# Sundial Created - Oaths Update 3

2025-09-14 - [54] 6:28

Back in October of last year for Winter Nights, I made a some oaths to be kept by this coming Winter Nights this next full moon.

Winter Nights 2024 - Oaths and Deleting My Mastodon Account [HTTPS]

## 5 Oaths

The 5 oaths I made were:

- Find and listen to at least 6 barely listened to albums from start to finish in the order intended by the artist without skipping through any songs (album song order)
- Actually read through all of "Godel, Escher, Bach: an Eternal Golden Braid" instead of constantly starting over and stopping at chapter 3 or 4
- Crochet a Winter hat by Yule
- Heavily clean my living quarters by Sigrblot, to the point where I'm not ashamed of people entering those living quarters
- Build a functioning sundial from scratch, no matter what material, and get an accurate time reading, accounting for the Equation of Time and Longitude

I have finally completed all 5 oaths (although my office could use a little bit of cleaning again), ending with making a sundial.

## Making the Sundial

The material used was cardboard pizza circles. I have access to countless numbers of these things, so I figured I would use them because they're already circles.

### Base

One pizza circle was used as the base of the sundial, which needs lines denoting the hours. To find those dial lines, I used the following equation.

    dialAngle = atan( tan(hourAngle) * sin(latitude) )

The value `hourAngle` of noon is 0, and each hour after noon is 15 degrees further around a circle, so 1 is 15 degrees, 2 is 30 degrees, 3.5 (3:30) is 52.5 degrees, etc...

Marking out these hours was a bit harder than expected, as I currently do not own a compass (the geometry tool, not the navigation tool). Instead, I took advantage of the fact that the base was a circle of a known diameter and marked everything out using a tape measure used for fabric-work. The tape measure used inches and 8ths of inches.

To figure out where to mark each hour, I essentially create a bunch of isosceles triangles. The 2 legs of the triangle are 5 inches long (the pizza circle is 10 inches in diameter) and the vertex angle is the dialAngle of the hour. I can use this information to determine the base length of the triangle and make a chord that is that long starting at the noon hour point (dialAngle = 0 degrees). That can be figured out with the law of cosines.

    c**2 = a**2 + b**2 - 2 * a * b * cos(C)

`a` and `b` are both 5 inches and C is the dialAngle. `c` is the base chord length we are trying to find. We can rearrange and slot in values to the law of cosines equation.

    baseLength = sqrt( 50 - 50 * cos(dialAngle) )

Once I got the base chord lengths, I rounded them to the nearest 1/8th of an inch and started marking the outside of the pizza circle, using the spot for noon as the reference. An issue would happen though that the further from noon, the more inaccurate the points will be, so I first found the 6 o'clock points and midnight point, which split the circumference in quarters. I would use noon to make the 6 AM through 6 PM hour points on the pizza circle and would use midnight to make the hour points before 6 AM and after 6 PM.

A horizontal sundial's (the kind of sundial I made) hour lines from 6 AM to 6 PM are a mirror image of the hour lines from 6 PM to 6 AM. Also, the hour lines from 6 AM to noon are a mirror image of the hour lines from noon to 6 PM. This meant I only needed to calculate the base chord lengths for noon through 6 PM as long as I had the midnight hour point marked as well.

### Gnomon

I used a second pizza circle for the gnomon. The gnomon needed to be the same angle as the latitude that the sundial is placed in so it can point to the celestial north (pointing essentially to the star Polaris). I made sure to cut the gnomon so the leg lengths of the gnomon were slightly smaller than 5 inches. This was so I could slice the noon line of the base and insert the gnomon.

## Accuracy

There is a lot of imperfection to this sundial:

- It's cardboard...
- The dial angle lines were made with a straight edge only, not a compass as it should have been
- The gnomon is only held straight into the base through friction alone
- The sundial isn't perfectly flat
- The gnomon angle isn't perfect

With all of those imperfections stated though... it's impressively accurate. I'd say it's accurate to within 5-10 minutes, possibly even more accurate than that. When I took this picture, the solar time in my area (accounting for my longitude and the equation of time) was 1:20 PM and the sundial certainly looked to be pointing at about 1:20 PM. Overall, I consider this a success and consider the oath completed!

## Contact/Reply

If you would like to reply to this post, feel free to send me an email.

Email: vi@vigrey.com [Email]
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