A B C D E F G H I J K
1 Noon Shadow Observation Project 1998    
2 Location City State Country Latitude Longitude Noon Shadow Length Sun Angle Equatorial Distance (km) Circumference Estimate (km) Error Distance (km)
3

Faubion Middle School

McKinney

TX

USA

33° 11' 51" N

96° 36' 54" W

65 cm

33°

3674

40080

72

4

Anne Frank Gymnasium

Werne

Nordrheinwestfalen

Germany

51° 40' N

7° 37' E

--

52.17°

5726

39628

380

5

Lynn English High School

Lynn

Massachusetts

USA

42.5°N

71.0°W

--

41.67

4704

40639

631

6

Stevens Institute of Technology

Patterson

New Jersey

USA

40.9° N

70.2° W

--

40.2

4531

40576

568

7

Im Ellener Feld

Bremen

--

Germany

53.06°N

8.92°E

RAIN

RAIN

5885

   
8

Moorestown High School

Moorestown

New Jersey

USA

39° 59.19'N

74° 56.59'W

--

39.6

4428

40254

246

9

Mt. St. Michael Academy

Bronx

New York

USA

40.9°N

73.8°W

--

39.79

4545

41121

1113

10

Holy Family Academy

Bayonne

New Jersey

USA

40.7°N

74.1W

--

38.93

4523

41826

1818

11

Käthe-Kollwitz Gymnasium

Wilhelmshaven

Lower Saxony

Germany

53.5°N

8.1°E

--

53.76

5946

39817

191

12

Northcote High School

Melbourne

Victoria

Australia

37.81°S

144.96°E

--

38.6

4202

39190

818

13

Serrano
High School

Phelan

California

USA

34.4°N

117.6°W

--

34.37

3823

40043

35

14

F.W. Reilly Elementary School

Chicago

Illinois

USA

41.9°N

87.6°W

--

39

4656

42978

2970

15 CP Center Essex &
West Hudson
Belleville New Jersey USA 40.8°N 74.2°W -- 41 4516 39653 355
16 The Governor
French Academy
Belleville Illinois USA Will participate next year.
17 Karl-von-Closen
Gymnasium
Eggenfelden Bavaria Germany 48.4°N 12.8°E -- 48.63 5362 39990 18
18 Warrensburg Middle School Warrensburg Missouri USA 38.8°N 93.6°W   38 4297 40708 700

Explanation of the Excel Spreadsheet Formula
Column by Column

by
Andrew W., Middle School Student
Faubion Middle School
April 2, 1998

Note: In the formula below, the highlighted variables labeled as column A, column F, etc., in Excel as in most spreadsheets are replaced by the actual cell name. Take for example, a cell in column G and row 7.  If the cell is in column G and in row  7 the cell is named G7.
So, the formula in Column J  below which is written =(360/Column H)*Column I, in Excel  actually is  written with the cell names.  The formula is written in cell J3 as: =(360/H3)*I3. A nice thing about spreadsheets is the fill option for formulae. To make the formula work in all the successive rows of Column J, we click on cell J3 to activate the cell, then without clicking, lay our mouse on the small square at the lower right-hand corner of the rectangle surrounding the active cell until the curser turns into a thin plus sign, click and hold down the left mouse button, and while holding the left mouse button down, drag down to fill our formula in the cells below. This is called a fill down.


Column A: Site Name — School Name


Column B: City


Column C: State


Column D: Country


Column E: Latitude - of reporting site.


Column F: Longitude -of reporting site.


Column G: Length of shadow of a meter stick at local noon time. (we will leave this one out next year — kc)


Column H: The angle of the Sun at noon. sungles3.gif (2449 bytes)


Column I: The Equatorial Distance-To understand what we are doing here, just think about why we take our readings at our local noon time. Imagine that we are lining up all of our schools at the same place on the globe, longitudinally, say at the Prime Meridian. The only distance between the schools would be the north-south distance. Instead of comparing the distances between the different schools as we have in the past, this year we are calculating using the equitorial distance, that is, the distance between each school and the Equator.
Now to find the circumference, we use Bali Online's site called HowFar is It, where we enter the latitude and longitude of the school and the the latitude and longitude corresponding point on the Equator directly north or south of the city.


Column J: Circumference Estimate-Now that we know the arc of the Earth formed by the distance from the school to the Equator, Column I, and the central angle of that arc which is the same as the Sun Angle, Column H, at Noon on the Equinox, we make our formula to find the circumference of the Earth.. (In this project the first site is the location of the school. The second site is the Equator. The distance is the perpendicular distance from the location of the school to the Equator. Since we chose our second site to be the point on the Equator closest to our first site and the time to be at Noon on the Vernal Equinox, the sun angle at our second site is 0°. Therefore, we do not need to do the subtraction that Eratosthenes did because we would be subtracting 0° from our sun angle. — kc)

You might remember that the size of an arc of a circle is the measurement of its central angle. Also, we chose the second site to be the point on the Equator closest to our initial site at the Vernal Equinox so that in this table, the central angle is the same as the sun angle. We posted a lesson to demonstrate this concept. Now to find the circumference estimate, multiply that one degree length by 360.

The Excel formula which we use is:
=(360/Column H)*Column I


Column K: The deviation from the Actual Circumference-To find this number we subtract the actual circumference from our estimate in column J, divide the answer by the actual circumference, 40008 km. Since we only want the distance and not the signed direction, we find the absolute value of it. Therefore, it won't be negative.

The Excel formula which we use is:
=ABS(40008-Column J)


Last update: 17 April 1998
Kenneth Cole
FMS Emerging Technology Teacher
kcole@ns.waymark.net
Edited and revised final copy
for posting at this location.

Andrew W.
Emerging Technology Club President
Student
Page creator
kidbert101@aol.com
Andrew's original pre-edited page


Brian B.
Student
Distance measurer bb84@hotmail.com


Background cropped from an original fractal
created and tessellated by 8th grader Kim H.

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