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Sundial, compass, spirit level. All-in-one time piece.

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Picture of sundial, compass, spirit level. All-in-one time piece.
Who wouldn't want to have a wearable sun-dial as part of a time traveller's outfit?
My sister and I always thought a wrist-mounted sun-dial would be completely impractical, Not so.
(although it's still nowhere near as convenient as a normal watch)
To have a functioning sun-dial outside of your garden, you need to know where north is..
Also, you need to keep it level.  How do you combine a shadow, a compass and a spirit-level, and fit it on a wristband?
Researching existing sun-dial designs, one type in particular caught my fancy: the equatorial dial.
It can function at any latitude (if you know what it is) and some of them actually give you true north when you line them up to read the time.
An afternoon later, I had a modified design that closely resembled a snow dome.. how could i resist?

This dial can read to within five minutes of local solar time if you etch the components accurately.

 
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Step 1: The Maths, yuck.

Don't worry, this will be over soon and there's no exam.  Everything vital will be covered when you mark out the plastic.

If you lived a few hundred years ago, you'd know that the earth is flat and the sun goes around the earth.  While wrong, it's a good starting point.
The sun passes the roughly same spot in the sky every 24 hours so it spends 12 hours above the base plate.  We need to divide the dome into 12 equal increments: one for each hour.  This is the equatorial line.

The circle on the base plate is a bit harder to grasp.  Every year, the sun wanders north and south, about 24 degrees above and below the equator.  As it turns out, this is very close to a sine wave so we'll call upon the unit circle:
The base plate is divided into 12 sections, one for each month.  Each month has a height above or below the equatorial line, this height follows the same sine wave the sun follows year after year.

The size of the circle is important too, the sun's rays have to hit the very top or very bottom of the circle at the solstice, making them about 24 degrees north or south of the very top of the dome.
Unfortunately, since this is basically a snow dome, we need to account for the refraction angle into the water.
A bit of mucking about with algebra tells you that the diameter of the circle needs to be about a third the diameter of the dome (0.312 times the size, to be precise).
(If you actually do the algebra, a plot of the sine of the incident angle vs the sine of the refracted light is slightly non linear, but it's only out by less than 1%)
[edit] This is a PDF of some of the algebra.

bubbledial.pdf(595x842) 137 KB
I made a solar compass too!
It came from my tracking solar cooker and clam shaped solar attempts.
I didn't expect the "2 north's" problem.
It took me completely by surprise!
Is there any way to quickly tell which north is the right one?
If you have a watch you could quickly tell which is which but if you don't it gets a bit harder.
Also, have you considered putting a demo video on the internet?
Survivalists are interested in compass stuff and they should have something much better than sticks in the ground.
Thanks
Brian
EGiR (author)  gaiatechnician3 years ago
As far as I know, you need to know which side of noon you're at.
It gets really hard near noon because the two norths get really close together.

The best fail safe method I know of is that one north will drift fairly quickly (twice as fast as the sun moves across the sky) while the other will stay put.

Here, you'll probably want a bigger dial though because it's hard to read this with resolution better than 30 mins.
The design was inspired by the equinoctical ring dial. Which should perform a lot better, but looks significantly less like a snow dome :( http://en.wikipedia.org/wiki/File:Ringsundial_open.jpg

because the working area is so small and the shadows are so fuzzy, it's really hard to photograph. A demo video would be cool but I'd have to re-build to get a more photogenic device.
Thanks. So basically, morning and evening, it is very accurate, and around noon, you got to be a bit careful, probably need to give it 15 minutes to identify the false reading. Do you know if the ring sundial can work as a compass too or is it strictly a timepiece? (I had a look, there is video too) but I couldn't tell if it works as a compass.
EGiR (author)  gaiatechnician3 years ago
The ring dial uses all of the same mathematics.
The bubble dial is basically an inside-out ring dial.

The sliding part in the middle of the ring dial works the same as the graduations on the face of the bubble dial.
The time written in the ring is the same as the time etched onto the dome.
you hang the ring dial on a string - same as lining up the bubble,

you rotate the system until the point of light (shadow of the sliding part) falls squarely on the ring, the ring with the time will be equatorial, the ring with the latitude will be north-south (ie, the axis of the largest ring is east-west)

It still has the two norths issue (and still needs a look-up table for the analemma), but it can be built bigger and with better resolution.

basically, every "self aligning" sun-dial will give you true north. These two dials are good examples of that.
I don't understand...how does it work as a compass?
EGiR (author)  alltootechnical4 years ago
Ok, so once you line up:
You've got the bubble under the dot that marks your latitude (2 degrees of freedom)
You've got the shadow from the line on the dome over a point on the centre line determined by the month. (the other degree of freedom)

Once you've done all that, the dial can only be facing one way (actually two, but one direction will give a time that's on the other side of noon)

When it's lined up, the line on the dome is parallel to the equator of the planet, and the centre line is parallel to the axis of rotation, that gives you true north.

