SUNDIALS: SUite of Nonlinear and DIfferential/ALgebraic Equation ...
15 Sundials CCB 2009color
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Transcript of 15 Sundials CCB 2009color
An early March sunset as seen on the Lawrence Hall of Science’s Bay Cam. This is one of my favorite web sites. (http://www.lhs.berkeley.edu)
Around the globe, civic structures like Stonehenge below often marked
landmark events in the heavens and their own place on earth.
In about 30 B.C. Marcus Vitruvius -Roman architect, contemporary of Julius Caesar, and muse to architects for millennia - described 13 different sundial designs used in Greece, Asia Minor,
and Italy.and Italy.
He lamented that by his day all possible forms of the art had been discovered.
Christopher Wren is best known as the architect of St. Paul's Cathedral and other London churches, but his first love was science and mathematics. During the first part of his career he worked as an astronomer.
JPL’s Mars
sundial
Currently
providing time
and color
calibration cues
to Martian
locations locations
The Mars dial as seen on Mars ….
and in an artist’s rendition that has Mars looking Mars looking remarkably like the American Southwest.
Yet more proof that the Earth revolves around it’s north-south
axis and the notion that there are time implications in this
fact.
Solar time is unique for each location according to longitude and time of year,
It is relatively straightforward to relate solar time to local standard time.
Local solar time (LSoT) is simply the local clock time adjusted for these factors:
LSoT = LST + (4 minutes * (LSTM - LL)) + EoT
Converting Solar Time
Step 1. Determine the local standard time, LST. This is clock time, adjusted
for daylight savings time if necessary. If daylight savings is in effect,
subtract one hour.
Step 2. Determine the local standard time meridian, LSTM.
Step 3. Determine the local longitude, LL.
Step 4. Determine the equation of time, EoT , adjustment in minutes.
Solar time is unique for each location according to longitude and time of year,
It is relatively straightforward to relate solar time to local standard time.
Local solar time (LSoT) is simply the local clock time adjusted for these factors:
LSoT = (LST – 1)+ (4 minutes * (LSTM - LL)) + EoT = (11:20 – 1)+ (4 minutes * (120 - 122)) + (-10) = 10:02
Converting Solar Time
Step 1. Determine the local standard time, LST. This is clock time, adjusted
for daylight savings time if necessary. If daylight savings is in effect,
subtract one hour.
Step 2. Determine the local standard time meridian, LSTM.
Step 3. Determine the local longitude, LL.
Step 4. Determine the equation of time, EoT , adjustment in minutes.
A visual tour through several types of sundial:
Horizontal
Flag pole
Polar
Vertical declining
Equatorial
Diptych
ScapheScaphe
Armillary sphere
Cylindrical
Analemmatic
Meridian
For each of these look for the landmarks of due
south, the earth’s north-south axis, the equatorial
plane, and the ground plane
Horizontal
Sundial
It is a dial on a horizontal plane, with a style inclined towards the pole. It gives the hour during all the day. the pole. It gives the hour during all the day. It is generally drawn on the ground or installed on a column in a garden. The angle between the style and the table of the dial is equal to the latitude of
the place.
Laying out a horizontal dial (1)Laying out a horizontal sundial in six easy steps:
1. Make a protractor by dividing a half circle with lines at an even 15º spacing.
2. Create a style from a right-angled sheet of stock. Cut at an angle that equals at an angle that equals latitude for the sundial site.
3. Glue the style to the north – south axis of the sundial’s base.
Laying out a horizontal dial (1)Laying out a horizontal sundial in six easy steps:
4. Slice a tube on its long axis and affix to the top of your style.
5. Lean your protractoragainst the north slope of against the north slope of your style and project the angles to the sundial baseplane using a string.
6. Connect the south base of the style to your projected points with straight lines.
Handwritten class notes on the construction of horizontal sundials by president in training James Madison
Polar Sundial
The polar dial sundial in which the dial plate is set along the East-West direction and inclines so that it is parallel with the polar axis. The hour lines are parallel. The polar dial can also be cylindrical.
Their biggest advantage is visibility from a distance. In Europe vertical dials can be found on walls of all
Declining Vertical Sundials
on walls of all orientations. Of course those on east- and west-facing walls only tell the time for part of the day and south-facing dials are useful for a larger time of the year.
