The finished product works nicely and looks smart. I can usually measure the time from the stars or sun to within about 10 minutes, and can measure true north within about 5 degrees or so.
As many sources on the internet point out (correctly!) that the astrolabe is a stereographic projection of the sky onto a plane that is tangent to the earth at one of the poles. For northern hemisphere astrolabes, such as mine, the plane is tangent to the north pole, and the projection point is the south pole. That makes the north pole (and the north star) the center of the instrument. Since stereographic projection turns circles on the earth into circles on the projection plane, nearly everything sketched on the astrolabe is also a circle. For instance, both the equator and the ecliptic, which is the path that the sun appears to move through the sky, are both circles. Since the ecliptic is almost concentric with the equator, but twisted off the equator by about 23.5 degrees (the tropics!), the ecliptic looks like an offset circle on the astrolabe.
I could do all these projections by geometric constructions, but decided that merely projecting points was easier. This I did in python, and to keep organized, I chose to design all of the curves and scales in a Jupyter notebook. The notebook produces SVG files as output that contain the various curves, stars, and scales, all at a fixed scale for printing. I edited each of the files by hand to add some more difficult annotations or to make aesthetic adjustments. For instance, the back of the instrument has an equation of time, to which I added some small glosses for "sun fast" and "sun slow" as well as the build date.
The front of the instrument consists of the rete (a simplified star chart), the tympan (a replaceable model of the sky's azimuth and elevation curves for local latitude), and a scale around the outer edge for time and compass directions. I used this file as the source of my star chart, from which I produced the rete file.
With the rete file in hand, I manually selected the ten brightest stars, and shaped the pointers. The idea is that the outer two rings go on the body of the instrument, while the rete, proper, starts at the inner two rings. The picture below is an earlier revision, with somewhat different scales on the rete. It also contains both front and back pointers.
This earlier revision uses mean solar time, from which the true position of the sun cannot be read directly. You need to use the equation of time to make this adjustment. I found that was too error prone. I prefer to have the front of the astrolabe show the true position of everything, and then correct for mean solar time afterwards if desired.
I printed two copies of this file, so that I would have clean copies of each for construction.
You need one tympan for each latitude. This one is for my local latitude.
This file contains the same outer scales as the rete so that the pages can all be scaled the same. These outer two scales are cut off and disposed, which is why I left some intersections. The bright red mark is the location of true north, common to all files.
It wasn't too difficult to arrange the lines of constant azimuth and elevation, though I noticed that there is very little documentation about how the "unequal hours" lines are traced. After playing with the models a bit, I realized that these lines are the horizon line rotated about the local north direction, not rotated about true north.
The unequal hours aren't particularly in a modern instrument, but were used for reckoning time in Italy until the introduction of weight-driven clocks. The idea is that day and night are divided into twelve hours of equal length, starting at sunset. The hours are therefore of unequal length throughout the year. During the day, the unequal hours can be read from the position of the sun. At night, the astrolabe is more useful. By turning the rete so that the stars are oriented correctly, the position of the sun in one of the unequal hours tells you the time. At least on my instrument, the sketching the unequal hours seemed to occupy unused space in a pleasing way.
The instrument was built using my usual paper-on-wood scroll saw technique. I used 1/8" birch plywood for the flat pieces. The tympan is merely a laminated sheet of paper, so that it is thin and sturdy. The two pointers were cut from oak.
Here is the astrolabe disassembled.
The instrument has a brass pin that holds all the parts on the common center (the north pole). The back pointer has a cutout that sets the pin into place.
This is important because you simultaneously want one edge of the pointer to align with the center of the mounting hole -- so that you can sight across it and then read an elevation on the scale -- and you want the pin there too. The pin has to fit back into the pointer to give clearance for the sight line.
The front pointer has a similar construction, but I made a small brass button to keep the pin end. Once the pin is installed, you merely bend the tip of the pin to retain it. The marks along the front pointer measure declination -- angular distance from the celestial equator.
Finally, I added a thumb ring that sets through a larger pin. I turned this with a small flourish, and silver soldered the ring closed.
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