International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 5

Number 3

September 2011

303

1 INTRODUCTION.

The compensation of deviation of magnetic compass

is usually carried out on the special aquatory

equipped by leading line. The primary compensation

of deviation is executed at an output of a vessel from

building shipyard. All factors of deviation is deter-

mined and compensated in this case. The determina-

tion of residual deviation and calculation of the table

is made after compensation of deviation. Such pro-

cedure can demand some hours of time. At annual

deviation's works the compensation of the most in-

constant factors of deviations B and C is made only.

These factors on new building vessels can reach val-

ues 9

0

÷ 12

0

. They are the most instable in storm

conditions, at ice navigation, at knock about a quay

on mooring, etc. As a rule, the table of deviation

guarantees high reliability of the data up to the first

heavy storm.

The most often used method for compensation of

factors B and C is the method of Airy, which is car-

ried out at 4 main magnetic courses. Accuracy of

compensation depends on accuracy of supervision,

on accuracy of operations by magnets - compensa-

tors, on hysteresis effects in the body of the vessel at

maneuvering by means of course. After compensa-

tion of deviation the definition of residual deviation

and calculation of the table is carried out.

Especially many problems are delivered at devia-

tions maneuvers to large-capacity ships such as su-

pertanker, big passenger ship, the big military ships

and submarines etc.

Every time even the minimal program of devia-

tion's work is connected to loss of operational time

and an additional overhead charge. The problem of

navigational safety is included in this case into the

contradiction with economic problems. The radical

decision of this question would be possible at pres-

ence of a method for destruction of deviation with-

out derivation of a vessel from the basic work. Such

statement of a question is possible only at presence

of a method for destruction of deviation on one any

course. The deviation's works at one course would

allow as considerably to exclude influence of hyste-

resis effects on accuracy of deviation's works. Thus,

the way of destruction of deviation on one any

course is the most effective way to liquidate unpro-

ductive expenses of time.

2 THE DEVIATION OF MAGNETIC COMPASS

AT CONTEMPORARY CONDITION.

At contemporary ships of symmetric design the con-

stant factor of deviation A and the factor of devia-

tion E depending from asymmetrical soft steel of the

ship are in limits 0,2

0

÷ 0,6

0

and are characterized by

extremely high stability [2]. The factor of deviation

D after compensation by the help of without induc-

tion’s sheet of a soft iron [1] does not exceed 0,25

0

and as differs very high stability.

It can to tell, that the values of these three factors

of deviation are situated at the same level as accu-

racy of supervision of courses and bearing. Howev-

Compensation of Magnetic Compass Deviation

at Single Any Course

E.M. Lushnikov

Szczecin Maritime Academy, Poland

ABSTRACT: The new method for compensation of deviation of magnetic compass at one any course is of-

fered. The theoretical substantiation of a method is given, the analysis of accuracy is made, corresponding

conclusions and recommendations are made. It allows to carry out a deviation’s works without interruption

from voyage.

304

er, according to rigid algorithm of Airy, these factors

without any need are determined and recalculated

anew for use in the new table of deviation [3].

All this operations can be qualified, as unproduc-

tive works with loss of time for measurements, pro-

cessing and calculations.

Exact expression for deviation of a magnetic

compass

δ

is implicit function from compass course

KK

and enters the name as:

)2()2(cos

δδδδ

++++++= KKECosKKDSinCCosKKBSinKKASin

(1)

where:

λλλλλ

2

;

2

;;;

2

bd

E

ea

D

H

fZQ

C

H

cZP

B

bd

A

+

=

+

=

+

=

+

=

−

=

thus:

H

- a horizontal component of force of terrestrial

magnetism;

Z

- a vertical component of force of terrestrial mag-

netism;

P

,

Q

- longitudinal and cross-section magnetic

forces from according hard ship's steel;

f,e,d,c,b,a

- parameters of Poisson, describing

constructions from soft ship's steel;

2

1

ea +

+=

λ

- factor of shielding of a magnetic

compass.

Parameters of Poisson a, b, c, d, e, f and as factor

λ, are functions of the sizes and forms of ship's soft

steel, his remoteness from a compass and magnetic

characteristics of a case material. All these charac-

teristics are constant constructive parameters of a

vessel, than high stability of factors A, D, E explains.

Taking into consideration this circumstance, fac-

tors of deviation A, D, E usually consider constant

and at performance of annual procedural works these

factors do not adjust. In this case the problem of an-

nual deviation's works is reduced to indemnification

of factors B and C and to calculation of the new ta-

ble of deviation. Such operations at annual devia-

tion's works are the established practice already for a

long time.

