SRV-04

Representative fraction

Ground distance = map distance × denominator S.

Reading speed

CartographyISO 19115

Governing equation

D_{\mathrm{ground}} = D_{\mathrm{map}}\times S

$D_{\mathrm{map}} \in \left[1, 400\right]$

where

D_{\mathrm{map}}: Map length (mm)
S: Scale denominator (—)
D_{\mathrm{g}}: Ground distance (m)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

D_{\mathrm{ground}} = D_{\mathrm{map}}\times S

$D_{\mathrm{map}} \in \left[1, 400\right]$

$D_{\mathrm{map}} = 1$ $D_{\mathrm{g}} = 25$

Along the curve

②

Domain of the variable — blue

D_{\mathrm{map}}_{\min} = 1,\quad D_{\mathrm{map}}_{\max} = 400

$D_{\mathrm{map}} \in \left[1, 400\right]$

$D_{\mathrm{map}} = 1$ $D_{\mathrm{map}} = 1$

Along the curve

③

Response curve — green

D_{\mathrm{ground}} = D_{\mathrm{map}}\times S

$D_{\mathrm{map}} \in \left[1, 400\right]$

$D_{\mathrm{map}} = 1$ $D_{\mathrm{g}} = 25$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}D_{\mathrm{g}}}{\mathrm{d}D_{\mathrm{map}}}

$D_{\mathrm{map}} \in \left[1, 400\right]$

$D_{\mathrm{map}} = 3.509$ $D_{\mathrm{g}}^{\prime} = 25$

Along the curve

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-04 — Representative fraction) is the form associated with ISO 19115. Working symbols: $D_{\mathrm{map}}$ , $S$ $\rightarrow$ $D_{\mathrm{g}}$ . A map scale 1:S is the ratio of a length on the map to the same length on the geoid, neglecting projection distortion.

Purpose

Purpose: compute

D_{\mathrm{g}}

from

D_{\mathrm{map}}

S

in Surveying via

D_{\mathrm{ground}} = D_{\mathrm{map}}\times S

Ground distance = map distance × denominator S. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

D_{\mathrm{map}} = 40.000\,\mathrm{mm}

S = 25000.000\,\mathrm{—}

, the governing relation

D_{\mathrm{ground}} = D_{\mathrm{map}}\times S

yields

D_{\mathrm{g}} = 1000.000\,\mathrm{m}

. Planar, no relief displacement. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Map length D_{\mathrm{map}}40 mmScale denominator S25000 —

Outputs

Ground distance D_{\mathrm{g}}1000.000 m

Reading speed

Watch on YouTube

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Narration of this film

Planar, no relief displacement.

A map scale 1:S is the ratio of a length on the map to the same length on the geoid, neglecting projection distortion.

Reading speed

Watch on YouTube