SRV-36

Earth curvature correction

c = D² / (2 R). How much a level line drops below the horizontal tangent.

Reading speed

LevellingEarth curvature

Governing equation

c=D^2/(2R)

where

D: Sight distance (km)
R: Earth radius (km)
c: Curvature drop (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-36 — Earth curvature correction) is the form associated with Earth curvature. Working symbols: $D$ , $R$ $\rightarrow$ $c$ . R ≈ 6371 km. Combined curvature-and-refraction is ≈ 0.0675 D² (D in km, c in m) with k ≈ 0.13.

Purpose

Purpose: compute

c

from

D

R

in Surveying via

c=D^2/(2R)

c = D² / (2 R). How much a level line drops below the horizontal tangent. 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 = 2.000\,\mathrm{km}

R = 6371.000\,\mathrm{km}

, the governing relation

c=D^2/(2R)

yields

c = 0.314\,\mathrm{m}

. A tangent, a curved earth, a drop c. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Sight distance D2 kmEarth radius R6371 km

Outputs

Curvature drop c0.314 m

Reading speed

Watch on YouTube

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Narration of this film

A tangent, a curved earth, a drop c.

R ≈ 6371 km. Combined curvature-and-refraction is ≈ 0.0675 D² (D in km, c in m) with k ≈ 0.13.

Reading speed

Watch on YouTube