Our NOON ANALEMMA SUNDIAL is a solar calendar. Each day the
Sun's path across the sky is a little higher or lower, depending on the season,
than it was the day before. The rays of the Sun passing through that south-facing
circular window (and through the APERTURE in the pointer in that window, called a
GNOMON), casts a bright spot on the floor of the INFOSCULPTURE. In the days
leading to the summer solstice the spot moves closer and closer to the south wall
(each day the Sun is rising higher in the sky), and as we move into winter it
works its way up toward the north banco (lower in the sky each day). The
"lopsided 8" design in the floor of the INFOSCULPTURE is called a NOON ANALEMMA
because it is derived from the path of the noontime solar spot throughout the year.
See it for yourself!
Terms You Need to Know
ANALEMMA - a figure-eight representing the sun's
position at 24 hour intervals throughout the year; a sundial; an instrument marking
the passage of the sun over time. APERTURE - opening or hole, in this case the small hole
in the GNOMON through which sunlight passes. AZIMUTH - the angle of an arc measured along the horizon
between a celestial point and your meridian; the angle of the horizontal position
of the sun relative to the local meridian; how far the sun's position is off from
being directly south. Azimuth is a "left-right" or "east-west" measurement.
[See DECLINATION] DECLINATION - the north-south angle as compared to the
earth's celestial equator. Declination is a "north-south" measurement. [See
AZIMUTH] EQUATION OF TIME - the explanation for the east-west
shift of the sun's position each day at noon; why the sun appears to move a little
faster or slower. EQUINOX - the point during the year when nighttime
hours and daytime hours are exactly equal: around March 21 and September 22. GNOMON - an index pointer that by its shadow or other
mark identifies the time of day; the pointer of a sundial. MERIDIAN - an imaginary north-south line on the earth's
surface; longitude. SOLSTICE - the point during the year when the apparent
northward or southward drift of the sun's daily path stops; around June 21
(farthest north; the longest day in the northern hemisphere) and around December
22 (farthest south; the longest night in the northern hemisphere).
This Information Center at Cerrillos Hills Historic Park has
been built to support a simple type of sundial called a noon analemma. A gnomon
("no' mon"), or pointer, has been mounted in the south-facing circular window. The
aperture (an opening or hole) in the center of the gnomon acts as a pin-hole lens
to project an image of the sun onto the floor of the Information Center (from
August 11 through April 30th) or the window sill (from May 1 through August 10th).
Below is a photograph of the kiosk floor.
Marks will be made on the floor corresponding to the position
of the sun's image at noon Mountain Standard Time (MST). During Daylight Savings
Time, marks will be made at one o'clock to correct for the time change. The marks,
over time, will trace out a figure-eight shape called an analemma. Once the
analemma is marked in, it will serve as a noon sundial because the sun's image
will cross it each day at noon MST. Additionally, it will serve as a calendar
because the date can be determined by where the suns image crosses the analemma.
Although we are creating a noon analemma, one could create an analemma for any
time of day provided that the sun would reach the gnomon and a suitable projection
area at that chosen time every day throughout the year.
NOTE: While you are observing this sundial,
please keep in mind that you should never look directly at the sun even with
darkly tinted films or glasses! Doing so could cause permanent damage to your
vision!
An analemma takes on a figure-eight shape because of two main
factors, the declination of the sun which governs the north and south movement of
the sun's image and the equation of time which accounts for the easterly and
westerly changes.
The sun's declination is its north and south angle as compared to the earth's
celestial equator. It determines the distance that the sun's image will fall to
the north of a point directly below our gnomon. Toward the winter solstice, the
sun's angle is more southerly, the sun appears lower in the sky and the declination
is less. The image will fall a longer distance north of the gnomon, nearly to the
north wall. Toward the summer solstice, the sun is higher in the sky and its image
will be so close to the point directly below the gnomon that it will fall on the
window sill. See an enlarged view of analemma path (left)
The east and west shift of the sun's image at noon is explained by something
called the equation of time. The equation of time results from two main factors,
1) the plane of the earth's equator is not the same as the plane of the earth's
orbit around the sun and 2) the orbit of the earth around the sun is an ellipse,
not a circle. For more on this topic and others, go to:
Because of the equation of time, the apparent length of our
days is not exactly 24 hours.
If you set an accurate watch to exactly noon one day when the sun is at its
highest point as it passes over our local meridian (this is often referred to as
the time at which the sun "souths"), and then you look at this watch the next day
and the next and so on each time the sun souths again, you will see that during
some times of the year, the sun arrives above the local meridian some seconds
before 24 hours and thus seems "fast" and the day seems shorter. At other times
of the year, the sun takes a bit longer than 24 hours to reach the meridian and
seems "slow" with an apparently longer day. These fast and slow times accumulate
each day to equal more than 14 or 16 minutes at some times of the year.
Table of slow or fast times.
