SRV-35

EDM slope to horizontal

H = S cos α, Δh = S sin α. Slope distance S, vertical angle α.

Reading speed

EDMEDM

Governing equation

H=S\cos\alpha,\quad \Delta h=S\sin\alpha

where

S: Slope distance (m)
\alpha: Vertical angle (°)
H: Horizontal (m)
\Delta h: Height difference (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-35 — EDM slope to horizontal) is the form associated with EDM. Working symbols: $S$ , $\alpha$ $\rightarrow$ $H$ , $\Delta h$ . A total station measures S and α (or zenith z = 90°−α). Atmospheric ppm and prism constants sit inside S.

Purpose

Purpose: compute

H

\Delta h

from

S

\alpha

in Surveying via

H=S\cos\alpha,\quad \Delta h=S\sin\alpha

H = S cos α, Δh = S sin α. Slope distance S, vertical angle 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

S = 186.420\,\mathrm{m}

\alpha = 4.200\,\mathrm{^{\circ}}

, the governing relation

H=S\cos\alpha,\quad \Delta h=S\sin\alpha

yields

H = 185.919\,\mathrm{m}

\Delta h = 13.653\,\mathrm{m}

. A slope ray, a horizontal, a Δh. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Slope distance S186.42 mVertical angle \alpha4.2 °

Outputs

Horizontal H185.919 m
Height difference \Delta h13.653 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 slope ray, a horizontal, a Δh.

A total station measures S and α (or zenith z = 90°−α). Atmospheric ppm and prism constants sit inside S.

Reading speed

Watch on YouTube