ATPL Theory

Charts

Map Projections — Overview

A map projection is a way of representing the Earth’s curved surface on a flat chart. Because the Earth is a sphere (actually an oblate spheroid), some distortion (in shape, distance, or area) is always introduced.


✈️ Main Types Used in Aviation

Projection Key Feature Advantages Disadvantages Common Use
Lambert Conformal Conic (LCC) Cone projection, intersects Earth along two parallels Preserves angles (conformal) → bearings are accurate Slight distance distortion near edges Most aeronautical charts (sectionals, enroute)
Mercator Cylindrical projection Straight rhumb lines (constant headings) Great circles appear curved; scale distortion at high latitudes Marine charts, some low-latitude maps
Transverse Mercator Cylinder turned 90° (tangent to a meridian) Accurate along central meridian Distortion increases east/west from center Used in local topographic and UTM grids
Polar Stereographic Plane projection touching at a pole Accurate near the pole Distorted away from the pole High-latitude and polar navigation charts
Gnomonic Projected from Earth’s center onto a plane Great circles are straight lines Severe distortion at edges Used for great-circle route planning (long-haul flights)

🧩 Quick Summary

Property Lambert Mercator Polar Stereographic Gnomonic
Conformal (angle-true)
Straight Great Circles
Constant Heading (Rhumb) Lines Straight
Used For Air charts Marine Polar Long-range planning

✈️ In short:

Lambert Conformal Conic is the standard for aviation charts — it keeps bearings and shapes accurate enough for navigation. Gnomonic charts are used only for plotting long great-circle routes.


Short review of the main aviation chart types


Aviation charts are specialized maps designed to help pilots navigate safely, showing terrain, airspace, radio aids, airports, and obstacles — all to scale and oriented to true north.


Main Types of Aviation Charts

Chart Type Scale / Coverage Used For Key Features
World Aeronautical Chart (WAC) ~1:1,000,000 Long-distance / overview navigation (now mostly replaced by digital charts) Terrain, airways, VORs, NDBs, limited detail
Sectional Chart ~1:500,000 VFR (Visual Flight Rules) navigation Detailed topography, landmarks, obstacles, airspace classes, airports
Terminal Area Chart (TAC) ~1:250,000 VFR navigation around busy airports More detail on airspace and obstacles near terminals
Enroute Chart (Low Altitude / High Altitude) Variable (~1:1,000,000) IFR (Instrument Flight Rules) navigation Airways (V, J, Q routes), navaids, reporting points, MEAs, MOCAs
Instrument Approach Chart N/A (one airport) IFR approach to land Runway layout, approach path, altitudes, frequencies, missed approach procedure
Standard Instrument Departure (SID) Chart N/A IFR departure procedure Initial climb, route to enroute structure
Standard Terminal Arrival (STAR) Chart N/A IFR arrival procedure Transition route from enroute to approach
Airport Diagram (Aerodrome Chart) N/A Ground operations Runways, taxiways, parking, frequencies, hotspots

Chart References

  • North reference: Most charts are oriented to true north; magnetic variation is shown.
  • Projection: Usually Lambert Conformal Conic, which preserves angles — great for navigation.
  • Elevation: Terrain colors, contour lines, and spot elevations help assess obstacle clearance.

Digital Charts

Modern pilots use:

  • Jeppesen charts (standardized for IFR)
  • Government/ICAO charts
  • EFB apps like ForeFlight, Garmin Pilot, SkyDemon, etc.

These combine sectionals, approach plates, and enroute charts digitally with GPS overlay.


Summary Table

Flight Type Chart Type Scale / Purpose
VFR Sectional (1:500,000) / TAC (1:250,000) Visual nav & airspace awareness
IFR Enroute Low- and high-altitude enroute charts Airways, navaids, routes
IFR Terminal SID / STAR / Approach plates Procedure-based navigation
Airport Aerodrome diagram Taxi & ground ops

lambodrome, loxodrome, orthodrome belong to spherical navigation and cartography, which are fundamental to aviation and maritime navigation


Orthodrome (Great Circle)

Definition: A path on the surface of a sphere that represents the shortest distance between two points.

Characteristics:

  • It’s the intersection of the Earth’s surface with a plane passing through the Earth’s center.
  • The direction (bearing) constantly changes along the route, except when following the equator or a meridian.
  • Shortest distance between two points → hence used for long-range flight planning.

In aviation:

  • Used for long-haul flights (e.g., intercontinental routes).
  • Appears as a curved line on a Mercator chart, but as a straight line on a gnomonic projection.

