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GELE Photogrammetry & CartographyMap ProjectionsCheat Sheet

One-page cheat sheet for GELE Photogrammetry & Cartography — Map Projections. Every formula, definition, and key fact you need for this chapter, condensed to a single printable page. Designed for the final review session before the GELE 2026.

Exam context

The Geodetic Engineer Licensure Examination is conducted by Professional Regulation Commission (PRC) — Board of Geodetic Engineering and is scheduled for September 2026. The Photogrammetry & Cartography subtest is marked as "Core" in the official pattern, and Map Projections appears in position 4th of 6 in the GELE Photogrammetry & Cartography review rotation. Passing mark: 70% weighted average, no sub-test below 50%. Recent GELE 2026 papers have drawn roughly a meaningful share of questions from this subject.

Map Projections - Cheat Sheet

Your last-minute revision companion for Map Projections in Photogrammetry & Cartography. Covers all formulas, classification schemes, Philippine standards (PPCS/UTM), and exam-critical concepts. Memorize the must_remember section first.

Sections

Formulas

Formula

k = Projected Distance / True (Ellipsoidal) Distance

Meaning

k = scale factor; projected/grid distance; true distance on ellipsoid; k = 1.0 only on standard line(s)

Watch Out

k < 1.0 at central meridian of TM/UTM (e.g., k₀ = 0.9996 for UTM), k > 1.0 at zone edges. Do NOT assume k = 1.0 everywhere

When To Use

Converting between ellipsoidal and grid (map) distances; assessing distortion at any location

Formula

Grid Distance = k × Ellipsoidal Distance

Meaning

Grid distance = plotted distance on map; ellipsoidal distance = true distance on reference surface; k = local scale factor

Watch Out

Apply k correctly with sign and direction. Forgetting k leads to coordinate errors ± 0.04% at zone edges

When To Use

Converting measured field distance to map coordinates; applying scale reduction to survey observations

Formula

Distortion Factor = k − 1.0 (in percentage: (k − 1) × 100%)

Meaning

Fractional or percentage change in distance due to projection; positive = extension, negative = compression

Watch Out

Distortion is NOT uniform across the map; always quote distortion at a specific location or line

When To Use

Assessing overall map accuracy; comparing projections; quality checks in PPCS/UTM applications

Common Values

Value

0.9996

Symbol

k₀

Quantity

UTM Scale Factor (Central Meridian)

Value

Symbol

Δλ

Quantity

UTM Zone Width

Value

500,000 m

Symbol

E₀

Quantity

UTM False Easting

Value

0 m

Symbol

N₀

Quantity

UTM False Northing (Northern Hemisphere)

Value

10,000,000 m

Symbol

N₀

Quantity

UTM False Northing (Southern Hemisphere)

Value

~0.04% (k ≈ 1.0004 at zone edge)

Symbol

k_max − 1

Quantity

Maximum Distortion in UTM Zone (±3° from CM)

Section Title

Projection Fundamentals & Classification

Important Facts

  • No single projection preserves all four properties (area, shape/angle, distance, direction) simultaneously.
  • Conformal projections preserve angles locally but distort area (especially at high latitudes). Shape is locally correct.
  • Equal-area projections preserve area but distort angles and shapes. Useful for choropleth and statistical maps.
  • Equidistant projections preserve distance along specific lines only; not a general property across the map.
  • Scale factor k varies smoothly across a projection. At standard lines, k = 1.0; away from them, k ≠ 1.0.
  • Transverse Mercator (TM) is conformal; used globally in UTM and in Philippines (PPCS). Central meridian is the standard line.
  • For TM/UTM, scale factor is set k₀ < 1.0 (typically 0.9996) at the central meridian to control distortion within the zone.
  • Distortion increases with distance from the standard line(s). UTM zones are ±3° wide to keep distortion < 0.04%.
  • Cylindrical projections wrap around like a cylinder (e.g., Mercator, TM); conic projections nest like nested cones; azimuthal (planar) projects radially.
  • Scale factor depends on position (latitude/longitude in the projection). Always check k at the location of interest.

