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GELE GeodesyFigure of the Earth and the Reference EllipsoidMemory Anchors

Filipino reviewers do well on Figure of the Earth and the Reference Ellipsoid once they have personal mnemonics — the anchors that make the concept local, memorable, and quick to surface under GELE time pressure. This page gathers the best-working anchors for Professional Regulation Commission (PRC) — Board of Geodetic Engineering's typical Geodesy items on this chapter.

Exam context

Professional Regulation Commission (PRC) — Board of Geodetic Engineering runs the Geodetic Engineer Licensure Examination on September 2026. Its Geodesy section sits under a "Core" weighting, and Figure of the Earth and the Reference Ellipsoid is the 1st chapter in the 6-chapter GELE Geodesy rotation. The GELE passing mark is 70% weighted average, no sub-test below 50%, and the most recent 2026 paper drew about a meaningful share of questions from Geodesy.

Figure of the Earth and the Reference Ellipsoid - Memory Anchors

Memory techniques can increase long-term recall by up to 400% compared to rote reading. The human brain stores information as networks of associations — vivid images, stories, sounds, and emotions. By attaching abstract geodetic formulas to concrete mental hooks (stories, acronyms, analogies), you create multiple retrieval pathways. When exam pressure hits and your mind goes blank, these anchors act like mental search-and-rescue ropes, pulling the right formula or concept back to the surface. Use these anchors actively: close your eyes, replay the story, see the image, say the rhyme out loud. The more senses you engage, the deeper the memory trace. Every anchor here is engineered for one purpose — to make sure that on PRC exam day, you never forget the Figure of the Earth.

Anchors

Tags

  • definition
  • concept
  • shape

Topic

Shape of the Earth

Concept

The Earth is an oblate ellipsoid — flattened at the poles, bulging at the equator

Anchor Id

A1

Difficulty

easy

Memory Aid

Imagine a slightly squished balon (balloon) — round but pressed gently on the top and bottom. Now imagine a Pinoy mango that someone sat on lightly. The mango is wider at the middle (equator) and flatter at the stem ends (poles). That is exactly the Earth's shape — an oblate ellipsoid. 'Oblate' comes from ob- (against) + latus (side) meaning 'pressed against the side.' The Earth is that mango.

Anchor Type

analogy

Why It Works

Concrete, familiar Filipino object (mango) creates a vivid, tactile image that maps perfectly to the geometric concept of oblateness.

Example Usage

Exam asks: 'What is the geometric shape of the Earth used in geodesy?' → See the mango → Answer: oblate ellipsoid of revolution, flattened at poles, bulging at equator.

Recall Trigger

Think: 'Philippine mango pressed lightly at top and bottom'

Tags

  • definition
  • formula
  • classification

Topic

Ellipsoid Parameters

Concept

Semi-major axis a (equatorial) and semi-minor axis b (polar) — a > b

Anchor Id

A2

Difficulty

easy

Memory Aid

Remember: 'A is for Around the equator, B is Below at the poles.' A (around) is the bigger radius; B (below) is the shorter one. Or use the alphabet: A comes before B, and A is always LARGER. Think 'A is Amazing and BIG; B is Beneath and smaller.'

Anchor Type

mnemonic

Why It Works

Alphabetic ordering + directional cues (Around/Below) create dual reinforcement for remembering which axis is larger.

Example Usage

Given WGS84: a = 6,378,137 m and b = 6,356,752.31 m. Which is bigger? A is Amazing → a = 6,378,137 m → correct, it is the bigger one.

Recall Trigger

A comes before B → A is larger → a is equatorial (bigger), b is polar (smaller)

Tags

  • formula
  • definition

Topic

Ellipsoid Parameters

Concept

Flattening formula: f = (a − b) / a

Anchor Id

A3

Difficulty

easy

Memory Aid

Recall the sentence: 'Flattening Finds how much the Big axis lost.' f = (a − b) / a. The numerator (a − b) is HOW MUCH was 'lost' from a to make b. The denominator a normalizes it. Think of f as the 'fraction of flatness' — how flat is it compared to the full equatorial radius? F = Flat fraction = (Axial difference) / (Anterior big axis).

Anchor Type

acronym

Why It Works

The word 'flattening' itself encodes the meaning of the formula — it IS the fraction of how much the ellipsoid has been flattened from a perfect sphere.