Built in the first half of the 1st century B.C. by the
astronomer Andronicos, this octagonal marble tower, still
standing; has 9 sundials, friezes of the 8 winds, and remains of an astronomical water-clock and reservoir
Equatorial Sundial
The equatorial or universal sundial is the easiest dial to make. The gnomon is parallel to the earth's axis and the dial plate lies in the plane of the equator. The hour lines are spaced at 15°, so that the face looks very much so that the face looks very much like that of a traditional clock except …..
The style in an equatorial sundial is tilted at an angle equal to the latitude, the high end of the style points north, and the disc is parallel to the earth’s equatorial plane.
A contemporary dial near the equator -- Hong Kong University of Scienceand Technology
Equatorial or polar?
A sundial using cylindrical focusing mirrors to project a sharply focused beam on the inside of a helix shaped scale.
Diptych
The meridian dial is a particular case of the vertical direct south dial which gives the hour only around local midday. This type of dial was used to synchronize clocks and portable watches with the Sun. The analemma curve is often drawn around the noon line, to visualize seasonal departures from mean time.
Scaphe
The conical, scaphe or bowl sundial uses the concave segment of a circular cone as the dial face. They are similar in appearance to the hemicyclium, which was invented by which was invented by the Greeks and then copied by the Romans
Armillary
Sphere
Armillary or ring sundials consist of a system of rings that represent the major circles of the terrestrial and terrestrial and celestial spheres. The hour lines are evenly spaced on the equatorial ring. The style is the axis of
the sphere
FLASH from the BBC 1/27/04:Made of three polished stainless steel towers, the Derbyshire Sundial will cast a shadow across a 60-metre base marked out to trace both time and the rotation of the earth. The main tower will point due south, while the other two will mark sunrise and sunset on the summer solstice.
Cylindrical or
pole sundials
Portable cylinder or pillar sundials are also called poke dials or shepherd's dials, because they used to be carried in the pockets (pokes) by shepherds. Another name for this dial is the traveler's dial. The dial is in the form of a dial. The dial is in the form of a cylinder with the gnomon attached to a movable top. The hour lines are in the form of curves inscribed or printed on the cylinder. To tell the time, the gnomon is set over the vertical line of the day and the time read off where shadow of the point of the gnomon falls on a hour line
Analemmatic
Sundial
It is an elliptic horizontal dial which has the characteristic to have a mobile style. This style must be moved according to the date along an axis (small axis of the an axis (small axis of the ellipse). This type of dial is often realized in great dimension on the ground and a person casts her shadow while being placed on the graduation corresponding to the date. There are also analemmatic dials with tilted styles.
Meridian Sundial
The meridian dial is a particular case of the vertical direct south dial which gives the hour only around local midday. This type of dial was used to synchronize clocks and portable watches with the Sun. The analemma curve is often drawn around the curve is often drawn around the noon line, to give the mean time. Many meridian have been installed on churches
The Jantar-Mantar of Delhi
The Indian astronomer Maharaja Sawai Jai Singh II (1688-1743 AD) built a series of stone observatories throughout India.
The Jantar-Mantar of Delhi
These are extraordinary structures – basically buildings and spaces as instruments of observation.
In Review: Solar Geometry variables from previous lectures
Solar Declination (δ) relative tilt of equatorial plane to ecliptic plane
Solar Altitude (Β)position of sun above horizon in a vertical plane
Zenith angle (Z)sun’s position referenced to the zenith in a vertical plane
Solar Azimuth (Φ)horizontal position of sun referenced to south
Solar –Surface Azimuth (γ)Angle in plan between the sun and a line normal to a surface.
Angle of Incidence (Θ)True angle (in three-dimensions) between the sun and a line normal to a surface.
Profile Angle (Ω)Position of sun translated into a two-dimensional vertical plane (as in section)
New this lecture: Solar Geometry variables
Angle of Incidence (Θ) Angle of sun to a line normal to the surface in question (time and orientation specific)
Solar-Surface Azimuth (γ)
.
Solar-Surface Azimuth (γ) Angle in plan between the sun and a line normal to the surface in question (time and orientation specific)
Surface Tilt (Σ)Tilt of a surface relative to the ground plane (orientation specific)
Sunsets from Benton’s officeSolar-Surface Azimuth (γ) Angle in plan between the sun and a line normal to the surface in question (time and orientation specific)