Key Definitions

Term

Map Projection

Example

UTM projection flattens the globe into 60 cylindrical zones, each ±3° from central meridian.

Definition

Systematic transformation of points on the curved Earth (ellipsoid) to a flat plane; always introduces some distortion.

Term

Developable Surface

Example

Transverse Mercator uses a cylinder; Albers uses a cone; Stereographic uses a plane.

Definition

Geometric shape (cylinder, cone, or plane) onto which the ellipsoid is projected; determines projection geometry.

Term

Standard Line (Standard Meridian / Standard Parallel)

Example

UTM uses central meridian as standard line; PPCS uses central meridian per zone.

Definition

Line(s) where projected distance = true distance (k = 1.0); distortion is zero there and increases away from it.

Term

Conformal Projection

Example

Mercator, Transverse Mercator (UTM/PPCS), Stereographic. Essential for surveying and navigation.

Definition

Preserves angles and shapes locally; k is constant in all directions from a point (but varies across the map).

Term

Equal-Area (Equivalent) Projection

Example

Albers Equal-Area Conic, Lambert Equal-Area. Used for thematic/statistical area maps.

Definition

Preserves area; all regions scale uniformly so relative sizes remain true. Angles/shapes are distorted.

Term

Equidistant Projection

Example

Equirectangular (preserves parallel spacing); Azimuthal Equidistant (preserves radial distance from center).

Definition

Preserves distance along certain lines (e.g., meridians or from a center point); not distances in all directions.

Term

Central Meridian (CM)

Example

UTM Zone 51 (Philippines) has CM = 123°E; PPCS zones use meridians at 119°, 121°, 123°, 125°, 127°E.

Definition

Reference meridian of a projection zone; typically the standard line in Transverse Mercator projections.

Term

False Easting / False Northing

Example

UTM: false easting = 500,000 m, false northing = 10,000,000 m (Southern Hemisphere) or 0 m (Northern).

Definition

Arbitrary offsets added to all x/y coordinates to avoid negative values; simplifies computations and avoids minus signs.

Diagrams To Know

  • Cylindrical projection (Mercator, Transverse Mercator): cylinder touching equator or central meridian.
  • Conic projection (Albers, LCC): cone touching along standard parallels; meridians converge toward apex.
  • Azimuthal projection (Stereographic, Orthographic): radial lines from center point on plane.
  • Scale factor curve for Transverse Mercator: U-shaped, minimum at central meridian (k₀), rising toward zone edges.
  • Distortion envelope for UTM: narrow band showing where distortion is <0.04% (within ±3° of central meridian).

Common Values

Value

1.0

Symbol

k₀

Quantity

PPCS Scale Factor (Central Meridian)

Value

119°E

Symbol

CM₁

Quantity

PPCS Zone 1 Central Meridian

Value

121°E

Symbol

CM₂

Quantity

PPCS Zone 2 Central Meridian

Value

123°E

Symbol

CM₃

Quantity

PPCS Zone 3 Central Meridian (Most Used)

Value

125°E

Symbol

CM₄

Quantity

PPCS Zone 4 Central Meridian

Value

123°E

Symbol

CM

Quantity

UTM Zone 51 Central Meridian (Philippines)

Value

~0.03%

Symbol

k − 1

Quantity

Maximum Distortion in PPCS (Zone Edge)

