ATPL General Navigation

Mercator Projection

From a Spherical Earth to a Conformal Cylindrical Chart

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TRAINING USE ONLY — EDUCATIONAL GEOMETRY AND FICTIONAL ROUTES

Introduction

The Mercator projection represents the spherical Earth on a rectangular chart. Meridians are shown as straight, parallel, equally spaced lines. Parallels are shown as straight lines at right angles to the meridians, but their spacing increases toward the poles.

This chapter primarily concerns the normal Mercator projection used in classical navigation theory.

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Learning objectives

By the end of this chapter, you should be able to:

  • 01Describe how a Mercator projection is formed.
  • 02Explain the role of the tangent cylinder.
  • 03Explain why meridians and parallels appear straight.
  • 04Explain why the latitude spacing increases towards the poles.
  • 05Define conformality and state what it does not mean.
  • 06Explain why a rhumb line is straight on a Mercator chart.
  • 07Explain why a great circle is normally curved.
  • 08Identify the special great circles that remain straight.
  • 09Calculate chart scale factor at any latitude.
  • 10Use the latitude scale to measure distance.
  • 11Explain and use meridional parts.
  • 12Calculate rhumb-line course and distance.
  • 13Compare Mercator with Lambert and Polar Stereographic charts.
  • 14Answer ATPL-style Mercator questions independently.

Wrap and Unwrap the Earth

Stage 1 of 8 · unrolled 0%
Route
The Earth, the tangent cylinder and the developing Mercator chartA spherical Earth inside a cylinder tangent at the Equator. The graticule and two routes are transferred onto the cylinder, which is then cut along a meridian and unrolled into a flat Mercator chart. The rhumb line is drawn as a solid red line and the great circle as a dashed purple line.N POLES POLEFTC1FTV2

Stage 1 — The spherical Earth

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A perfectly round Earth, with both poles, the Equator, the Prime Meridian and a graticule of meridians and parallels. Two positions are marked: the red line joining them is a rhumb line, crossing every meridian at the same angle, and the purple line is the great circle, the shortest route over the surface. Neither is straight on a sphere.

Speed
Routes

Projection note

The visual rays explain the projection concept. The exact Mercator latitude is calculated mathematically.

The mathematics driving every frame

The height of a parallel on the cylinder is the analytical Mercator ordinate, so the spacing you see is calculated, not drawn by eye:

x = R (λ − λ₀)

y = R · ln[ tan(π/4 + φ/2) ]

Unrolling keeps arc length constant — an isometry — so the flat chart at the end of the timeline has exactly these coordinates. As φ → 90°, y → ∞, which is why the poles can never appear on a Mercator chart.

Medium haul · Training leg (fictional)

Calder Bay (FTC1) 22°00′N 034°00′W to Vantor East (FTV2) 54°00′N 026°00′E. The chapter's fictional demonstration leg, chosen to show the geometry clearly.

Rhumb linesolid

A rhumb line crosses every meridian at the same angle. Mercator preserves angles, so a constant-angle track must plot as a straight line — that is the whole purpose of the projection.

Distance
3,358 NM
Constant true track
055°
Great circledashed

A great circle is the shortest route over the surface, but its true track changes continuously. Because Mercator shows local direction faithfully, that changing track appears as a curve bowing towards the nearer pole.

Distance
3,294 NM
Initial true track
038°
Final true track
079°
Rhumb-line penalty
65 NM

Next in this chapter: meridian and parallel demonstrations, conformality and Tissot indicatrices, scale-factor and departure tools, meridional parts, rhumb-line course and distance, the virtual protractor and divider, the synchronised Mercator-versus-Lambert animation, worked examples, practice and the knowledge check.