Drafting the Astrolabe 6: The Zodiac Scale

OK, yes, that was tedious. But now it is done.

I have started work on the back of the astrolabe: The first scale, the zodiac ring, is finished.

Drawing this used a combination of geometric construction and fudging with the compass. First, draw the outside edge of the astrolabe (set the compass using the finished front drawing). When this is done draw 4 more circles of diminishing radius to make the scale. Then trisect the four quadrants. This divides the scale into the twelve astrological signs. Fudge with the compass to divide each sign into three parts, giving you the ten-degree marks. Then next, bisect the 10-degree angles to give the five-degree marks. Finally manually divide each five degree section into five one-degree ticks.

The Back of the Astrolabe

The scales should be marked as follows: The top half of the outermost ring should be marked 0-90 degrees on each side (zero for the horizontal and counting up to 90 for the vertical). This is the elevation scale, used to measure elevation above the horizon.

The innermost scale needs to be marked with the zodiac (I used the symbols, but spelling the names out is also used): Starting with Ares on the right side above the horizontal line and working counter-clockwise through the rest of the zodiac in order. Finally, each zodiac section has to have the 10 and 20 degree ticks marked (note that these are marked counter-clockwise as well).

Next up: Adding the Calendar.

Drafting the Astrolabe 5: A Recipe for Fudge(ing)

The next big chore will be creating the major scales for the back of the astrolabe. This will involve drawing one set of rings representing the Zodiac and another set representing the Calendar.
Drafting the zodiac is straight-forward, if tedious. The circle needs to divided into 360  one-degree ticks. The process is the same one I used to create my protractor (link).
The next step will be -um- interesting. The calendar scale sits inside the zodiac ring and is oriented such that when placed on a date, the adidade pointer will also point to the position of the sun on the zodiac for that date. Unfortunately, where 360 divides up well, 365 does not. in fact, the only divisors other the 1 and itself are 5 and 73. Now I can divide the circle into 5 equal parts (quintrants?)by cheating with the compass, but after that 73 is prime and not divisible equally. In addition the year is not 365 days…. it is 365.25.
So I looked at my sources. Stoeffler has this to say:
“Make the subdivisions of the days and of the months in this way. Set the rule on the center E and on the 20th degree of Capricorn and draw a line segment crossing all the eccentric circles. It will point out the beginning of January and be marked with a G. Starting from it, in the opposite direction to the succession of the Signs, count around 5 degrees 20 minutes. Set the rule between this point and the center E. Draw a line from the first eccentric circle to the second, which will be H. The remaining arc must now be divided (this small arc excepted) into 360 equal parts…”(Stoeffler:67)
Hummm. Clever.
So I am to remove the angle equivalent of 5.25 days from the circle, and divide the remaining arc into 360 ticks. Much easier. Or rather somewhat easier; as the 360-day section of the circle is NOT 360 degrees, I will not be able to quarter it and trisect etc. like I will the zodiac. I will need to bisect repeatedly and do some fudging with the compass when I need to divide an angle other than in half.
Question: Am I dividing into 365 or 365.25?
It occurs to me that at the finished diameter of my astrolabe, the .25 day tick will be approximately the same as the width of the line used to mark it. If I remove the .25 and use 365 ticks, each tick will be thrown off a bit: By approximately .0007 of the width of the space. This is not going to be measurable with this instrument.
An examination of the backs of several period astrolabes shows that leaving out the .25 is a regular practice. In fact, going back to Stoeffler: “The GH arc will be divided into 5 parts and 1/4, if it is held to precision” (Stoeffler:67). So for this project I’ll go with 365 days.

Drafting the Astrolabe 4: The Front

Back to work on this project:

I got several tasks done today.

When I am finished drafting my astrolabe, I plan on photocopying it onto card stock, and assembling and laminating it in order to compare it’s accuracy to a computer-generated version. I tested the photocopy process today.

First, I printed out the front of the computer-generated version of the astrolabe and then photocopied the printout. Then I measured the two with my point-scaled ruler (Note: PostScript measures in points: 1/72 of an inch).

