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Presentation title: Sundials and Solar Geometry Sundials and Solar Geometry Lecture 15. Geometry

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Presentation title: Sundials and Solar Geometry

Sundials and Solar Geometry

Lecture 15.

Geometry

ARCH. 140 Midterm 2009

Grade Distribution

C (~15%) B (~50%) A (~25%)

9 February 5 March

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.

Back to Earth where it is diagrammatically summer

above the equator

Summer above the arctic circle in photographs

4 am 6 am 8 am 10 am noon 2 pm

Summer above the arctic circle in photographs

4 pm 6 pm 8 pm 10 pm midnight 2 am

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.

Time zones

Standard meridians run at roughly 15° intervals

Time zones

Standard meridians run at roughly 15° intervals

The analemma conveys both declination

and the equation of time

Solar Analemma photographs taken in Greece by Anthony Ayiomamitis

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.

Isogonic chart for the US Mainland

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.

Horizontal Sundial

Nomenclature

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

Another type of horizontal sundial uses a vertical gnomon

– often called Flagpole Plots

Flagpole plots for many latitudes are available in

Sun, Wind, and Light.

Did the Arch. 140

Sundial Exercise

precipitate the

Berkeley parking

meter crisis?

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.

Polar sundials under close guard in England

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.

A contemporary vertical

sundial in glass

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

Vertical declining dialon a house in Pustertal, Austria circa 1576

Two of the eight dials on the façade

of the Louis le Grande High School in

Paris

Contemporary vertical dials

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.

An equatorial

sundial in India’s

lower latitudes

A contemporary dial near the equator -- Hong Kong University of Scienceand Technology

Equatorial or polar?

This small equatorial dial

made for shading models

has an adjustable hour

scale

But wait -- it is time for the 7th inning stretch

And then there is the

issue of precision in

timekeeping

An analemmic gnomon

Heliochronometers with sighting mechanisms,

gears, and dial indicators.

A sundial using cylindrical focusing mirrors to project a sharply focused beam on the inside of a helix shaped scale.

The sundial’s base features handsome latitude wedges

A contemporary Gunning heliochronometer

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.

Sunsets from Benton’s office

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

A Korean sundial circa 1875

An Italian equatorial scaphe dial circa 1600

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

How many sundial landmarks can you spot on this armillary sphere?

Sundials as graphic design objects by Analemma

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

Former Arch. 140 GSI Hugh Tuffley with some cylindrical dials from Arch. 140 past.

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.

Schema for

Equidistant

Sun Path Diagram

Got to here at a pretty

fast clip in 2004

Benton

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)

Solar-Surface Azimuth (γ)

Profile Angle (Ω)Position of sun translated into a two-dimensional vertical plane (as in section)

Profile Angle (Ω)

Profile Angle (Ω)

Profile Angle (Ω)

Excel worksheet via WWW

site if there is time