SIERRA COLLEGE OBSERVATIONAL ASTRONOMY

LABORATORY EXERCISE

NUMBER    VI.A.       TITLE: The Sundial Project

DATE-                             PRINT NAME/S AND INITIAL BELOW:             GROUP

                                                               

DAY-                                      

                                                                               

LOCATION

 

INTRODUCTION

Each student in Astronomy 11 is expected to design and build a sundial.  The sundial may be done individually or as part of a group effort.  The completed sundial is due as indicated by the instructor.  Check with the instructor prior to this date for any questions on the design or function of the sundial.  The sundial is worth 20 points with the points divided between:  1) Technical Accuracy [10 points]; 2) Quality of Written Report [5 points]; and 3) Aesthetic Appearance [5 points].

DESIGN AND CONSTRUCTION POINTERS

The instructor will give a brief lecture on the technical features of the sundial construction.  The student is then expected to incorporate these technical features in an original and aesthetic design.  There are sundial models on display in the laboratory to help spark an idea or two.  In any case, the primary technical features to pay close attention to are as follows:

·  Be sure the sundial base is level

·  Be sure the style is made of thin but study material

·  Be sure style angle is equal to local latitude

·  Be sure the face of the style is perpendicular to the sundial base

·  Be sure style base is oriented North-South (the style edge points toward the North Star)

·  Be sure the vertices of all the hour lines are located at the style vertex

·  Be sure the hour angles are measured from the noon line at the style base

·  Be sure the hour lines are symmetrical to both the E-W and N-S lines of the sundial

WRITTEN REPORT

Each student must individually submit a written report addressing the following points regarding the proper use and set-up of a sundial.  Each report must be typed (double spaced).

·  Does the base of the sundial have to be level in order to operate properly?

·  In what direction must the tip of the style or gnomon point for a properly oriented sundial?

·  The angle of the style to the plate of a conventional sundial must equal the observer’s                 ?

·  Give three reasons why the sundial time (local apparent solar time) does not always agree exactly with the Pacific Standard Time (PST).  Assume the sundial is constructed properly and set up correctly.

·  Determine what time (PST) a properly constructed and oriented sundial will register 2 PM on December 17.

·  On what date(s) would a sundial located in Rocklin, CA, agree (within 30 seconds) with an accurately set local clock (PST)?

·  If your sundial was part of a group effort, what part did you play in its design and construction?  If you were not part of a group effort, please indicate this in your report.

ADDITIONAL SUNDIAL SPECIFICATIONS

·  Constructed for:       local latitude = 39O     longitude =     121O

·  Hour range must be from 5 AM to 7 PM local apparent solar time

 

CONSTRUCTING THE HOUR LINES – THE ‘TRIG’ METHOD

·        Sundial may be constructed for a horizontal or vertical base.  For a horizontal base, the equation for the hour lines is:

tan(At) = tan(t) • sin(L)

 

·        For a vertical plate sundial the equation for the hour lines is:

  tan(At) = tan(t) • cos(L)

where At is the angle from the style base (North-South Line) to the hour of interest, t. The hour of interest (t) is expressed in degrees (15 degrees for each hour before or after noon), and L is the sundial’s latitude.  Caution:  When using a calculator, be sure the degree mode is set ON.   Compute the angles for 1, 2, 3, 4, & 5 PM, enter them in the table below and then complete the table.

 

HOUR

At
HOUR

At
1PM

 

11AM

 

2PM

 

10AM

 

3PM

 

9AM

 

4PM

 

8AM

 

5PM

 

7AM

 

6PM

 

6AM

 

7PM

 

5AM

 

CONSTRUCTING THE HOUR LINES – THE GEOMETRIC METHOD

For this method, you will need a straight edge, drafting compass, protractor, sharpened pencil, and an 11” x 17” sheet of paper.  In the following steps, refer to the diagram on the back of this page.

 

·         In the center of the 11x17 paper or base of your sundial, draw a vertical line, NS, to represent the north-south line. This will be the meridian and direction of the shadow at local apparent noon.

·         Near the bottom of NS, draw a line through point A at right angles.  This is the east-west line, EW, and will be marked 6a.m. and 6p.m., since it marks the direction of the shadows at those times.

