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B) Permanent & Induced Magnetism and

Coefficients
Objective:

Understand the concept of permanent and

induced magnetism, their coefficients and
their effects magnetic compass

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Deviation
Magnetism acquired
by steel structures of
a ship

Hard Iron Magnetism

Soft Iron Magnetism
(Permanent
(Induced Magnetism)
Magnetism)

Horizontal Soft
P • Fore & Aft Horizontal component Iron Vertical Soft Iron
• Athwartship Horizontal component (induced by Z)
Q (induced by H)

R • Vertical Component
Athwartship Soft Fore & Aft
vary with change Iron Soft Iron
of ship’s head,
latitude &
hemisphere Nine Imaginary soft iron rods

δ = A + B sin co + C cos co + D sin 2co + E cos 2co

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Coefficient B
• Coefficient B is the max. value of the semicircular
deviation which varies as the sine of the compass
course.
• It is caused by the horizontal, fore and aft
component of the magnetic field due to the ship
at the compass position.

Coefficient B

Permanent B Induced B
(PB) + (iB)

Force ±𝑃 rod ±𝑐 (V. S. I. )

(+PB, -PB) (+iB, - iB)
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Coefficient B
Coefficient
B

+B -B

• Due to the ship’s field acting towards • Due to the ship’s field acting towards
the bow the stern

• Result of deviation: • Result of deviation:

1. Easterly Deviation on Easterly Course 1. Westerly Deviation on Easterly Course
and and
2. Westerly Deviation on Westerly Course 2. Easterly Deviation on Westerly Course

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Permanent B (PB) (Due to Hard Iron)

[ Regardless of Hemisphere ]
• Ship built heading Magnetic North:

• Ship built heading Magnetic South:

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Permanent B (PB)
• Force causing permanent B is P and is constant,
but the deviation due to this force changes with
both latitude and course.

+ PB
How the
change in δ
due to
change of
course?

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Permanent B (PB)

• How about ?
- PB

• How a ship acquired –PB?

• How is the change of deviation due to change of
course?
• Could you illustrate with sketches the deviations
on various ship’s heading produced by –PB and
hence draw the deviation curve and symbol?

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Effect of ship’s course on deviation due to PB:

• δ due to PB: nil at 000° & 180°, max. at 090° & max.
of the opposite name on 270°.
• δ varies as sin comp. co ( δ ∝ sin comp. co. )

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Effect of change of Latitude on

Deviation due to PB:
• Force P causing the deviation remains constant,
but as the latitude of the ship changes, H also
changes.

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Effect of change of Latitude/Hemisphere on

Deviation due to PB:
• The deviation caused by PB will be max. at the
magnetic poles and least near the equator.
𝟏
• PB ∝
𝐇
• H has the same direction in the Northern and the
Southern hemisphere, it always acts towards
magnetic North.
• Deviation due to PB does not change sign when
crossing the magnetic equator.

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• Definition of Coefficient B
• Condition give rise to Coefficient +B, -B
• Deviation associated with the Coefficient
permanent B varies with change of
✓ ship’s course
✓ magnetic latitude
✓ hemisphere

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• PB Equations
• PB Correction approach
• PB Calculations
• Deviation associated with the
Coefficient Induced B varies with
change of
✓ ship’s course
✓ magnetic latitude
✓ hemisphere

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Correction for PB : How?

• Basic principle: “to cure like with like”.
• To ensure the correction made holds good for all
latitudes and all course.
• PB to be corrected by using F & A permanent
magnets, placed horizontally, such that they
produce a permanent magnetic field at the
compass, exactly equal to and opposite to that of
the ship, nullified and eliminated PB.
• When the ship has a +PB, place permanent
magnets with their red ends ford; -PB will be
their blue ends ford.
1
• Deviation caused by a magnet ∝
𝑑𝑖𝑠𝑡.3
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Correction for PB

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B & C Correctors
B : correctors are in ship´s longitudinal direction ,
magazine on both sides port & starboard with each 10 positions

C : correctors are in ship´s cross direction, only one magazine with 10

position aft of binnacle colum
In total there are 6 bar magnets included to correct about 40°deviation.
The different positions will be used at adjustment as necessary
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Correction for PB

• Use of single magnets is not advisable and better

correction by uniform field can be achieved by
the use of a number of magnets placed at
varying distance from the needle.
• The corrector magnets are not to be placed
nearer than twice their length to enable uniform
magnetic field.

