True direction is what is shown on maps — the direction to the geographic North Pole.
An INS (Inertial Navigation System) finds True direction by detecting Earth's rotation. Most aircraft, however, use magnetic compasses as primary heading references, with INS as a standby or supplement.
The Earth behaves as though a huge, slightly bent bar magnet runs through it, with its magnetic poles approximately (but not exactly) aligned with the True poles. This misalignment creates the need to convert between True, Magnetic, and Compass headings in flight planning.
Figure 1 — The Earth's True Poles and Magnetic Poles — not coincident, causing variation
2. Variation — Definition & Observer Geometry
🔎 Definition
Variation is the angular difference between the directions of True North and Magnetic North at any point.
Measured in degrees East or West from True North. Suffix: E or W.
A line joining points of equal variation is an Isogonal (shown as a pecked/dashed line on charts).
The isogonal of zero variation is the Agonic Line.
Figure 2 — Idealised model of world variation — how the observer's position geometry determines the direction and magnitude of variation
How Observer Position Determines Variation
The variation at any point depends on the geometry of the observer, the True North Pole, and the Magnetic North Pole:
Observer A: Magnetic North Pole is to the right of True North → Easterly variation
Observer B: Magnetic North Pole is to the left of True North → Westerly variation
Observer C/D: Further from both poles → smaller angle of variation
Observer E: On the Great Circle joining True and Magnetic Poles → zero variation (on the Agonic Line)
Figure 3 — Idealized geometry of True and Magnetic North Poles — showing the 0° and 180° variation lines
3. Situation at the Poles — Maximum Variation
For an observer on the arc of the Great Circle between the True North Pole and the Magnetic North Pole:
True North points one way (toward the True Pole)
The compass needle points in exactly the opposite direction (toward the Magnetic Pole)
The variation at such a point is exactly 180°
⚠ Maximum Variation = 180°
The maximum possible value of variation is 180°. It occurs between the True and Magnetic Poles.
At the True Poles themselves, isogonals converge and variation is indeterminate (all directions are either only North or only South).
4. The Real Variation Map — Isogonals & Agonic Lines
The real magnetic field is more complex than the idealised model — it resembles a bent bar magnet.
The North Magnetic Pole (NERC 2000 survey) was at approximately 81°N 110°W; the South Magnetic Pole at approximately 63°S 135°E — they are not antipodal.
There are two Agonic Lines (zero-variation lines), both starting from the True North Pole:
One runs southward through Western Europe → Stuttgart, Germany → Central Africa → back via North-Central Asia → Australia → South Magnetic Pole
The other runs southward through the USA → South America → True South Pole
Figure 4 — Actual variation distribution around the North Pole — isogonals converge on both the True and Magnetic PolesFigure 5 — Actual variation distribution around the South PoleFigure 6 — Variation at the North Pole showing the two Agonic Lines and the 180° variation line between the poles
⚠ Key Exam Facts — Isogonals
Isogonals converge on all four poles — both True (Geographic) AND both Magnetic poles
Isogonals are NOT the same as magnetic field lines — they show the difference between local field direction and True North
Zero variation (Stuttgart area) does NOT mean no magnetic field — it means Magnetic North = True North at that point
5. Changes in Variation Over Time
Variation at any point changes with time because the Magnetic Poles are moving.
There are several overlapping cycles:
Type
Period
Cause
Magnitude
Secular
Long-term drift
Movement of molten magma in the Earth's core; Magnetic Pole moving westward & northward
~1°/9 years at some locations
Annual
~1 year
Earth's orbit round the Sun (sinusoidal)
Small
Diurnal
~1 day
Daily changes in ionosphere height as Earth rotates
Up to ~0.1°
Solar activity
11-year sunspot cycle (unpredictable)
Solar flares hitting the ionosphere — "magnetic storms"
Up to 7° observed
Local anomalies
Constant
Magnetic rock deposits or formations below surface
Variable
📚 Practical Accuracy
It is very difficult to know the instantaneous variation to better than about ±2°.
Over a period of time with careful correction, accuracy of ±0.5° is achievable.
This is why INS (accurate heading from gyros) was a major advance in the 1960s–70s.