The printed out version is a uniform 503 points in diameter, horizontally, vertically and obliquely (45 degrees). The photocopied version is 501 points horizontally and vertically, and 504(!) obliquely. Obviously my home photocopier is distorting the image a bit. If the hand-drawn version is going to be distorted for testing, it will skew the results.

Two possible options suggest themselves:

1. Test other, commercial, photocopiers for distortion an see if I can use them instead.

2. For testing, photocopy the computer generated version as well. If the distortion is uniform, as I suspect it will be, it will be the same for both test and control.

Next I got out the drawing tools and drew up a template for the climate plates. The three tropic rings will be the same for each plate, so constructing them each time is a waste of effort. The compass can instead be set from the template and the rings transferred to the individual climate sheets.

Template for the construction of astrolabe climates

Next. I drafted up the front of the mater. First I drew a line down the center of the paper. then erected an perpendicular bisecting line using Method 1. I then transferred the lines for the inner and out edges of the mater limb from the printout of the computer generated example, to the paper using the compass. Four additional circles were drawn between these two circles to mark the various lengths of tick marks for the time scale.

The limb is to be marked in hours, half hours, quarter hours and five-minute ticks. To accomplish this I then used Method 6 to trisect the 4 quadrants, dividing the limb into 12 two-hour sections. I then bisected (Method 5) the angles giving me 24 one-hour sections. These 24 sections I marked across all four scale lines. I then again bisected the hour angles into half hours, and marked these across 3 rings. Bisecting again gave me my quarter-hour lines. marked over two rings.

Finally I abandoned the compass and straight-edge and eyeballed the division of the quarter=hour sections into three 5-minute sections (marked over two lines). I cleaned up the result by erasing most of the construction lines; and I inked the result carefully with a 0.1 mm drafting pen.

Front of the astrolabe mater,
The result is not the prettiest thing I’ve seen. But I’m not an artist. It does appear to be useable, however.
Next: Drafting the zodiac scale on the back.
Note: For methods of construction used see post: Drafting the Astrolabe: 2. Methods of geometric construction

Astrolabe Generator: Done For Now

I have just uploaded the last tweak I’m planning on making to version 2 of the Astrolabe Generator. I’ve done a lot of work on it over the last few weeks, and I’m happy with the results. I will still be planning to add more scales and functionality in the future, but it is time to shift my focus to other parts of the project…

I spent part of today going over the sadly neglected Astrolabe Manual. I’ll be working on that during most of my spare time for the next few weeks, so keep stopping back for updates, or subscribe to the RSS feed (See the link on the right).

In addition, I’ll be doing more work on the Astrolabe Drafting project. I think I have a good idea of what scales and detail I want to include now. More importantly, I can now use the Astrolabe Generator to print out a computer generated version of my design so I can compare accuracy.

So no more updates to the generator for a while, but more work on the other aspects of the Astrolabe Project.

If there is anything you would like to suggest to improve the site, bugs to report, functionality to add, etc. I’m posting an email address in the links menu.

 

Added a Horizons Plate

I did some doodling today and added a Horizon Plate to the Astrolabe Generator options.Astrolabe horizons plate

The plate covers latitudes from 10 degrees to 70 degrees in 5 degree intervals. This allows more portability for the astrolabe, at a cost of some of the functionality.

Astrolabe Generator Update (minor)

I updated the thumbnail graphics to make them easier to see.

Astrolabe Generator Update

I have added new more features to the Astrolabe Generator (http://astrolabeproject.com/build/). There is now a front degree scale option and I have added a new set of limb markings: Alphabetical (based on a 1370 astrolabe shown here).

Major Update

I just uploaded the latest changes:

  • The classic rete now has pointers as it should
  • The settings are now driven from a config file
  • Predefined astrolabe settings are available from a menu
  • Added a background (was getting tied of the Flex default)

Houses of Heaven

I have added two new scales: The Houses of Heaven are now an option for the front. I have also added a horizontal shadow scale option on the back.

The Houses are the first astrology-only scale I’ve added. Look for more in the future.

The new shadow scale differs from the shadow squares in that it shows the shadow length in units of gnomon-length, not porportion.

Another update

I’m definitely in a coding mood. I just uploaded another change. I’ve added a Quadratum Nauticum to the Astrolabe Generator “mater-only” option:

printOptionCbo