SRV-09

Bowditch linear misclosure share

Correction on a side ∝ its length. δE_i = − (ℓ_i / Σℓ) ΔE.

Reading speed

SurveyBowditch

Governing equation

\delta E_i=-\dfrac{\ell_i}{\sum\ell}\Delta E

where

\ell_i: Side length (m)
\sum\ell: Perimeter (m)
\Delta E: Easting misclosure (m)
\delta E_i: Correction (m)

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-09 — Bowditch linear misclosure share) is the form associated with Bowditch. Working symbols: $\ell_i$ , $\sum\ell$ , $\Delta E$ $\rightarrow$ $\delta E_i$ . Assumes equal precision in angle and distance — a compass-rule hypothesis.

Purpose

Purpose: compute

\delta E_i

from

\ell_i

\sum\ell

\Delta E

in Surveying via

\delta E_i=-\dfrac{\ell_i}{\sum\ell}\Delta E

Correction on a side ∝ its length. δE_i = − (ℓ_i / Σℓ) ΔE. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\ell_i = 120.000\,\mathrm{m}

\sum\ell = 600.000\,\mathrm{m}

\Delta E = 0.240\,\mathrm{m}

, the governing relation

\delta E_i=-\dfrac{\ell_i}{\sum\ell}\Delta E

yields

\delta E_i = -0.0480\,\mathrm{m}

. A closed traverse, a residual vector split along the sides. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Side length \ell_i120 mPerimeter \sum\ell600 mEasting misclosure \Delta E0.24 m

Outputs

Correction \delta E_i-0.0480 m

Reading speed

Watch on YouTube

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Narration of this film

A closed traverse, a residual vector split along the sides.

Assumes equal precision in angle and distance — a compass-rule hypothesis.

Reading speed

Watch on YouTube