Section Title

Philippine Coordinate Systems: PPCS & UTM

Important Facts

  • The Philippines uses PPCS (4 zones on CM 119°, 121°, 123°, 125°E) and UTM (primarily Zone 51, partly 50 and 52).
  • PPCS and UTM are both conformal Transverse Mercator projections; PPCS is national standard (RA 4374), UTM is global standard.
  • PPCS false easting = 500,000 m (like UTM); false northing = 0 m (north of equator).
  • UTM false easting = 500,000 m; false northing = 0 m (Northern Hemisphere, as Philippines is wholly north of equator).
  • PPCS scale factor k₀ at central meridian = 1.0 (unlike UTM which uses 0.9996). Maximum distortion in PPCS ≈ 0.03% at zone edges.
  • RA 4374 (Decree Creating PPCS) mandates PPCS for all national surveys; RA 8560 adopts PRS92 as official datum.
  • Cadastral surveys (PD 1529) and land registration (CA 141) increasingly require PPCS or UTM coordinates for legal descriptions.
  • UTM Zone 51 covers most of central Philippines (121°–125°E): Luzon, Visayas, central Mindanao. Zone 50 covers Palawan; Zone 52 covers eastern Mindanao.
  • Confusion alert: PPCS k₀ = 1.0 (no scale reduction), but UTM k₀ = 0.9996 (significant reduction). Different standards for different zones.
  • When converting PPCS ↔ UTM: apply appropriate scale factors and false values for the specific zone/system.

Key Definitions

Term

Philippine Plane Coordinate System (PPCS)

Example

Zone 1: CM = 119°E, Zone 2: CM = 121°E, Zone 3: CM = 123°E, Zone 4: CM = 125°E (plus Zone 5 at 127°E for extended coverage).

Definition

National grid system based on Transverse Mercator projection in 4 zones; referenced to PRS92 (WGS84-derived ellipsoid). Defined under RA 4374.

Term

UTM (Universal Transverse Mercator)

Example

Zone 51: CM = 123°E, encompasses central Philippines. Zone 50: 117°E (western edge). Zone 52: 129°E (eastern edge).

Definition

Global conformal grid system with 60 zones (each 6° wide); Philippines occupies Zones 50–52 (partly 51, 52). k₀ = 0.9996 at each central meridian.

Term

Central Meridian (CM) for Philippine Zones

Example

PPCS Zone 3 (most common): CM = 123°E. UTM Zone 51: CM = 123°E. Both are standard for central Luzon and Mindanao.

Definition

Reference meridian for each PPCS zone; scale factor k = 1.0 there. Meridians to east/west have k > 1.0.

Term

PRS92 (Philippine Reference System 1992)

Example

All PPCS and modern UTM coordinates in the Philippines reference PRS92; older surveys used Luzon 1911 datum (now deprecated).

Definition

National geodetic datum based on WGS84 ellipsoid; official reference for geodetic surveys in the Philippines per RA 8560 and DENR guidelines.

Diagrams To Know

  • Map of Philippine Zones: PPCS 4 zones (119°, 121°, 123°, 125°E) overlaid on UTM zones 50, 51, 52.
  • Scale factor profile for PPCS Zone 3 (CM 123°E): k = 1.0 at CM, k ≈ 0.9997 at ±1.5°, k ≈ 0.9988 at ±3°.
  • Scale factor profile for UTM Zone 51 (CM 123°E): k = 0.9996 at CM, k ≈ 0.99976 at ±1.5°, k ≈ 1.0004 at ±3°.
  • False Easting/Northing grid overlay: 500,000 m E, 0 m N origin at CM and equator, with coordinate labels.

Section Title

Projection Types & Developable Surfaces

Important Facts

  • Cylindrical projections have uniform scale along parallels (latitude lines) and varying scale along meridians.
  • Conic projections have parallel lines as concentric arcs and meridians converging toward apex. Two standard parallels give better fit.
  • Azimuthal projections preserve distances and bearings from a central point (radially). Good for polar regions.
  • Transverse Mercator (TM): best for north-south-oriented regions (like the Philippines). Minimal distortion ±3° from CM.
  • Mercator: worst for area representation but excellent for navigation (loxodromes are straight lines). Avoid for statistical maps.
  • For surveying/mapping: Conformal projections (TM, LCC) are strongly preferred because angles/bearings are preserved.
  • Scale factor in conformal projections is isotropic (same in all directions from a point) but varies spatially.
  • Conic projections are best for mid-latitude regions with wide east-west extent; cylindrical better for north-south.
  • Universal coverage: use azimuthal for poles, cylindrical for equatorial/tropical zones, conic for mid-latitudes.
  • Exam trick: 'Which projection for a map of Europe?' → LCC (conic, mid-latitude). 'Which for navigation?' → Mercator or TM.