Example Usage

Board problem: WGS84, a = 6,378,137 m, b = 6,356,752.31 m. f = (6,378,137 − 6,356,752.31) / 6,378,137 = 21,384.69 / 6,378,137 ≈ 1/298.257.

Recall Trigger

Flattening = fraction of how much was flattened → (a − b) / a

Tags

  • definition
  • classification
  • formula

Topic

WGS84 Parameters

Concept

WGS84 defining parameters: a = 6,378,137 m and 1/f = 298.257223563

Anchor Id

A4

Difficulty

medium

Memory Aid

Chunk the semi-major axis as: '6-37-8-137.' Read it as: 6 | 378 | 137. Story: 'Six jeepneys (6) carry 378 passengers to 137 barangays.' For 1/f = 298.257...: chunk as '298 point 257.' Say it as: 'Two-ninety-eight point two-fifty-seven.' Drill: '6,378,137 — sixty-three-seventy-eight — one-thirty-seven. And the flattening inverse is two-ninety-eight.'

Anchor Type

chunking

Why It Works

Chunking reduces working memory load from 10 individual digits to 3-4 meaningful chunks. The jeepney story adds an emotional Filipino anchor.

Example Usage

Examiner asks: 'What is the semi-major axis of WGS84?' → Six jeepneys → 6,378,137 m. What is the inverse flattening? → Two-ninety-eight → 298.257223563.

Recall Trigger

Six jeepneys → 6,378,137 m. Two-ninety-eight → 1/f = 298.257

Tags

  • formula
  • definition

Topic

Eccentricity

Concept

First eccentricity squared: e² = (a² − b²) / a² = 2f − f²

Anchor Id

A5

Difficulty

medium

Memory Aid

Remember the phrase: 'Eccentricity is Easy — it's the big minus small over big, all squared.' e² = (a² − b²) / a². Or the alternate form: '2f minus f-squared' — think '2 Flat minus Flat-Flat.' Imagine paying 2 times the flat rate but getting a discount of flat-times-flat: 2f − f². For WGS84: e² ≈ 0.00669438. Memory hook: '669 — six-six-nine after the decimal zeros' → e² ≈ 0.00669438.

Anchor Type

mnemonic

Why It Works

The phrase '2 Flat minus Flat-Flat' directly mirrors the algebra 2f − f² and makes the formula self-narrating.

Example Usage

Given f = 1/298.257, compute e²: e² = 2(1/298.257) − (1/298.257)² = 0.006694380 − 0.0000112 ≈ 0.00669438.

Recall Trigger

e² → '2 Flat minus Flat-Flat' → 2f − f². WGS84 value: 'six-six-nine' → 0.00669438

Tags

  • formula
  • definition

Topic

Eccentricity

Concept

Second eccentricity: e'² = (a² − b²) / b²

Anchor Id

A6

Difficulty

medium

Memory Aid

First eccentricity uses 'a-squared' in the denominator — it sees the world from the equator's perspective (the big boss). Second eccentricity uses 'b-squared' in the denominator — it sees the world from the pole's perspective (the small one looking up). Think: 'First e uses the big house (a); Second e' uses the small house (b) as base.' They both have the same numerator (a² − b²) — same difference, different base.

Anchor Type

analogy

Why It Works

House size analogy (big vs. small house as denominator base) gives a concrete image for remembering which squared term goes in the denominator.

Example Usage

e'² = (a² − b²)/b². For WGS84: e'² = (6,378,137² − 6,356,752.31²) / 6,356,752.31² ≈ 0.006739497.

Recall Trigger

First e: big house (a²) below. Second e': small house (b²) below.

Tags

  • definition
  • formula
  • classification

Topic

Radii of Curvature

Concept

Prime vertical radius of curvature N — applies East–West direction

Anchor Id

A7

Difficulty

medium

Memory Aid

N is for 'North-East-West No — actually East-West!' But more powerfully: N is the radius that holds up the NORMAL to the ellipsoid — and the Normal in the prime vertical plane runs East-West. Memory hook: 'N is Ninety degrees from the meridian' — East and West are 90° from the North-South meridian. So N governs the perpendicular (East-West) direction. Also: N ≥ M always, so 'N is Never smaller than M' — N is the 'Nicer bigger' one.

