SOURCE: MAGNETIC COMPASS DEVIATION AND CORRECTION BY **CAPT. A.N. COCKROFT**

Welcome, folks!!!

It’s been more than 2 months since my last article that’s because I was focused on other stuff. We all are familiar with magnetic compasses onboard, but we rarely use it because gyro can provide more accurate directions. And you can make a magnetic compass at home just take a needle and rub it against a magnet. Then take a Thermo coal piece and put it in a bowl of water and needle on top of it. The needle will point towards magnetic north. But can we do that on a ship? No because of ships magnetism the needle won’t show the magnetic north but point towards a resultant of the magnetic field of earth and ship. So to make a magnetic compass work we should have an idea of ships magnetism. Let’s discuss that

The aim of this post is that so that you can appreciate the beauty of research done in the field of ship’s magnetic compass which we never cared about.

## SHIPS MAGNETISM

There are two categories of magnetic materials first is magnetically hard and another one is magnetically soft. Magnetically hard are those which if comes under influence of magnetic field become permanent magnets and other ones are those which when comes under magnetic field become magnets and loose their magnetism as soon as the magnetic field is removed. **The ship is primarily made up of mild steel which is neither magnetically hard nor magnetically soft but a mixture of both**. So there are two components to the magnetic field of a ship first is permanent magnetism other one is temporary magnetism. Just to give you an idea of how complex ships magnetic field is let me tell you factors affecting it.

- Type of material used
- Alignment of ship frames(plates) to earth’s magnetic field while building the ship which controls how the permanent magnetic field of ship behaves
- Magnetic field induced due to welding, hammering, and vibration in ships hull
- Magnetism of plates when they arrive building site
- Magnetic anomaly at building site
- Weather conditions i.e. in case lightning strikes the ship it changes ships magnetism alters considerably.

## PERMANENT MAGNETISM

As building process takes some time the earth magnetic field induces permanent magnetism in the ship. It mainly depends upon the orientation of ship when it’s built with respect to the magnetic field of earth at that place. The ship permanent magnetism can be visualized as a bar magnet with north and south pole and. The picture below will clear the matter further

Now the question is that how does this permanent magnetism affect the magnetic compass needle. Magnetic compass needle can be thought as a small piece of the permanent magnet which have only 2 degrees of freedom i.e. along x-axis and y-axis (in a plane of compass card).

**If a ship is built in northern hemisphere its blue pole(south) will be the upward side of structure irrespective of ships heading. **Because earth acts like a bar magnet and magnetic field line will start from north pole of earth and terminate at south pole so if the ship is built in northern hemisphere the vertical component of magnetic field lines will cut the hull from downward direction making the bottom of hull a north pole(red) and upper part will be south pole(blue).We divide this into two components horizontal and vertical. The vertical component will still be divided into two components one is in the plane of and other is directly below compass card. The component directly below it will have no effect on compass needle(when the ship is upright) as it is only allowed to move in the plane of compass card. The image below will clear the matter further.

Please note that the horizontal component shown in the figure above need not to be at the center line of the ship and itself have to be divided into components(x and y). But if it happens to be at centerline in a particular case then the compass will show no deviation when on northerly or southerly course and will show a westerly deviation on the westerly course and easterly deviation on the easterly course.

The image above only discuss the vertical component of ships permanent magnetism but the horizontal component will have a similar effect. The component directly below the compass card causes the **heeling** **error when the ship is not upright.** So the conclusion of the whole discussion is that “*The effect of ship permanent magnetism on deviation is such that, while the ship is upright the deviation appears to be caused by a horizontal permanently magnetized material lying in the horizontal plane through the compass.*”

## SHIP INDUCED MAGNETISM (TEMP. MAGNETISM)

Lets discuss the effect of ships temporary magnetism on the compass needle. Ships temporary magnetism is that which changes as soon as the ships orientation changes with respect to earth magnetic field i.e. as soon as the ships heading change. To understand its effect we divide it into nine components. Pay attention here it may be a little bit confusing. Ships induced magnetism is divided into 3 components. Fore and aft, athwartship and vertical. And each of these can be divided into 3 components as before making it a nine components game. Let’s understand it from some other dimension the earth field can be divided into 3 components fore and aft, athwartship and vertical. So for simplicity assume these 3 different components will create 3 different magnets. One in fore and aft direction, 2^{nd} is in athwartship direction and the 3^{rd} one in the vertical direction. Now each of these magnets will have the magnetic field at the position of the compass which can be further divided into 3 components. So it makes it total 9 components. Basically, these 9 components are nothing but force acting at compass needle. So to visualize is in a better a let’s assume 9 soft iron rods of no thickness and infinite length (so that they can only be magnetized through their lengths and only one pole effect the at one time). Here comes a figure for what I just said but believe me it won’t help to clarify the matter further but instead it is going to make it more confusing. But I will explain it in a bit.

The picture was taken from the book of A.N. Cockroft MAGNETIC COMPASS DEVIATION AND CORRECTION.

Let’s see here first of all each rod is named as a,b,c,d,e,f,g,h,k respectively.(why i and j are omitted?).Now a is fore and aft component of fore and aft component of a ship induced the magnetic field and b is athwartship component of fore and aft component of the induced magnetic field and the list goes on like this. Now these rods are also given a sign +ve or –ve. That is to fit them in the coordinate system. Forward, starboard and down directions are considered +ve and aft, port, and upward direction are considered –ve. To understand how the signs work read carefully. Each rod has 2 ends one is near end and other is far end to the compass position. First, we need to know which rod it says we have a –f rod, now by name we know that it is a vertical component of athwart ship component. So it must be a vertical rod. First, name the near end of the rod as per the main component which is athwartship it means rod’s near end will be -ve if it is in the port of the ship and +ve if it is on stbd side of the ship. Now name the far end according to the minor component i.e. vertical component that means far end will be positive if it is downward and it will be negative if it is upward of compass positions. Now the product of far end and near end signs will give the actual sign of the rod.

