## Astrolabes on YouTube

- on 03.07.12
- Astrolabes General, Random Jottings
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- on 03.07.12
- Astrolabes General, Random Jottings
- Comments Off on Astrolabes on YouTube

- on 02.26.12
- Astrolabe Project, Drafting The Astrolabe
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The next step, and the last scale to be added to the back of my astrolabe, is the unequal hour scale.

In the middle ages, there where several timekeeping systems in use, as opposed to the single one we use now. This next scale was designed to convert between two of these systems: The Equal Hour and Unequal Hour systems.

The Equal Hour system is the one you are familiar with; 24 hours of 60 minutes each. The Unequal Hour system is different: The day (sunrise to sunset) and the night (sunset to sunrise) are each divided into 12 hours, regardless of the time of year. Therefore in Summer an hour of daylight is longer than an hour of darkness, and in Winter the reverse is true. The sun rises at the start of the first hour of the day and sets at the end of the 12th hour of the day, which is also the start of the first hour of the night; and local noon marks the end of the 6th hour.

Further discussion and examples can be found in my class handout.

The completed scale looks like this:

Depending on the astrolabe the scale may be on either or both sides, as it is symmetrical.

Drawing the unequal hour arcs is relatively straightforward once you understand the trick. The following is adapted from Stoeffler and Morrison (see recommended reading ).

First, draw an arc just inside the innermost ring; centered on the center of the astrolabe, and forming a half-circle above the shadow squares.

Next divide the arc into twelve equal parts. Stoeffler suggests that you use the outer elevation scale and make a mark every 15 degrees.

Now look at the figure above. Note that because the scale is symmetrical, the center of each arc will lie somewhere on the vertical center-line. Note also that each arc touches two points: The astrolabe central pivot, and one of the marks just made, therefore these two points must be an equal distance from the arc center.

This means that you can find the center of each arc by raising a perpendicular bisector to the line between the two points and marking where it crosses the center line (see Drafting the Astrolabe: 2. Methods of geometric construction).

Step1: Draw a light construction line from Point A (the astrolabe center) to Point B (any one of the twelve fifteen-degree hour lines).

Step 2: Erect a perpendicular bisector from line AB to the astrolabe mid-line and mark it Point C.

Step 3: Place the point of your compass at Point C and draw an arc from Point A to Point B (mirrored on both sides if that is your wish).

Step 4: Repeat until all the arcs are drawn. Erase construction lines and label the arcs as shown above.

As some of you might have noticed, the Joomla site for Astrolabe: The Missing Manual is gone. Like the original wiki it replaced, it was not meeting my needs, so I nuked it. Do not despair! The manual still exists, and is still being added to regularly (more regularly than this blog lately). I replaced an overly complicated site with a simple PDF. The link is on the right as “Astrolabe Manual”… I will update this file as I add to the manual, and will provide version information inside the front cover.

I stumbled across this today at Thingverse: A plastic working astrolabe. The creator made it back in June 2010, and didn’t stumble across my site until afterword. Here’s hoping that someone will be inspired to make more…

Or there will be soon. I was contacted by a developer who is working on an iPad app that simulates various medieval astronomical devices. He will be using files made with the Astrolabe Generator. I’ll post information here when it becomes available.

- on 02.20.12
- Astrolabe Project, Drafting The Astrolabe
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- on 01.21.12
- Random Jottings
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For those of us that like to put the science into Arts and Sciences, Artisan’s Row at Pennsic this year will have a day devoted to scientific instruments and tools.

I have been asked by the Artisan’s Row Dean to organize a day devoted to the tools and instruments of the sciences. I am looking for like-minded artists and artisans who are involved in making and using such tools to spend a few hours displaying their work and sharing their knowledge. I’m being very broad in my definition of both science and tool here: For example, someone willing to demonstrate medieval methods of casting astrological natal charts would be welcome.

So, If your interest is in the scientific tools and instrumentation of the period, be it navigation, timekeeping, surveying, alchemical glassware, weights and measures, astronomical, etc. Please get in touch with me.

Please repost to any discussion lists you think might be interested.

Master Richard Wymarc

wymarc(at)hotmail.com

- on 01.16.12
- Astrolabe Project, Drafting The Astrolabe
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Getting the zodiac and calendar rings done was probably the worse, most finicky part of this project; the rest of the tasks remaining might require careful measurement, and attention to detail, but orders of magnitude less work than the last section.

The next task is to finish off the rear of the astrolabe. Two scales remain to be drawn, the Unequal hours and the shadow squares.

Drafting the shadow squares is straight-forward: Two square boxes in the bottom half of the astrolabe back, each side divided into a set number of sections. The only trick bit will be finding the correct size for the boxes. I want the shadow squares to be as big as possible, as larger means more accurate to draw and to use, but they also need to fit into the remaining space inside the calendar ring. Because the calendar ring is offset, I have to take that offset into account

The largest dimension of the shadow square is its 45 degree diagonal, so if I draw a line at 45 degrees from the center to the right bottom side of the astrolabe, stopping at the inside edge of the calendar ring, I can use that point to erect the rest of the square.

