A use I had not thought of…

I present to you the astrolabe cake…

http://nuri148.blogspot.com/2011/09/la-torta-mas-nerd.html

A working astrolabe cake

Made using the files produced by the Astrolabe Generator.

Looks Delicious.

Drafting the Astrolabe: 3. The Protractor

After Stoeffler

This does seem a bit extreme, but the purpose of this project is to see what can be done with just a straightedge and compass. Building my own protractor serves two purposes. One: It proves to me that an accurate tool can be made this way. Two: It gives me a chance to play with the tools and techniques I will need later on in the project.

Step 1: Using the straight edge, draw a horizontal line roughly 2/3 of the way down the paper.

Step 2: Use Method 1 to erect a perpendicular line at the center of the first line.

Step 3: Use the compass to draw four arcs as follows:
Set the point of the compass at the intersection of the two lines.
Set the width of the compass to the radius you wish for the protractor (bigger is more accurate).
Draw a half-circle arc beginning and ending at the first line. This is the outside edge of the protractor.
Decrease the width of the compass a bit and draw second half-circle arc inside the first. The space between will be for degree increments.
Decrease the width of the compass a bit and draw third half-circle arc inside the second. The space between will be for 5 degree increments.
Decrease the width of the compass a bit and draw fourth half-circle arc inside the third. The space between will be for 10 degree increments.

Step 4: Trisect the right angles:
Work on one half of the protractor at a time.
Use Method 6 to trisect the right angle. This will give you lines at 30 and 60 degrees. Mark these across all four arcs.

Step 5: Bisect the 30 degree angles:
Work on one half of the protractor at a time.
Use Method 5 to bisect the 30 degree angles. This will give you lines at 15, 45 and 75 degrees. Mark these across the three outermost arcs.

Step 6: Trisect the 15 degree angles:
It is not possible to trisect a 15 degree angle by construction, therefore we have to fudge a bit.
Adjust the width of the compass until it can divide a 15 degree section of the outermost arc into three equal sections. Take your time and be as precise as possible.
With the compass so set, mark the entire outer edge of the protractor. then use the straightedge to draw a line at each mark toward the center (Note some will be 5 degree lines and some 10, work it out…). This gives you a mark every 5 degrees.

Step 7: Mark the degrees
Now for the really tedious part. The compass is not going to be accurate enough to mark the degrees, so you will have to eyeball it.
On the outermost arc mark each 5 degree section into five 1 degree sections. Be as patient and accurate as possible.

Finally, label the scale as desired.

Congratulations, you have invented the protractor.

To finish mine I laminated the page in a 5 mil laminating envelope and carefully cut it out. It is now durable enough to use.

Basic construction finished

Basic construction finished

Cleaned up and labeled

Cleaned up and labeled

Laminated and cut

Laminated and cut

Drafting the Astrolabe: 2. Methods of geometric construction

Hartmann’s Practika is a collection of writings by the 16th century instrument maker Georg Hartmann. These detail the steps to design a range of sundials, and extensive notes on astrolabe construction. Hartmann begins by demonstrating the geometrical construction techniques he will be using. Given how complex some of the design work will be, this seems a good place to start

Adapted from Hartmann:

Method 1: Erecting a centered perpendicular.

Given line AB: Place the pivot of the compass at point A and draw two arcs, one above and one below the line as shown. Without changing the size of the compass, move the compass pivot to point B and draw two more arcs, intersecting the first two arcs. With a straight-edge, draw a line through the two intersections. The resulting line will be perpendicular to AB and centered between points A and B.

Method 2: Erecting a perpendicular at one end of a line.

Given line AB: Place the pivot of the compass at point A and draw an arc of radius r as shown. Mark the point where the arc crosses AB as point C. Keeping the compass set to radius r, move the pivot to point C and draw another arc, intersecting the first arc. mark this intersection point D. Using a straight edge, draw a line from point C past point D. Keeping the compass set to radius r, move the pivot to point D and draw another arc intersecting line CD at point E. Using a straight edge, draw a line from point A to point E. Line AE is perpendicular to line AB.

