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Procedure for LEOC Calculations

 

PROCEDURE FOR CALCULATING L.E.O.C.

The procedure uses the calculated latitudes and departures to determine the Linear
Error of Closure (LEOC).
Step 1                Sum  the North Latitude column (926.1908). Sum the South Latitude column
                          (926.1124). Sum the East Departure column (1271.5510). Sum the West Departure
                          column (1271.6325). See the summation line in the next Table.
Step 2                Determine the difference between the summations of the North and South
                          Latitudes (that is, Closure in Latitude = 0.0784). Determine the difference between
                          the summations of the East and West Departures (Closure in Departure = 0.0815).
Step 3                Insert the differences into the Pythagorean Theorem (A²+B²=C²) to calculate the Linear Error
                          of Closure (LEOC) for the traverse.


                                          LEOC²= 0.0784² + 0.0815²
                                          LEOC = 0.1131

PRECISION CALCULATION AND ANALYSIS

Once the Linear Error of Closure is determined, the precision of the traverse can
be determined.  Precision is a simple ratio determined from the proportional
relationship between the LEOC and the total distance around the traverse.

Formula

Using the LEOC and the distance measured, a ratio called the precision is
calculated.

Procedure

Sum the distances measured around the traverse to determine the perimeter and
then substitute into the formula. For this continuing example:
Linear Error of Closure

Analysis

After measuring 3739 feet, the traverse had an LEOC of 0.1131 feet. Expressed as
a ratio, 1 foot in 33000 feet means that if the field crew had measured 33000 feet
using the same techniques and precision, they would have been off 1 foot. By using
a typical construction total station (5-second instrument) and good techniques, this
is an acceptable precision for this traverse. If this were a traverse in which a transit
and chain were used, a precision of around 1:5000 would have been expected.


This has been an excerpt from a chapter of Wesley Crawford's book, "Construction Surveying and Layout" 3rd Edition.  You can purchase this helpful book online!
Construction Surveying and Layout Wesley G CrawfordBuy the Book

 


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