Greetings to any of you who have found me as a result of the Astronomer’s Workbench article in Sky & Telescope. As the article in question was limited in length, I wanted to take this opportunity to expound more on my project as the quadrant is only a small portion of a much larger project as well as answer some questions I expect you may have.
What is the SCA?
The SCA is a medieval recreation organization that spans the entire US and Canada and has a presence in many other countries. It was started in $1966$ in Berkley, CA as a backyard party, but they had so much fun with it, it just kept growing.
Unlike a renaissance faire, which is done as a performance that attendees view from the outside, the SCA is all about learning by doing and being an active participant. This means that if there is a trade or skill that was done in the period we cover1, there is likely someone doing it in the SCA. This covers everything from clothing to combat to cooking. To my knowledge, I’m the only person doing anything quite like this.
The SCA is organized into kingdoms, which cover several states, as well as smaller groups which are usually aligned with cities. For example, I live in the Barony of Three Rivers which is St. Louis, MO, and is within the kingdom of Calontir which is Missouri, Iowa, Nebraska, Kansas, and the northwest corner of Arkansas.
Each kingdom is presided over by sovereigns chosen by right of arms and while somewhat ceremonial, sovereigns do have the ability to bestow awards and titles in recognition of achievements within the group. For example, I am a member of the order of the Leather Mallet which was given for my work in astronomy – a science. I’m also a member of the order of the Golden Swan for my bardic skills and costuming which are considered arts, as well as the order of the Torse which is bestowed for service. Generally these awards vary by kingdom although the highest levels are always the same.
On a regular basis, local groups will hold local meetings, often for specific purposes, such as fighter practice or an archery night. But at other times, groups will hold larger events which draw attendees from a wider region. The largest events, wars, can draw participants internationally. The biggest of these can have several thousand attendees.
How long have you been involved in the SCA?
I started in the SCA sometime around 1998. Mostly because the Star Wars prequels were getting ready to come out and this seemed like the closest thing to lightsaber fighting I could find at the time. I have taken several breaks during that time period for college, jobs, etc… but have been heavily involved for the past six years.
What got you interested in medieval astronomy?
I have always been interested in astronomy in general. So much so that I have a Bachelors of Science in the field. However, for a long time I did not think that there was much that could be done with medieval astronomy as the general story was that there was the Ptolemaic geocentric model, nothing for ~1500 years, and then the Renaissance happened and it was replaced by the heliocentric model. What got me to really start reconsidering this was encountering an image of an astronomical toolkit like the one below.
This got me wondering how it would be used. Although not well shown here, you can see there is a set of tables in the back compartment of the panel. This would tell the position of planets in the sky or other useful astronomical data, but how did astronomers of the time mathematically work this out? I wanted to know so I could produce my own tables following period methods. Learning by doing.
What is the overall project?
The end goal of my project is to be able to create the sort of planetary prediction tables that would be featured in such a toolkit. But this is easier said than done and necessitates other steps to achieve. The first reason is that the tables are built from mathematical models which are in turn, built on observations. So while understanding the models is important, I also decided that I’d like to use my own observations on instruments similar to those used in period as opposed to getting the necessary data from Stellarium or other modern tools. This is what led to the construction of the quadrant.
But it turned out that understanding the models was much more challenging than I anticipated. I had immediately honed in on Kepler’s work since I already knew that his heliocentric model was essentially right. But when I sat down to try to read through his Astronomia Nova it only took me a few chapters before I was unable to follow2 – The context in which he was working was fundamentally different than how we think of astronomy today.
As such, before trying to understand Kepler, I knew I’d need to firmly ground myself in the astronomical thinking of the day which was still largely based on Ptolemy’s Almagest. I first started on that work in May 2018 and after nearly three years of work, I am barely one third of the way through.
Once I finish the Almagest, I will continue working towards Kepler chronologically: I have a few books in my library regarding the Islamic golden era of astronomy (which aren’t nearly as technical), then Copernicus and finally Kepler.
In the meantime, the quadrant sees a fair amount of use, but not directly to this end. While the positions of the planets will be useful for the model in the end, astronomers actually made use of very few observations to set the models. Instead, I mostly use the quadrant to record stellar positions. The quadrant takes measurements in Altitude and Azimuth, so these get converted to RA-Dec to map out as a side goal will be to create star maps similar to John Bayer’s $1603$ Uranometria which was based on Tycho Brahe’s data. In addition, converting lets me compare against the true vales to understand how accurate the quadrant really is.
How do you actually use the instrument?
The idea of this instrument is dead simple. It measures two things: How high above the horizon an object is, and where along the horizon it is. This is known as the altitude and azimuth respectively.
To sight an object, I simply look down the straight edge of the quadrant arm (that reddish orange part). It is fitted with a pair of metal posts that has a “v” shape cut into them – one nearer to my eye and one at the other end. The idea being that if I looked from the near one to the far one and the star rested in the bottom of both v’s, it was aligned. Essentially the same as a basic rifle sight.
However, this is challenging because in the dark, you can’t see those sights. As such, we use red headlamps and will flip them on and off to get a good alignment. Yes, this is obviously a modern solution, but they certainly would have used candles in period3. Alternatively, I’ve had the best success ignoring the sights all together and placing my eye level with the near end of the quadrant arm. That near end will be out of focus to my eye and appears as a fuzzy band. I can then move the arm up and down, keeping my eye at the right position until the star winks out behind the far end. At that point, I know the altitude is aligned well. I still have to use the sights for the azimuth though.