The last ministry's instruction of Russia “Rec-

ommendations to navigation's service” of 1989 year

do not define the time of actuality for a table of de-

viation. Only the level of accuracy according to re-

quirements of IMO is formulated at this instruction.

At the same time “Recommendations to navigation's

service for a ships of a fishing fleet” contains record

about the maximal 1 year interval of actuality of the

deviation’s table. These departmental distinctions

emphasize complexity and a urgency of this prob-

lem.

Progress in development of satellite systems of

navigation and gyrocompasses has led to that mag-

netic compasses on sea vessels basically carry out

reserving and monitoring function. Unproductive

expenses of time for deviation's works stimulates a

negative attitude of ship-owners and captains of

ships.

Modern market conditions demand optimization

of production and the proved time expenses. It is

natural, that such optimization should be made in

view of safety of navigation.

3 PRECONDITIONS TO DESTRUCTION OF

DEVIATION WITHOUT INTERRUPTION OF

VOYAGE.

If the factors of deviation A, D, E are small and con-

stant, there is no need to spend time for determina-

tion of these factors anew. It is necessary to take into

account their values from the previous table.

The same logic can be continued further. Factors

B and C at carrying out of deviation's work can be

not destroyed up to zero, and to restore their former

residual tabulated values [4].

Such step gives the basis to consider, that after

restoration of factors B and C all factors of deviation

correspond(meet) to values of the old table of devia-

tion and to expect the new table there is no necessi-

ty.

Validity of the former table in this case can be

prolonged for one year. All deviation's works will be

reduced in this case only to restoration of factors B

and C without expenses of time for 8 courses for de-

termination and calculation of all five factors. Also

there is not necessity for calculation of new devia-

tion's table . Such actualization of the former table of

deviation can be made during 4÷5 years.

However the determination of factors B and C for

the purpose of their return to former tabulated values

demands not less than two equations, that is, at least,

two courses. Otherwise it means, that compensation

of two factors B and C at one course is impossible.

It is possible to notice, however, that in navi-

gating practice exists essentially various two ways of

determination of deviation. The first way bases on

use of navigating measurements. The second way

bases on physical measurements of magnetic forces

with the subsequent calculation on this basis of de-

viation's factors.

Simultaneous use of these two essentially various

methods allows to receive the missing information

for the determination of a task in view on destruction

of two factors deviations B and C at one course.

305

4 DETERMINATION OF FACTORS B AND C

AT ONE ANY COURSE.

The set of navigating ways and means for determi-

nation of deviation of a magnetic compass on an any

course of a vessel is known. For this purpose it is

possible to use a terrestrial leading line, celestial ob-

ject, remote reference points, systems AIS and gyro-

compasses. The deviation of a magnetic compass

δ

determined by navigating way can be written down

as implicit function of compass course КК as ex-

pression 1.

Taking into account, that in terms of 1 set sizes

are deviation

δ

(measured by navigating way),

compass course КК, and as factors A, D and E (from

the previous table), the expressi0n 1 can be copied to

more compact kind:

1

cossin ∆=+ KKCKKВ

(2)

where:

)2cos()2sin(cossin

1

δδδδ

+−+−−=∆ KKEKKDA

(3)

Thus, the equation 2 connects two unknown fac-

tors of deviation B and C by means of measurement

of deviation

δ

.

As the second missing equation can be used equa-

tion of total ship's magnetically force of compass H

K

. It is known [2], that the value of measured force H

K

looks like:

)]2sin()2cos(sincossin[cos

δδδδλ

+−++−++= KKEKKDKKCKKBAHH

K

(4)

Expression 4 can be copied to more compact kind:

2

sincos ∆=− KKCKKB

(5)

where

)2sin()2cos(sincos

2

δδδδ

λ

+++−−−=∆ KKEKKDA

H

H

k

(6)

Thus, the system of two equations 2 and 5 at two

unknown factors B and C is received:

2

1

sincos

cossin

∆=−

∆=+

KKCKKВ

KKCKKВ

(7)

The solution of this system of the equations

gives:

KKKKC

KKKKB

sincos

cossin

21

21

∆−∆=

∆+∆=

(8)

At essential changes of these factors they must be

restoring by means of regulators B and C of compass

before former table's values. For restoration of for-

mer values of factors B and C the value of correction

∆B and ∆C is calculated under formulas:

CCC

BBB

Т

Т

−=∆

−=∆

(9)

where B

T

and

C

T

- values of factors B and C from

the table of deviation.

If factors of correction ∆B and ∆C are positive,

readout of each regulator increases before the corre-

sponding value and on the contrary.

Thus, joint application of navigating and physical

measurements allows to solve a problem which all

time was considered insoluble.

