Goals: The student will|
- Know the design, principle and orientation of a sundial, the type with a gnomon pointing towards the pole of the heavens.
- Construct a model sundial from paper.
Stories and extras: The historical reason for the "clockwise" direction of the hands on a clock.
The "Sundial Bridge" across the Sacramento River in Redding, California.
Start asking the class--does anyone have a sundial in the garden, or seen one in a public place? How well did it work?
Some tourist shops--e.g. in Valley Forge Park, Pennsylvania--sell folding pocket sundials, mounted on top of a magnetic compass. Why the combination, can anyone guess? (Because the pointer--the "gnomon"--must be directed northward for the dial to work).
After this, present the material. The questions below may be used in the presentation, the review afterwards or both
At a suitable time (as part of the lesson, or afterwards) have the students construct paper sundials. Distribute templates, preferably copied onto construction paper. To make the copies, feed the sheets to a xerox machine one by one, by hand: feeding the machine from a stack could jam it. Instructions are found on the "Stargazers" site, but for the convenience of the students, printed copies should also be distributed.
Students should have scissors available, also rulers and ballpoint pens, for scoring along the broken lines. Have a few extra templates ready, for students who spoil theirs by incorrect cuts. Students with shop skills may want to build some from more durable materials and perhaps to their own designs.
Guiding questions and additional tidbits
(Suggested answers in parentheses, brackets for comments by the teacher or "optional")
-- How does the shadow of a flagpole appears to move across the ground, in the continental US or in Europe?
On average, the Sun rises in the east, crosses south at noon, and sets in the west. The shadow therefore points to the west in the morning, north at noon and to the east in the evening.
-- Does the shadow move clockwise or counterclockwise?
(Optional demonstration in class)
-- If you are south of the equator, will the shadow move clockwise too, or counterclockwise?
Let the students find out by themselves! Bring out one student in front of the class to demonstrate the motion of the Sun and the shadow. Let her (or him) represent a vertical pole, and let her face the left of the students. That direction will be now called "east"--it may be different outside, but indoors we can choose what is convenient. East is also where the Sun rises, on either side of the equator.
Now let the student stretch out both arms--the right one above her shoulder, the left one below. The high arm traces the motion of the Sun--it rises in front (east; raised arm points forward, gradually rising). It passes its highest point on her right (in the south direction, where it is at noon), and it sets on the side where her back is, in the west (arm descending again towards her back).
The other arm, the low one, is always kept exactly opposite the high arm. That is the shadow. How does the shadow swing? Clockwise, of course.
Next, let us go south of the equator. The Sun still rises in the east and sets in the west, but now it passes to the north.
Very well: so let the student raise her left arm above her shoulder and lower her right arm below her shoulder, the opposite of what she did before. Now the right arm traces the motion of the Sun: rising in the east (in front), passing north at noon, when it is highest, and setting in the west, behind the person.
The lower, right arm again stays opposite, and again marks the shadow of the vertical pole--backwards in the morning, forewards in the evening, always opposite the Sun. How does the shadow rotate? Counterclockwise.
If this seems too complicated, the teacher can demonstrate. Or else, the teacher demonstrates first, then some student(s) try it.
-- Will the sundial you build work anywhere ?
No. Only if it is pointed at the pole of the heavens can it work equally accurately at all seasons. The sundial cut out here is designed to work at latitude 38°, corresponding to the middle of the continental US.
-- A visitor to an equatorial country saw a strange sundial which the natives constructed out of 3 water pipes--a horizontal one held at its ends by two vertical ones [Draw it on the board as you describe it]. The vertical support pipes were embedded in a concrete pavement, and painted on the concrete were marks for the hours. The time was read off from the position of the shadow of the horizontal bar.
Would such an arrangement work?
Yes. The horizontal pipe is the gnomon, pointing at the Pole Star. On the equator the pole star only appears on the horizon, so a horizontal gnomon is appropriate.
-- I compared my watch to a sundial in a public park, and the two disagreed. What might be the reasons?
- (a) Your watch is set for daylight saving time
- (b) The sundial is incorrectly aligned
- (c) the sundial is correctly aligned to north, but is located at the edge of a time zone. For convenience, local time is averaged in hourly time zones: these may not give the exact local time.
- (d) A discrepancy of a few minutes exists, the "equation of time", due to the uneven motion of the Earth in its orbit.
If time remains, a student who prepared beforehand may tell about the Sundial Bridge in Redding, California (details and links on the web page)
It has an interesting design. Older "classical" bridge like the Golden Gate Bridge in San Francisco or the George Washington Bridge in New York City (also the Verrazano Narrows Bridge) have large cables running from tower to tower, the ends of each cable anchored on the land in a very heavy chunk of concrete. The bridge then hangs from those cables.
Here, individual cables run to different parts of the bridge, a more modern design which is cheaper. Usually (e.g. Charles River Bridge in Boston) the cables descend symmetrically from both sides of a vertical tower. In the Sundial Bridge, the cables run to only one side, and the tilt of the tower helps counteract the uneven strain. Since the tower points north, it also serves as the gnomon of a giant sundial.
The grand-daddy of all big suspension bridges is the Brooklyn Bridge in New York. Next time you look at its picture, note it has both systems of cables. When it was built, its designer could not calculate the stresses very accurately, and to play it safe included two independent systems of cables!