Key Definitions

Term

Cylindrical Projection

Example

Mercator (standard cylinder), Transverse Mercator (rotated cylinder along CM). UTM and PPCS are cylindrical/Transverse.

Definition

Ellipsoid projected onto a cylinder; cylinder can touch at equator (standard) or wrap around a meridian (Transverse Mercator).

Term

Conic Projection

Example

Albers Equal-Area Conic (two standard parallels), Lambert Conformal Conic (one or two standard parallels, conformal).

Definition

Ellipsoid projected onto a cone with apex; meridians converge toward apex, parallels are concentric arcs. One or two standard parallels.

Term

Azimuthal (Planar) Projection

Example

Stereographic (conformal), Orthographic (perspective), Azimuthal Equidistant (equidistant from center).

Definition

Ellipsoid projected radially onto a plane tangent at a point; meridians radiate from center, parallels are concentric circles.

Term

Transverse Mercator (TM)

Example

UTM and PPCS both use Transverse Mercator. Preserves angles/shapes locally; ideal for surveying where angles matter.

Definition

Conformal cylindrical projection with cylinder rotated 90° to touch along a meridian (central meridian); scale factor = 1.0 on CM.

Term

Mercator Projection

Example

Historical nautical charts and navigation. NOT suitable for area-based comparisons. Distortion → ∞ at poles.

Definition

Conformal cylindrical projection with cylinder touching the equator. Grossly exaggerates area at high latitudes (Greenland appears huge).

Term

Albers Equal-Area Conic Projection

Example

US state maps, continental-scale thematic maps. Shape is distorted but areas are correct.

Definition

Conic projection preserving area; two standard parallels. Used for thematic maps where area comparisons are critical.

Term

Lambert Conformal Conic (LCC)

Example

Mid-latitude country maps, aviation charts. Better shape preservation than Albers but area is distorted.

Definition

Conic projection preserving angles/shapes; one or two standard parallels. Suitable for mid-latitude regions (airlines use LCC for flight charts).

Diagrams To Know

  • Cylindrical projection: globe with vertical cylinder wrapped around; tangent along equator (Mercator) or meridian (TM).
  • Conic projection: globe with cone-shaped surface; apex above/below pole; standard parallels marked as tangent/secant lines.
  • Azimuthal projection: globe with plane tangent at pole; radiating meridians and concentric parallels.
  • Property comparison table: Mercator (conformal, equator standard), TM (conformal, meridian standard), Albers (equal-area, two parallels), LCC (conformal, conic).

