SRV-31

Prismoidal volume

V = (h/6)(A1 + 4 Am + A2). End areas plus a mid-section.

Reading speed

VolumePrismoidal

Governing equation

V=\dfrac h6(A_1+4A_m+A_2)

where

h: Station interval (m)
A_1: Start area (m²)
A_m: Mid area (m²)
A_2: End area (m²)
V: Volume (m³)

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-31 — Prismoidal volume) is the form associated with Prismoidal. Working symbols: $h$ , $A_1$ , $A_m$ , $A_2$ $\rightarrow$ $V$ . Exact for a prismoid (planar ends, ruled sides). Earthwork between two stations uses this or the average-end-area shortcut.

Purpose

Purpose: compute

V

from

h

A_1

A_m

A_2

in Surveying via

V=\dfrac h6(A_1+4A_m+A_2)

V = (h/6)(A1 + 4 Am + A2). End areas plus a mid-section. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

h = 20.000\,\mathrm{m}

A_1 = 12.000\,\mathrm{m^{2}}

A_m = 18.000\,\mathrm{m^{2}}

A_2 = 9.000\,\mathrm{m^{2}}

, the governing relation

V=\dfrac h6(A_1+4A_m+A_2)

yields

V = 310.0\,\mathrm{m^{3}}

. Two end areas, a mid area, a volume. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Station interval h20 mStart area A_112 m²Mid area A_m18 m²End area A_29 m²

Outputs

Volume V310.0 m³

Reading speed

Watch on YouTube

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Narration of this film

Two end areas, a mid area, a volume.

Exact for a prismoid (planar ends, ruled sides). Earthwork between two stations uses this or the average-end-area shortcut.

Reading speed

Watch on YouTube