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Levitating Potato
Level 3: 301 points
Alltime Score: 1751 points
Last Logged In: June 28th, 2015
TEAM: Societal Laboratorium TEAM: SCIENCE! TEAM: Lab Coats! TEAM: Level Zerø TEAM: Probot

15 + 100 points

Sundial I by Levitating Potato, teucer

January 18th, 2008 10:59 AM / Location: 35.914982,-78.93453

INSTRUCTIONS: Make a sundial. Use it!

Intro: I decided I wanted to go one step beyond this and make sundial-making ubiquitous among SF0 players. I came up with the idea of making a polar sundial out of a single piece of paper small enough that, when folded in the places it needs folds anyway, it would fit into your wallet. I then needed some way of angling it so that it would sit above horizontal at an angle equal to the latitude you're using it at - which, I decided, called for some more paper to be folded at a spot found by some simple trigonometry.

I enlisted the help of Levitating Potato to produce the actual pieces, because he has a nice cad program that gave him the precise measurements we needed and I don't. He's also the one who had the clever idea of giving lines on the stand for cities we know have active SF0 players rather than just every ten degrees.

Once the dial design was finished, we of course constructed our own sundials... but that really isn't the point. The point is to make a design you can print out on cardstock (or copy paper, in a pinch), cut out, and fold quite easily into something that fits in your wallet. Now no SF0 player will ever have an excuse for being without a polar sundial.

Assembly Instructions: Print out the design and cut out both pieces.

Fold the dial plate along the central line such that the lines are on the outside. Then fold it the other way along both noon lines (the line closest to the center on either side). It may be somewhat tricky to fold along a line that needs to be on the inside of the crease, so the other trick to help you is knowing that the central piece will come up exactly to the 1500 and 0900 lines. The section of the dial plate between the noon lines is the gnomon - the part of the sundial which casts the shadow you use to tell time. We recommend keeping it from spreading apart at all by gluing the inside of the gnomon to itself with glue stick.

For storage in your wallet, those creases need to be folded all the way, leaving a flat piece the size of a driver's license. For use, the noon lines should be unfolded to a right angle, so that the dial plate is flat and perpendicular to the sides of the gnomon.

Fold the stand along the line corresponding to your latitude. If your latitude isn't marked, estimate where that line would go based on other lines that are. Whether the lines on the stand are in or out is immaterial, as is which hemisphere you're in.

For wallet storage, we recommend that the crease for your latitude be folded all the way and the stand be folded around the open end of the dial plate. However, if you travel from one latitude to another regularly, you may wish to avoid strengthening such a crease and prefer to store the stand unfolded; for this reason even unfolded it is no larger than a driver's license. For use, the stand will need to be creased there to a 90 degree angle.

Operating Instructions: First, set up the stand. It should be folded at one place only - the line corresponding to your latitude. That fold needs to form a right angle; we recommend using a table top as a square. Now put the two ends of the stand on a flat surface that gets full sunlight. (In other words, it forms a right triangle with the flat surface as a hypoteneuse.)

Next, open out your dial plate so that the two sides form a single plane and the gnomon sticks up perpendicular to them. Place this on the inclined side of the stand, on the side that has the lattitudes higher than 45 degrees. (Exception: if you are on the 45th parallel, it does not matter which side of the stand you put your dial plate on.) The dial should be on the steep side if your latitude is more than 45, and on the shallow side closer to the equator.

Now, rotate the whole assemblage such that the side of the stand you have your sundial on is south of the other side, the latitude marks on the stand run east-west, and the hour lines run north-south.

Finding North: Your sundial needs the top of its gnomon, and its hour lines, to run directly north-south to tell accurate time. (In fact, because of the angle it's sitting at, they will be exactly parallel to the earth's axis.)

The method previously described here for using the dial itself to find north, turns out not to work. We hereby call upon anyone who's better at the relevant math to help us find an alternative method using only the sundial, or a proof that none is possible.

Telling LAST: Having set up the sundial, telling the local apparent solar time is quite simple - just look at the shadow of the gnomon on the dial plate; the edge of the shadow will be read the current local apparent solar time. This is the kind of time the sundial is meant to read, as are most dials, but with a bit of extra know-how you can get other kinds of time with it too.

Telling LMST: Local mean solar time is just LAST with a correction added for the so-called Equation of Time - a formula which predicts for each day how many minutes fast or slow your sundial will be. In practice, the formula is quite ungainly - so look up the correction on a handy-dandy table and add or subtract the resulting number of minutes from the LAST as indicated by your sundial. (Note that in fact this varies by significant fractions of a minute from one year to the next - but using one average table like the one I linked to is good enough for the level of precision our sundials will produce.)

Telling ZMST: Zonal mean solar time is the local mean solar time at a specific longitude line, and is the same for everybody in the same time zone. Making the longitude correction requires you to know both what your longitude is, and what longitude you'd have to be at for ZMST to equal LMST (called the standard meridian). The standard meridian is fifteen degrees times the number of hours you have to add or subtract to GMT to get your time. (If you're subtracting, your standard meridian is in the western hemisphere; if adding, it's in the eastern hemisphere.) Every degree of longitude between you and the standard meridian for your time zone represents four minutes that you have to either add (if west of the standard meridian) or subtract (if east). This number need only be calculated once and memorized, as it is constant throughout the year.

For example, San Francisco is at a longitude of 122° 26′ - or almost exactly 122.5° - west. Its time zone is GMT - 8 hours, with a standard meridian of 120°. SF is two and a half degrees west of that, so residents should add ten minutes to their LMST calculations to get ZMST.