Section Title

Worked Examples & Numerical Calculations

Important Facts

  • Example 1 (Scale Factor, Grid Distance): Ellipsoidal distance 5000.00 m, k = 0.99960 → Grid = 0.99960 × 5000.00 = 4998.00 m (compression of 2.00 m).
  • Example 2 (Projection Choice): National land-area statistics map → Equal-area projection (area preserved, shapes sacrificed).
  • Example 3 (Surveying & Conformal): Survey grids (UTM/PPCS) use conformal TM because angles/bearings are preserved locally.
  • Example 4 (Distortion Check): Line measured in field as 8000 m, k = 1.00012 at location → Grid distance = 1.00012 × 8000 = 8000.96 m (extension of 0.96 m, ~0.012%).
  • Example 5 (PPCS vs UTM): Same survey location (123°E, central Philippines): PPCS Zone 3 has k = 1.0 (no reduction), UTM Zone 51 has k = 0.9996 (reduction applied).
  • Example 6 (False Easting/Northing): UTM coordinate (123°E, 15°N) at CM maps to easting ≈ 500,000 m (false), northing varies with latitude.
  • Example 7 (Zone Edge Distortion): Point ±3° away from CM (at zone edge) has k ≈ 1.0004 for UTM (extension ~0.04%), or k ≈ 0.9988 for PPCS (compression ~0.12%).
  • Example 8 (Conversion k): If measured distance in field is 1234.56 m and k_local = 0.99988, then grid distance = 0.99988 × 1234.56 = 1234.44 m.
  • Example 9 (Property Trade-off): Mercator preserves angles but wildly distorts area (area error → ∞ at poles). Albers preserves area but distorts angles.
  • Example 10 (Survey Reduction)): Instrument height 1.50 m, vertical distance 850.00 m → horizontal projected distance ≈ 850.00 m; then apply k to get grid distance.

Section Title

Common Pitfalls & Exam Traps

Important Facts

  • PITFALL 1: Assuming k = 1.0 everywhere. Reality: k = 1.0 only on standard lines; k ≠ 1.0 elsewhere. Always check location.
  • PITFALL 2: Confusing k < 1.0 (compression) and k > 1.0 (extension). At CM of TM/UTM, k₀ < 1.0 (compression); at edges, k > 1.0 (extension).
  • PITFALL 3: Forgetting to apply k when converting between ellipsoidal and grid distances. Leads to ~0.04–0.12% coordinate errors.
  • PITFALL 4: Thinking conformal = equal-area. Conformal preserves angles; equal-area preserves area. Never both at once.
  • PITFALL 5: Mercator distorts area terribly but students wrongly choose it for thematic area maps. Always use equal-area for area comparisons.
  • PITFALL 6: Confusing PPCS (k₀ = 1.0) with UTM (k₀ = 0.9996). Different scale factors; different distortion profiles.
  • PITFALL 7: Not knowing that PPCS has 4 (or 5) zones while UTM has 60 zones globally. Use correct zone for calculation.
  • PITFALL 8: Ignoring false easting/northing. Coordinates always include 500,000 m E and 0 m N offset (or 10,000,000 m N in Southern Hemisphere).
  • PITFALL 9: Assuming azimuthal projections are suitable for large-area maps. They distort severely away from center point.
  • PITFALL 10: Forgetting that UTM/PPCS are designed to keep distortion within acceptable bounds (< 0.04% for UTM). Within zones, use conformal TM for surveying.

Must Remember

  • Scale factor k = Projected Distance / True Distance; k = 1.0 ONLY on standard lines (e.g., central meridian in TM). Away from standard lines, k ≠ 1.0, causing compression (k < 1) or extension (k > 1).
  • Grid Distance = k × Ellipsoidal Distance. Always apply k when converting field measurements to map coordinates. Forgetting k causes ~0.04–0.12% errors depending on location and projection.
  • Conformal projections preserve ANGLES and SHAPES locally (used for surveying/navigation); Equal-Area projections preserve AREA (used for thematic/statistical maps). They are mutually exclusive — no projection preserves both.
  • Transverse Mercator is the projection used by BOTH PPCS (Philippine standard, k₀ = 1.0) and UTM (global standard, k₀ = 0.9996). Always verify which system and k₀ value apply.
  • PPCS has 4 zones (CM: 119°, 121°, 123°, 125°E); Zone 3 (CM 123°E) is most common in central Philippines. UTM has 60 global zones; Philippines spans zones 50–52, with Zone 51 (CM 123°E) covering most of the country.
  • False Easting = 500,000 m and False Northing = 0 m (in both PPCS and UTM for Northern Hemisphere) are offsets to avoid negative coordinates. Always include them in coordinate conversions.
  • Maximum distortion in UTM is ~0.04% at zone edges (±3° from CM); in PPCS, ~0.03–0.12% depending on zone width. Within these bounds, use conformal TM for surveying where angles/shapes matter.
  • Cylindrical projections (Mercator, TM) suit equatorial/tropical regions; Conic projections (Albers, LCC) suit mid-latitudes; Azimuthal projections suit polar regions. Match developable surface to latitude of the region.
  • Mercator projection preserves angles but GROSSLY distorts area at high latitudes (Greenland appears much larger than it is). Never use Mercator for thematic area maps; use Equal-Area Conic or Equal-Area Azimuthal instead.
  • RA 4374 mandates PPCS for national surveys; RA 8560 adopts PRS92 (WGS84) datum; PD 1529 and CA 141 increasingly require PPCS/UTM coordinates for land titles and cadastral records. Know these legal frameworks.