So let’s try drawing –f rod.

## PRACTICAL APPLICATION OF RODS

Let’s look at a practical application of these rods. Suppose there is a soft iron derrick(AB) at the centerline of the ship and slightly below the compass deck. As you can see from image derrick is a slanting structure and its magnetism can be disintegrated into to two magnets one horizontal(BD)and other vertical(BE). Now the horizontal component will act on forward and downward direction. So to study its effect on compass position we can use two horizontal rods instead one in the plane of the compass and one directly below it. These rods will have the same effect on the compass as the component BD had. Of course from the table, you can find these rods are +a and +g rods. Similarly, for vertical component BE we can use two rods +c and +k. So the whole effect of the derrick can be boiled down to these 4 rods which make it easier to understand and allows us to make a mathematical modal which we will discuss now.

## THE MATHEMATICAL MODAL

The horizontal component of the magnetic field of earth say H at the position of the compass can be defined into 3 components X- fore and aft, Y- athwart ship, Z- vertical. The fore and aft rods a,d,g will derive their force from X component of the induction of earth’s magnetic field, therefore, the force can be considered as aX, dX, and gX where a,d and g are constant quantities depending upon magnetic quality of soft iron used for building the ship. Similar arguments can be given for other rods also. Also, the magnetic field due to the permanent magnetism of ship in fore and aft, athwartship and vertical direction can be represented by P, Q, and R respectively. The total magnetic field at the compass position say H’ can be defined as 3 components X’, Y’and Z’.

So the total magnetic force in fore and aft dirn at compass position can be written down as.

X’= (x component of earth’s magnetic field)+(fore and aft component of ship’s induced magnetism)+(x component of ship’s permanent magnetism)

X’= X+ aX + bY + cZ + P …… (1)

Similarly

Y’= Y + dX + eY + fZ + Q …….(2)

Z’= Z + gX + hY + kZ + R …….(3)

These are the fundamental equation on which whole theory is based. Please note that the “”+” sign here is just indicative that quantities are additive for any specific these can be negative.

Now lets consider for a moment X and Y components of earth’s horizontal force H. Let the magnetic course be α. X is acting toward bow so its positive and Y toward ports so conventionally negative.

From the figure it is clear that

X = H.cosα

Y= -H.sinα

Similar reasoning can be given for X’ and Y’.

X’= H.cosβ

Y’=H.sinβ

Where β is the compass course.

Note that here α-β = γ **which is the deviation of the magnetic compass.** Also, note that Z/H =tan θ. Where θ is the angle of Dip of earth magnetic field.

Now substituting the values of X, Y, X’ and Y’ and then dividing both sides by H we will get

H’= total magnetic field of the ship.

H= horizontal component of earth’s magnetic field

a,b,c,d,e,f = constants to indicate magnetic nature of material used in building ship(soft iron)

P, Q = constant to indicate permanent nature of ship’s magnetism(hard iron)

**Equation 6 and 7 gives the total magnetic force in direction of magnetic east and magnetic north why? Let’s see.**

In above figure, H is magnetic north and AB is magnetic east and γ is deviation so H’cosγ =OA which is in magnetic north dirn. Similarly H’sinγ = AB which is in magnetic east dirn.

It is worth noting that mean of all angles of sine and cosine from 0 to 360 degree is zero so the average of total magnetic force in east is

This is the equation which gives the deviation explicitly in terms of magnetic course if the value of exact coefficients is known. Please also note that λ is the mean value of total directive force towards north for all headings. Though the expression above is quite complicated but our aim here is to reduce the value of deviation. And that depend upon magnetic course α and we cant do anything about that we have to apply error manually for that but the others factor affecting it such that exact coefficient can be reduced with the help of corrector so it will be useful to know the practical significance of these expressions.

λ : the value of lambda is usually given by the arrangement of –a and –e rods in which –e is more effective as it deals with athwartship component of magnetic field whose induced poles will be nearer than the compass position than longitudinal poles

D bar : This is mainly caused by –e rod and as its poles will be near so we soft iron corrector for reducing the value of d bar it also increases the value of λ because they increase the effect of +e rods.

A bar and E bar : A bar is the coefficient of constant part of deviation and E bar is the constant of quadrantal deviation. Why? I literally don’t know!!! Sorry guys. But it is clear that if soft iron of ship is symmetrically distributed along a vertical plane passing through fore and aft line of the value of both d and b rod is zero and so that of A bar and E bar. So the position of the magnetic compass is chosen such that the value of A bar and E bar are minimum.

B bar and C bar : These are called coefficient of semicircular deviation and from the equation 4 and 5 it can be seen that the mean value magnetic force toward bow is λHCbar and mean of total magnetic force towards starboard is λHBbar.

**The main disadvantage of equation 10 is that it gives the deviation in terms of magnetic course and we require in terms of compass course.**

## DEVIATION IN TERMS OF COMPASS COURSE

From the equation 10, we can rearrange the terms to get the new equation 11 which we write as this

FUN FACTS: I read this book when I was doing GMDSS and I really appreciate his efforts.But unfortunately, this book is available on amazon for 6000 rupees. And I can’t tell you that this book is available for free on the internet because this will encourage piracy. I tried down to boil down the whole book in few page. How successfully it went. You be the judge of that. Some important topics are missing from it like heeling and pitching error and how to correct the magnetic compass which I can not include to keep it short. if you want to read that i will write about it and make a part 2 of it.