Anchor Type

mnemonic

Why It Works

The letter N linked to 'Normal' (which is geometrically correct — N is the radius of curvature in the prime vertical normal section) plus the 'Never smaller' trick gives two independent memory hooks.

Example Usage

Exam asks: 'Which radius of curvature is used for the East-West direction?' → N is Ninety from meridian → N (prime vertical radius).

Recall Trigger

N = Normal direction (East-West), Never smaller than M

Tags

  • definition
  • formula
  • classification

Topic

Radii of Curvature

Concept

Meridian radius of curvature M — applies North–South direction

Anchor Id

A8

Difficulty

medium

Memory Aid

M is for Meridian and for Moving North-South. Think of M as 'Me going to Maynila (Manila) from Mindanao' — you travel North-South along a meridian. M is always the SMALLER radius (harder to bend N-S because the ellipsoid is flatter there). And M has a more complex formula with (1-e²sin²φ)^(3/2) — the 3/2 power makes it more 'bent' and thus smaller. 'M is the Modest, smaller radius, going between Mindanao and Maynila.'

Anchor Type

analogy

Why It Works

Filipino geographic reference (Mindanao to Maynila = North-South travel) makes the direction immediately intuitive. 'Modest/smaller' encodes the M < N relationship.

Example Usage

Exam asks: 'Which curvature radius governs North-South geodetic computations?' → Me going to Maynila = Meridian = M.

Recall Trigger

M = Meridian = Mindanao to Maynila (N-S). M is Modest (smaller than N).

Tags

  • formula
  • process

Topic

Radii of Curvature

Concept

Formula for N: N = a / √(1 − e²sin²φ)

Anchor Id

A9

Difficulty

hard

Memory Aid

Walk through a house mentally. At the FRONT DOOR: you see 'a' (the big equatorial number, 6,378,137 — the address of the house). In the LIVING ROOM: you see a giant square root sign hanging from the ceiling like a chandelier. Under the chandelier: '1 minus e²sin²φ' written on the floor like a carpet. The fraction is the house itself: a (roof/numerator) over the square root (floor/denominator). Every time you think of N, walk through that house: door (a) → chandelier (√) → carpet (1 − e²sin²φ).

Anchor Type

method_of_loci

Why It Works

Method of loci (memory palace) encodes the formula spatially. The house metaphor gives a physical structure to an abstract equation.

Example Usage

φ = 45°, WGS84: N = 6,378,137 / √(1 − 0.00669438 × sin²45°) = 6,378,137 / √(0.99665281) ≈ 6,388,838.3 m.

Recall Trigger

Walk into the house: front door = a, chandelier = √, carpet = 1 − e²sin²φ

Tags

  • formula
  • process

Topic

Radii of Curvature

Concept

Formula for M: M = a(1 − e²) / (1 − e²sin²φ)^(3/2)

Anchor Id

A10

Difficulty

hard

Memory Aid

Compare N and M side by side. N = a / W, where W = √(1−e²sin²φ). M = a(1−e²) / W³. The key differences: (1) M has an extra (1−e²) in the numerator — 'M has a Modifier up top'; (2) M uses W-cubed (power 3/2) instead of W-squared (power 1/2) — 'M is More powerful below (3/2 vs 1/2).' Rhyme: 'N is simple a-over-W; M modifies a and cubes the W.' The 3/2 power makes M smaller — more denominator, less result.

Anchor Type

mnemonic

Why It Works

Contrast learning (N vs M) is highly effective. The rhyme and structural comparison encode the differences between the two most-confused formulas in this chapter.

Example Usage

At φ = 30°, WGS84: W = √(1 − 0.00669438 × sin²30°) = √(0.998326) = 0.999163. M = 6,378,137(1 − 0.00669438) / (0.999163)³ = 6,378,137 × 0.993306 / 0.997491 ≈ 6,351,376 m.

Recall Trigger

M has Modifier (1−e²) on top AND cubed W below (3/2 power)

Tags

  • formula
  • process
  • classification

Topic

Radii of Curvature – Special Cases

Concept

At the equator (φ = 0°): N = a and M = a(1−e²)

Anchor Id

A11

Difficulty

medium

Memory Aid

Story: Imagine you are standing exactly on the equator — the 'waistline' of the Earth-mango. At this special point, sin(0°) = 0, so the e²sin²φ term vanishes completely. The formula simplifies beautifully. N falls back to just 'a' — the equatorial radius itself — as if the Earth is briefly pretending to be a perfect sphere in the East-West direction. But M shrinks to a(1−e²) because the meridian curves MORE at the equator (sharper bend). Lesson: 'At the equator, N is at its minimum (= a) and M is at its minimum too, even smaller than N.'