Last Minute Tips

  • EXAM TIP 1: If asked 'which projection preserves area?' → immediately answer Equal-Area or Equivalent (e.g., Albers, Lambert Equal-Area). If asked 'which preserves angles?' → Conformal (e.g., Mercator, TM, LCC).
  • EXAM TIP 2: For any grid distance calculation, write Grid = k × Ellipsoidal as your first formula. If k is missing, ask yourself 'where am I on the projection?' — k changes with location. At the central meridian of PPCS, k = 1.0; at the CM of UTM, k = 0.9996.
  • EXAM TIP 3: Philippines-specific: If a problem says 'PPCS Zone 3' or '123°E', assume central Luzon/Mindanao. If it says 'UTM Zone 51', it is the same region. Both use Transverse Mercator but with different k₀ values (1.0 vs 0.9996), leading to different grid distances.
  • EXAM TIP 4: When choosing a projection for a scenario, first identify the critical property: Does the map prioritize angles (surveying) → Conformal. Area (statistics) → Equal-Area. Distance from a point (navigation) → Equidistant. Match the property to the use case, not the region.
  • EXAM TIP 5: Scale factor k is NEVER exactly 1.0 across an entire map (except on standard lines). If a problem gives you k = 1.0 everywhere, it is a trick or an approximation. Real-world k values vary smoothly, so distortion increases away from standard lines. Always compute/check k at the actual location.

Comparison Tables

Rows

Values

  • YES (locally)
  • NO
  • NO
  • Surveying, Navigation, Engineering
  • Mercator, Transverse Mercator (UTM/PPCS)

Property

Conformal

Values

  • NO
  • YES
  • NO
  • Thematic Maps, Area Statistics, Census
  • Albers Equal-Area Conic, Lambert Equal-Area

Property

Equal-Area (Equivalent)

Values

  • NO
  • NO
  • YES (along certain lines)
  • Distance-Important Maps, Azimuth from Center
  • Azimuthal Equidistant, Equirectangular

Property

Equidistant

Values

  • NO
  • NO
  • NO
  • Great-Circle Routes (Navigation)
  • Gnomonic (great circles are straight lines)

Property

Gnomonic

Columns

  • Projection Type
  • Preserves Angles?
  • Preserves Area?
  • Preserves Distance?
  • Best Used For
  • Example

Table Title

Projection Property Comparison: What Each Preserves

Rows

Values

  • Tangent or Secant (line/circle)
  • Straight, Parallel Lines
  • Straight, Parallel Lines
  • Equatorial (0°–±30°)
  • Mercator, Transverse Mercator, Oblique Mercator

Property

Cylinder

Values

  • Tangent or Secant (1–2 parallels)
  • Straight, Converging Toward Apex
  • Concentric Circular Arcs
  • Mid-Latitude (30°–60°)
  • Albers Equal-Area Conic, Lambert Conformal Conic

Property

Cone

Values

  • Tangent at Single Point (Pole or Equator)
  • Radiating Straight Lines from Center
  • Concentric Circular Arcs Centered at Pole
  • Polar Regions (>60°N/S)
  • Stereographic, Orthographic, Azimuthal Equidistant

