SRV-21

Stadia distance

D = k s + C. k = f/i ≈ 100, s the staff intercept, C the additive constant.

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TacheometryStadia

Governing equation

D=ks+C

where

k: Stadia constant (—)
s: Staff intercept (m)
C: Additive constant (m)
D: Horizontal 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-21 — Stadia distance) is the form associated with Stadia. Working symbols: $k$ , $s$ , $C$ $\rightarrow$ $D$ . Similar triangles in the telescope. The stadia hairs subtend a fixed angle; intercept s scales as distance.

Purpose

Purpose: compute

D

from

k

s

C

in Surveying via

D=ks+C

D = k s + C. k = f/i ≈ 100, s the staff intercept, C the additive constant. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

k = 100.000\,\mathrm{—}

s = 1.240\,\mathrm{m}

C = 0.300\,\mathrm{m}

, the governing relation

D=ks+C

yields

D = 124.30\,\mathrm{m}

. A staff, two hairs, a distance. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Stadia constant k100 —Staff intercept s1.24 mAdditive constant C0.3 m

Outputs

Horizontal distance D124.30 m

Reading speed

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Narration of this film

A staff, two hairs, a distance.

Similar triangles in the telescope. The stadia hairs subtend a fixed angle; intercept s scales as distance.

Reading speed

Watch on YouTube