Method 3: Erecting a perpendicular from a line to a given point not on the line.

Given a line and point A not on the line: Place the pivot of the compass at point A and draw an arc intersecting the line in two places. Mark these intersections as point B and point C. Place the pivot of the compass at point B and draw two arcs, one above and one below the line as shown. Without changing the size of the compass, move the compass pivot to point C and draw two more arcs, intersecting the first two arcs. With a straight-edge, draw a line through the two intersections. The resulting line will be perpendicular to line BC and pass through point A.

Method 4: Finding the common center of three points.

Given three points A, B, and C, not on a line: Place the pivot of the compass at point A and draw an circle of radius r as shown. Repeat for point B and Point C. Radius r should be set such that the three circles overlap as shown. With a straight-edge, draw lines through the two sets of intersections. These two lines will cross at point D, which is the common center of points A, B, and C.

Method 5: Bisecting any angle.

Given angle BAC where point A is the point of the angle: Place the pivot of the compass at point A and draw an arc intersecting the sides of the angle as shown. Move the compass pivot to point B and adjust the compass radius to just past the center of BC. Draw an arc as shown. Keeping the compass set to the same radius, move the pivot to point C and draw a second arc. With a straight-edge, draw a line through the two intersections and point A. This line bisects the angle BAC.

Method 6: Trisecting a right angle.

Given right angle BAC where point A is 90 degrees: Place the pivot of the compass at point A and draw an arc of radius r intersecting the sides of the angle as shown. Without adjusting the compass radius, move the compass pivot to point B and draw an arc that intersects the first arc as shown. Mark this as point E. Move the compass pivot to point C and draw another arc. Mark this intersection as point D. With a straight-edge, draw lines AD and AE. These lines trisect the angle BAC.

Drafting the Astrolabe: 1. Planning the Project

The first step has to be making myself a protractor. I was going to create one as a proof of concept then switch to a commercial model, but I have changed my mind. If I can make a reasonably accurate tool, I can laminate it and use it; getting rid of the need to ‘cheat’.

I’m tempted to jump right into the climate plates next; but I think that they really need to be much further down the list. The construction of the climates is the most complex and confusing and I will have to lay a lot of groundwork before I am ready to start documenting that process.

My rough schedule is as follows:

  • Explain the geometric construction techniques to be used. Number them to allow me to refer to them later.
  • Draft the protractor
  • Rough out the design for the astrolabe as a whole. I can then use this rough model to transfer measurements from for the various parts.
  • The front of the mater:
    • time scale
    • interior scale
    • throne
  • The back of the mater:
    • zodiac scale
    • calendar scale
    • unequal hour scale
    • shadow scales
    • throne
  • The climate plates.
  • The rete.
  • The alidade and rule.

Drafting the Astrolabe: Defining the project

Allowed tools:

  • Straight-edge: NOT a ruler, I need to find a nice (straight!) length of hardwood with no markings. I may cheat and use a steel yardstick.
  • Compass: I have a nice Staedtler compass, but it will not be big enough for some of the arcs required. I may add a beam compass or experiment with cord. There may be clues in the references as to how large, shallow arcs were drawn in period.
  • Dividers: I have a nice pair of dividers that may be useful in transferring measurements.
  • Paper: 8 1/2 by 11 good quality drawing paper.
  • Eraser
  • Protractor: Cheating a bit here. I will demonstrate that I can construct a protractor before I start using a commercial one, but drawing out one by hand each time I need one seems excessive, unneeded and probably not what was done in period.
  • Astronomical tables and measurements – These would have been available to an instrument maker in period.

Technique:

  • For drawings requiring excessive geometrical construction (climate plates for example), work will be done on a working copy and transferred to a clean copy.

Sources:

  • Hartmann, Georg. Hartmann’s Practika, English translation by John Lamprey, Classical Science Press, 2002
  • Morrison, James. The Astrolabe, Janus, 2007
  • Stoeffler, Johannes. Stoeffler’s Elucidatio – The Construction and Use of the Astrolabe, English translation by Alessandro Gunella and John Lamprey, Classical Science Press, 2007

Parts:
Overall, based on astrolabes from Hartmann’s era.