When the sun is "running slow", it will be to the east of our local meridian at
noon on the watch and it will throw an image to the west of the analemma's center
line. When the sun is "running fast", the sun will have already crossed to the
west of the local meridian at noon on the watch. Its image will then be projected
to the east of the analemma's center line. Thus, the east and west fluctuations
of the analemma are formed.
Standard vs. Local Meridian
A meridian is an imaginary line on the earth that runs north
and south from pole to pole. It is also known as a longitudinal line. A standard
meridian is one chosen for setting our clocks. Mountain Standard Time's meridian
is located at longitude 105° west of the Greenwich, England meridian, which is
longitude 0°.
A local meridian is the meridian line for a local longitude. The meridian for
this Information Center is approximately longitude 106° 7' W. (The Information
Center's latitude is approximately 35° 27' north of the equator.)
Calculated vs. Empirical Analemma
This analemma will be laid out empirically; that is, we will
let the sun show us where to put the marks. However, to estimate the approximate
path that the analemma would take, calculations were used. The location of each
point on the analemma was determined trigonometrically by first looking up the
altitude (A) and azimuth (a) for latitude 35° 27' N longitude 106° 7' W
on a given date at the U.S.Naval
Observatory From there, the following calculations were made. (Refer to the
diagram below.)
CS = 90 - A
COT A = TAN(VCS)
VS = d COT A
y = BV = VS COT a
x = BS = BV TAN a
The values y and x were then plotted. Value "y", being the
distance the sun's spot would fall to the north of point V directly below the
gnomen and "x", being the distance to the east or west of point B.
Three Ways that the Real-Life Analemma Will Vary from the Calculated One
1. Effect of Floor Height:
The gnomon's height above the floor plays
a role in the north/south position of the sun's image. The image of the sun is
projected at an angle from the gnomon to the floor (see the image above).
If the floor is raised, the sun's image location will be closer to the south wall.
If it is lowered, the location will be farther to the north.
At the south wall the floor is approximately 82" below the height of the gnomon's
aperture. However, the floor is graded to be lower toward the north wall. This
causes the analemma to stretch farther north than it would had the floor been
level. Additionally, various points on the floor are a bit higher or lower or
slightly uneven which will cause variation in the analemma track. This will be
more noticeable toward the winter solstice when the sun is at a lower angle.
By calculation, on December 21, a one-inch change in floor height will result in
a 1.6 inch change in the northerly distance of the sun's image on the floor.
Toward the summer solstice, a one-inch change in floor height will have less
impact, 0.4 inch on August 15 for example. (Note the widths of the green lines
in the profile view above.)
2. Effect of Leap Year:
Because our years are not exactly 365 days
long and some are 366, the analemma marks will vary somewhat over a four-year
period. Waugh's book, Sundials, Their Theory and Construction"
(see notes), recommends using the year after
a leap year when making calculations as this is a more average year than others.
For this reason, the year 2005 was used to calculate the probable path of the
analemma.
By calculation, the difference in points from year to year seems to move fairly
little, no more than an inch. The variations also seem to move along the analemma
path rather than out of it. That is, a point on a north-south portion of the
analemma line moves north-south rather than east-west. So, although year to year
marks may move along the analemma track, the overall size and shape of the
analemma is not expected to be affected significantly.
3. Accuracy of Positional Reading:
A sundial's latitude and longitude is needed
in order to calculate points on an analemma. Our position on the globe was
estimated from maps and may not be entirely accurate.
If you happen to have GPS, and wish to contribute your more accurate reading of
this location, please contact this
address. Thank-you!
The Path Described by the Sun Spot on the Floor of the Kiosk
The sun is highest in the sky during the summer. From May 1st
through August 10th the high angle of the sun will cause the sun spot to fall on
the sill of the kiosk rather than on the floor. See the profile
diagram.
The sinuous red ribbon separates Standard Time from Daylight Savings Time. The
top portion of this analemma above the red ribbon represents the sun spot's
location at one o'clock clock time (Mountain Daylight Time), and the portion of
the analemma below the red ribbon is the sun spot at twelve noon clock time
(Mountain Standard Time).
The blue line is the NOON MARK for Cerrillos; Cerrillos Mean Noon. See more on
the Noon Mark. Cerrillos and the kiosk are not located in the
center of the Mountain Time Zone, but are about 63 miles west of that center.
Therefore, the position of the sun at Mountain Time "clock midday" in Cerrillos
is slightly east of overhead, and the noon analemma path on the floor of the
kiosk is slightly west of the Cerrillos NOON MARK (the blue line). The sun spot
produced by the gnomon will reach the Cerrillos NOON MARK about 4.5 minutes later.
The sun "souths" (or Cerrillos has its local noon) four and a half minutes later
than your Mountain Time clock says it is noon.
If you understand all of this then you have a potential excuse the next time you
arrive somewhere a little late. "What do you mean, I'm late? According to my
local analemma I'm right on time."
This website is maintained by the Cerrillos
Hills Park Coalition
and is dedicated to the creation, enhancement and stewardship
of an historical, recreational, and cultural open space in
the
Cerrillos Hills, Santa Fe County, New Mexico, USA