Anchor Type

micro_story

Why It Works

The story gives a physical intuition for why the formulas simplify at φ = 0°, preventing the common error of misapplying the general formula at special latitudes.

Example Usage

Board shortcut: If φ = 0°, immediately write N = a = 6,378,137 m and M = a(1−e²) = 6,378,137 × 0.993306 ≈ 6,335,439 m without using the full formula.

Recall Trigger

Equator: sin(0°) = 0 → N = a (minimum), M = a(1−e²) (also minimum, smaller than N)

Tags

  • formula
  • classification

Topic

Radii of Curvature – Special Cases

Concept

At the poles (φ = 90°): M = N = a(1−e²)^(1/2) / (1−e²)^... = a(1−e²)/b² × b = b²/a

Anchor Id

A12

Difficulty

hard

Memory Aid

At the poles, M = N — the two radii of curvature become EQUAL. Visualize the two parallel rails of a railroad track (M and N) that are always separate, but at the very tip of the pole, the track converges to a single point. They merge. The common value at the poles = a²/b (a common result). Visual: two tracks → one point at the pole. Also memorize: at poles, curvature is MAXIMUM (smallest radius means tightest curve — the ellipsoid is most 'curved' at the pole tip).

Anchor Type

visual_association

Why It Works

The railroad convergence metaphor is a powerful spatial image for why two normally different values become equal at the poles.

Example Usage

At φ = 90°: M = N = a²/b = 6,378,137²/6,356,752.31 ≈ 6,399,594 m. Note this is LARGER than N at equator (6,378,137 m) — confirms N increases with latitude.

Recall Trigger

Railroad tracks converging at the pole tip → M = N at φ = 90°

Tags

  • formula
  • definition

Topic

Mean Radius of Curvature

Concept

Mean radius of curvature: R = √(MN) — the Gaussian mean

Anchor Id

A13

Difficulty

medium

Memory Aid

R = √(MN) is the geometric mean of M and N — the same formula you use for the geometric mean of two numbers in basic math. Think of it this way: M and N are two friends of different heights. R is the 'fair average height' that represents both — not the arithmetic average (M+N)/2, but the geometric mean √(MN). This R is used to approximate the Earth locally as a sphere for small-area computations. 'R is the Representative radius — the Reasonable compromise between M and N.'

Anchor Type

analogy

Why It Works

Connecting Gaussian mean to the familiar concept of geometric mean from basic mathematics creates a bridge to prior knowledge, making the formula intuitive rather than arbitrary.

Example Usage

At φ = 14° (Manila area), compute M and N separately using WGS84 formulas, then R = √(MN) ≈ the local sphere radius used in plane surveying approximations.

Recall Trigger

R = geometric mean of M and N = √(MN). Two friends, fair average height.

Tags

  • definition
  • classification

Topic

Common Pitfalls

Concept

Flattening is tiny: f ≈ 1/298 ≈ 0.00335, NOT 0.298 or 1/3

Anchor Id

A14

Difficulty

easy

Memory Aid

Story: A board exam taker (let's call him Kuya Rodrigo) mistakenly wrote f = 0.298 — confusing 1/f = 298 with f = 298. His entire answer fell apart. The Earth looks almost perfectly round to the naked eye — it is only about 1 part in 298 flatter than a sphere. That is less than 0.4% flatter. If you scaled the Earth to a basketball, the flattening would be invisible to your eye. Kuya Rodrigo's lesson: '1/f = 298 means f is ONE over 298, not 298 itself. Big number below means tiny fraction above.'

Anchor Type

micro_story

Why It Works

A cautionary story activates emotional memory and directly addresses the most common board exam mistake. The basketball analogy gives physical intuition for the smallness of f.

Example Usage

If a problem gives 1/f = 298.257, immediately compute f = 1/298.257 = 0.003352811 — never use 298 as f itself.

Recall Trigger

Kuya Rodrigo's mistake → 1/f = 298 → f = 1/298 ≈ 0.00335 (SMALL!)