Both factors B and C depend from correction a

component

∆

1

and

∆

2

. Navigating component

∆

1

, ap-

parently from expression 4, depends on accuracy of

definition of deviation δ and from accuracy of tabu-

lated factors A, D, E. Correction component

∆

2

, ap-

parently from expression 7, demands knowledge of

exact values of resulting compass force

H

k

, a hori-

zontal component of terrestrial magnetism H, factor

λ, and as deviation δ and factors A, D, E. Except for

accuracy of the navigating data the exact data of

physical measurements here are required. Accuracy

of attitude

H

k

/H can be provided with use of the

same deflector for measurements on coast and on a

vessel.

Accuracy of factor λ in usual circumstances never

represented special interest. In this case of accuracy

of knowledge of this factor are demanded much.

The situation is facilitated by that it needs to be

determined accuracy once as his stability as is ex-

tremely high as stability of factors A, D, E.

Believing, that deviations are characterized by ra-

ther small angles, that usually corresponds to the va-

lidity, both settlement components

∆

1

and

∆

2

at high

accuracy can be simplified to a kind:

KKEKKD

H

H

KKEKKDA

k

2sin2cos1

2cos2sin

2

1

+−−=∆

−−−=∆

λ

δ

(10)

In view of these simplifications the correction ∆B and ∆C

will become:

KKD

H

H

KKEAC

KKD

H

H

KKEAВ

k

k

sin1cos)(

cos1sin)(

+−−−−=∆

−−++−=∆

λ

δ

λ

δ

(11)

Final record of factor ∆B and ∆C can be submitted as:

KKV

H

H

KKUC

KKN

H

H

KKMB

k

k

sincos)(

cossin)(

−−−=∆

−+−=∆

λ

δ

λ

δ

(12)

where:

306

.1

;

;1

;

DV

EAU

DN

EAM

−=

+=

+=

−=

Factors M, N, U, V it is necessary to calculate at

once after full indemnification of deviation and cal-

culation of the table of residual deviation. Formulas

12 and value of factors M, N, U, V are used at the

further annual procedural works on compensation of

deviations factors B and C.

Substitution of these numerical values in before-

hand prepared formulas allows to calculate quickly

values of correction's factors ∆B and ∆C and to enter

them with the help of corresponding regulators.

Application of such method directly at a cargo

mooring, as a rule, is not expedient owing to pres-

ence on a mooring and in designs of a mooring of

the big iron weights, and as positions of ship iron not

in a marching way.

The method is the most expedient for applying at

an output of a vessel from port when it is situated on

leading line. Such operation can be executed by de-

viator so as ship's navigator. For performance of

works it is required no more than 10 minutes. In this

case disappears necessity of special aquatory and

additional time for deviation's work.

All this process can be named as a process of res-

toration or process of actualization of the former ta-

ble of deviation. The most important in all it is that

this actualization can be made on one any course

without interruption of voyage.

5 THE ANALYSIS OF ACCURACY OF A

METHOD

It is obvious, that accuracy of restoration of the table

of deviation depends on accuracy of determination

of proof values ∆B and ∆C. They, in turn, depend on

accuracy of measurement of deviation δ, from accu-

racy of the information about tensions of magnetic

fields

H

K

and H, and as from accuracy of factor λ.

Regular error of actualization of deviation's

table. For an estimation of a regular error of restora-

tion of the table of deviation it is necessary to exe-

cute differentiation of expressions (11) therefore it

turns out:

KK

H

dHHdHHHdH

KKdCd

KK

H

dHHdHHHdH

KKdBd

kkk

kkk

sincos

cossin

22

22

⋅

−−

−⋅=∆

⋅

−−

+⋅=∆

λ

λλλ

δ

λ

λλλ

δ

(13)

Believing, that measurement of force H on coast

and force

H

K

on a vessel was made by means of the

same deflector and by the same observatory these

measurements can be qualify as the same accuracy.

k

dHdH =

In this case expression (13) corresponds to a kind:

KK

H

dH

H

dHHH

KKdCd

KK

H

d

H

H

dHHH

KKdBd

kk

kk

sin

)(

cos

cos

)(

sin

22

22

⋅

−

−

−⋅=∆

⋅

−

−

+=∆

λ

λ

λ

δ

λ

λ

λ

δ

(14)

Apparently from expression (14), accuracy of res-

toration of the table of deviation depends on accura-

cy of a navigating component of measurements d δ,

a technical component of measurements dH, and al-

so an information component d λ.

