NOTE: This post is actually being posted in December $2020$, as when I was writing my year end post, I was reminded I’d never posted this. This was largely due to having not decided what to actually do with the data for reasons you’ll see. Ultimately, I’ve decided to exclude the data completely.
In addition, since I hadn’t posted this, the discussion of the enhancements to the quadrant was actually featured in a post from July. But for readers who may read this in chronological order, I have instead moved that portion to this post.
It’s been awhile since I’ve posted about observing. Due to COVID, it’s been extra challenging to do any observations given the quarantine I’ve been doing my best to observe. I do still have a few friends that I see in a very small social circle, but between that and the weather last month, there hasn’t been a lot of opportunity. So when the weather called for a near-perfect night for observing and one of the people I trust was willing to assist, there was no way I was going to miss observing.
In addition, this night was extra special because it was going to allow me to test two new upgrades to the quadrant which I’ll start by introducing.
The first upgrade to the quadrant was an attempt to resolve the issue of needing an assistant to observe. This was required because one person would aim the quadrant arm, but would have to hold it in place while another person took the reading on the scale which was perpendicular.
To solve this, a set of “wings” was added directly behind the quadrant arc.
The quadrant arc would rest on this and, once the object was sighted, a clamp could be applied to hold quadrant firmly in place. This should be fairly easy to do since the scale of the arc has a gap behind it.
The second upgrade was finally adding an azimuth scale. I’d been debating about this for quite some time. I reasoned that, since the quadrant itself was a $90º$ wedge of a circle $6$ feet in diameter, it would only make sense to add if I could get one comparable in size. In which case, where would an observer even stand. But eventually, I realized that the scatter I was seeing in determining when things crossed the meridian was larger than the units I could put on a scale of a circle only $3$ ft in diameter. Thus, there was no reason not to do so.
Previously, the quadrant could only measure a star’s altitude, so to take data, we had to wait for a star to cross the meridian. Then we would know it’s either due north or south and its right-ascension would be equal to the sidereal time. While this gave solid results, it was a huge waste of time. Depending on which part of the sky we were looking at as well as the sky conditions, this would often mean $10-20$ minutes between observations.
This new azimuthal ring rotates on an inner ring so it can be aligned to north once the quadrant is set up each time. Then a pointer was added to the ring for the central pillar which rests on the inner ring and points to the azimuth on the outer. The azimuth ring is divided into the obvious $360º$ with each $10º$ mark being in bold, and the $5º$ marks being “half bold” where only the outer and inner edges are bold. Each degree is further subdivided into $4$ parts on a transversal, although I’ve not found them particularly useful as they’re too far away from the pointer to be readable.
The scale on this was created in the same manner as I did for the quadrant arm wherein it was mocked up in AutoCad and printed full scale on several sheets of paper that were then carefully reassembled. This was then laid on the unmarked ring and slits were cut lightly into the wood for the degrees and the transversal dots were punched using a nail and hammer. This was all then traced in sharpie to make it readable.
These are both still in a prototype phase so I haven’t stained or painted everything, but overall I’m quite happy with how they look1:
The wings are entirely unobtrusive and the azimuth ring is an elegant addition to the overall look2. But the real test would be how they performed.
So instead of my usual observing at Broemmelsiek park, we headed out to Danville Conservation Area which is twice as far out with significantly darker skies, and planned to stay the night so we brought tents instead of trying to make it home.
Since Count Yseult was assisting, we didn’t immediately test the wings. Instead I started by sighting the north star and adjusting the azimuth ring to $0º$ where it was pointing. Because I wasn’t feeling overly confident, we agreed that for each star, both of us would observe it and record the observations. This was certainly slower, but it would let us to compare against one another to ensure the results were in the same ballpark.
Generally, the numbers we came up with were quite similar. But on our $13^{th}$ observation I suddenly noticed something was wrong. Most of the stars we’d observed so far were about half way up the sky or $~45º$ altitude. But for this observation, Yseult had sighted in on one of the stars in Scorpio which was not particularly high above the horizon. But somehow the reading came out as $>60º$ altitude. Something was obviously wrong.
After a few minutes of reflection, it occurred to me that we’d been sighting down the wrong arm of the quadrant. This is quite easy to do because both arms have sights on them. This was because, when the quadrant was built to just observe along the meridian, this would allow for observations to the north. You would just need to subtract the angle from $90º$. Thus, this was the case for these first measurements.
In addition, we took the opportunity to check the alignment of the azimuth ring. Somehow it was off by $7º$. Given that last time I observed, I sighted a star other than Polaris to align, it’s entirely possible that happened here again, but I’m pretty certain that wasn’t the case this time. So we wondered if the ring had been bumped at some point. However, the friction between the inner and outer ring is quite significant right now, so we thought it was unlikely. As such, we simply made a note of this to take into consideration when we reviewed the data.
