Introduction: 15-minute Paper-craft Sundial

This is a 15-minute paper sundial in two senses: it takes 15-minutes to make and is labeled to the nearest 15-minutes.  It is made of paper, but I designed the gnomon to have a three-dimensional base for greater stability, tapering to a thin top for better accuracy around noon.

The hard work was my doing the trigonometry for the three-dimensional paper-craft gnomon and writing a perl script that generates a pdf file for a particular location.  But with the script written, you should be able to print out a sundial from the generator on my website and construct it in fifteen minutes.

Ingredients and tools:
  • Two sheets of paper, ideally cardstock or some other heavy stock.
  • Scissors
  • Paper glue (I use Aleene's)
  • Printer
  • Ruler
  • Something pointy, e.g., a pen with no ink or a small screwdriver
  • Computer with internet access, PDF viewer, and printer
The script I used was based loosely on the one in my large patio/driveway analemmatic sundial Instructable.  This is a much simpler project.  The last one I assembled took 12 minutes once I had the design printed out and all the tools in place, and that's counting periodic stops to take photographs.

You can load the PDF file into a vector drawing application like Inkscape and make it fancier.  Just make sure that if you resize the dial, you resize the gnomon (the pointer) in the same proportions.  The script is open source so you can modify it as you see fit.

You can presumably trace the printout on copper sheets to make a fancier dial and gnomon.  I'd love to see it.

This would make a good classroom project at various levels, depending on how deep you get into explaining how it works.

Note: The script currently works for latitudes between 24 degrees (north or south) and 65 degrees (north or south).  (That covers all of the contiguous 48 states in the U.S., much of the populous parts of Canada and Europe, all of South Africa, much of India, etc.)  The limitations are due to the way the gnomon is designed to work both when shadows are short and when they are long, and its having a wider base.

Step 1: Enter the Data

You will need the following information:

  • your zip code (if you're in the US) or latitude/longitude (this site should help)
  • your timezone
  • whether your location has daylight savings time (time change between winter and summer time).

Now go to my script's website Enter the above information. If you have daylight savings in your location, you will need to decide if you want your dial to show winter or summer time. You can leave the colors as-is for a black-and-white sundial, or you can enter HTML color codes to customize. I customized by setting the dial and hour backgrounds to C6DEFF (a light blue), the gnomon to 2B60DE (a royal blue) and the hour text to 000000 (black). You can also choose whether you want Arabic or Roman numerals and whether you want 4 shown as "IIII" or as "IV". If you don't want some element, like the time correction table, you can set its color to be the same as the background it's on.

Print both pages of the PDF file, ideally on heavy paper, e.g., card stock.

Step 2: Cut Out the Dial

Cut out the dial circle.  If you like, you can glue it on a harder backing.

Step 3: Score the Gnomon

The gnomon is the pointer that casts the shadow.

The gnomon is on the second page of the pdf file and has five dashed/dotted lines (depending on your color choices, they may be hard to see; you might want to put a black and white version on screen for references).  The lines that have only dashes (_ _ _ _ _ _ _) are valley folds--you will fold so that the dashed line is at the bottom of the crease.  The lines that have dashes and dots (_ . _ . _ . _ .), i.e., the central line and the lines for the outside flaps, are mountain folds--you will fold so that the dashed and dotted line is at the top of the crease.

Before folding, however, you need to score all the fold lines to make an accurate gnomon.  To do that, use a ruler and draw over them with a pointy object, like a small sharp screwdriver.  Try to remember which lines are mountain and which are valley folds or have the PDF file on your computer screen for reference, since the scoring may make it hard to see the dots and dashes.

After scoring, cut out the gnomon's outer edges.  (I find it easier to score before cutting.)

Step 4: Fold and Glue the Gnomon

Make all the creases in this step nice and sharp.  It will be difficult to keep them sharp as you reach the end where they come together.  Using a ruler may be helpful.

Start by folding the gnomon in half along the central mountain-fold line, and pressing the halves together (photo 1).  Make the halves line up nicely.

Then fold back (in the opposite direction to the first fold) along the next two lines, which are valley-fold (photo 2).

Next, carefully glue together the two triangles on either side of the central mountain-fold line, up to the valley-folds you just did (photo 3).  Don't use too much glue--you want a very flat and straight joint.  Wait for the glue to set a bit before the next step.  If you want the gnomon to be stronger, you can embed a wire extracted from a wire-tie along the crease.

Finally, you have two small flaps which will be used to glue the gnomon to the triangular (or, more precisely, diamond-shaped) area on the dial.  They are attached with mountain folds--crease them so they join up but do not overlap (photo 4).  

Step 5: Attach and Adjust Gnomon

Go back to the gnomon and put glue all over the two small triangular flaps on the bottom of the gnomon, and glue them down into their positions on the dial.  Make sure the flaps don't overlap, but join evenly.  Try to align them as carefully and as symmetrically as you can with the triangles for them on the dial, and glue the flaps down neatly along the creases..  

Optionally, for more precise alignment, you can first cut out the "Gnomon sizer" triangle.  Then while the glue on the gnomon flaps is still tacky, play with adjusting the exact gnomon height (it goes up if you move the flaps slightly together and down if you move them slightly apart).  The gnomon height should be the same as the height of the "Gnomon sizer" triangle (with the word "Gnomon sizer" being horizontal), and the distance from the center of the dial to where the tip of the gnomon overhangs should be the same as the length of the sizer.

Step 6: Aligning the Dial

To use the dial, you need to place it on a level spot (e.g., a sunlit table) and align the "N" arrow with geographic or true north (in the northern hemisphere, the gnomon will also point north; in the southern hemisphere, it will point south).  Unfortunately, geographic or true north is not the same as the magnetic north shown by a magnetic compass.  

The simplest way to align is simply to look at a watch and turn the dial until the shadow shows the correct time.  (You may also want to do an Equation of Time adjustment when reading the time shown on the dial--see the next step.  Also, make sure you make a daylight savings adjustment if the dial is not printed for the current season's time.)  There are other methods.  You can use a magnetic compass and correct for magnetic declination, as described in my other sundial Instructable.  Or you can wait for night and align with the north star.  I just used the fact that I already had one large aligned sundial.

Step 7: Reading the Sundial

You read the sundial by looking where the edge of the shadow is, or more precisely where the edge of the shadow further from the gnomon.  Except near solar noon (which may be more like 1 pm in the summer if you have daylight savings), that shadow line should be a straight line from the center of the dial out.  Near solar noon, because of the wider base of the gnomon, there will be a bend in the shadow line--use the outermost portion of the shadow line.

For greater precision, you can add the number of minutes indicated in the correction table for a date close to your current date.  This is an Equation of Time correction that every sundial needs to make.  If you aligned and leveled the dial well (mine wasn't that well aligned--the excellent match with time in photo 1 was probably a fluke;  in photo 2, I had the dial--actually a different copy of the dial--in a slightly different location).

And of course you may need to add or subtract an hour to correct for Daylight Savings--if you used the right Daylight Savings option when entering data into the script, there will be a reminder printed on the dial--since the earth doesn't know about Daylight Savings and doesn't change its rotation to suit.

Note that the script that produced the dial adjusts for where your longitude lies within a time-zone--it shows your time-zone time, not local solar time.  (For instance, solar noon is at about 12:30 pm winter time and 1:30 pm summer time at my location.)

Finally, you can always use the sundial in reverse, as a solar compass.  Just align it so it's level and shows the correct time, and it'll point you north or south.  However, be careful, since the sundial is set for your particular latitude and longitude.  
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