6. Updating Isogonals on Charts
For frequently republished radio-navigation charts, isogonals are usually current enough.
For topographical maps republished every 5–10 years, pilots may need to update isogonals during flight planning.
Charts show the year of origin and the annual change in one of two ways:
Figure 7 — Isogonal update — annual change shown by an arrow indicating the direction and distance of movementFigure 8 — Isogonal update — annual change shown as a stated value on the chart
7. Magnetic Dip — Angle, H and Z Components
The Earth's magnetic field acts along a total force vector T, which is directed into the Earth at an angle to the horizontal. This angle is the Angle of Dip.
Figure 9 — Lines of magnetic force around the Earth — showing how the dip angle varies from 0° at the magnetic equator to 90° at the magnetic polesFigure 10 — The Angle of Dip — total force T resolves into horizontal component H (compass-useful) and vertical component Z (useless for direction)
Resolving T into H and Z
Component
Symbol
Direction
Compass use
Total force
T
Along field line (into Earth at dip angle)
—
Horizontal component
H
Horizontal — toward Magnetic North
USEFUL — the directive force
Vertical component
Z
Vertical — into the Earth
USELESS — causes dip errors
Figure 11 — Effect of latitude on H and Z: at the magnetic equator H ≈ T and Z ≈ 0; at the magnetic poles H ≈ 0 and Z ≈ T
Relationship Between Dip and H
At the magnetic equator: Dip = 0°, H ≈ T (maximum — compass most effective)
As latitude increases toward the poles: Dip increases, H decreases, Z increases
At the magnetic poles: Dip = 90°, H ≈ 0 (compass unreliable)
At a typical mid-latitude UK location: Dip ≈ 66°
⚠ Two Problems Caused by Z (Vertical Component)
1. Compass dip: Z causes the compass needle to hang down from the horizontal, creating turning and acceleration errors (partially corrected by pendulous suspension — residual ~2° at a typical mid-latitude location).
2. Soft-iron deviation increase: Z induces vertical soft-iron magnetism in the aircraft structure, adding to deviation.
Magnetic field strength is measured in microteslas (µT). H is the directive force.
A line joining points of equal magnetic dip is an Isoclinal.
The isoclinal of zero dip is the Aclinic Line (the magnetic equator).
8. The 6 µT Threshold & Compass Reliability
The accepted threshold below which H is too weak to reliably drive a magnetic compass is 6 microteslas (µT).
Inside the 6 µT zone, compass reliability cannot be guaranteed.
Figure 12 — The 6 µT zone around the North Magnetic Pole (Arctic polar projection, ~1950) — compass unreliable within this regionFigure 13 — The 6 µT zones around both the North and South Magnetic Poles (NERC survey, Jan 2000)Figure 14 — World dip angle distribution — the magnetic equator (zero dip) and the regions of high dip near the magnetic poles
📚 Exam Tip
The 6 µT zone exists around BOTH the North AND South Magnetic Poles. The 6 µT threshold is the notional figure — actual threshold depends on compass design.
Maximum dip = 90° directly over either magnetic pole.
9. Deviation — Definition & Sign Convention
🔎 Definition
Deviation is the angle measured at a point between the direction indicated by a compass needle and the direction of Magnetic North. Termed East or West according to whether Compass North lies to the East or West of Magnetic North.
The aircraft itself contains magnetic influences (metal structures, electrical currents, equipment) which deflect the compass needle from its ideal alignment with Magnetic North.
The compass then points to Compass North — not Magnetic North.
Sign Convention (±)
Convention
East deviation
West deviation
Directional suffix
E (e.g. 3°E)
W (e.g. 3°W)
Algebraic sign
+ (positive)
− (negative)
Applied to Compass heading to give Magnetic heading: Hdg(M) = Hdg(C) + Deviation (using algebraic sign). Equivalently: From Compass to Magnetic, the signs are true — East is +, West is −.