For estimating calculations it is possible to count

that Н≈H

K

, λ≈1. In view of told, for an estimation of

accuracy as a first approximation expression (14)

can be simplified to a kind:

KKdKKdCd

KKdKKdBd

sincos

cossin

⋅+⋅=∆

−⋅=∆

λδ

λδ

(15)

From this expression it is visible, that the main

factors of regular errors are accuracy of navigating

supervision and accuracy of knowledge of factor λ.

The regular error of determination of deviation at

leading line is extremely small. In this connection

the basic role belongs to a component depending on

factor λ. For maintenance of accuracy at a level 0,5

0

relative error of factor λ should not exceed 0,8 %.

Such requirement is high enough, but quite real. De-

termination of factor λ is carried out by measure-

ment of compass force

H

k

on four main and four in-

termediate course's with the subsequent calculation

under the formula:

H

H

k

8

8

1

∑

=

λ

The requirements of Register to accuracy of com-

pensation of deviation is δ≤ 3

0

. The relative method-

ical error of determination of factor λ will be not

worse, than 0,12 % . Such accuracy is more than suf-

ficient.

Exact value of factor λ should be determined at

descent of a vessel to water. The information on fac-

tors A, D, E and as about factor λ it should be kept

carefully on a vessel before the next complex check

and compensation of deviation. At capital recon-

struction of a vessel, replacement of the engine these

factors should be determined anew.

Casual errors of actualization of the table of

deviation. Influence of casual errors of supervision

and measurements is estimated by the help of stand-

ard error under the formula:

307

2

2

2

2

2

2

2

1

...

21 n

X

n

XXx

m

x

f

m

x

f

m

x

f

m ⋅

∂

∂

++⋅

∂

∂

+⋅

∂

∂

=

Using as function f expressions (11), we shall re-

ceive standard errors of the proof data ΔB and ΔC

as:

KK

H

mH

H

mH

H

m

KKmm

KK

H

mH

H

mH

H

m

KKmm

kHkk

H

C

kHkk

H

B

2

24

22

42

22

22

2

22

2

24

22

42

22

22

2

22

sincos

cossin

+++=

+++=

∆

∆

λλλ

λλλ

λ

δ

λ

δ

(16)

For estimated calculations it is possible to accept

;1; ≈≈

λ

HH

k

. At such assumptions of expression

(16) become simpler to a kind:

( )

( )

KKm

H

m

H

m

KKmm

KKm

H

m

H

m

KKmm

H

k

k

H

C

H

k

k

H

B

2

2

2

2

22

2

2

2

2

22

sincos

cossin

+

+

+=

+

+

+=

∆

∆

λδ

λδ

(17)

From these expressions it is visible, that casual

errors of compensation of factors B and C depend on

relative errors of all three factors – navigating, tech-

nical and information.

At standard error of deviation at the level

0

5,0=

δ

m

, at relative accuracy of magnetic forces at

the level of 1 % and at relative accuracy of factor λ

also at the level of 1 % a standard errors ΔB and ΔC

is not lower 1

0

. Schedule of standard errors

B

m

∆

and

C

m

∆

for such initial data is submitted in figure 1.

Fig. 1 The standard errors and depending from compass course

at

B

m

∆

C

m

∆

0

5,0=

δ

m

and

01,0===

λ

λ

m

H

m

H

m

k

H

H

k

From figure it is visible, that casual errors of res-

toration of factors B and C are in limits

00

0,15,0 ÷

.

The additional errors from instability of factors A,

D and E are small, and stability of them is very high.

Such accuracy of actualization of deviation's table is

quite sufficient.

Not always the innovation gives a prize without

by-effects and additional expenses. This case just

does not entail any additional questions and prob-

lems.

6 THE CONCLUSION

1 The offered method for compensation of devia-

tion of a magnetic compass on one any course of

a vessel is essentially new method allowing to re-

duce a routine work of a vessel, connected with

financial expenses.

2 The method differs exclusive simplicity. It can be

applied by navigators in conditions of voyage.

3 For introduction of a method in practice of navi-

gation it should find reflection in corresponding

program of educational institutions.

THE LITERATURE

1. V.V. Voronov, N.N. Grigoriev., A.V. Jalovenko. Magneti-

cally compass. Sankt-Petersburg. “ALMOR”, 2004.

2. Kozuchov V.P., Voronov V.V, Grigoriev N.N. Magnetically

compass. Moskov.: Transport, 1981.

3. E.M. Lushnikov. Compensation of magnetic compass devia-

tion at contemporary conditions. International scientific

conference «Innovation in scientific and education –2008»

Kaliningrad, KGTU, 2008.

4. E.M. Lushnikov. The problem of magnetic compass devia-

tion at contemporary condition. International Navigational

Symposium “TRANSNAV 09”. Gdynia, Maritime. Univer-

sity 2009. p.219-224.