SRV-27

Forward coordinate

E = E0 + ΔE, N = N0 + ΔN. A new station from a known one.

Reading speed

CoordinatesGrid coordinates

Governing equation

E=E_0+\Delta E,\quad N=N_0+\Delta N

$\Delta E \in \left[-500, 500\right]$

where

E_0: Start easting (m)
N_0: Start northing (m)
\Delta E: Departure (m)
\Delta N: Latitude (m)
E: Easting (m)
N: Northing (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

E=E_0+\Delta E,\quad N=N_0+\Delta N

$\Delta E \in \left[-500, 500\right]$

$\Delta E = -500$ $E = 49500$

Along the curve

②

Domain of the variable — blue

\Delta E_{\min} = -500,\quad \Delta E_{\max} = 500

$\Delta E \in \left[-500, 500\right]$

$\Delta E = -500$ $\Delta E = -500$

Along the curve

③

Response curve — green

E=E_0+\Delta E,\quad N=N_0+\Delta N

$\Delta E \in \left[-500, 500\right]$

$\Delta E = -500$ $E = 49500$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E}{\mathrm{d}\Delta E}

$\Delta E \in \left[-500, 500\right]$

$\Delta E = -493.7$ $E^{\prime} = 1$

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-27 — Forward coordinate) is the form associated with Grid coordinates. Working symbols: $E_0$ , $N_0$ , $\Delta E$ , $\Delta N$ $\rightarrow$ $E$ , $N$ . The traverse update. Close the loop and Bowditch-adjust ΔE, ΔN before storing the station.

Purpose

Purpose: compute

E

N

from

E_0

N_0

\Delta E

\Delta N

in Surveying via

E=E_0+\Delta E,\quad N=N_0+\Delta N

E = E0 + ΔE, N = N0 + ΔN. A new station from a known one. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

E_0 = 50000.000\,\mathrm{m}

N_0 = 120000.000\,\mathrm{m}

\Delta E = 85.400\,\mathrm{m}

\Delta N = -32.100\,\mathrm{m}

, the governing relation

E=E_0+\Delta E,\quad N=N_0+\Delta N

yields

E = 50085.400\,\mathrm{m}

N = 119967.900\,\mathrm{m}

. A known point, a vector, a new station. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Start easting E_050000 mStart northing N_0120000 mDeparture \Delta E85.4 mLatitude \Delta N-32.1 m

Outputs

Easting E50085.400 m
Northing N119967.900 m

Reading speed

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Narration of this film

A known point, a vector, a new station.

The traverse update. Close the loop and Bowditch-adjust ΔE, ΔN before storing the station.

Reading speed

Watch on YouTube