  • The Front:
    • Show throne, mater and limb.
    • Limb marked in hours as the class example is.
    • Mater hollow should display traditional scale.
  • The Back:
    • Elevation scale.
    • Zodiac Ring.
    • Calendar Ring (offset).
    • Unequal Hour lines.
    • 7 and 12 shadow squares.
  • Climate plates
    • At least 5. Based on the standard set listed in Stoeffler. Adding a Pennsic Plate (40-58).
    • 5 Degree intervals on both almucantar and azimuth lines.
    • 18 degree twilight line.
    • Unequal hour lines.
    • Possibly the lunar houses if I get (more) ambitious.
  • Rete
    • Drawn properly in gothic style, pointers to major stars.
    • Zodiac ring
  • Rules and alidade
    • Drawn with proper scales.
    • Both single and double rule.
    • Alidade designed with sights.

This Year’s Project

During my vacation, I spent a few hours one afternoon with a straight-edge, a compass, and my copy of Stoeffler’s Elucidatio – The Construction and Use of the Astrolabe. I was able to draw out a basic climate plate very easily; in fact I was surprised at how straight-forward it was. I am inspired to draw an astrolabe from scratch using the techniques described in the book, and to display the result at the Arts and Sciences Display during Pennsic 41.

Project: Drafting the astrolabe with straight-edge and compass

  • Using only a straight-edge, compass, and pencils, design a complete set of plans for an astrolabe.
  • Create front, back, rete, rules, and a climate plate set
  • Photocopy the above, assemble and laminate for testing.
  • Step-by-step examples of how the climates are drawn.
  • Document the whole process in this blog over the course of the year.

This project, besides being a fun challenge, will give me a more in-depth understanding of how an astrolabe works. Moreover, it will provide insight into the minds and techniques of period instrument makers, and (hopefully) provide other students a clear set of instructions for designing their own instruments.

Pennsic Postmortum

I’m back from Pennsic War XL. Still coughing up the dust, tired and happy. So starts another 50 week town run.

My two Astrolabe classes were well attended, especially in view of the fact that one was late in the day and the other was scheduled very late in the war. If I remember correctly, there were 17 people in the first and at least 16 in the the second. As usual there was a wide range of students, including a forensic astronomer in the first and a jeweler in the second (the latter wanted to know about design and construction details, she has access to a rapid prototyper and injection molding. We may have some astrolabes for sale at the war yet…)

The updated handout worked much better, as did the simplified astrolabe. The flow of the classes was smoother, and I had to spend much less time sorting out confused students.

Based on my impressions, I’m going to be overhauling the handout once again. This time, instead of a basic and advanced section, I’m going to break it into chapters; with one or two concepts per chapter. Each chapter will build on the concepts in previous chapters, and will include multiple detailed examples for each new concept, as well as a review. I’m removing the discussion on time-keeping and prayer times to an appendix, and will just reference the information I need for the examples. This will allow me to cover the basics smoothly and to adjust the class time as needed: I can cover chapters until I run out of time, some classes are faster than others; so I cover what I can and make the handout clear enough that it allows a student to work on what we couldn’t cover.

The current version of the astrolabe is pretty solid. I’m probably going to keep it as it is.

Class Handouts Posted!

The new, updated handout and set of astrolabe files to be used in my upcoming Pennsic War class can be found linked on the right.

Upcoming Pennsic Classes!

My class: The Astrolabe in Theory and Practice, will be taught at the Pennsic War. I am teaching the class twice: August 7 at 5pm and August 12 at 1pm. Handouts are limited to 15 per class with a fee of $5. Auditors welcome. The handout and the astrolabe files will be posted here the week before Pennsic at the latest.

More Updates

I made more changes to the generator. The azimuth lines are now optional, and I added an option to print just the sine scale on the back.