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.
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.
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.
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.
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.
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.)
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.