Notes on Magnetism and Formulas

Hard Iron Deviation

• 1 A ship built in North /South direction will have only PB.

• 2 A ship built in East/West direction will have only PC.

• 3 The heading $180^\circ$ away from the direction in which it was built is called the direction of Natural Zero

• 4 The heading in which the ship was built and natural zero course are called Neutral Courses

• 5 No deviation on Neutral Courses.

• 6 Maximum deviation $90^\circ$ away from it ( Westerly for left side and Easterly for right side).

• 7 Maximum Hard Iron Deviation $\sqrt( PB^2+PC^2)$.

• 8 Angle $\theta$ between meridian and Neutral course

  $$\tan \theta = \frac{PC}{PB}$$

• 9 Hard Iron deviation in any heading = maximum deviation due to hard iron + angle between ship’s head and natural zero

• 10 Hard Iron deviation (\ \propto \frac{1}{H}).

• 11 The angle of ship’s head is measured clockwise from ship’s Natural Zero.

Heeling Error

• 1 Heeling error consists of two parts Permanent Heeling Error and Induced heeling error .$HE = PHE +IHE$

• 2 $PHE \propto cos (compass course) \propto i(angle of heel) \propto \frac{1}{H}$

• 3 IHE is composed of-

    flowchart TD
    A[ Induced Heeling Error] 
    A -->|One| D['k' rod heeling error]
    A -->|Two| E['e' rod heeling error]
    A -->|Three|F['g' rod heeling error ]
    A -->| Four|G['c' rod heeling error]
  

k rod heeling error

*1 $IHE_k \propto cos (compass course) \propto i ( angle of heel) \propto Z \propto \frac {1}{H}$ *2 If Directive force is large then $IHE_k$ is small.

e rod heeling error

*1

g rod heeling error

*1

No effect of Latitude change.

c rod heeling error

*1

Heeling error correction

$\lambda_1$ is the ratio between the mean directive force at the compass position , towards magnetic North and the directive force ashore, before the spheres are placed to correct the Coefficient D.

$\lambda_2$ is the same ratio after coefficient D has been correctly compensated by the spheres.It is also called the Ship’s Multiplier.

always.

The soft iron spheres always increase the mean directive force.

$\mu$ is the ratio between the mean vertical force at the compass position and the vertical force ashore before correction of heeling error.

$\mu_2$ is the ratio between the mean vertical force at the compass position and the vertical force ashore after the correction of the heeling error.

The target of heeling error correction $\lambda_2 = \mu_2$

Vertical force instrument

The heeling error correction done on Easterly / Westerly heading.

Directive Force

Directive force is maximum when heading towards the Blue Pole.

Presuming Ship to be in Northern Hemisphere with +P,+Q,+a rod +c rod and +e rod.

Directive force on Northerly heading:

This means H = Horizontal Field of Earth at the Latitude. P = Induction force in the fore and aft direction. aH = a rod as induced by Horizontal field of Earth. cZ = c rod induced by Vertical field. on East :

on South: H-P+aH-cZ on west : H+Q+eH.

Horizontal Vibrating Needle

Where H = Horizontal field of Earth. T = time period of vibrations of the horizontal needle. n = number of vibrations of the needle counted in a fixed time.

Mean DF on board = Mean of $H_1 cos \delta$ on any number of equidistant magnetic headings.$delta$ = deviations.

Where $H_E$ = Horizontal component of Earth’s Field , ashore. $H_1$= Horizontal component , on board , in the direction of the compass North.