SRV-34

Magnetic declination

TN = MN + δ. True bearing from magnetic bearing and declination (east positive).

Reading speed

CompassMagnetic declination

Governing equation

\mathrm{TN}=\mathrm{MN}+\delta

$\delta \in \left[-30, 30\right]$

where

MN: Magnetic bearing (°)
\delta: Declination E+ (°)
TN: True bearing (°)

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

\mathrm{TN}=\mathrm{MN}+\delta

$\delta \in \left[-30, 30\right]$

$\delta = -30$ $TN = 12$

Along the curve

②

Domain of the variable — blue

\delta_{\min} = -30,\quad \delta_{\max} = 30

$\delta \in \left[-30, 30\right]$

$\delta = -30$ $\delta = -30$

Along the curve

③

Response curve — green

\mathrm{TN}=\mathrm{MN}+\delta

$\delta \in \left[-30, 30\right]$

$\delta = -30$ $TN = 12$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}TN}{\mathrm{d}\delta}

$\delta \in \left[-30, 30\right]$

$\delta = -29.62$ $TN^{\prime} = 1$

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-34 — Magnetic declination) is the form associated with Magnetic declination. Working symbols: $MN$ , $\delta$ $\rightarrow$ $TN$ . Declination is the angle from true north to magnetic north. It wanders; IGRF models it year by year.

Purpose

Purpose: compute

TN

from

MN

\delta

in Surveying via

\mathrm{TN}=\mathrm{MN}+\delta

TN = MN + δ. True bearing from magnetic bearing and declination (east positive). Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

MN = 42.000\,\mathrm{^{\circ}}

\delta = -2.400\,\mathrm{^{\circ}}

, the governing relation

\mathrm{TN}=\mathrm{MN}+\delta

yields

TN = 39.60\,\mathrm{^{\circ}}

. A compass rose, two norths, a δ. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Magnetic bearing MN42 °Declination E+ \delta-2.4 °

Outputs

True bearing TN39.60 °

Reading speed

Watch on YouTube

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Narration of this film

A compass rose, two norths, a δ.

Declination is the angle from true north to magnetic north. It wanders; IGRF models it year by year.

Reading speed

Watch on YouTube