you are standing on the equator on the day of an equinox, the Sun is directly overhead, 90 degrees up, at your zenith. The same is true of our miniature Earth. This is why the armillary is such a powerful and fascinating tool. It is essentially an accurate representation of the entire Earth that you can put in your own backyard. The Sun moves the exact same way relative to the sundial that it does to Earth as a whole.
I hope I have not bored you, dear reader. But if you have made it to the end, thank you for putting up with this little nerd-rant of mine. As I said, I am a man of obsessions, and sometimes I cannot help but share things I am passionate about. If you are interested in armillary sundials, the kind that I have is produced by a brand called Good Directions, and it is sold on Amazon. There are also metallurgists who can custom-make them to work at your location, but these can be extremely expensive. Alternatively, there is a man on YouTube (with a wonderful ASMR voice, by the way) who has a video which explains how to make an inexpensive homemade armillary, along with visualizations (including the suspended mini-Earth) which can help you better understand how an armillary works. I highly recommend it.
Thank you for reading, and as Neil DeGrasse Tyson says, keep looking up.
John J. South
*The Earth is, of course, rotating from west to east, which is what creates this effect, although once again the Greeks thought the Earth was stationary. I thought a footnote would help avoid confusion.
Helpful links:
The North American Sundial Society’s website has an informative page on armillary sundials, including a diagram of a much more complex one than mine: https://sundials.org/index.php/teachers-corner/sundial-construction/200-armillary-sundial.html
Info about time zones, medians, etc: https://www.flightliteracy.com/latitude-and-longitude-meridians-and-parallels-part-one/
Calculate your local solar time, or convert local solar time back to clock time: https://koch-tcm.ch/en/uhrzeit-sonnenzeit-rechner/
