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Index/Surveying/SRV-26

SRV-26

Traverse latitude and departure

ΔN = L cos θ, ΔE = L sin θ. Whole-circle bearing from north.

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TraverseTraverse ΔE ΔN

Governing equation

ΔN=Lcos⁡θ,ΔE=Lsin⁡θ\Delta N=L\cos\theta,\quad \Delta E=L\sin\theta

where

L
Length (m)
\theta
Azimuth from north (°)
\Delta N
Latitude ΔN (m)
\Delta E
Departure ΔE (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-26 — Traverse latitude and departure) is the form associated with Traverse ΔE ΔN. Working symbols: LL, θ\theta →\rightarrow ΔN\Delta N, ΔE\Delta E. Plane surveying on a projected grid. Azimuth clockwise from north, so easting takes the sine.

Purpose

Purpose: compute ΔN\Delta N, ΔE\Delta E from LL, θ\theta in Surveying via ΔN=Lcos⁡θ,ΔE=Lsin⁡θ\Delta N=L\cos\theta,\quad \Delta E=L\sin\theta ΔN = L cos θ, ΔE = L sin θ. Whole-circle bearing from north. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given L=145.200 mL = 145.200\,\mathrm{m}, θ=42.000 ∘\theta = 42.000\,\mathrm{^{\circ}}, the governing relation ΔN=Lcos⁡θ,ΔE=Lsin⁡θ\Delta N=L\cos\theta,\quad \Delta E=L\sin\theta yields ΔN=107.905 m\Delta N = 107.905\,\mathrm{m}, ΔE=97.158 m\Delta E = 97.158\,\mathrm{m}. A course, a bearing, a ΔE and ΔN. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • Latitude ΔN \Delta N107.905 m
  • Departure ΔE \Delta E97.158 m
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SRV-26 · gauge
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Narration of this film

A course, a bearing, a ΔE and ΔN.

Plane surveying on a projected grid. Azimuth clockwise from north, so easting takes the sine.

Reading speed

Watch on YouTube