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.
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.
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.
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.
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 ).
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.