SRV-08

Plane grid distance

D = √(ΔE² + ΔN²) on a projected grid.

Reading speed

CoordinatesUTMISO 19111

Governing equation

D=\sqrt{(\Delta E)^2+(\Delta N)^2}

where

\Delta E: Easting difference (m)
\Delta N: Northing difference (m)
D: Grid distance (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-08 — Plane grid distance) is the form associated with UTM · ISO 19111. Working symbols: $\Delta E$ , $\Delta N$ $\rightarrow$ $D$ . On a conformal projection the grid distance is Euclidean in easting and northing; a scale factor later recovers the ellipsoid.

Purpose

Purpose: compute

D

from

\Delta E

\Delta N

in Surveying via

D=\sqrt{(\Delta E)^2+(\Delta N)^2}

D = √(ΔE² + ΔN²) on a projected grid. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\Delta E = 150.000\,\mathrm{m}

\Delta N = 80.000\,\mathrm{m}

, the governing relation

D=\sqrt{(\Delta E)^2+(\Delta N)^2}

yields

D = 170.000\,\mathrm{m}

. No scale factor applied (grid, not ground). Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Easting difference \Delta E150 mNorthing difference \Delta N80 m

Outputs

Grid distance D170.000 m

Reading speed

Watch on YouTube

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Narration of this film

No scale factor applied (grid, not ground).

On a conformal projection the grid distance is Euclidean in easting and northing; a scale factor later recovers the ellipsoid.

Reading speed

Watch on YouTube