Sundial

Template for Horizontal Sundial at Ripon’s Latitude

sundailface

        Face:  Time numbering begins  at left horizontal line as 6 AM (7 AM Daylight Time) and increases clockwise to 7, 8, 9, 10, 11 AM, 12 noon (shown), 1 pm, etc. to 6 PM  (horizontal line to the right)

To distinquish Standard Time and Daylight Savings Time, you might use Arabic and Roman numbers, respecitively .

gnomon

                                                          cut on each line

Construction:

Cut around gnomon and cut between tabs.

Fold tabs along angle base line, alternating bending right and left.

Align gnomon with 12:00 ST (due North) line, placing  the acute angle marked above at the point where dial angles cross.

Tape or glue in place. Straighten gnomon so it is perpendicular to face.

To use:

Place on horizontal surface in full sunlight with 12:00 ST line pointed toward celestial North.

Sundial Design 

Since very early times, the sun has been used to tell time during the day because, as we now know, as the Earth rotates, the position of the sun in the sky changes.  This simple technology has applications and connections in many disciplines.

  • History of technology
  • Mathematics:

If Earth makes one rotation in 24 hours, each hour represents a rotation of 15 degrees, the hour angle h. The hour angle is 0 at noon, -15 degrees (15 degrees counterclockwise from the noon line) for 11:00 a.m., +15 degrees (15 degrees clockwise from the noon line),  for 1:00 p.m., and so on.  For a horizontal sundial at a particular latitude L, the angle A of a shadow line from the line to due north (noon line) is given by

tan(A)= sin(L) tan(h).

The gnomon—shadow casting element-angle is L.

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For a vertical south dial, such as Ripon’s Farr Hall sundial shown above, the angles are given by

tan(A)=sin(90-L) tan(h),

and morning hour angles are measured clockwise from the downward vertical noon line while afternoon ones are measured counterclockwise..

The gnomon angle is (90-L) for a vertical south dial.

A sundial–vertical, horizontal, or whatever–measures solar time (or local apparent time), which is related to local mean time by the following relationship:

Solar time=Local Mean Time + Equation of Time  (3)

and Local Mean Time to Clock Time (Zone Time) by

Local Mean Time=Zone Time +(CML-LL)4 minutes.  (4)

CML is the longitude of the time zone’s central meridian (90 degrees for Central Time) and LL is the local longitude (88deg. 50’ 24” for Ripon).  Locations east of the central meridian experience local noon before clock noon and locations west experience it after clock noon.  In equation 3, the equation of time–a correction that may be as large as +/-16 minutes–occurs because the Earth’s orbit around the Sun is not quite circular.  This results in a variation of speed of Earth in its orbit which in turn causes a variation in the apparent position of the sun at local noon.  Thus a sundial at a particular location (e.g. Ripon) may indicate a time as much as 20 minutes different from clock time because of a combination of equation of time and local vs. zone time effects.

The equation of time is shown in the following graph**:

 equation of time

**Source:  Wikipedia article on the Equation of Time.

Design Note:  The plane of the gnomon of either a horizontal or vertical south sundial must be perpendicular to the face of the dial and aligned with the noon line.

  • Art and Design:  The Farr Hall sundial (installed in 1997) was a collaborative project in which art students under the direction of Professor Gene Kain designed the hour markers to represent the signs of the Zodiac (plus a sun/moon marker at noon designed by Prof. Kain) and Prof. Mary Williams-Norton (Physics) provided the angle calculations.
  • Science/ Science Education:  Sundials provide a simple and interesting way of studying shadows and the position of the sun in the sky throughout the day and year.

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Farr Hall of Science sundial (Ripon College) designed byProf.  Mary Williams-Norton, Prof. Gene Kain, and his art students