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Correction of PB : Which Course?

• Correction of each coefficient is carried out with

the ship heading on course on which that
coefficient produces maximum deviation.
• Since PB produces maximum deviation when
heading E or W, this correction is carried out with
the ship heading E or W.

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Summary of PB
Change of Effect of change on deviation

Course 𝛅 ∝ sin comp. co.

Hemisphere No effect

Latitude Varies inversely as H ( 𝛅 ∝

𝟏
)
𝐇

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Induced B

• Due to c rod, i.e. the induced magnetism in the

vertical soft iron, ford or abaft of the compass
that influencing horizontal fore and abaft
magnetic field at the compass.

Ship is at
a. Northern
Hemisphere
b. Equator
c. Southern
Hemisphere ?
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Induced B

• The installation of compass at merchant ships is

on a level with the top poles of the masts and
funnel. (∴ ignore the bottom poles)
• As the funnel is the largest vertical S.I. on board
and situated close, abaft the compass, it
produces predominant effect at the compass.

Northern Blue abaft the Resulting:

Hem. compass
-iB EW

Southern Red abaft the Resulting:

Hem. compass
+iB WE

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-iB
• Change of deviation due to change of course

Curve of Deviation
due to -iB

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Effect of course/latitude on deviation due to iB:

• Deviation due to iB varies directly as sin comp.
co. δ ∝ sin comp. co.
• When considering the effect of change of latitude
on deviation due to iB, two changes have to be
considered.
• The vertical S.I. is induced by Z. From equator
to higher latitude, Z is increasing, induced
magnetism of V.S.I. increasing => deviating field
increasing ∴ deviation increasing.
• So, δ ∝ Z

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Effect of latitude/Hemisphere on deviation due

to iB:
• This deviation disappears on the magnetic
equator and reappears in a S latitude with the
opposite sign, because the direction and sign of Z
changes.
• Plus, the deviation will vary inversely as H, just
like in the case of PB deviation.
1
• So, δ ∝
H
• Combining these two changes, the result is:
𝑍
Deviation due to V.S.I. varies as or tan dip.
𝐻

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Effect of course/latitude on deviation due to iB:

• δ ∝ sin comp. co.

• δ∝Z
1
• δ∝
H

iB2
iB1
Dip & Z : +ve Northern Hem.
• Note: Dip & Z : -ve Southern Hem.

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Summary of iB
Change of Effect of change on deviation

Course 𝛅 ∝ sin comp. co.

Hemisphere Northern Hem. Blue abaft the compass

Southern Hem. Red abaft the compass

Latitude Varies inversely as H ( 𝛅 ∝
𝟏
) and
𝐇
Varies as Z (𝛅 ∝ Z)

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PB and iB Corrections

• Need to consider PB and iB separately as they do

not vary together.
• Need to correct the compass for PB and iB
separately, with PB using permanent magnet and
iB using Soft Iron Flinders Bar.

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Flinder´s bar, B2 Corrector

The wooden spacers are to lift the iron cylinders so that

their pole is horizontal to the magnetic sensing element.

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Correction of Induced B (V.S.I. Flinders bar)

• Apply correction principle “ to cure like with like”.
• iB is caused by induced magnetism V.S.I. To correct
it , apply an equal and opposite field produced by
induced magnetism in V.S.I.
• The correction will hold good for all positions,
headings and hemisphere.
• The value of magnetism of V.S.I Flinders bar depend
upon its length.
• Increase Flinders bar length if it is under
compensating.