10. Applying Variation & Deviation — CADIZ Rules
Figure 15 — Westerly Variation (left) and Easterly Variation (right) — how Magnetic North shifts relative to True North, changing the heading readoutFigure 16 — Variation application tables — Heading True, Variation, Heading Magnetic for both Westerly and Easterly cases
The CADIZ Chain: C → D → M → V → T
Apply deviation to Compass → get Magnetic; apply variation to Magnetic → get True
VARIATION WEST — MAGNETIC BEST (Magnetic heading > True heading)
VARIATION EAST — MAGNETIC LEAST (Magnetic heading < True heading)
DEVIATION WEST — COMPASS BEST (Compass heading > Magnetic heading)
DEVIATION EAST — COMPASS LEAST (Compass heading < Magnetic heading)
Worked Examples — Variation
Heading True
Variation
Heading Magnetic
Rule
105°(T)
17°W
122°(M)
West → M best (add)
105°(T)
17°E
088°(M)
East → M least (subtract)
Figure 17 — Westerly Deviation (left) and Easterly Deviation (right) — how Compass North shifts relative to Magnetic NorthFigure 18 — Deviation application tables — Heading Magnetic, Deviation, Heading Compass for Westerly and Easterly cases
Worked Examples — Deviation
Heading Magnetic
Deviation
Heading Compass
Rule
125°(M)
10°W
135°(C)
West → C best (add)
125°(M)
10°E
115°(C)
East → C least (subtract)
Full T → M → C Example
°True
Variation
°Magnetic
Deviation
°Compass
100°(T)
25°W
125°(M)
10°W
135°(C)
100°(T)
25°W
125°(M)
10°E
115°(C)
✎ ± Notation Example
Deviation 3°E = +3. Heading(M) = 263°. Find Heading(C):
"Deviation East → Compass Least" → C = M − 3 = 260°(C)
Check: C + deviation = M → 260 + (+3) = 263 ✓
11. All Definitions
Term
Definition
Heading
Direction of the fore-and-aft axis of the aircraft. May be measured from True, Magnetic, or Compass North.
Variation
Angle between True North and Magnetic North at a point. East if MN is East of TN; West if MN is West of TN.
Deviation
Angle between Magnetic North and the direction indicated by the compass. East if Compass North is East of MN; West if West.
Isogonal
Pecked line on a chart joining places of equal magnetic variation.
Agonic Line
Isogonal joining places of zero variation.
Angle of Dip
Angle in the vertical plane between the horizontal and the Earth's total magnetic force at a point.
Isoclinal
Line on a chart joining places of equal magnetic dip.
Aclinic Line
Isoclinal joining places of zero dip (the magnetic equator).
📚 Note on Isoclinals / Aclinic Lines
Isoclinals and Aclinic Lines do NOT appear on standard navigation charts. They appear only in specialist geomagnetic publications.
📚 Quick Revision — Chapter 3
Three North datums: True, Magnetic, Compass
Variation = True North to Magnetic North; Deviation = Magnetic North to Compass North
CADIZ: Var West = Mag Best; Var East = Mag Least; Dev West = Comp Best; Dev East = Comp Least
Max variation = 180° (between True and Magnetic poles)
Isogonals converge on all four poles (True N, True S, Mag N, Mag S)
Dip = 0° at magnetic equator; Dip = 90° at magnetic poles
Compass most effective where H is maximum — midway between magnetic poles (magnetic equator)
(a) inversely proportional to the horizontal component of the Earth's magnetic field
(b) proportional to the horizontal component of the Earth's magnetic field ✓
(c) inversely proportional to the vertical component of the Earth's magnetic field
(d) inversely proportional to the vertical and horizontal components of the Earth's magnetic field
▶ Show answer & explanation
Correct Answer: (b)
The compass needle is driven by the horizontal component H. The larger H is, the greater the directive force and the more reliably the needle aligns with Magnetic North. Sensitivity is therefore proportional to H — more H means a more sensitive, reliable compass.
Distractor Analysis: (a) Inverse of H would mean the compass works better near the poles — the opposite of reality. (c/d) Z is the vertical component — it is unhelpful (causes dip errors) but sensitivity is not inversely proportional to it.
Instructor's Note: Source key: b. Verified. No discrepancy.
(a) The angle between the direction indicated by a compass and Magnetic North
(b) The angle between True North and Compass North
(c) The angle between Magnetic North and True North ✓
(d) The angle between Magnetic Heading and Magnetic North
▶ Show answer & explanation
Correct Answer: (c)
Variation is defined as the angular difference between True North and Magnetic North at a given point. More precisely, it is measured from True North to Magnetic North and termed East or West accordingly.