Tags

  • classification
  • definition
  • sequence

Topic

Radii of Curvature

Concept

N ≥ M everywhere on the ellipsoid (prime vertical radius always ≥ meridian radius)

Anchor Id

A15

Difficulty

medium

Memory Aid

Rhyme: 'N is Never beaten by M; M is always the Modest gem. East-West N stands big and tall; North-South M is not as tall. At the equator the gap is wide; at the poles they stand side by side.' This rhyme encodes: (1) N ≥ M always, (2) N is East-West, M is North-South, (3) maximum difference at equator, (4) they converge at poles.

Anchor Type

rhyme

Why It Works

Rhymes engage phonological memory, making the entire relationship memorable as a unit. The rhyme encodes four facts simultaneously.

Example Usage

Any latitude on WGS84: N = 6,388,838 m at 45° vs M = 6,367,489 m at 45°. N > M confirmed. At poles: N = M ≈ 6,399,594 m.

Recall Trigger

Sing the rhyme: 'N is Never beaten by M...'

Tags

  • formula
  • classification

Topic

Eccentricity

Concept

e² uses a² in the denominator (first eccentricity); e'² uses b² in the denominator (second eccentricity)

Anchor Id

A16

Difficulty

medium

Memory Aid

Use the phrase: 'FIRST is Famous (uses a — the famous equatorial radius). SECOND is Shy (uses b — the less famous polar radius).' Or: 'First e: A-grade denominator. Second e': B-grade denominator.' The prime symbol on e' (like a graduation mark) signals it uses b (also starts with a 'b' sound: b-prime). Together: e² = (a²−b²)/a², e'² = (a²−b²)/b².

Anchor Type

mnemonic

Why It Works

Grading analogy (A-grade vs B-grade) with the letter correspondence (a→A, b→B) creates a logical mnemonic that is self-checking.

Example Usage

WGS84: e² = (a²−b²)/a² ≈ 0.00669438. e'² = (a²−b²)/b² ≈ 0.00673966. Note e'² > e² because b < a means smaller denominator means bigger result.

Recall Trigger

First e: A-grade (a²) below. Second e': B-grade (b²) below.

Tags

  • formula
  • definition

Topic

Ellipsoid Parameters

Concept

The relationship b = a(1 − f)

Anchor Id

A17

Difficulty

easy

Memory Aid

Think of 'a' as your original salary. Flattening 'f' is the percentage cut your boss takes from you. Your take-home pay is a(1 − f) = b. The Earth's polar radius b is the 'take-home pay' after flattening takes its cut from the full equatorial radius a. If f is small (like 1/298), then b is almost as large as a — just slightly less, like a tiny salary deduction.

Anchor Type

analogy

Why It Works

Financial analogy is universally relatable. Salary and deductions are concrete real-world concepts that map naturally to a, f, and b.

Example Usage

WGS84: b = 6,378,137 × (1 − 1/298.257) = 6,378,137 × 0.996647 = 6,356,752.31 m.

Recall Trigger

b = salary after deduction = a(1 − f)

Tags

  • definition
  • classification

Topic

Introduction to Geodesy

Concept

Geodesy definition: science of Earth's size, shape, and precise point positions

Anchor Id

A18

Difficulty

easy

Memory Aid

Use the acronym SSP: 'Geodesy = Size, Shape, Positions (precise).' Or expand: 'Geo-DESY studies: Does Earth's Size yield Positions?' Alternatively: think of a GPS device — it gives you a POSITION. How does GPS work? It uses a model of Earth's SIZE and SHAPE. So: GPS → Size, Shape, Position → Geodesy. The word 'Geodesy' itself: Geo (Earth) + desia (division/measurement) → measuring/dividing the Earth.

Anchor Type

acronym

Why It Works

The GPS connection is immediately relevant to practicing geodetic engineers and makes the definition memorable through a tool they use daily.

Example Usage

Exam: 'Define Geodesy.' → GPS mnemonic → 'The science that determines the Size and Shape of the Earth and the precise Positions of points on its surface.'

Recall Trigger

GPS = needs Size + Shape + Position → Geodesy

Tags

  • classification
  • definition

Topic

Historical Ellipsoids

Concept

Clarke 1866 ellipsoid — used by old Philippine surveys before PRS92/WGS84

Anchor Id

A19

Difficulty

medium

Memory Aid

Story: In the old days (1866), a British geodesist named Alexander Ross Clarke measured the Earth very carefully. His ellipsoid (a = 6,378,206.4 m, b = 6,356,583.8 m) was used by Philippine survey maps for over a century — it powered the old Luzon Datum of 1911. Think of Clarke 1866 as the 'old NAMRIA maps lolo/lola used' — the pre-digital Philippine cadastral surveys. When the Philippines shifted to PRS92 (based on GRS80/WGS84), Clarke was retired. 'Clarke is Classic; WGS84 is Current.'