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Correction of Induced B (V.S.I. Flinders bar)

• Wooden pieces are placed at the bottom of the
brass case so flinders bar effective pole is in level
with the compass card.
• Usually, predominance of V.S.I. is abaft the
compass, so flinders bar is placed forward of the
compass.
• Flinders bar used is large:
• Flinders bar used is very short:

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• Total Coefficient B
• Approaches of Correcting Coefficient B
• PB and iB Calculations

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Total Coefficient B
• The value of total B is found by taking the mean
of the deviation on E and W by compass after
reversing the sign of the deviation on W.
𝛿 𝑜𝑛 𝐸 − 𝛿 𝑜𝑛 𝑊
• Total Coefficient B =
2
• Example: On East heading, the deviation is 10°W
and on West heading, the deviation is 6°W.
Calculate the Coefficient B.
− 10° −(−6°) −4°
• Coefficient B = = = -2°
2 2
• Coefficient B = 2° W
• Total Coefficient B = PB + iB
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Approaches of Correcting Coefficient B

(Not at equator)
• To be able to know individual values of PB and iB
of Coefficient B, the values of total B at two
places with different H and Z values are required.
• In practice, correction is done at one place.

• Find total B: (𝛿 𝑜𝑛 𝐸 − 𝛿 𝑜𝑛 𝑊)/2

One

• Assess iB and adjust Flinders bar

Two

• Remaining PB corrected by horizontal

fore and aft permanent magnet
Three
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Approaches of Correcting Coefficient B

(At equator)
• If the vessel is on the magnetic equator:

• Existing dev. due to PB alone. Correct

with permanent magnet
One

• At other place, check if dev. still

present. If yes, this will due to iB alone
Two

• Correct iB using appropriate amount of

Flinders bar
Three

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Accept the challenges ….

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Ex. 1
• The following deviations were observed on an
uncorrected compass. Calculate the value of
Coefficient B and the deviation due to Coefficient
B on a compass course of 330°.
• Answer: Coef. B = +10°, 5°W
Heading N NE E SE S SW W NW
by
compass
Deviation 6°W 19.5°E 15°E 1.5°W 4°E 12.5°E 5°W 22.5°W

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Ex 2:
• Permanent B is +4° and induced B is -2° at a
position (1), where H = 30 A/m and Z = 40 A/m.
Find the deviation due to these coefficient when
heading 250° © at position (2) where H = 20
A/m and Z = -30 A/m.
• Answer = 7.75° W

PB2

PB1

iB2
iB1
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Ex.3:
• At a position A, on the magnetic equator, H = 30
A/m, the deviation on heading of 090° © was 4°
W. At a position B, where (H = 20 A/m, dip
+62°), the deviation on a heading of 090° © was
7° W. Find the value of PB and iB at the second
position. Further, state how it should be
corrected. (Assume Coefficient A, C, D & E are
fully corrected)

PB2

PB1

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Important Approaches
1. When working problems on splitting of B, C or
Heeling Error, where permanent and induced
components are present, it is best to start work
with the position, where the separate
components are required.
2. This rule does not hold good if one of the
positions given is on the Magnetic Equator. In
that case, we start with the position on the
Magnetic Equator.
3. In problems involving correction of compass,
find PB and iB and PC and iC of ship alone.

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Important Approaches
4. In case the problem requires adjustment or
readjustment of the correctors, we have to find PB,
iB, PC, iC of ship and corrector together.

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Ex. 6

• At a position (1), where H = 30 A/m, dip = 55°,

a total coefficient B of +5° was observed with no
correctors in place. At position (2), where H =
25 A/m, dip = -64° a total coefficient B of +1.5°
was observed. What correction should be made
at the second place with permanent magnets and
what corrections should be made by means of
Flinders Bar at place (2).

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Ex. 7

• At place P (H = 15 A/m; Z = 30 A/m), deviation

on 090 ° © = 12° W. This is allowed to remain
un-corrected. At a place Q ( H = 22 A/m, Z = 15
A/m), deviation on 090° © was 4° W. The
compass was still not corrected. Find the
deviation at a place R (H = 20 A/m, Z = -25 A/m,
when heading 090° ©.

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Exercises:

• Pages 92 (Ship’s Magnetic Compass by Capt. T.K.