·         Select some point, B, on NS and draw another line at right angles to NS.  Call it CC’.

·         Draw a line, AD, from point A which makes an angle BAD = L with the line NS, where L is the latitude of the sundial.   Then drop a perpendicular BD from B to the line AD.

·         Lay off a distance, BP, on line NS equal to the distance BD.  P represents the celestial pole.

·         Draw a circle (or half-circle) with P as its center.  Mark off on the circle points which are 15o apart; that is, one hour apart.  Draw radii of the circle from P through the points marked off on the arc. Where they intersect the line CC’, mark the points C1, C2, C3, - - -.

·         Connect each of the points C1, C2, C3, - - - with the point A. The angles BAC1, BAC2, BAC3, - - - are the At angles in the trig formula and table on the previous page.  This array of lines marks the position of the shadows for the afternoon hours (using Roman Numerals) as shown in the figure on the next page.  The morning hours can be marked similarly at the same angles on the left side of AB and marked accordingly, XI, X, IX, - - -.  In the figure, only the first three lines were drawn by construction, since the paper was not large enough to draw the lines for the later hours.  The later hours must be drawn using a larger sheet of paper, like 11” x 17” provided at your request.

CORRECTIONS TO THE SUNDIAL

Adjacent to each date below is the corresponding Standard Time a sundial would register NOON.  As a further correction for longitude, add 4 minutes for every degree your sundial is located west of the Standard Time meridian.  For any other time of day, simply add or subtract the appropriate number of hours and minutes from the NOON time.

Example:  What time (PST) would the shadow produced by a sundial located at 122° W longitude register 4 PM on July 10?  Solution:  By the table below, sundial noon occurs at 12h05m.  Add 8 minutes to correct for local longitude.  We now have sundial noon occurring at 12h13m.  Now add 4 hours for time of day.  Thus, at 4:13 PM PST, the sundial will register exactly 4 PM.

Jan    1        12h 03m 32s

Apr    1        12h 03m 56s

Jul      5        12h 04m 31s

Oct    3        11h 49m 06s

          6        12h 05m 49s

          6        12h 02m 28s

        10        12h 05m 18s

          8        11h 47m 37s

        11        12h 07m 54s

        11        12h 01m 05s

        15        12h 05m 55s

        13        11h 46m 18s

        16        12h 09m 44s

        16        11h 59m 50s

        20        12h 06m 19s

        18        11h 45m 13s

        21        12h 11m 17s

        21        11h 58m 43s

        25        12h 06m 30s

        23        11h 44m 23s

        26        12h 12m 32s

        26        11h 57m 49s

        30        12h 06m 26s

        28        11h 43m 50s

        31        12h 13m 27s

 

 

 

 

May   1        11h 57m 06s

Aug   4        12h 06m 06s

Nov    2        11h 43m 36s

Feb    5        12h 14m 01s

          6        11h 56m 36s

          9        12h 05m 31s

          7        11h 43m 41s

        10        12h 14m 15s

        11        11h 56m 20s

        14        12h 04m 42s

        12        11h 44m 08s

        15        12h 14m 09s

        16        11h 56m 18s

        19        12h 03m 39s

        17        11h 44m 56s

        20        12h 13m 46s

        21        11h 56m 31s

        24        12h 02m 25s

        22        11h 46m 06s

        25        12h 13m 06s

        26        11h 56m 58s

        29        12h 01m 00s

        27        11h 47m 34s

 

        31        11h 57m 36s

 

 

Mar    2        12h 12m 12s

 

Sep    3        11h 59m 25s

Dec    2        11h 49m 21s

          7        12h 11m 06s

Jun    5        11h 58m 24s

          8        11h 57m 44s

          7        11h 51m 22s

        12        12h 09m 49s

        10        11h 59m 21s

        13        11h 56m 00s

        12        11h 53m 37s

        17        12h 08m 25s

        15        12h 00m 22s

        18        11h 54m 13s

        17        11h 56m 01s

        22        12h 05m 57s

        20        12h 01m 28s

        23        11h 52m 27s

        22        11h 58m 30s

        27        12h 05m 26s

        25        12h 02m 33s

        28        11h 50m 44s

        27        12h 00m 59s

 

        30        12h 03m 35s

 

        32        12h 03m 24s