For the azimuth, the ring must be set each night. So as I start each observing session, I first find the north star, point the quadrant at it as if I were taking a reading, and then wherever the pointer is, I rotate the ring to $0º$. While the north star isn’t perfectly north as it rotates around the north celestial pole with a radius of about $0.85º$, it’s good enough to get set up and if the alignment is particularly bad due to this, I can simply apply a mathematical correction as I process the data, adjusting for how far off north we were due to the Polaris not being due north.
How do you know what you’re pointing at?
In period, stars were often described by where they were in the constellation. For example, “Orion’s right shoulder” would be Betelgeuse. This is painfully cumbersome, so I use the Bayer designation which is the one that sounds like “Alpha Orionis”. Interestingly, this designation system started in John Bayer’s Uranometria, from $1603$ and used Brahe’s data.
When actually observing, I don’t really worry about any such things. Rather, I have a printout from Stellarium, and I will simply number the stars as I observe them, and figure out what they were later.
How do you transport the quadrant?
One of the reasons that I chose the great quadrant from the many instruments Brahe featured in his Astronomiae Instauratae Mechanica, was that it was something that I immediately saw how it could be disassembled for transport.
The bottom of the base has holes in the corners where the legs simply drop in. When it was first built, these fit quite tightly and so each was actually numbered so it would fit well. The wood has worn in the past few years so it’s not as important which leg goes in which hole. Once the legs are inserted, the top with the azimuth ring is placed on.
The center column is fitting a square peg in a round hole, so it has a collar that slides on. This collar also has the azimuth pointer. Once the column is inserted, the quadrant arm is placed on it.
Here is a video showing the setup process:
The whole set-up process generally takes about 10 minutes. The most tedious part is leveling the instrument which is done with a set of screws near the corners which you can see me adjusting near the end.
And here’s how it all fits in my car:
Not shown is the legs: They just go in the back seat well and tend to live in my car. It’s hard to catch, but before inserting the center column, I place a towel across my dashboard where it will rest, to keep it from scratching anything.
How accurate is the instrument?
There’s a few different ways to answer that. The first is simply assuming ideal circumstances and is essentially the division on the scale. The altitude scale measures in tenths of a degree and it’s quite easy to see when the wire is hanging between two increments. As such, it can be read to $\frac{1}{20}º$ or $3$ arcminutes. In the article, it mentioned that Tycho boasted his instruments were accurate to $\frac{1}{6}$ of one minute of arc and this is where he came up with that number. Modern reviews of his data have shown this was a generous estimate as his best ones were only accurate to about $\frac{4}{6}$ of a minute of arc. Human error and all that.
Second, I can compare against the true position of the stars once converted to right-ascension and declination which I can look up from modern sources. If I do and average the results for the ~$850$ observations to date, I average about $12$ minutes high in right-ascension (which is $\frac{1}{5}º$) and $0.04º$ low in declination.
Lastly, we can talk about the scatter in those comparisons against the true values by looking at the standard deviations of the individual errors. While the average is only $12$ minutes high in right-ascension, there is a lot of scatter and one standard deviation is $0.74º$. In other words, I’m about $68$% sure that my answer falls within $0.74º$ of the average. For declination, the standard deviation is a bit better at $0.44º$.
This is a bit biased because if an observation is really bad4, I throw it out. This occasionally happens in crowded fields of stars where I simply confuse myself on what I was observing.
Where do you observe?
My most common location recently has been Danville Conservation area. It’s a good balance of dark skies and reasonable drive from St. Louis, being about and hour and twenty minutes from me. Previously, I’ve also used Broemmelsiek Park’s astronomy site. However, there’s a lot of sky glow there from St. Louis, St. Charles, and other nearby cities and at this point, I’ve mapped most of the stars bright enough to be seen from there.
How do you process the data?
Measurements in altitude and azimuth aren’t really all that helpful because those values will change minute to minute. As such, the data needs to be converted to a coordinate system that rotates with the sky. In period, the ecliptic coordinate system was favored, but I use the equatorial system because that’s what it’s easiest to find the true values in for comparison.
To convert, I need two other pieces of information in addition to the altitude and azimuth which is the latitude of where I’m observing (looked up online) and the sidereal time (which I get from an app on my phone). This all gets entered into a Google Sheet which does the conversion and then compares to the true values. I walk through the derivation of that conversion here and do an example here.
Why did you paint it red/orange?
When Brahe printed his book, it was initially black and white copper plate engravings. However, some were hand colored as gifts for important potential patrons5. Thus, the reddish color is simply based on the color that it likely actually was. Before choosing the exact shade, I discussed period paints and colors with my friend Konstantia and they recommended this particular shade which is modernly nicknamed “Dragon’s Blood.” So obviously that’s what I went with.
Do you have plans that I could use to build my own?
Sadly, no. The construction was really made up as we went along.
Are you available to give a talk to my class/club/etc…?
Probably. I can be reached at VoijaRisa @ gmail dot com.
How can I get involved in the SCA?
Generally, start by finding out which kingdom you’re in. From there, find a local group near to you. Larger groups will have a Chatelaine which is the official newcomer person who will help answer any questions you may have. For local meetings, there’s generally no requirements to attend. Our official events often have a site fee and a requirement of an “attempt” at period clothing.
During the pandemic, the larger events are on hiatus until at least June, but local meetings my still be occurring. But in the meantime, there is a plethora of online content to be found.
- The original premise was $600$ to $1600$ but that has gotten pushed on both ends.
- You can find the first few posts I wrote in this blog where I’d started on this under the relevant tag.
- Indeed, an illustration of Brahe’s mural quadrant shows them doing just this.
- More than about $\frac{3}{4}º$ usually.
- Brahe published that work because he was trying to woo new patrons after being effectively exiled from his home country.