Distractor Analysis: (a) Describes Deviation, not Variation. (b) The angle between TN and Compass North is the combined effect of Variation + Deviation. (d) Magnetic Heading relative to Magnetic North would simply be the heading itself — not meaningful.
Instructor's Note: Source key: c. Verified. No discrepancy.
The magnetic equator (Aclinic Line) is defined as the line of zero dip. At the magnetic equator, the total field T is horizontal — Z = 0 and H = T (maximum). Compass reliability is highest here.
Distractor Analysis: (b) Variation is zero only on the Agonic Line, which does not follow the magnetic equator. (c) Deviation depends on the aircraft's own magnetic properties — unrelated to magnetic equator. (d) The isogonal at the magnetic equator is not an Agonic Line (except where the magnetic equator and Agonic Line happen to intersect).
Instructor's Note: Source key: a. Verified. No discrepancy.
Q4. Which of these is a correct statement about the Earth's magnetic field?
(a) It acts as though there is a large blue magnetic pole in Northern Canada ✓
(b) The angle of dip is the angle between the vertical and the total magnetic force
(c) It may be temporary, transient, or permanent
(d) It has no effect on aircraft deviation
▶ Show answer & explanation
Correct Answer: (a)
In conventional magnetic labelling, a blue pole is a South-seeking pole (the end a compass South needle would point to). The Earth's geographic north region acts as a magnetic south pole — attracting the north-seeking (red) end of a compass needle. So 'blue magnetic pole in Northern Canada' correctly describes the Earth's field configuration near the Magnetic North Pole.
Distractor Analysis: (b) Wrong — dip angle is between the horizontal and the total force T, not the vertical. (c) Describes aircraft deviation categories, not the Earth's field. (d) Wrong — the Earth's field induces magnetism in the aircraft, directly causing deviation.
Instructor's Note: Source key: a. Verified. No discrepancy.
(a) About midway between the Earth's magnetic poles ✓
(b) In the region of the magnetic South Pole
(c) In the region of the magnetic North Pole
(d) On the geographic equator
▶ Show answer & explanation
Correct Answer: (a)
The compass is most effective where H (horizontal component) is greatest. H is maximum at the magnetic equator, which lies approximately midway between the North and South Magnetic Poles. There H ≈ T and Z ≈ 0.
Distractor Analysis: (b/c) At either magnetic pole, dip = 90°, H ≈ 0 — compass is least effective. (d) Geographic equator ≠ magnetic equator. The geographic equator passes through regions of varying dip.
Instructor's Note: Source key: a. Verified. No discrepancy.
The maximum possible variation is 180°. This occurs at points between the True and Magnetic Poles where TN and MN point in exactly opposite directions. The Agonic Line (zero variation) is unrelated to the magnetic equator.
Distractor Analysis: (a) Zero variation occurs on the Agonic Line — not on the magnetic equator. (c/d) Both wrong — variation can theoretically reach 180°.
Instructor's Note: Source key: b. Verified. No discrepancy.
(a) is midway between the magnetic North and South poles
(b) follows the geographic equator
(c) is the shorter distance between the respective True and Magnetic North and South poles
(d) follows separate paths out of the North polar regions, one currently running through Western Europe and the other through the USA ✓
▶ Show answer & explanation
Correct Answer: (d)
The text describes two Agonic Lines from the North pole region: one running through Western Europe (Stuttgart, Germany) and the other through the USA. Both pass through the poles. This is due to the complex, non-ideal shape of the Earth's magnetic field ('bent bar magnet' analogy).
Distractor Analysis: (a) Midway between the magnetic poles would be the magnetic equator — the Aclinic Line, not the Agonic Line. (b) The geographic equator has nothing to do with zero variation. (c) The 180° variation line (not the Agonic Line = 0°) runs between True and Magnetic poles.
Instructor's Note: Source key: d. Verified. No discrepancy.
Q8. The angle between True North and Magnetic North is known as:
Variation is precisely the angle between True North and Magnetic North. Deviation is between Magnetic North and Compass North. Dip is the angle between horizontal and the total magnetic force.