Anchor Type

micro_story

Why It Works

Philippine historical context (Luzon Datum, NAMRIA, PRS92 transition) makes this directly relevant and emotionally resonant for Filipino geodetic engineers.

Example Usage

Clarke 1866: a = 6,378,206.4 m, b = 6,356,583.8 m. f = (a−b)/a = (21,622.6)/6,378,206.4 ≈ 1/295.0. Used in pre-PRS92 Philippine cadastral work.

Recall Trigger

Clarke = Classic old Philippine surveys (Luzon Datum 1911). WGS84 = Current PRS92.

Tags

  • formula
  • process

Topic

Radii of Curvature

Concept

The denominator term W = √(1 − e²sin²φ) appears in both N and M formulas

Anchor Id

A20

Difficulty

hard

Memory Aid

Visualize W as a 'weight machine' at the gym. When latitude φ = 0° (equator), sin(0°) = 0, so W = √1 = 1 — the machine shows 'no weight added.' When φ = 90° (pole), sin(90°) = 1, W = √(1−e²) — maximum weight is added. The W value lies between √(1−e²) and 1. In the N formula, W is in the denominator once (W¹). In M, W is cubed (W³). Higher power of W below = smaller result = M < N. 'W is the Weight that reduces both N and M, and it Weights M more (W³) than N (W¹).'

Anchor Type

visual_association

Why It Works

The gym weight machine metaphor makes the variable W concrete and shows intuitively why it appears in both formulas and why its higher power in M produces a smaller value.

Example Usage

At φ = 14°: W = √(1 − 0.00669438 × sin²14°) = √(1 − 0.00669438 × 0.05843) = √(0.999609) = 0.999804. Use W to compute both N and M efficiently.

Recall Trigger

W = weight machine at gym. W¹ for N, W³ for M → M gets heavier burden → M < N

Revision Game

Semi-major axis a

Clue

I am the equatorial waistline of the Earth. On WGS84, I am exactly 6,378,137 meters. What letter names me?

Memory Link

A2 — A is Amazing and BIG (equatorial radius)

Flattening f (f ≈ 0.00335, not 0.298)

Clue

I am a tiny fraction — about 1 part in 298. I measure how squashed the Earth is. Kuya Rodrigo once wrote me as 0.298 — and failed. What am I?

Memory Link

A14 — Kuya Rodrigo's cautionary tale: 1/f = 298, so f is ONE over 298

Prime vertical radius of curvature N

Clue

I govern East-West curvature. My formula has 'a' on top divided by a square root. I am never smaller than my meridian cousin. Who am I?

Memory Link

A7 — N is Never smaller, N is Ninety degrees from meridian (East-West)

Mean radius of curvature R = √(MN)

Clue

I am the geometric mean of M and N. I approximate the ellipsoid as a local sphere. My formula is simple — just take the square root of two friends multiplied. What am I?

Memory Link

A13 — R is the Representative radius, geometric mean, two friends of different heights

Prime vertical radius N

Clue

At the equator, I equal exactly 'a' — nothing more. At the poles, I grow to my maximum. I am the BIGGER radius of curvature at every latitude. What am I?

Memory Link

A11 — At equator: N = a (minimum), grows toward poles

Second eccentricity e'²

Clue

I use b-squared in my denominator — the 'B-grade' base. My first cousin uses a-squared. We share the same numerator: (a²−b²). Who am I?

Memory Link

A16 — Second e': B-grade denominator (b²). First e²: A-grade denominator (a²)

Clarke 1866 ellipsoid (Luzon Datum 1911)

Clue

I was the reference ellipsoid for Philippine surveys before PRS92 arrived. My semi-major axis is 6,378,206.4 m — a bit larger than WGS84's. Lola's cadastral map used me. Who am I?

