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Magnetic Declination Formula

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  • Last Updated : 26 May, 2022
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The angle on the level plane between magnetic and true north is known as magnetic declination. When the magnetic north is east of the true north, the declination is positive, and when it is west of the true north, the declination is negative. Let’s have a look at the magnetic declination formula.

What is Magnetic Declination?

On the horizontal plane, magnetic declination is defined as the angle formed between magnetic north and true north. 

It is not constant and changes with the earth’s position and time. We refer to magnetic declination as a magnetic variation and use the Greek letter δ as a symbol. In addition, the declination is positive when the magnetic north is east of true north and negative when the magnetic north is west of true north.

Isogonic lines are some of the other terminologies we employ. When the lines along the declination remain constant, this is called a constant declination. Then there are agonic lines, which are zero-length lines that run parallel to the declination.

Types of North

The north is divided into three categories:

  • True North: True north is the direction along the globe’s surface that leads to the true North Pole, also known as the topographical North Pole. It’s also known as geodetic north, and it’s distinct from magnetic north, which is the direction shown by a compass, and grid north, which is the journey taken via network lines to the north.
  • Grid North: On a guide projection, grid north is the direction along the framework lines that points northwards. The divergence of the grid north from true north is extremely small, hence this phrase is used for routes.
  • Magnetic North: Because of the earth’s magnetic field, the compass needle points north. Because the world’s magnetic poles are not stable in relation to its pivot, the difference between true north and magnetic north fluctuates from place to place.

Magnetic Dip

The magnetic dip is defined as the horizontal edge of the world’s magnetic field lines. Georg Hartmann discovered it in 1544 and named it dip angle or magnetic inclination.

When the inclination is positive, it indicates that the world’s magnetic lines are pointing lower or downwards in the northern portion of the globe, and when the inclination is negative, it indicates that the world’s magnetic lines are facing vertically or upwards in the southern portion of the globe.

Robert Norman invented the dip circle, a means of determining the dip angle or magnetic inclination, in the year 1581. Isoclinic lines (when the shape lines at the world’s surface are comparable) and aclinic lines (when the shape lines are not comparable) are two terminologies employed (when the locus of the focus are having zero dips).

Magnetic Declination Formula

The following methods can be used to determine magnetic declination:

  • From the Declination Calculator: The declination calculator is a simple tool for determining the declination of any location on the globe. The calculator calculates the declination using magnetic reference field models by entering the year, degree, and longitude of a specific region.
  • From the Declination Chart: A magnetic declination chart is a tool for calculating declination. The magnetic fields of the world are depicted on the chart. Finding magnetic declination is made simple using this method.
  • From the Compass: True, magnetic, and compass bearings are the three types of bearing available. The phrase:

T = M + V

M = C + D

T = C + V + D

where, T = True bearing, M = Magnetic Bearing, C = Compass Bearing, D = Compass Deviation, V = Variation.

  • V, D > 0  …(Easterly Variation and Derivation)
  • V, D < 0  …(Westerly Variation and Deviation)

The magnetic and compass bearing formula is given below:

Magnetic Bearing = True Bearing – Variation

Compass Bearing = Magnetic Bearing – Deviation

The magnetic and true bearing formula is given below:

Magnetic Bearing = Compass Bearing + Deviation

True Bearing = Magnetic Bearing + Variation

As a result, when we use a compass to find the north direction, the needle is pointing to the world’s magnetic north, not the genuine/true north.

Sample Questions

Question 1: What Is Magnetic Declination and Why Is It Important?

Answer:

The exact route should consider magnetic declination. A compass will always point to magnetic power lines (which join on what are known as the magnetic poles). The declination is the angle formed by the direction of power and the bearing of the geographic north pole. Declination is positive or east if a compass in your area focuses on the right side of true north, and negative or west if it focuses on the other side. To demonstrate the direction of magnetic north from true north, this is expressed in degrees and minutes east or west.

Question 2: How to Work Out Declination at Any Place?

Answer:

  • Declination maps are one approach. Declination values, unfortunately, are always changing due to secular fluctuation. When printed maps were the primary source of this information, declination values were often out of date by the time the maps reached the general public. The angle between the magnetic and geological meridians at any location, according to Nathaniel Bowditch, an American practical navigator.
  • Making a prediction is another option. This should be based on a detailed model of the deep streams as a whole. The model reflects a highly predictable rate of progress and, on average, will be more precise than a guide and never less precise.

Question 3: Where the horizontal and vertical components of the earth’s magnetic field are identical, what is the angle of dip?

Answer:

Angle of dip is,

δ = tan-1(BV/BH)

Here,

BV = The magnetic field’s vertical components,

BH = The magnetic field’s horizontal components.

Therefore, BV = BH

∴ δ = tan-1(1)

= 45o

Question 4: The North point of a magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has a 60° angle to the horizontal. The earth’s magnetic field has a horizontal component of 1.2 G at this location. Calculate the magnitude of the earth’s magnetic field at your location.

Answer:

Given: δ = 60o, H = 1.2 G

Since,

Be = H / cos δ 

∴ Be = 1.2 / cos 60 

= 1.2 / (0.5)

= 2.4 G

Question 5: The northern point of a magnetic needle free to rotate on a vertical plane parallel to the magnetic meridian is at 45 degrees with the horizontal. At the location, the horizontal component of the earth’s magnetic field is known to be 0.8 G. Calculate the magnitude of the earth’s magnetic field at the given location.

Answer:

Given: δ = 45o, H = 0.8 G

Since,

Be = H / cos δ

∴ Be = 0.8 / 0.7071

= 1.1314 G

Question 6: A magnetic needle can freely revolve in a vertical plane and orients itself vertically to a certain location on the planet. What do you consider to be the values of

  • The earth’s magnetic field’s horizontal component, and
  • At this point, what is the angle of dip?

Answer:

  1. Because the coil can move freely in the vertical plane, the horizontal component of the earth’s magnetic field is zero.
  2. Angle of Dip is 90 degrees.
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