Here in Oz, the southern end of the dial points higher than the northern one so it's easier to be facing true south when you read it.
Thanks.
Do you use Mathematica? And what version?
EGiR (author)  alltootechnical4 years ago
 Yes, version 7 for Linux with a student licence from uni. 
Really useful stuff but it's a pain when the licences expire every year though.

 I'm using a 15-day trial and I kept replacing the licenses over and over. xD
EGiR (author)  alltootechnical4 years ago
nice.
i always thought that, if a wrist-sundial were to be attached to a compass, it would automatically orient itself north.
usb key4 years ago
according to WIKIPEDIA! WOOT WOOT!!!1 the summer solstic is either the 20th or the 21st and the winter solstic is the 21st or 22nd depending on wether or not its a leap year. doesnt really make a difference, just felt like correcting you
Fred826644 years ago
lol Oh man I am late for wok ,,,, My dial did not go off and wake me up lol  but all jokes a side This is cool !  I would do this one trying to make use of those Gum ball toy case things ,,,,,,,Those cases them rings and cheap toys you can get out of gum ball machanes for $0.50 to $0.75 . I call them Short Term  Grand Kid Bribers.    
EGiR (author)  Fred826644 years ago
 haha nice, they'd probably be really good for this.
wocket5 years ago
I might try this with silver and a floating hollow lens filled with water to make it true steampunk, I'll let you know how i go!
EGiR (author)  wocket4 years ago
Yes, the next step would definitely be to make it pretty!
Brass and leather is always good... look forward to seeing it dolled-up!
Wow, I've seen a handheld sundial, but never a wrist mounted one!
 
Parapegma5 years ago
 BTW, I forgot to add is that this is the best wrist sundial I've ever seen, bar none. 
EGiR (author)  Parapegma5 years ago
 thanks for the feedback!
hurtzmyhead5 years ago
I love it! great idea and great execution in the building!
EGiR (author)  hurtzmyhead5 years ago
Thanks,
If i ever make another attempt, I might try for some metallic trim here and there.
Parapegma5 years ago
 Depending on your Longitude, solar time and Local time (time in your time zone relative to GMT) can be as much as two hours off. You also have to correct for the equation of time for your latitude/longitude, so there can be quite a difference. In addition, true north and magnetic north vary considerably world wide.

I don't want to get too much into this, but this is why we use watches now a days (and presumably when time traveling) instead of sun dials.
EGiR (author)  Parapegma5 years ago
Under Making it Work, I did mention these corrections and posted a link to a table of the equation of time calculated for every day of the year.
Watches are great for travelling through space, but considering the number of time travel errors that play out in fiction, I'd hate to have to re-set my watch every time I park.
the only other niggling error is the fact that the solstices change over time. However, you'd need to take the Gregorian calendar to the dawn of time for this to be a problem, at which point orbital mechanics are completely different and you need a new dial anyway.
Parapegma EGiR5 years ago
 Unless I misread " making it work," you did not include a correction between zone time and solar time. Perth is pretty close to 115 degrees , so I think your correction is only a few minutes plus or minus for zone time plus equation of time.  You need both that and your equation of time to correct from solar time to zone time (as in time zone) . Equation of time also changes over the years because of changes in the earth's orbit and other factors. Astronomy does not use the Gregorian calendar but instead  uses the Julian calendar in a modified form which enables it to place events anywhere in time / space  from the big bang onward. This includes the solstices. Because change in orbital mechanics  is pretty regular and pretty predictable, you should have no problem figuring them out.
Kiteman5 years ago
Oh, this is so...

Well, the only thing that could make it better would be a shot of it actually telling the time (with visible shadows and what-not).

Highly creative - well done.
EGiR (author)  Kiteman5 years ago
Thanks Kiteman!
I'll get onto that when the sun comes out.
EGiR (author)  EGiR5 years ago
done, step8.
 Awesome, I've always wanted a wearable sundial. 

The line drawing and marking process is slightly confusing, could you post a template of some sort?
EGiR (author)  mad_scientist5 years ago
Thanks for that, I'll see about knocking up a PDF.
EGiR (author)  EGiR5 years ago
There's a .png on step4 now, it has all the important lines on it.  embellish it all you like. The scale isn't important, just blow it up to fit your dome.
Oblivitus5 years ago
I had the same idea when I was in Middle School. I didn't have the skills to actually make one then though. Good job.
EGiR (author)  Oblivitus5 years ago
Nice, childhood fantasies are our speciality.
(that sounded weird)
Thanks
Oblivitus EGiR5 years ago
Indeed it did, your welcome.