Memory Link

A19 — Clarke is Classic (old lola's maps), WGS84 is Current

W — the denominator factor W = √(1 − e²sin²φ)

Clue

I appear inside every radius of curvature formula. I equal √(1 − e²sin²φ). At the equator I equal 1; at the poles I equal √(1−e²). I am the gym machine that adds weight to the denominator. What letter am I called by?

Memory Link

A20 — W is the Weight machine at the gym

Formula Mnemonics

Formula

f = (a − b) / a

Mnemonic

Flattening is the Fraction of the gap (a minus b) relative to the Full equatorial radius (a). 'Flat Fraction = Gap over Grand radius.'

When To Use

When you need to find flattening from the two axes, or when deriving b from a and f (rearranged as b = a(1−f)).

What Each Part Means

f = flattening (dimensionless, ≈ 1/298 for WGS84); a = semi-major axis (equatorial radius); b = semi-minor axis (polar radius); (a − b) = the actual polar shortfall in meters

Formula

e² = 2f − f² = (a² − b²) / a²

Mnemonic

'2 Flat minus Flat-Flat' for the f-form. 'Big-squared minus Small-squared over Big-squared' for the axes form. WGS84 value: remember '669' → e² ≈ 0.00669438.

When To Use

Use e² = 2f − f² when only f is given. Use e² = (a²−b²)/a² when both axes are given. e² appears inside every radius of curvature formula.

What Each Part Means

e² = first eccentricity squared (dimensionless); the two forms are algebraically equivalent; e measures how much the ellipse deviates from a circle (e = 0 is a perfect sphere)

Formula

e'² = (a² − b²) / b²

Mnemonic

Second eccentricity = same numerator as e², but B-grade denominator (b²) instead of A-grade (a²). 'e-prime uses the Prime (polar) base.' e'² > e² always because b < a.

When To Use

When problems specifically ask for second eccentricity, or in advanced geodetic computations involving series expansions for arc length.

What Each Part Means

e'² = second eccentricity squared; b² in denominator makes this larger than e²; used in some geodetic series expansions and in certain conformal projection formulas

Formula

N = a / √(1 − e²sin²φ)

Mnemonic

'a over root of (1 minus eccentricity-latitude blend).' The HOUSE formula: a (roof) over √(1−e²sin²φ) (foundation). N governs East-West. At φ=0°: N=a (simplest value).

When To Use

For any computation involving East-West distances, parallel lengths, geographic coordinate conversions, and UTM/PPCS projection scale factors.

What Each Part Means

N = prime vertical radius of curvature (m); a = semi-major axis; e² = first eccentricity squared; φ = geodetic latitude; the denominator W = √(1−e²sin²φ) varies from 1 (equator) to √(1−e²) (pole)

Formula

M = a(1 − e²) / (1 − e²sin²φ)^(3/2)

Mnemonic

'M has a Modifier (1−e²) on top, and cubed W below (power 3/2).' Compare to N: M adds (1−e²) numerator and raises denominator to 3/2 instead of 1/2. M governs North-South. M < N always.

When To Use

For North-South distance computations, arc-to-chord corrections in N-S direction, meridian arc length calculations, and geographic coordinate to metric conversions.

What Each Part Means

M = meridian radius of curvature (m); a(1−e²) = semi-latus rectum of the meridian ellipse; denominator (1−e²sin²φ)^(3/2) = W³ where W = √(1−e²sin²φ); M is smallest at equator and largest at poles

Formula

R = √(MN)

Mnemonic

'R is the Root of M times N' — geometric mean. 'R is the Representative sphere radius.' Used locally to approximate the ellipsoid as a sphere for small-area plane surveying.

When To Use

For converting between geodetic and plane coordinates in small areas, for computing corrections in local plane surveys, and as the 'Earth radius' in first-order approximations.

What Each Part Means

R = mean radius of curvature (m), also called Gaussian mean radius; M = meridian radius; N = prime vertical radius; R is the radius of the sphere that best fits the ellipsoid at a given latitude

Formula

b = a(1 − f)

Mnemonic

'b is the pay after deduction': start with full salary a, deduct fraction f, get take-home b. Rearranging: f = (a−b)/a and a = b/(1−f).

When To Use

When you have a and f (like in WGS84 definition) and need b. Or to check consistency between given a, b, and f values.

