SRV-21

Stadia distance

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

Reading speed

TacheometryStadia

Governing equation

D=ks+C

$s \in \left[0.1, 4\right]$

where

k: Stadia constant (—)
s: Staff intercept (m)
C: Additive constant (m)
D: Horizontal 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.

00:0 / 00:08

①

Governing law — red

D=ks+C

$s \in \left[0.1, 4\right]$

$s = 0.1$ $D = 10.3$

Along the curve

②

Domain of the variable — blue

s_{\min} = 0.1,\quad s_{\max} = 4

$s \in \left[0.1, 4\right]$

$s = 0.1$ $s = 0.1$

Along the curve

③

Response curve — green

D=ks+C

$s \in \left[0.1, 4\right]$

$s = 0.1$ $D = 10.3$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}D}{\mathrm{d}s}

$s \in \left[0.1, 4\right]$

$s = 0.125$ $D^{\prime} = 100$

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-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

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

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