Objective: To build and use a working sundial
Background: Sundials are the oldest known instruments for keeping track of time. It is also one of the most ancient scientific instruments, requiring knowledge of the motion of the Sun over the course of years, knowledge of Polaris, the North Star, and not inconsiderable mathematics for civilizations that had yet to invent the number zero.
The first attempt at marking time, perhaps around 5000 BC, was probably a stick in the ground to cast a moving shadow, the precursor of a sundial's gnomon. By 2500 BC Babylonians and Egyptians were building obelisks (the Washington Monument is an obelisk) that functioned as clocks, dividing the day into before and after noon. They also indicated the longest and shortest day of the year.
The oldest extant sundial was built almost 3000 years ago in Egypt. It had six inscribed time demarcations on the base and a crosspiece to align the device east-west. The crosspiece casts a shadow to give the time.
By 250BC the Greeks produced complex and more accurate sundials using their knowledge of geometry. Their expertise led to the Tower of the Winds in Athens in 100BC. Its eight faces each contained a sundial.
A great improvement to sundial development came circa 100AD with the slanted gnomon, rather than a vertical rod. If the slant causes the gnomon to be parallel with the Earth's rotational axis, the shadow cast will be the same size at any hour. About this time the Greeks started to employ trigonometry to make hour lines more simple to read. The technology was now mature.
Until the invention of mechanical clocks in the 14th century sundials were the best way of telling time (during the day, of course). Even after they were supplanted by mechanical timepieces, sundials remained in use as functional decorations to homes, gardens, and parks.
Types of Sundials: A stick and a board can be made (poorly) into a sundial. Here are some better variations:
Egyptian Shadow Clock
Bill Nye's Design for Seattle
Wall Sundial, U. of Washington
This is just a small sampling of what people have designed over 7000 years! In fact, one of our retired Astronomy faculty now runs Sunlight Designs in Arroyo Grande. Here's a sample of his work:
"An 8 foot square opening in a patio cover allows an awning with a sundial . Located at 35.13 N 120.58 W, the opening declines about 35 degrees to the west. The sundial employs a slotted gnomon design. Time is read at the eastern edge of the slot's shadow. The nodus is at the point of the diamond shaped shadow."
Assignment: Build and use a Sundial. It must be transportable as you will be showing it off in class.
Method: I will suggest one method, but the internet is filled with variations on this theme. You can keep it simple or make it elegant, but accuracy will be paramount. A stick stuck onto some scribbled notebook paper will be worth all that the materials and time cost: zero! You can make your sundial out of any materials you wish, anything with which you are familiar: wood, metal, cardboard, plastic. What follows below is a set of instructions for the classic version.
1. A sundial needs two things: a set of markings that indicate the time, and something to cast a shadow onto those markings. If you were a primitive proto-human, a bone stuck in the ground and some rocks might do. You wouldn't have to know anything about the Earth's rotation, anything about its revolution about the Sun, and nothing about the tilt of its axis or precession of the tilt, for that matter. But your erstwhile sundial would be woefully inaccurate for this reason: the Sun changes its position in the sky over the course of a year.
The tip of the shadow cast by the bone might work for a few days, but then the shadow would wander. Moreover, the length of the shadow changes over the course of a day. Of course, you can spread out the markings to account for this change, but then there's that long term variation to consider.
So the best thing to do is to angle the shadow-caster, the gnomon (N0`mon) AND spread out the markings. By angling the gnomon to align with the tilt of the Earth you correct for the long term variation, and by spreading the pattern you correct for the daily length change of the shadow.
2. Let's tackle the angle first. The Earth is tilted 23.5o, but the angle is related to the latitude where you plan to use your Sundial. The following diagram comes from the University of Miami, my alma mater:
I've modified it just a bit (the four heavy black lines). For this diagram to really work you have to realize that Polaris is WAY FAR away, so the heavy black line actually aims at Polaris. Then the angle between the horizon and Polaris is the same as your latitude (arrowed line).
To make a long story short, if you align your gnomon with the rotational axis of the Earth, you've fixed the wandering shadow problem. So you have to find North, you have to know the desired latitude, and you have to design your angle.
For North you'll need a compass (see #4).
The latitude at this school is 34o. If you plan to use this elsewhere, you'll have to ask someone (or use your GPS).
To get the correct angle for the gnomon you'll have to use a protractor:
If you've never used one before, it's easy. You could take the gnomon rod, place one end at the zero point (the red dot) and angle it up to 34o, propping it up temporarily until you build something permanent. Alternately, you can make a triangle like the one below:
If the gnomon edge is 12 inches long, the base of the triangle will be 10 inches and the height will be 6 3/4 inches. You can double or triple the dimensions, or cut them in half, and still have 34o.
A couple of other things: it's good if you have some shape at the top of the gnomon or apex of the triangle to cast a distinct shape on the markings (called the nodus). Also, make the gnomon or triangle thin so the shadow doesn't smear out.
Do you see how a split in the markings will be necessary for a wide gnomon?
3. Now for the markings. The Sun will cast a shadow every day it shines, so you could just place your blank sundial out and check it hourly, noting where the shadow is and checking it with a regular clock. Since the shadow motion and length will vary, be prepared to set aside 8-10 hours for this process! Furthermore, because of the variations, you can't just mark off the hours evenly. You need some MATH!
Yikes! XHL is the angle to draw your corrected hour lines, theta is your latitude, and T is the time in 24 hour mode. Set your calculator to degrees. Yikes again!
Well, I'm not going to let you suffer. Click this link to open an Excel spreadsheet. Enter the value for latitude in the correct cell and a table of correct angles will be generated.
Look at the narrow/wide gnomon pictures just above; let these be your guide. See how the lines are not all the same angle apart? This is why you need the generated table. Imitate the narrow or wide pattern you see, drawing the lines at the correct angle using your protractor. Be sure the lines are long enough for all year long!
Wait! How can you figure that out? What is the day of the year in the Northern Hemisphere that the Sun is lowest in the sky? Winter Solstice! You want to make sure that your noon line is long enough for the shadow to reach on December 21. But what if it's cloudy that day? What if you don't want to wait until half a week past Beethoven's birthday?
Here's a math fix:divide the height of your gnomon by 0.62 and that will tell you the longest noon line. By the way, you do understand that your noon shadow is the shortest of the bunch, right? All the others must be even longer!
4. In use: Put your sundial in a place that's sunny most of the day. If your construction is not weatherproof you'll have to bring it in should things turn inclement. Get out your compass. It will look something like this:
The needle suspended inside always points North. Align your sundial so that the tilted gnomon tilts up and is aligned with North. As a further check, your 6AM mark should point East and your 6PM mark should point West.
5. Over the course of the rest of the semester, check the time on your sundial against your cellphone clock (it checks in with standard time regularly). Keep a generous log of the time your construction reports along with the cellphone time. Record any problems you encounter. I will ask to see your sundial towards the end of the semester.
Finally, something else to consider: each time zone is wide!
This means our clocks say noon from Mesquite, NV to Santa Cruz, CA. But the Sun can't be at noon along that whole line at the same time! So you can't take your sundial East or West, or North or South! There is a math fix for this too, but you would not like it! (Use your sundial here in SoCal.)