Aeronautical Map Projections for Air Navigation

061-04-02Pablo Asensio Martínez2026-04-014 min

Navigating the world requires translating a three-dimensional sphere (the Earth) to a two-dimensional flat map. This process is carried out through projections, and each one has its own rules and distortions. Below, we explain in a simple way how the main projections used in aviation work, integrating all the essential theoretical and mathematical concepts.

Fundamental Navigation Concepts

Great Circle vs Rhumb Line

Before studying maps, we must understand how lines and angles behave on the Earth's surface:

  • Orthodrome (Great Circle): It is the shortest distance between two points on a sphere. Its direction changes constantly as we cross meridians. In most charts, we seek for these routes to appear as straight lines.
  • Loxodrome (Rhumb Line): It is a line that maintains a constant direction, cutting all meridians at the same angle. It is easy to fly (you just follow a fixed heading on the compass), but it is not the shortest route. On polar charts, it is a curve concave toward the pole.
  • Convergence (Convergency): It is the angle of inclination between two meridians. On Earth, meridians meet at the poles.
    • Formula: $\text{Convergence} = \text{Change in Longitude} \times \sin(\text{Mean Latitude})$
  • Conversion Angle: It is the angular difference between the direction of the Orthodrome and the Loxodrome.
    • Key rule: $\text{Conversion Angle} = \frac{1}{2} \times \text{Convergence}$

1. Polar Stereographic Projection

This chart is created by imagining a flat plane that touches the Earth at one of the Poles (point of tangency). It is ideal for navigation at high latitudes.

  • Graticule (Geographic Network): The meridians are straight lines radiating from the pole. The parallels are concentric circles whose distance increases when moving away from the pole.
  • Convergence Factor (n=1): In this chart, convergence is maximum and identical to polar reality.
    • $\text{Chart Convergence} = \text{Change in Longitude}$
  • Route Behavior:
    • A straight line drawn passing through the pole is a meridian.
    • Orthodromes (great circles) are almost straight near the pole, but technically are slightly concave curves toward the pole.
    • Loxodromes are pronounced curves, always concave toward the projection pole.
  • Scale: It is correct only at the Pole. It expands as we move away (proportional to the secant squared of half the co-latitude).

2. Lambert Conformal Conic Projection

Lambert Conformal Conic Projection

It is the standard chart for aviation at mid-latitudes. A cone is used that "cuts" the Earth, intersecting it at two Standard Parallels.

  • Origin Parallel: It is the central mathematical latitude of the projection, located halfway between the two standard parallels. Here the chart convergence equals the Earth convergence.
    • Calculation: $\frac{\text{Standard Parallel 1} + \text{Standard Parallel 2}}{2}$
  • Cone Constant (n): It defines how much the cone has been "flattened" (0 is a cylinder, 1 is a plane).
    • $\text{Cone Constant} = \sin(\text{Origin Parallel})$
  • Chart Convergence: It is constant throughout the map.
    • $\text{Convergence} = \text{Change in Longitude} \times \text{Cone Constant}$
  • Scale: It is exact on the standard parallels. It contracts (reduces) between them (minimum at the origin parallel) and expands (increases) outside them. The scale error is typically kept below 1%.
  • Orthomorphic: Yes, like all navigation charts, it preserves angles and shapes in small areas.

3. Direct Mercator Projection

Mercator Projection

It is a cylindrical projection where the cylinder wraps the Earth touching the Equator (its origin parallel).

  • Graticule: The meridians are straight parallel lines uniformly spaced. The parallels are straight parallel lines that separate more as they move away from the Equator.
  • Zero Convergence: Since the meridians are parallel, they never touch. The chart convergence is zero.
  • Routes:
    • Loxodromes are perfect straight lines (its great advantage).
    • Orthodromes are convex curves toward the pole (concave to the Equator).
  • Variable Scale: The scale is correct only at the Equator and increases rapidly toward the poles (like the secant of the latitude).
  • The "ABBA" Formula: To calculate distances or scales at different latitudes on a Mercator, we use this mathematical relationship:
    • $ \text{Distance A} \times \cos(\text{Latitude B}) = \text{Distance B} \times \cos(\text{Latitude A}) $

Practical Direction Rules

To solve direction problems between two points (A and B):

  1. Calculate Convergence: Depending on the projection (Change in Longitude for Polar; Change in Longitude × Sine of Latitude for Lambert).
  2. Calculate Conversion Angle: Divide the convergence by 2.
  3. Apply the Hemisphere Rule:
    • The Orthodrome is always closer to the Pole than the Loxodrome.
    • On a Lambert or Polar chart, the Orthodrome is the straightest line; the Loxodrome curves toward the equator.
    • $ \text{GCT (Great Circle Track)} = \text{RLT (Rhumb Line Track)} \pm \text{Conversion Angle} $