(2A) The Sundial
Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern
This lesson plan supplements: "The Sundial," section #2a: on disk Sundial.htm, on the web
Template of a sundial: on disk Sfigs/Sdial3.gif, on the web
"From Stargazers to Starships" home page and index: on disk Sintro.htm, on the web
Goals: The student will|
Stories and extras: The historical reason for the "clockwise" direction of the hands on a clock.
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.
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?
-- Does the shadow move clockwise or counterclockwise?
The shadow varies with the season of the year--that will be discussed at a later time.
(Optional demonstration in class)
-- If you are south of the equator, will the shadow move clockwise too, or counterclockwise?
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 ?
-- 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?
-- I compared my watch to a sundial in a public park, and the two disagreed. What might be the reasons?
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!
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Author and Curator: Dr. David P. Stern
Mail to Dr.Stern: stargaze("at" symbol)phy6.org .
Last updated: 30 August 2004