Joseph):
✓ Question No. 15, 16, 18, 20, 21, 24, 25

• Page 102 (Ship Magnetism and the Magnetic

Compass by F.G. Merrifield)
✓ Question No. 1 - 8

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Page 102 (Ship Magnetism and the Magnetic

Compass by F.G. Merrifield) PB & iB exercises

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Page 102 (Ship Magnetism and the Magnetic

Compass by F.G. Merrifield) PB & iB exercises

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• Splitting B: PB and iB Calculations (no correctors

in place)
– Info given: One of the place is at equator
– Info given: None of the places from equator
• Calculate PB and iB at the place of interest
• Approach to do the correction

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• Splitting B: PB and iB Calculations

– Adjustment of correctors
• In case the problem requires adjustment or
readjustment of the correctors, we have to find
PB , iB, of ship and corrector together

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Over or Under Correcting ?

• At place (1) … is corrected by fore and aft magnets,
red end forward, leaving no deviation on any course.
… Then, at place (2) PB (ship) and magnet = +3°.
Over or under correcting at place (1)?
• At place (1) where H = 20 A/m, Z = 40 A/m zero
deviation obtained with Flinders Bar forward of the
compass …Then, at place (2) where H = 30 A/m, Z =
20 A/m, iB and F/B = + 3°. Over or under correcting
at place (1)?
• At place (1) where H = 20 A/m, Z = 40 A/m zero
deviation obtained with Flinders Bar forward of the
compass …Then, at place (2) where H = 30 A/m, Z =
- 20 A/m, iB and F/B = + 2°. Over or under correcting
at place (1)?
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Ex. 10

• At place (1), where H = 20 A/m, Z = 40 A/m, a

ship’s compass is corrected and zero deviation
obtained with Flinders Bar forward of the
compass and fore and aft magnets inserted in the
binnacle with red ends forward. At place (2),
where H = 30 A/m, Z = 20 A/m, a coefficient B of
+ 2.5° was observed. How should the correctors
be readjusted at the second place?
• Also state what would be the value of coefficient
B at place (3), where H = 20 A/m, Z = -25 A/m,
if the correctors were not adjusted.

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Ex. 11
• A vessel’s compass was adjusted off River Clyde
(H=12 A/m, dip = 70°), the fore and aft magnets
being placed with their red ends aft, and the
Flinders Bar situated ford of the compass. On
completion of adjustment, no deviation was
observed on any heading. Subsequently when
off River Plate (H = 28 A/m, dip = -30°), the
deviation on East was observed to be 5° E and on
West it was 3° W. How should the correctors be
readjusted to effect proper compensation of
coefficient B at River Plate.

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Page 102 (Ship Magnetism and the Magnetic

Compass by F.G. Merrifield) Readjustment of PB & iB

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MCQ questions

• The ship has corrector Fore and Aft permanent

magnet inserted in binnacle with red end forward
and Flinders bar forward with zero deviation
observed at H = 0.2 oe and Z = - 0.5 oe. Later
at H = 0.9 oe and Z = 0, it was found the
Coefficient B is +4°. How should we adjust the
Flinders bar when ship head East?

• a. increase the length of Flinders bar

• b. not require to adjust the Flinders bar
• c. decrease the length of Flinders bar
• d. shift the Flinders bar aft of compass
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Exercises:

• Pages 92 (Ship’s Magnetic Compass by Capt. T.K.

Joseph):
✓ Question No. 15, 16, 18, 20, 21, 24, 25
✓ Question No. 22, 23, 26, 33, 34

• Page 102 (Ship Magnetism and the Magnetic

Compass by F.G. Merrifield)
✓ Question No. 1 – 8
✓ Question No. 11, 12, 15, 16 25%
in LA 2

B Permanent & Induced Magnetism and Coefficients A1MC Part 2 / Gyro & Magnetism / Jan. 2023/ / CKM 94
[Open]
Shaping Maritime Leaders Of The Future

Exercises:

• Pages 92 (Ship’s Magnetic Compass by Capt. T.K.

Joseph):
✓ Question No. 22, 23, 26, 33, 34

• Page 102 (Ship Magnetism and the Magnetic

Compass by F.G. Merrifield)
✓ Question No. 11, 12, 15, 16

B Permanent & Induced Magnetism and Coefficients A1MC Part 2 / Gyro & Magnetism / Jan. 2023/ / CKM 95