INGENIA
Index/Surveying/SRV-35

SRV-35

EDM slope to horizontal

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

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EDMEDM

Governing equation

H=Scos⁡α,Δh=Ssin⁡αH=S\cos\alpha,\quad \Delta h=S\sin\alpha

α∈[−30,30]\alpha \in \left[-30, 30\right]

where

S
Slope distance (m)
\alpha
Vertical angle (°)
H
Horizontal (m)
\Delta h
Height 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.

SRV-35 · gauge
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①

Governing law — red

H=Scos⁡α,Δh=Ssin⁡αH=S\cos\alpha,\quad \Delta h=S\sin\alpha

α∈[−30,30]\alpha \in \left[-30, 30\right]

α=−30\alpha = -30H=161.4H = 161.4

②

Domain of the variable — blue

αmin⁡=−30,αmax⁡=30\alpha_{\min} = -30,\quad \alpha_{\max} = 30

α∈[−30,30]\alpha \in \left[-30, 30\right]

α=−30\alpha = -30α=−30\alpha = -30

③

Response curve — green

H=Scos⁡α,Δh=Ssin⁡αH=S\cos\alpha,\quad \Delta h=S\sin\alpha

α∈[−30,30]\alpha \in \left[-30, 30\right]

α=−30\alpha = -30H=161.4H = 161.4

④

Rate of change — amber

dHdα\frac{\mathrm{d}H}{\mathrm{d}\alpha}

α∈[−30,30]\alpha \in \left[-30, 30\right]

α=−29.62\alpha = -29.62H′=1.608H^{\prime} = 1.608

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: SS, α\alpha →\rightarrow HH, Δh\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 HH, Δh\Delta h from SS, α\alpha in Surveying via H=Scos⁡α,Δh=Ssin⁡αH=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 mS = 186.420\,\mathrm{m}, α=4.200 ∘\alpha = 4.200\,\mathrm{^{\circ}}, the governing relation H=Scos⁡α,Δh=Ssin⁡αH=S\cos\alpha,\quad \Delta h=S\sin\alpha yields H=185.919 mH = 185.919\,\mathrm{m}, Δh=13.653 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

Outputs

  • Horizontal H185.919 m
  • Height difference \Delta h13.653 m
Reading speed

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SRV-35 · gauge
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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