Hands-On Activity (submitted by Joe Jordan)
Intuitive Illustration of Sun Paths on Sky
All Grade Levels (but useful in particular for solar designers)
There are various nifty tools now used in solar site assessment, such as the
Solar Pathfinder or the digital SunEye, but these don't give the kind of direct
"seat-of-the-pants" understanding of the sun's path on the sky that could come
in handy for a solar designer (or just a home/building owner) who happens to
be without one of the fancy commercial tools when trying to get a rough idea
of the solar energy potential for some site.
The purpose of this activity is to promote a real sense for the paths the sun
takes across the sky as a function of both your location (latitude) and the time
of year. (With Pathfinder and SunEye, e.g., you're looking down, at reflections
or silhouettes superimposed on upside-down sun-path lines, or at a computer
screen -- instead of up in the sky, where the sun goes!)
The classroom (or outdoor) activity is to handle the little invention (that I hope
to have built a preliminary version of, to bring to this SEET thing), and explore
how the configuration of its essential piece changes with the desired latitude
to be represented. (Maybe an educational tool like this already exists, but I'm
not aware of one -- though I haven't searched particularly hard yet, either!)
This gizmo is not intended to yield the kind of detailed quantitative information
that can be obtained from the commercial tools, on percentages of maximum
theoretical sunlight received at a given site for all times of year; rather, it's just
to give a qualitative feel for the way the sun appears to move in the sky. One
puts this thing over one's head and looks up and around, and sees the actual
paths the sun will trace on the sky at the set latitude, at both solstices and either
equinox. (On those key dates of the year, one could actually follow the path of
the sun as it appears to move right along the arcs built into this demonstrator.)
If there are trees or buildings in the way of parts of the arcs displayed by this
tool, you'll see exactly everywhere that they'll be blocking the sun, just by
looking right at them.
[If you get lost partway through the paragraph beginning right here, go ahead
and read on beyond it (and then you might try coming back to this one). The
rest of this document after this paragraph should be pretty clear and engaging.
What this paragraph needs is drawings and/or photos to accompany it -- but
that's not going to happen in time for posting this item on-line for SEET. Best
of all would be seeing the actual physical model -- and at the workshop,
hopefully, that will be available. It's not nearly as complicated as it might
sound, from the following verbiage!]
Here's a quick description of the simple, basic model represented by this tool.
There's a big horizontal hoop (maybe 20 inches across), and your head (eyes,
in particular) should be centered in the middle of that. (You hold the hoop at
its left and right sides, with your hands.) This hoop represents the horizon.
Screwed into this hoop, at points diametrically opposed (just outside your
left and right temples, basically) -- and able to pivot (with some resistance)
about those two connection points, is another hoop that fits just outside the
horizontal one. But this second hoop can go in any plane, from the vertical
to the horizontal. And that second hoop has two slightly smaller hoops in
parallel planes on either side of it -- precisely as the earth's equator has the
two tropic lines in parallel planes above and below it -- and these three hoops
swing as a unit, just as if you're holding a globe with one finger of each
hand at diametrically opposite points of the equator, and swiveling the globe
about those two antipodes. The three hoops of this swivelable "cage"
represent the paths the sun will appear to take on your sky (if you're looking
at them from inside, at the center of the horizon hoop), at the equinoxes
(center hoop) and the two solstices (the slightly smaller hoops to either side
of the center hoop, analogous to the tropic lines on a globe). When the three
hoops of this "cage" are all in the vertical plane, you're seeing what you'd
see at the earth's equator. (There, the sun rises straight up from the horizon.)
When the hoops are all in the horizontal plane, you're seeing the sun's arcs as
viewed at the poles (where the sun appears to go around the sky, parallel to
the horizon). To get the view from any desired latitude, simply swivel the
"cage" of parallel hoops to an angle from the vertical equal to your latitude.
On the equinoxes, the sun rises due east and sets due west, everywhere on the
planet. And those two days are the only days of the year when the sun rises
due east and sets due west, anywhere. The rest of the year, it's rising north or
south of east (and setting north or south of west), by varying amounts that
depend on your latitude. The sun's daily arc on the sky meets the horizon at an
angle from the vertical equal to your latitude. (If you're on the equator, latitude
zero, then the sun's path is always in the vertical plane -- zero angle from vertical.
If you're at a pole, the sun's path is horizontal -- ninety degrees from vertical -and your latitude is ninety degrees.) In the northern hemisphere, the sun rises
along an arc that goes up and to the right from the eastern horizon. South of
the equator, it rises up and to the left. (When you see a movie that's supposed
to be set in Australia, say, and they show a scene with time-lapse of a dramatic
sunset with the sun going down to the right, then you know that either the
filming was actually done somewhere north of the equator, or it really is south
of the equator but they ran the film backwards and it's actually a sunrise they're
showing!)
All of this will become abundantly clear once you see and play around with the
little educational model I hope to bring to the workshop. One fine point: The
"cage" of three parallel hoops will come up against the back of your neck and
shoulders if you try to swivel it to an angle too close to vertical. So instead of
fully circular arcs, each of these three hoops should have a section of maybe 90
degrees or more cut out of it, so you can freely swing the whole assembly
through the full range from horizontal all the way up to vertical -- especially
since you can't see the parts of the sun's arcs that go below your horizon,
anyway (which are thus behind your head when you're facing south, if in the
northern hemisphere). This tool will also nicely and quite naturally illustrate
the fact that every day, the sun is due south at the highest point of its diurnal
arc across the sky (if you're in the northern hemisphere).
By the way, the equator-and-two-tropics image for the "cage" of three parallel
hoops is more than just an analogy. On the equinoxes, the sun is overhead all
day at the equator, as it circles all around directly above it. On the summer
solstice (northern hemisphere), the sun is overhead at the Tropic of Cancer;
and at northern winter solstice it's overhead at the Tropic of Capricorn. So the
two slightly smaller hoops to either side of the central one in our "cage" really
are each 23-1/2 degrees away from that central hoop (on an imaginary sphere),
just as the tropics are from the equator on the real globe -- because these hoops
are simply the extensions of the equator and the tropics out onto the sky!
Finally, an astronomical note relating to all this: The sun is always in front
of some stars; and the zodiac (named for a bunch of animals, like a zoo) is
simply the band of constellations that the sun gets in the way of, as we move
around the sun during the course of the year. A fun party fact, most probably
unknown to even your most educated friends, is that at the time of the year
when your birthday rolls around, you can't see the constellation of your
astrological "sign", because it's behind the sun! (The sun is "in" that
constellation -- in front of it, ... in the way of it.) ... OK, so which zodiac
constellation do you think the sun is in front of at northern summer solstice,
when it's overhead at the Tropic of __?__ ? (So now you know why those
tropics have those names!)
(It's all off by about a month now, though. In mid-June nowadays, the sun's
actually closer to being in Gemini rather than Cancer, because the 26,000-year
wobble of the earth's rotational axis -- "precession" -- has shifted everything
about one sign westward along the zodiac, in the roughly 2,000 years since this
whole system was originally set up!)
(The "Age of Aquarius" refers to the fact that nowadays at spring equinox,
the sun's in front of Aquarius, instead of Aries or Pisces, as it was formerly.)