Telling Clock Time: If you've actually bothered with the equation of time and such needed to tell ZMST, clock time is the easiest thing in the world. Take the ZMST result and add an hour if it's daylight savings time. That's it.

Note that you won't get perfect answers out of your sundial even after all those corrections. The stand in particular is not likely to hold its perfect right angle, and of course it's very hard to get your folds positioned perfectly in the first place.

- smaller



The measurements for producing the dial plate. Astute players will note that our dial plate is actually two tenths of a millimeter shorter than this says it should be; that's to make it fit in a wallet.



This is the spreadsheet used to calculate where the lines go for the stand.



and the same thing for lame Microsoft customers



This is the actual sundial. Print it out, cut the parts out, and follow our directions. Voila, you have made a sundial.



Opening the stand to a right angle. It's folded along the SF/Seoul line, because that's also the latitude I'm at.



The dial plate, reading a local apparent solar time of about 1315.



Today, the equation of time and longitude corrections add up to twenty-six minutes difference. It's 1345, and the dial is reading 1315 - so, despite the imprecision of the sundial, I'm only off by about 5 minutes.



The CAD file used to generate the PDF.

20 vote(s)

Favorite of:



19 comment(s)

(no subject)
posted by Levitating Potato on January 18th, 2008 11:46 AM

We'd be happy to add more cities if we missed any. The middle latitudes are kinda crowded as is, though.

I had meant to upload the dxf file that the pdf was generated from, but the uploader doesn't take those. If there's interest I can ask SSI to change that.

(no subject)
posted by susy derkins on January 18th, 2008 11:49 AM

I want to cry! This is so impossibly good!

(no subject)
posted by GYØ Ben on January 18th, 2008 12:04 PM

An excellent completion. Loving it lots.

(no subject)
posted by teucer on January 18th, 2008 12:54 PM

By the way, we'd love it if somebody with more knowledge of astronomy than us could check our way of finding north. How do we fix it?

(no subject)
posted by Burn Unit on January 18th, 2008 1:28 PM

Check our way of finding north??
Just always know where it is, suckas!!!1!!

(no subject)
posted by teucer on April 29th, 2009 7:18 PM

At this point in time I heartily endorse this recommendation.

(no subject)
posted by teucer on January 18th, 2008 1:35 PM

See, that's a lot harder when you aren't in Minneapolis.

We think we have an improved version, but it's hard enough to implement that we'd like to make sure there isn't a better one first.

(no subject)
posted by Sean Mahan on January 18th, 2008 3:10 PM

BAM! dxf, dwf, dwg and skp are all uploadable now, so go ahead and get your CAD on.

(no subject)
posted by Levitating Potato on January 18th, 2008 3:26 PM

Awesome. DXF uploaded. Not too complicated, but if anyone wants to modify this for their own use, it should now be convenient to do so.

(no subject)
posted by susy derkins on January 18th, 2008 6:16 PM

Would it work for Loki in Antarctica?
Are there even shadows moving at all in the summer?

(no subject)
posted by rongo rongo on January 18th, 2008 6:22 PM


(no subject)
posted by Burn Unit on January 18th, 2008 7:55 PM

Everywhere is north when you're in Antarctica!

(no subject)
posted by teucer on January 18th, 2008 8:01 PM

At the south pole, everywhere is north and there isn't really a meaningful local apparent solar time. For the rest of Antarctica, of course the shadows are moving. (And we've included a line on their for the latitude of McMurdo Station; if Loki's at a different locale we can add that line instead.)

(no subject)
posted by Levitating Potato on January 18th, 2008 8:13 PM

The shadows at the pole proper would move, even in the summer. The sun would be above the horizon, but it would travel in a circle around the sky at the same apparent elevation every 24 hours, with that elevation slowly rising until the summer solstice, then falling to the horizon at the equinox, below the horizon until the next equinox, and then back to maximum (not all that high, of course) for the solstice.

On other planets and moons (including our own) it's more interesting -- some of them have craters at the poles that are perpetually in shadow. There's been some talk of the Lunar south pole as an interesting spot for a manned base since you can build perpetually-lit solar towers, and there might well be ice in the shade.

(no subject)
posted by teucer on January 18th, 2008 9:35 PM

Yeah, at the pole proper I imagine you could point the sundial toward north along the standard meridian for any time zone and have it read the (apparent) time in that zone.

Nicely done.
posted by Loki on January 20th, 2008 4:09 AM

Way cool, guys.

And, the discussion here has anticipated what I was planning as my first task of the era. If I can find a printer, I will try your sundial out in addition to my (much more crude, fixed location) one.

For anyone who cares, I arrived at the pole a few days ago. Have been incredibly busy working since the moment I arrived, but should have a few spare hours soon for tasking and praxis browsing. Can't wait to catch up with my friends here.

(no subject)
posted by teucer on January 20th, 2008 8:33 AM

We're assuming you need multiple observations. Our old method involved rotating the dial to find the maximum shadow length - a step we think may be involved in a more correct algorithm also - and that's essentially equivalent to taking infinite observations.

(no subject)
posted by susy derkins on January 20th, 2008 12:01 PM

Hey guys, didn´t you shortchanged yourselves of 60 points? You completed this task. Almost. We need to compensate that in votes.

(no subject)
posted by teucer on January 20th, 2008 2:11 PM

Neither of us is level four, so we couldn't sign up.

But we feel that although we didn't use it to the exclusion of all other timekeeping devices, we made having a sundial for that purpose very easy - for ourselves and others.

Not that I'd mind people compensating in votes, mind you.