🛫 Example: A flight from London to Los Angeles follows an orthodromic route, curving over Greenland on the map but minimizing distance and fuel.


Loxodrome (Rhumb Line)

Definition: A line crossing all meridians at a constant angle (constant bearing or heading).

Characteristics:

  • The aircraft maintains a constant compass heading.
  • It spirals toward the poles (never reaches them) if extended infinitely.
  • Longer than the orthodrome between two distant points.

In aviation:

  • Easier to fly and navigate since the heading is constant.
  • Preferred for shorter routes, or in lower latitudes where the curvature effect is small.
  • Appears as a straight line on a Mercator chart, which simplifies navigation.

🛫 Example: A flight between Paris and Rome can use a loxodromic path with one constant heading.


Lambodrome

This one is less standard and often confused. Historically, lambodrome is a French or old nautical term occasionally used as a variant or approximation of loxodrome. In most English and modern navigation contexts:

Lambodrome ≈ Loxodrome (Rhumb Line)

So — in aviation, you can treat “lambodrome” as an outdated synonym for a constant-heading (rhumb line) course.


Comparison Summary

Term Type of Curve Heading Distance Chart Appearance Common Use
Orthodrome Great Circle Changes continuously Shortest Straight on Gnomonic Long routes
Loxodrome Rhumb Line Constant Longer Straight on Mercator Short routes, easy nav
Lambodrome (Obsolete) Same as Rhumb Line Constant Longer Straight on Mercator Historical/academic
Equirectangular / Parallel path Parallel of latitude Constant latitude Not shortest Straight on Equirectangular Often local routes or headings

In Practice (Modern Aviation)

Modern flight computers and FMS (Flight Management Systems):

  • Plan and fly great circles (orthodromes) automatically.
  • Display rhumb-line bearings for readability.
  • Constantly update headings to stay on the great-circle route.

So, while pilots may see a constant bearing on the display, the aircraft is technically flying an orthodromic path optimized for efficiency.


⚓️ 1. Historical Context

Before precise geodesy and spherical trigonometry were widely available (roughly pre-18th century), sailors and early navigators used practical, graphical methods on flat charts to steer courses.

These charts — especially the Mercator projection (introduced in 1569 by Gerardus Mercator) — had a magical property:

Any straight line on the Mercator chart corresponds to a constant compass bearing.

That straight line was what navigators drew and followed — a loxodrome (rhumb line).

But before the word “loxodrome” became standard in English, different languages and traditions used other names for this same idea — among them:

  • Lambodrome (from French lambodrome, or lambodromie)
  • Rumb line (from the old nautical word rumb meaning compass point or direction)

So “lambodrome” was originally a seaman’s practical path — a line of constant heading drawn on a chart. Later, mathematicians formalized it as the loxodrome on the sphere (a logarithmic spiral toward the pole).


Why "Approximately"?

Because early navigators treated Earth as flat for local or regional sailing.

  • They plotted a straight line on their chart (a “lambodrome”) using a constant heading.
  • On the sphere, that path is not exactly constant in terms of true direction and distance — it’s a loxodrome approximation.

So the lambodrome was a practical, flat-map path, while the loxodrome was the exact spherical equivalent that crosses all meridians at the same angle.

Hence:

“Lambodrome” ≈ “Loxodrome” because the lambodrome is the planar approximation to the spherical rhumb line.


Evolution of Terms

Era Common Term Meaning
16th–17th centuries Lambodrome (French nautical term) Constant heading line drawn on chart
17th–19th centuries Rhumb Line or Loxodrome Mathematical constant-angle curve on the sphere
Modern usage Loxodrome or Rhumb Line Exact definition used in navigation theory

By the time spherical navigation matured (18th–19th centuries), lambodrome faded, and loxodrome became the accepted scientific term.


In Aviation Context

Aviators inherited both:

  • Rhumb-line navigation from marine charts (Mercator style)
  • Great-circle navigation from geodesy (orthodrome)

So in old manuals (especially French, Portuguese, or early ICAO literature), you might find “lambodromic navigation” meaning “constant bearing flight” — essentially rhumb-line flying.


In Short

Why lambodrome ≈ rhumb line:

  • “Lambodrome” was the older, practical term for constant-heading paths used by sailors and early aviators.
  • “Loxodrome” is the mathematically exact version of that same concept on the sphere.
  • Thus, a lambodrome is a flat-chart approximation of a loxodrome.