It looks like there is indeed a $7º$ offset to these first $13$ stars, so it definitely wasn’t a case of it being bumped between observations or slowly getting out of alignment. But regardless of how it happened, this was a simple correction to the data to account for it.
Once the azimuth ring was realigned, we continued on until Yseult went to bed around $1$am. I’ve been up late quite a bit recently due to our Friday night online bardics during COVID, so I still had quite a bit of energy left and wanted to see how it worked to use a clamp to lock the quadrant arc to the wings.
It definitely took a bit of a learning curve. I found the best way for me, was to use one hand to do an initial rough lining up. Then I’d place the other hand on the wing and quadrant arm to do a more fine adjustment and, once aligned, would hold the two tightly together while I reached for the clamp and applied it.
Once worked out, this seemed to go quite smoothly for stars at intermediate altitudes. But anything below about $20º$ it became quite difficult for two reasons. The first was that this would extend the quadrant arm farthest from the center line making the wing harder to reach to hold on to while grabbing the clamp. Second, this extra distance from the center of gravity means more torque, so it was more weight to try to hold still while getting the clamp and putting it on. There were several observations I had to redo due to it slipping slightly before I could get the clamp applied.
I also found that tring to apply the clamp would also often result in some horizontal motion which could throw the azimuth off. So my solution was to first line up the star in azimuth, step down, record the azimuth, and then sight it more carefully on the altitude, clamp, step down, record the altitude. Once I got into the groove, this led to each observation taking about $3-4$ minutes. This will certainly introduce a bit of error due to the star moving in this amount of time, but it shouldn’t be overly problematic.
At the end of the night, we ended up observing $46$ objects, $3$ of which were planets.
Since this was the first time we’d used the azimuth ring, I looked up the altitudes and azimuths for each object in Stellarium to determine how far off we were. Unfortunately, it looks like there were problems. Even after making the correction of $7º$, those observations still had an average error of $-0.85º$ (i.e., notably leftwards). And the observations after we realigned were worse, averaging $-1.94º$. Something is obviously wrong. To help do some analysis, I took the data and compared it with the true values (taken from Stellarium) to graph the error as a function of azimuth. It shows a fairly clear pattern.
Here it’s apparent that the error is worst right around $180º$. While we didn’t take many measurements in the north east, it’s still pretty easy to see overall that this looks like an upside-down bell curve with a lot of scatter with an apparent minimum was off by about $2 \frac{1}{2}º$ at $180º$.
To validate this, I went out a few nights later and set $0º$ on polaris again, then rotated the quadrant and sighted the same star down the other quadrant arm. If this was indeed due to the azimuth scale being off, then on the second measurement should not be at $180º$ but off by about this amount.
Sure enough, it was:
So what could cause this?
There’s two ways I could see this happening. The first is that the azimuthal ring is drawn correctly, but the center of the ring on which it rotates is slightly off from the true center of rotation of the pillar as drawn here:
This is very similar to what we’ve seen in the Almagest in which the center of the eccentre is offset from the observer.
Alternatively, the center could be fine, but the angles could be off as follows:
So which is it?
To answer that question, I took the azimuth ring and top of the base back into the workshop. First, I checked to make sure all the angles on the ring were good. To do so, what I really wanted was a giant T-square so that I could lay it across $0º$ and $180º$ and ensure that the right angle would fall right on $90º$ and $270º$.
Since I didn’t have one I put one together from a right angle bracket and a piece of scrap wood that had a sharp angle on it giving a well defined edge.
If the ring was made correctly, then I should be able to place the wood portion across $0º$ and $180º$ and, sliding it left and right, it should lie well across the mark for $90º$.
It did. Thus, the expectation was that the center ring it rotated on was off center. To test this, I determined the center of one side. I carefully lined up 0º there and then measured where $180º$ lay. It was off by about $\frac{2}{3}$ inches. This was about right as a $2º$ error measured from the center would imply a $0.62$ inch error since the radius is $18$ inches. Thus, this sounded like the right issue. So it was time to remove the ring. I’d only attached it with some wood glue, so a wedge and a hammer popped it off pretty quickly.
This time, I made a mark on the side of the base where $0º$ and $180º$ should be, and then lined the ring up while on the inner ring. The inner ring was then screwed down. As a further test, I tried it at several different orientations to make sure that whatever was at the side I originally put $0º$ at, whatever was at the mark on the other side was $180º$ away.
It seems there’s still a small issue because the inner ring and outer ring aren’t perfect circles. Thus, as it’s rotated, it can push it slightly out of alignment. However, after numerous checks, this never seemed to throw it off by more than $0.5º$. That’s still far more than I’d like, so I’ll probably rebuild both rings at some point, but it’s a significant improvement!
To see if this resolved the issue, I’ll have to go observing again and process the data.
- Thanks to Yseult for the impressively badass pictures!
- The two square blocks sitting inside the azimuth ring are not one of the additions. The base has $4$ screws that can be adjusted to level the instrument and those blocks are used to give the screws something to push against instead of sinking into the soil.