March 2014 Problem

Surveyors of the Lost Arc

North and south PLS township lines originally were run in as true lines of latitude so they were curved.  The diagram shows the south line of T23N R18W 4th PM, Badger County, WI.  All the corners along the township boundary line are lost except for those at the SW corner of Section 31 (A) and SE corner of Section 36 (B).

township line

You’re re-establishing the SE corner of Section 33 by proportionate measurement between A and B. The approximate latitude and longitude of the corner location are 44°25' N and 92°30’ W. The horizontal distance between A and B is 31,693.25 ft.
What is the offset to the south from the chord AB to the latitudinal arc at the SE corner of Section 33? To minimize roundoff error, compute to nearest 0.1 link.

offset to arc

 

Solvers

 Name

Date
rec'd

S

D

 B

Total 

Comments 
Bill Holme

03 Apr

4

10

5

19 

Used arc geometry & trig but answer off a bit because he
used an approx earth radius only good to the nearest mile.   

Alex Durkin

03 Apr

6

8

5

19

 Tried trig first, then reverted to the Standard Field Tables to get correct answer.
Dave Tlusty

14 Apr

6

6

2

14

Correct answer with this explanation: "As long as you didn’t use the word “compute”, I just looked it up!"

Mick Heberlein

30 Apr

6

4

5

15

Correct answer using the 1973 Manual's Tangent Method
Mick's Solution
Chris Ruetten

1 May

6

2

5

13

Correct answer using the 1973 Manual's Secant Method 
 

 

 

 

 

 

 

 

 

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