Drafting the Astrolabe 12: The climates part 1

Drawing the climate part 1The first step in drafting the astrolabe climate plate is to lay out the Tropics and the Equator, along with the meridian. As these markings will be the same for all the plates, it makes sense to draw each line on all the plates before moving on to the next line. This way, I can set the compass once for each line, and I only have to draw construction lines on a single sheet.
Step 1:
Draw a horizontal line to become the true east-west line; and erect a perpendicular line at its center point to become the meridian. Repeat this on all the climate sheets. Next, use the compass to draw a circle the desired diameter of the plate (remember to get this measurement from the finished astrolabe front drawing, the plate will need to fit in the mater hollow). Without changing the setting of the compass, repeat for all plates. Finally, set the compass to a slightly smaller diameter and draw the circle for the Tropic of Capricorn. Repeat on the other plates.
Note: The space being left at the edge of the plate allows room for the outer edge of the rete. Some astrolabes have this space some do not.
When done with this set all the plates should look like A in the figure to the right.
Step 2: 
The current obliquity (angle to the equator) of the Ecliptic is approximately 23 degrees 26 minutes [Morrison]. The next step is to project the circle for the Equator, so at an angle of 23.5 degrees (rounding off to the nearest half degree as my tools are no more accurate than that) I draw a light construction line from the center of the plate to the circle representing the Tropic of Capricorn (#1 on the right).
As I already have the Tropic of Capricorn defined, the first circle to project will be the Equator. To do this, place one end of the straightedge on the place where the true east-west line (the horizontal line) crosses the Tropic of Capricorn, and the other end on the point where the construction line intersects the same circle. Draw a second construction line (#2).  The point where this construction line crosses the meridian (the vertical line), marks the radius of the Equator circle. Place the point of the compass at the center and draw a circle at this point. Repeat this circle on the other plates.
Step 3:
Repeat this process to project the circle of the Tropic of Cancer: This time using the intersections with the Equator circle (See B on the figure to the right).
After the construction lines are removed, all five plates should look like C in the figure to the right.
The next step will be more complicated: Drawing the almucantars.

Drafting the Astrolabe 12: Planning the climates

Before I tackle the next bit I need to plan out what I want to do. I want a set of five climate plates, one for each of five different latitudes. One of these will need to be for the latitude of Cooper’s Lake, the site of the annual Pennsic War. Another should be the latitude of my home, of course. For the other three I will select from latitudes of Major cities I have visited.
This gives me the following list:
  • 39 degrees – My home latitude
  • 41 degrees – Pennsic War
  • 49 degrees – Paris
  • 52 degrees – London/Cambridge
  • 56 degrees – Copenhagen
As for drawing the plates themselves, it occurs to me that a lot of the work is going to be either identical or very similar for each plate. This suggests to me that doing all five plates at once, that is, completing each step on all five plates before moving on, will be the most efficient way forward.
The process for creating a climate plate breaks down as follows:
  1. Draw the outer edge of the plate. Add the Meridian and east-west line. Draw the Tropics and Equator.
  2. Draw the almucantars (circles of elevation) to include the horizon and the twilight line.
  3. Draw the azimuth arcs
  4. Draw the equal hour arcs
As I did with the front and back of the astrolabe I will detail each step as I go along.
Watch this space!

Drafting the Astrolabe 11: The Unequal Hour Arcs – Completed

The unequal hours arcs have now been added to the back of the astrolabe. With the exception of what little decoration I’m planning, this completes work on the back of the project.

Unequal hours completed

Unequal hours completed

With the front and the back now finished, the next step is designing a set of climate plates. Doing five of those will get a bit tedious, perhaps, so I’ll probably take a break part-way through to do the rete and then the alidade and rule.

There’s an App for That: An astrolabe for the iPad

As I mentioned a while back, there is a developer out there using the output of the Astrolabe Generator to create an astrolabe app for the iPad. Well, version 1 is complete and available for free on the App Store. The website is: http://taucetisystems.com/. I have not had a chance to look at it yet, as I don’t have an iPad, but it looks very nice: Just the kind of thing I was hoping the Generator would inspire.

Phaeton for iPad

Phaeton for iPad

Bug Swatting and New Options

One of the Astrolabe Generator’s users, Jürgen Hoefeld, spotted a problem with the alignment of the Houses of Heaven, the intersection point should be on the horizon, and was not. I have it fixed now and the changes checked in to SourceForge. I have posted the updated generator to the site as well. In addition to the fix I have included two new options for the back, both still works in progress:

There is now an option to show the Lunar Mansions inside the Shadow Squares; and in the upper right quadrant drop-down there are options to display the Arcs of the Signs.

Astrolabes on YouTube

Two videos I ran across on YouTube:

The first is a good, quick introduction to the tool LINK.

The second is a very nice breakdown of a practical use of the astrolabe LINK.

Drafting the Astrolabe 11: The Unequal Hour Arcs

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:

Unequal Hours Example

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.Drawing the unequal hour lines

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.

 

Random Jottings

The Missing Manual has gone missing!

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.

Plans and instructions for making a plastic astrolabe

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…

There’s an app for that

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.

Drafting the Astrolabe 10: The Shadow Squares – Completed

I thought I posted this two weeks ago… Work and life have gotten busier than I realized it seems.

Anyway, here is the completed shadow square section. Next up will be the unequal hours scale and then the back will be done.

Astrolabe: Completed shadow squares

Pennsic: Scientific Instrument Day on Artisan’s Row

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