Step 1: Draw the 45 degree diagonal from the center down and right to where it touches the inside of the calendar ring on the bottom right side of the astrolabe back. Mentally label this point “A” (See Figure A).

Step 2: Erect a vertical line from point A to the horizontal center line of the astrolabe (see Figure B).

Step 3: Erect a line parallel to the horizontal center line of the astrolabe, running from point A to the left side of the astrolabe (see Figure C).

Step 4: Draw the 45 degree diagonal from the center down and left to where it touches the line drawn in the previous step. Mentally label this point “B” (see Figure C).

Step 5: Erect a vertical line from point B to the horizontal center line of the astrolabe as you did in step 2 (see Figure D).

Step 6: Draw a scale line inside the box you just drew (see Figure E).

Step 7: Divide and label the Shadow Squares.

- on 01.09.12
- Drafting The Astrolabe
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- on 01.04.12
- Astrolabe Project, Drafting The Astrolabe, Tools
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In working with a compass and a straight-edge I’m finding that there are techniques that can be used to improve the accuracy of the drawing.

When drawing arcs to bisect lines or angles it is best to set the compass radius so that the construction arcs cross as close to 90 degrees as possible. The shallower the angle of incidence, the less defined the intersection, and the greater chance of the line drawn between the intersections being off by a (small, admittedly) amount.

When using the Compass to measure distances, it is easier to transfer large distances than small ones with accuracy. If I need to draw a line and mark a point 1/32 of the way along it, I can do this with good accuracy by repeatedly dividing the line in half by construction. But if I want to transfer that 1/32 distance, it is easier and more accurate to transfer the 31/32 measurement. The mark ends up in the same place, but adjusting the compass accurately is easier.

When dividing a circle it is better to work each stage in the division over the whole circle then move to the next. If I need to divide a circle into 24 sections, I should first quarter the whole circle, then trisect all four quarters, then bisect all twelve sections. I could try to save time by trisecting one quarter, and bisecting one section of that; then use the compass to copy the arc of that 1/24 section 24 times. But I find that small errors in measurement compound if you do it that way. Working the whole circle at once tends to cancel out small errors.

- on 01.04.12
- Astrolabe Project, Drafting The Astrolabe
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Well… That was a bit more intense than I expected.

I was expecting that drawing the calendar ring on the back of my astrolabe would be rather involved, but actually doing it took more patience than I expected. This was definitely the hardest part so far.

Drawing the offset ring was straight-forward. As described previously computing the direction and distance of the offset is fairly simple, once you have the equations, and drawing the lines presents no problem. Where the difficulty lies is dividing the calendar ring. As described earlier, I need to mark off a section equal to the equivalent 5.25 days and then divide the remainder of the circle into 360 parts. Because I’m no longer working with a full circle, I can’t just quarter and then trisect like i did with the zodiac ring. Here I have to bisect each angle, and fudge “trisection” with the compass. Fudging the trisection by adjusting the compass to mark off 1/3 of the arc by eye is full of potential for small errors. Moreover, the first bisection that has to be made is to divide a huge arc – It was harder to do that accurately than I expected. I had to invent techniques to make it easier to divide accurately. After much cussing and erasing, I have a result that is fairly accurate, I need to ink and label it and then I will post a scan of the result.

- on 12.26.11
- Astrolabe Project, Drafting The Astrolabe, Tools
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While I’m working on this project, I’m also researching the tools and techniques used by the instrument makers who made these astrolabes. The two period manuals I am working from assume a certain shared level of knowledge, and do not mention tools or engraving techniques, except in passing.

I am finding the art of the period a better resource; in particular, I found a very nice portrait by Hans Holbein the Younger:

(*Note: WikiMedia is listing this image as Public Domain, if anyone claims the rights to the photograph, please contact me at the email to the right and we can discuss it*)

The original image can be found here.

The subject of the portrait is shown with several tools and a partially completed sundial compendium similar to those described in Hartmann. The tools for designing and laying out the lines of a sundial are the same ones that would be needed in designing and laying out an astrolabe.

Identifiable in the portrait are two straight-edges (one on the table, one hanging), two scribing compasses (on the table and hanging), a set of dividers (by the hammer on the right), a scriber (in front, right of center), some scissors and some other tools whose use is not immediately evident.

My friend Miguel, of Spanish Peacock was nice enough to make me a very nice straight-edge out of hardwood, based on the one in the painting:

A bit later, I stumbled across a two pairs of scribing dividers at a Harbor Freight sale.

I’m currently looking into buying a good scriber, and I will be ready to start playing with brass. I have neither the time nor skill to build a complete astrolabe from scratch, but I’m thinking a brass version of one of the climate plates might be instructive to attempt.