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Index/Surveying/SRV-33

SRV-33

Meridian convergence

γ ≈ Δλ sin φ. Grid north vs true north, first-order on a TM projection.

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GeodesyMeridian convergence

Governing equation

γ≈Δλsin⁡φ\gamma\approx\Delta\lambda\sin\varphi

where

\Delta\lambda
Longitude from CM (°)
\varphi
Latitude (°)
\gamma
Convergence (′)

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-33 — Meridian convergence) is the form associated with Meridian convergence. Working symbols: Δλ\Delta\lambda, φ\varphi →\rightarrow γ\gamma. Meridians converge toward the pole. On a Transverse Mercator, γ is the angle between the projected meridian and grid north.

Purpose

Purpose: compute γ\gamma from Δλ\Delta\lambda, φ\varphi in Surveying via γ≈Δλsin⁡φ\gamma\approx\Delta\lambda\sin\varphi γ ≈ Δλ sin φ. Grid north vs true north, first-order on a TM projection. Use it when a real surveying question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given Δλ=1.500 ∘\Delta\lambda = 1.500\,\mathrm{^{\circ}}, φ=34.000 ∘\varphi = 34.000\,\mathrm{^{\circ}}, the governing relation γ≈Δλsin⁡φ\gamma\approx\Delta\lambda\sin\varphi yields γ=50.33 ′\gamma = 50.33\,\mathrm{′}. Two meridians, a φ, a small γ. Move a slider: the numbers are this situation, not a canned story.

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Inputs

Outputs

  • Convergence \gamma50.33 ′
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SRV-33 · gauge
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Narration of this film

Two meridians, a φ, a small γ.

Meridians converge toward the pole. On a Transverse Mercator, γ is the angle between the projected meridian and grid north.

Reading speed

Watch on YouTube