Property

Azimuthal (Plane)

Columns

  • Surface Type
  • Contact with Ellipsoid
  • Meridians Appear As
  • Parallels Appear As
  • Best Latitude Range
  • Projection Examples

Table Title

Developable Surfaces: Cylinder vs. Cone vs. Azimuthal

Rows

Values

  • Transverse Mercator (Conformal)
  • Transverse Mercator (Conformal)

Property

Projection Type

Values

  • PRS92 (RA 8560)
  • WGS84 (Global Standard)

Property

Datum

Values

  • 4 zones (CM: 119°, 121°, 123°, 125°E)
  • 3 zones (50: 117°E, 51: 123°E, 52: 129°E)

Property

Philippine Zones

Values

  • 1.0 (No Reduction)
  • 0.9996 (Intentional Reduction)

Property

Scale Factor at CM (k₀)

Values

  • 500,000 m
  • 500,000 m

Property

False Easting

Values

  • 0 m
  • 0 m (Northern Hemisphere)

Property

False Northing

Values

  • ~0.03% at Zone Edge
  • ~0.04% at Zone Edge

Property

Max Distortion

Values

  • National Standard (RA 4374)
  • Global Standard, Widely Accepted

Property

Legal Status (Philippines)

Values

  • Cadastral, National Surveys, Land Titles (CA 141, PD 1529)
  • International, Military, GIS, Cross-Border Work

Property

Best For

Values

  • Varies (~2°–3°)
  • 6° (Standard)

Property

Zone Width

Columns

  • Attribute
  • PPCS (Philippine Plane Coordinate System)
  • UTM (Universal Transverse Mercator)

Table Title

PPCS vs. UTM: Philippines Standard Grids

Rows

Values

  • 1.0000
  • 1.0000
  • ~0.9988
  • k decreases away from CM
  • Compression ~0.12%

Property

PPCS

Values

  • 0.9996
  • 0.9996
  • ~1.0004
  • k increases away from CM
  • Extension ~0.04%

Property

UTM

Values

  • 1.0000
  • 1.0000 (at Equator)
  • k → ∞
  • k increases dramatically toward poles
  • Extreme at high latitude

Property

Mercator (Standard)

Values

  • 1.0000 (on parallels)
  • Varies (not at a meridian)
  • Adjusted for area preservation
  • Area preserved; k ≠ 1 elsewhere
  • Angle distortion instead

Property

Albers (Equal-Area)

Columns

  • Projection
  • k at Standard Line
  • k at Zone Center (CM)
  • k at Zone Edge (±3°)
  • Behavior
  • Distortion at Edge

Table Title

Scale Factor k: Behavior Across Projections

Rows

Values

  • Angles/Bearings
  • Conformal
  • Preserves angles → traverse and angular measurements transfer accurately
  • Survey grids, property surveys (PPCS, UTM)

Property

Surveying & Engineering

Values

  • Direction/Angles
  • Conformal (Mercator or TM)
  • Angles preserved, loxodromes straight (Mercator)
  • Nautical charts, aviation charts

Property

Navigation & Compass Bearings

Values

  • Area
  • Equal-Area
  • Area preserved so province/country sizes compare truthfully
  • Census maps, thematic area maps, choropleth

Property

Statistical Area Comparisons

Values

  • Distance from Center
  • Azimuthal Equidistant
  • Preserves distance from central point; good for radiating routes
  • Distance rings from a city, polar navigation

Property

Distance Along Radii

Values

  • Balanced Distortion
  • Conformal Conic (LCC) or Transverse Mercator
  • Moderate distortion across region; balanced shape/area
  • Country maps, regional atlases

Property

General-Purpose National Map

Columns

  • Map Purpose
  • Property Priority
  • Suitable Projection(s)
  • Why?
  • Example Use

Table Title

Decision Tree: Choosing the Right Projection

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