SRV-07

Linear traverse closure

e = √(Ex²+Ey²), precision = e / perimeter.

Reading speed

TraversingFGCCISO 17123

Governing equation

e=\sqrt{E_x^2+E_y^2},\quad p=e/\sum L

where

E_x: Easting closure (m)
E_y: Northing closure (m)
\sum L: Perimeter (m)
e: Linear misclosure (m)
1:N: Relative precision N (—)

Lecture brief

Historical brief

From chain and theodolite through Bowditch’s compass-rule (1802) to GPS PDOP, surveying is the propagation of small errors across a network. These sheets close traverses, reduce stadia and state map scale. This sheet (SRV-07 — Linear traverse closure) is the form associated with FGCC · ISO 17123. Working symbols: $E_x$ , $E_y$ , $\sum L$ $\rightarrow$ $e$ , $1:N$ . Vector closure of a polygon is the residual of summed latitudes and departures; relative precision is e over the perimeter.

Purpose

Purpose: compute

e

1:N

from

E_x

E_y

\sum L

in Surveying via

e=\sqrt{E_x^2+E_y^2},\quad p=e/\sum L

e = √(Ex²+Ey²), precision = e / perimeter. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

E_x = 0.120\,\mathrm{m}

E_y = -0.080\,\mathrm{m}

\sum L = 1200.000\,\mathrm{m}

, the governing relation

e=\sqrt{E_x^2+E_y^2},\quad p=e/\sum L

yields

e = 0.1442\,\mathrm{m}

1:N = 8321\,\mathrm{—}

. Closed loop. Enter component closures and perimeter. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Easting closure E_x0.12 mNorthing closure E_y-0.08 mPerimeter \sum L1200 m

Outputs

Linear misclosure e0.1442 m
Relative precision N 1:N8321 —

Reading speed

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Narration of this film

Closed loop. Enter component closures and perimeter.

Vector closure of a polygon is the residual of summed latitudes and departures; relative precision is e over the perimeter.

Reading speed

Watch on YouTube