Distractor Analysis: (a) Deviation = MN to Compass North. (c) Not a standard term in navigation. (d) Dip = angle of field from horizontal.
Instructor's Note: Source key: b. Verified. No discrepancy.
Q9. The value of magnetic variation on a chart changes with time. This is due to:
(a) Movement of the magnetic poles, causing an increase
(b) Increase in the magnetic field, causing an increase
(c) Reduction in the magnetic field, causing a decrease
(d) Movement of the magnetic poles, which can cause either an increase or a decrease ✓
▶ Show answer & explanation
Correct Answer: (d)
The secular movement of the Magnetic Poles changes the relative geometry between observer, True Pole, and Magnetic Pole. Depending on the direction of pole movement and the observer's location, variation can either increase or decrease — it is not universally one or the other.
Distractor Analysis: (a) Says movement always causes an increase — wrong, it depends on location. (b/c) The total field strength is not the mechanism for changing chart variation.
Instructor's Note: Source key: d. Verified. No discrepancy.
(b) At the North and South Magnetic and Geographical Poles ✓
(c) At the North and South Magnetic Poles
(d) At the Magnetic equator
▶ Show answer & explanation
Correct Answer: (b)
Isogonals converge at all four poles — both True (Geographical) poles AND both Magnetic poles. This is because near any pole, all isogonals must converge as the pole is a singular point for direction. The text states explicitly: 'Isogonals converge on both the True and the Magnetic North and South Poles.'
Distractor Analysis: (a) Only the North Magnetic Pole — incomplete. (c) Both Magnetic Poles but not the Geographical Poles — incomplete. (d) The magnetic equator is where isoclinals converge (zero dip), not isogonals.
Instructor's Note: Source key: b. Verified. No discrepancy.
Q11. What is the maximum possible value of dip angle?
Maximum dip = 90°, occurring directly over either Magnetic Pole where Z = T and H = 0. The field lines enter the Earth vertically.
Distractor Analysis: (a) 66° is a typical dip angle at mid-latitude UK — a specific local value, not the maximum. (b) 180° is the maximum possible variation, not dip. (d) 45° has no physical significance here.
Instructor's Note: Source key: c. Verified. No discrepancy.
Q12. What is the dip angle at the South Magnetic Pole?
At either magnetic pole (North or South), the field lines are vertical — dip = 90°. The horizontal component H = 0 at both magnetic poles.
Distractor Analysis: (a) 0° is the dip at the magnetic equator (Aclinic Line). (c) 180° is maximum variation, not dip — dip cannot exceed 90°. (d) Not a recognized standard value.
Instructor's Note: Source key: b. Verified. No discrepancy.
An isogonal connects points of equal magnetic variation. An isocline (or isoclinal) connects points of equal dip. An isogriv connects points of equal Grid Variation (used in polar grid navigation). 'Isovar' is not a standard aviation term.
Distractor Analysis: (a) Isocline = equal dip, not equal variation. (c) Isogriv = equal Grid Variation (polar navigation only). (d) Not standard terminology.
Instructor's Note: Source key: b. Verified. No discrepancy.
Variation is defined as East or West according to whether Magnetic North lies East or West of True North. If Variation is West, Magnetic North is West of True North — therefore True North is East of Magnetic North.
Memory check: 'Variation West, Magnetic Best' — M > T numerically. If MN is West of TN, a pilot facing TN would need to look right (East) to see TN relative to MN. So TN is East of MN. ✓
Distractor Analysis: (a) True North West of Magnetic North would mean Easterly variation. (b) Compass North relative to Magnetic North is Deviation, not Variation. (d) Magnetic North West of Compass North is Easterly Deviation.
Instructor's Note: Source key: c. Verified. No discrepancy.
Q15. Fill in the blank spaces in the TVMD table below. Part A uses East/West notation; Part B uses ± notation (+ = East, − = West).
DGCA CPL/ATPL General Navigation Study Notes
Chapter 3 — Earth Magnetism Capt. Pankaj Pahil | www.ghostaviator.com For personal study use only. Ghost Aviator Interactive Colour Edition.
