SRV-25

Differential levelling

Δh = BS − FS. Rise and fall; a loop misclosure is ΣΔh around the circuit.

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LevellingDifferential levelling

Governing equation

\Delta h=\mathrm{BS}-\mathrm{FS}

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

where

BS: Backsight (m)
FS: Foresight (m)
\Delta h: Level difference (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

\Delta h=\mathrm{BS}-\mathrm{FS}

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

$BS = 0.1$ $\Delta h = -1.002$

Along the curve

②

Domain of the variable — blue

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

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

$BS = 0.1$ $BS = 0.1$

Along the curve

③

Response curve — green

\Delta h=\mathrm{BS}-\mathrm{FS}

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

$BS = 0.1$ $\Delta h = -1.002$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta h}{\mathrm{d}BS}

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

$BS = 0.125$ $\Delta h^{\prime} = 1$

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-25 — Differential levelling) is the form associated with Differential levelling. Working symbols: $BS$ , $FS$ $\rightarrow$ $\Delta h$ . A collimated H.I. = BS + known RL. Foresight down to the next point. Collimation and curvature cancel in a balanced BS/FS.

Purpose

Purpose: compute

\Delta h

from

BS

FS

in Surveying via

\Delta h=\mathrm{BS}-\mathrm{FS}

Δh = BS − FS. Rise and fall; a loop misclosure is ΣΔh around the circuit. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

BS = 1.456\,\mathrm{m}

FS = 1.102\,\mathrm{m}

, the governing relation

\Delta h=\mathrm{BS}-\mathrm{FS}

yields

\Delta h = 0.3540\,\mathrm{m}

. A level, two staves, a Δh. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Backsight BS1.456 mForesight FS1.102 m

Outputs

Level difference \Delta h0.3540 m

Reading speed

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Narration of this film

A level, two staves, a Δh.

A collimated H.I. = BS + known RL. Foresight down to the next point. Collimation and curvature cancel in a balanced BS/FS.

Reading speed

Watch on YouTube