What Each Part Means

b = semi-minor axis (polar radius, m); a = semi-major axis (equatorial radius, m); f = flattening (dimensionless fraction); (1−f) is the fraction of a that b represents

Quick Recall Chains

Chain Title

WGS84 Key Numbers Chain

Recall Test

Without looking: What is the WGS84 semi-major axis? Inverse flattening? Semi-minor axis? e²? Recite the jeepney story from start to finish.

Memory Chain

Story chain: 'Six jeepneys (6) with 378 seats (378) carry 137 barangay captains (137) — that is a = 6,378,137 m. Their meeting is at Room 298 (1/f = 298.257). The meeting discusses a 0.335% budget cut (f ≈ 0.00335). After the cut, they have 6,356 pesos and 752 centavos (b ≈ 6,356,752 m). The eccentricity of their argument: 669 decibels (e² ≈ 0.00669).'

Items To Remember

  • a = 6,378,137 m
  • 1/f = 298.257223563
  • f ≈ 0.00335281
  • b ≈ 6,356,752.31 m
  • e² ≈ 0.00669438

Chain Title

Ellipsoid Parameter Derivation Sequence

Recall Test

Starting only from a and f, can you write all 8 derived quantities in order without notes? Time yourself — should take under 3 minutes in an exam setting.

Memory Chain

The ROAD to curvature: 'A Fine Base (a, f) → Build the B-road (b) → E-squared on the road (e²) → E-Prime diverges (e'²) → W is the Weight on the road (W) → N is the North-East overpass (N) → M is the Meridian underpass (M) → R is the Roundabout (R = √MN).'

Items To Remember

  • Start with a and f (defining parameters)
  • Compute b = a(1 − f)
  • Compute e² = 2f − f²
  • Compute e'² = e²/(1 − e²)
  • Compute W = √(1 − e²sin²φ)
  • Compute N = a/W
  • Compute M = a(1 − e²)/W³
  • Compute R = √(MN)

Chain Title

Radii of Curvature at Special Latitudes

Recall Test

Fill in the blanks: At φ = 0°, N = ___ and M = ___. At φ = 90°, N = M = ___. Which is always larger, N or M?

Memory Chain

'Zero at equator: N is just a, M is a with modifier. Forty-five is middle ground: N = 6.388M and M = 6.367M (remember 8 and 7 at the end — N ends in 8, M ends in 7). Ninety at poles: the rails merge, N = M = a²/b.'

Items To Remember

  • At φ = 0° (equator): N = a, M = a(1−e²), M < N
  • At φ = 45°: N ≈ 6,388,838 m, M ≈ 6,367,489 m for WGS84
  • At φ = 90° (poles): N = M = a(1−e²)^(1/2) / (1−e²)^(1/2) = a²/b

Chain Title

Common Ellipsoids in Philippine Geodesy

Recall Test

Which ellipsoid is the basis of PRS92? Which is used by GPS/GNSS? What is common between GRS80 and WGS84? What was the Luzon Datum 1911 ellipsoid?

Memory Chain

'Philippine ellipsoid history: CLASSIC Clarke (old lola's maps, 1866) → GRS80 (basis of PRS92, same a as WGS84 but slightly different 1/f) → WGS84 (GPS era, current). Same a = 6,378,137 for both GRS80 and WGS84 — the equator never changed, only the fine details of flattening differ by the 7th decimal place.'

Items To Remember

  • Clarke 1866: a = 6,378,206.4 m — used in Luzon Datum 1911
  • GRS80: a = 6,378,137 m, 1/f = 298.257222101 — basis of PRS92
  • WGS84: a = 6,378,137 m, 1/f = 298.257223563 — basis of GNSS
  • Clarke 1880: used in some old Mindanao surveys

Chain Title

Eccentricity Forms and Relationships

Recall Test

Write the formula for e² in two ways. Write the formula for e'². What is the relationship between e'² and e²? Which is larger?

Memory Chain

'Eccentricity family: FIRST born uses the A (a²) surname. SECOND born uses the B (b²) surname. They have the same numerator (a²−b²) — same parents, different last names. The relationship: e-prime-squared = e-squared divided by (1 minus e-squared) — second born is always slightly bigger because the family name B is smaller, making the fraction bigger.'

Items To Remember

  • e² = (a² − b²) / a² [first, A-grade denominator]
  • e'² = (a² − b²) / b² [second, B-grade denominator]
  • e² = 2f − f² [from flattening]
  • e'² = e² / (1 − e²) [relationship between first and second]
  • e'² > e² always
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