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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 ANALYSISOnce 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.
FormulaUsing the LEOC and the distance measured, a ratio called the precision is
ProcedureSum the distances measured around the traverse to determine the perimeter and
then substitute into the formula. For this continuing example:
AnalysisAfter 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!