Date: Sun, 17 Mar 1996 20:00:03 -0600
To: noon@lynx.ed.uiuc.edu
From: ksmith@ncsa.uiuc.edu (Kathleen Smith)
Subject: SSheet Info

Dear Noon Folks,

Here are the formulas for the Noon Calculation Spreadsheet.
I can also send you a copy of the spreadsheet if you do not
have access to it on the web site:
        <http://www.ed.uiuc.edu/courses/satex/sp96/noon-project/>  
You need to let me know what software package you have that
runs a spreadsheet and I will see if I can send you a
compatable sheet.   The proportion that we use to calculate
the circumference is:
   "The difference in the angles of the sun between the two
sites is to 360 degrees as the north south distance between
the two sites is to the total circumference."
   When setting up the spreadsheet the site that is placed
in the top row is then compared to every site below it.  We
run a different spreadsheet for each site, putting that site
in the top row, so that they can see how they did with every
other site.
    What you do is enter the site name in column 1, the
latitude (positive if above equator, negative if below) in
column 2, the shadow mesaure in column 3 and then the
following formulas: in columns 4 through 7  ( columns 5
through 7 are blank for the site at the top)

Column 4: The formula to compute the angle, 
    =90-ArcTan(column 3/100)*57.3*(Sign of lattitude from column 2)
 (The 57.3 changes radians to degrees)

Column 5: The formula for the north/south distance
             =Abs(lattitude of site in first row minus
lattitude of site in current row)*(111.133)
(The 111.133 is the distance in km for one degree latitude)

Column 6: The formula for the circumference estimate
            =Abs(column 5*360/(difference in the angles
between the top site and the current row))
(This comes from the proportion listed above.)

The formula for the % error, to be placed in G4:
        =((Column 6-40008)/40008)*100
(40008 km is the correct circumference) 

  If this makes sense to you then you should go into the
business to deciphering secret codes!  If you  use
spreadsheets, however, it is pretty straight forward once
you have a sheet in front of you and follow along. Below I
have pasted some results from last year's running so you can
plug them into your sheet to see that it works.

Noon Observation Project 
Site     Lat    Shad   Angle    N/S   Circum        %
AUS   -23.38   46.2    114.8    (km)    Est      Deviation
CA     34.13   65.14    56.92   6391   39751       -1
WI     43.17   91.5     47.54   7396   39586       -1 
NY     42.93   90       48.01   7369   39719       -1
CA     36.53   67       56.18   6658   40888        2
IL     40.07   81.67    50.76   7051   39637       -1 
NZ    -43.53   96.6    134.01   2239   41959        5


You will notice that I used a site at the top that produced
excellent results.  Oh, that we could all be as good as Rex
in Rockhampton, Australia!


Kathleen Smith
Mathematics Teacher
Central High School
Champaign, Illinois   61820