We’re getting very close to the end of construction, so it’s the point where it’s down to a lot of small details. To start, here’s a better picture of the axle assembly:
I’d shown a picture last time, but today, we added a brass fitting to help tighten the portion that goes through the central column, and using a pipe wrench, tightened the portion that will go through the arm so it cannot rotate, forcing the quadrant arm to rotate on it whereas during the test assembly last time, the arm caused the axle itself to turn. The cap on the end still goes on finger tight so it can easily be removed to disassemble the instrument for transport.
That cap, however, is where the plumb will need to be hanging from, since the line needs to hang just in front of the quadrant arm. Close enough that it can easily be read, but not so close as to get caught on the arm, disturbing its position.
To do that, we determined the mathematical center and carefully drilled a hole that went through the pipe cap and the pipe:
Small improvements were made to the central shaft by adding a bit of shelf edging to the portions that will rotate so it wasn’t bare wood on wood. This included the collar (shown below) and disc at the bottom:
With that done, it was time to test fit the arm:
With the arm attached, the first test was to ensure that, when the sighting arm was raised to be level with the ground, the plumb hung straight down the inner edge of the opposing arm. To determine this, we clamped a level to the sighting arm, raised it, and it came out nearly exact. It was a tiny bit off center, likely from slightly uneven rasping to enlarge the axle hole. However, the discrepancy is less than $\frac{1}{16}$”.
Next we wanted to check how the arm was hanging. Since there is a bit of a gap between it and the central post, we expected it would tend to hang back towards the post along the bottom. Sure enough it did, although you can’t see it well from this picture.
To correct for this, it was time to move on to a piece that we nearly overlooked from the original drawing: Containing the plumb bob is a small box. My presumption was that this was to help shield it from any stray breeze. But as we worked to ensure that the central column was perfectly vertical, we realized this box should also contain a mark over which the plumb bob should sit to mark level. In addition, the top of the box in Brahe’s etching shows small tabs that extend in front of (and presumably behind) the quadrant arm to prevent it from tilting. Thus, we constructed a plumb box out of some scraps:
Here, we worked first to ensure that the column was level by use of a bubble level and shims beneath the corners, in order to verify that the plumb bob fell directly over the mark. Roughly 1″ holes are drilled in either side of the box so it’s easy to verify that the bob is hanging over the mark in that direction. To keep the mark from being hidden we elected to use a polyurethane on the interior of the box, and the same stain/sealant on the outside. We still haven’t added the tabs to constrain the arm, but we want to get some felt to back them with so they don’t scratch the scale.
Meanwhile, everything else got a second coat of stain/sealant with the exception of the quadrant arm which we’re painting to match the overall color scheme from the original1. I asked the SCA hivemind on my friends list which color of (modern) paint I should use and decided on “Dragon’s Blood” which was recommended to me by Konstantia. This color can be dated to the proper period and I think has a better look than cadmium red.
With that done, we tackled one of the pieces I have been most fearing: the scale. This, along with the alignment of the center of rotation of the arm (and from that, the plumb), is the most critical piece to ensure accuracy.
Since the arm’s arc is 90º of a circle of radius of 36″, that meant that each 1º should be 0.628318″ from the next. Not exactly an easy number to measure. It comes out to ~$\frac{10.05}{16}$”, but that niggling 0.05 would add up after 20º to be a full sixteenth of an inch off. It doesn’t sound like much, but my hope is to get down to an accuracy of less than 10 arcminutes and I’m really thinking 3-6 should be in reach which would put this on par with Tycho’s.
After all the Ptolemy I’ve been working through, I’d considered using a chord length. The advantage there would be that it would be a straight line measurement instead of curved, along the arc, but still didn’t excite me.
Ultimately, while I’d wanted to use a method that could have been used in period, I decided my pursuit of accuracy was too great. Thus, we drew up the scale in AutoCad:
Here, you can see the lower portion of the arc. Each line is 1º and every tenth we colored blue to make it easier to see. The zig-zag lines are based on a transversal scale from Brahe’s Astronomiae Instauratae Mechanica, the book with etchings of his instruments.
In ours, we only zigged once every degree whereas in the figure above, Tycho’s went back and forth 6 times for each degree. Since our model is somewhat smaller than Tycho’s, I felt that would get too cluttered and pared it down. Another thing to note is that in Tycho’s scale, the dots zig-zag a total of 6 times with 10 dots each. This means each dot is separated by one arc minute. Ours, only zigging once, means each dot is separated by 6 minutes of arc. I figure that the line should be thin enough to allow for it to read be read between dots, which would be give a precision of 3 arcminutes. For reference, review of Tycho’s data suggests he was able to have accuracy down to ~30-40 seconds of arc. But again, his instruments were significantly larger.
To compensate for the point at which the plumb hangs over the scale being slightly off when level, we measured the actual center of the hole for the axle to ensure all marks were in relation to that.
Our scale was then printed on several sheets of 13×19″ paper and then reassembled:
This ended up being quite easy to do since each sheet had some overlap with the next which allowed us to line up numerous lines to ensure a good fit. However, the real test would be when we got to the end, if that final 90º line fell where it should.
And it did. Spot on. So we trimmed the excess paper off and taped it down:
Here’s a detailed shot of our scale:
From here, we will be scoring through the paper to make marks on the wood underneath, which we can then paint to transfer the scale. I should note, that this scale is likely to only be temporary as many friends have suggested that I replace a painted on scale with a much nicer etched brass one at some point.
So the instrument is very nearly ready for use. At this point the major to do’s include transferring the scale (which may wait until after I’ve taken the instrument out once to make a few test measurements against stars of known altitude), adding the sights, and adding the tabs to stabilize the arm.
One thing that will be done later is to add screws to the base to assist in leveling. This is something Tycho had on many of his instruments as seen in this picture:
The pieces on the end of each foot can be raised or lowered via the screw to adjust the level. To keep the wood look, we elected to go with some threaded wood dowels and other parts that we had to special order, so they’re unlikely to be here in time for the opposition, but, as this is intended to be a prototype, we fully expect to be making improvements as we go.
T minus 22 days.
Oh yes. It was still stupid hot in the workshop:
- I haven’t been able to verify that the colors shown in the picture we’re working from actually date to period. While the etching itself certainly is, I have been unable to find any information on whether the colors were added in period, or were added in later renditions. However, I quite like it, so it’s what I decided on.