SRV-02

Stadia horizontal distance

D = k s cos²α + C cos α.

Reading speed

TacheometryStadia tacheometry

Governing equation

D = ks\cos^2\alpha + C\cos\alpha

where

k: Stadia constant (—)
s: Staff intercept (m)
\alpha: Vertical angle (°)
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-02 — Stadia horizontal distance) is the form associated with Stadia tacheometry. Working symbols: $k$ , $s$ , $\alpha$ , $C$ $\rightarrow$ $D$ . The stadia interval s subtended by the hairs is proportional to slant range; multiplying by cos²α reduces it to horizontal.

Purpose

Purpose: compute

D

from

k

s

\alpha

C

in Surveying via

D = ks\cos^2\alpha + C\cos\alpha

D = k s cos²α + C cos α. 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 = 1.250\,\mathrm{m}

\alpha = 8.000\,\mathrm{^{\circ}}

C = 0.300\,\mathrm{m}

, the governing relation

D = ks\cos^2\alpha + C\cos\alpha

yields

D = 122.876\,\mathrm{m}

. External-focusing telescope, k ≈ 100, C additive constant. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Stadia constant k100 —Staff intercept s1.25 mVertical angle \alpha8 °Additive constant C0.3 m

Outputs

Horizontal distance D122.876 m

Reading speed

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Narration of this film

External-focusing telescope, k ≈ 100, C additive constant.

The stadia interval s subtended by the hairs is proportional to slant range; multiplying by cos²α reduces it to horizontal.

Reading speed

Watch on YouTube