Marine Magnetic Compass adjustment:analysis of a table of deviations;

Excellent question. Analyzing a table of deviations is the core of marine magnetic compass adjustment. It’s how a compass adjuster diagnoses the ship’s magnetic “illness” before prescribing the “cure” with magnets and soft iron correctors.

Let’s break it down step-by-step, from the basics to a full analysis of a sample table.

1. The Fundamentals: Why We Need This

A ship is a large steel mass, creating its own magnetic field that interferes with the Earth’s magnetic field. This interference causes the ship’s compass to point to a direction called Compass North (CN) instead of Magnetic North (MN).

The angular difference between Magnetic North and what the compass shows is called Deviation (D).

• Goal of Adjustment: To reduce the deviation to a minimum (ideally less than 2-3 degrees on any heading).
• The Tool: The Table of Deviations, created by “swinging the ship” (turning it in a full circle and recording the compass heading against a known magnetic heading at regular intervals, e.g., every 15 or 30 degrees).

2. The Sources of Deviation

Deviation isn’t a simple, constant error. It’s a complex sum of errors caused by two types of magnetism on the ship:

1. Permanent Magnetism (Hard Iron): Magnetism “baked into” the ship’s steel during construction (due to hammering, welding, and sitting in one orientation in the Earth’s magnetic field). This causes Semicircular Deviation, meaning the error is maximum on two opposite headings and zero on the two headings 90° away.
2. Induced Magnetism (Soft Iron): Temporary magnetism induced in the ship’s soft iron components by the Earth’s magnetic field. This magnetism changes as the ship changes heading. This causes Quadrantal Deviation, meaning the error is maximum on the four intercardinal headings (NE, SE, SW, NW) and zero on the cardinal headings (N, S, E, W).

3. The Analysis: Deconstructing Deviation with Coefficients

To analyze the deviation table, we use a mathematical technique (a simplified Fourier analysis) to break down the total deviation into its component parts. These parts are known as Coefficients A, B, C, D, and E.

The approximate formula for deviation (δ) on any compass heading (H_c) is:

δ ≈ A + B·sin(H_c) + C·cos(H_c) + D·sin(2H_c) + E·cos(2H_c)

By calculating these coefficients from our table, we can understand the exact nature of the ship’s magnetic field and how to correct it.

4. Example: Analysis of a Table of Deviations

Let’s imagine we have just swung the ship and produced the following table. The deviation is found by subtracting the Compass Heading from the known Magnetic Heading (Dev = Mag - Comp).

(Note: West deviation is negative (-), East deviation is positive (+). This is crucial for calculations.)

Calculating the Coefficients

Here’s what each coefficient means and how to calculate it from our table.

Coefficient A (Constant Deviation)

• What it is: A constant error on all headings.
• Cause: Misalignment of the compass bowl, lubber line not parallel to the keel, or asymmetrical arrangement of soft iron.
• Calculation: The average of all deviations.
  • A = (-2 + -2 + -6 + 2 + 4 + -2 + 5 + 2) / 8
  • A = 1 / 8
  • A = +0.125°
• Analysis: This is a very small constant error. It can be physically corrected by rotating the compass bowl slightly. If small enough, it’s often left uncorrected.

Coefficient B (Semicircular Deviation)

• What it is: Deviation that is maximum on East and West headings.
• Cause: Permanent fore-and-aft magnetism in the ship.
• Calculation: The average deviation on East minus the average deviation on West, all divided by 2.
  • B = (Dev on E - Dev on W) / 2
  • B = (-6 - (+5)) / 2
  • B = -11 / 2
  • B = -5.5°
• Analysis: This is a large negative value. A negative B indicates that the forward part of the ship has “blue” magnetism (the pole that attracts the North-seeking pole of a magnet).
• Correction: This is corrected by placing permanent fore-and-aft magnets in the binnacle, in this case with their “red” ends forward to counteract the ship’s “blue” magnetism.

Coefficient C (Semicircular Deviation)

• What it is: Deviation that is maximum on North and South headings.
• Cause: Permanent athwartships (side-to-side) magnetism in the ship.
• Calculation: The average deviation on North minus the average deviation on South, all divided by 2.
  • C = (Dev on N - Dev on S) / 2
  • C = (-2 - (+4)) / 2
  • C = -6 / 2
  • C = -3.0°
• Analysis: This is a significant negative value. A negative C indicates that the starboard side of the ship has “blue” magnetism.
• Correction: This is corrected by placing permanent athwartships magnets in the binnacle, in this case with their “red” ends to starboard to counteract the ship’s “blue” magnetism.

Coefficient D (Quadrantal Deviation)

• What it is: Deviation that is maximum on the intercardinal headings (NE, SE, SW, NW).
• Cause: Induced magnetism in asymmetrical horizontal soft iron.
• Calculation: The average deviation on intercardinal headings (NE, SW) minus the average deviation on the other intercardinals (SE, NW), all divided by 2.
  • D = (Avg Dev on NE & SW - Avg Dev on SE & NW) / 2
  • D = ((-2 + -2)/2 - (+2 + +2)/2) / 2
  • D = (-2 - 2) / 2
  • D = -4 / 2
  • D = -2.0°
• Analysis: This is a notable quadrantal error. A negative D is less common and suggests that the soft iron is concentrated along the NW-SE axis. A positive D (more common) suggests soft iron concentrated along the fore-aft and athwartships lines (like beams).
• Correction: This is corrected by placing soft iron spheres (Quadrantal Correctors) on the sides of the binnacle. For a negative D, the spheres would need to be placed on the fore-and-aft line from the compass, which is usually not possible. In practice, a large D is almost always positive and corrected by moving the spheres closer to or further from the compass.

(Note: There is also a Coefficient E, another quadrantal error, but it’s typically very small and often ignored in initial analysis.)

Summary of the Analysis and Action Plan

Based on the calculation of coefficients from the deviation table, the compass adjuster now has a clear picture:

1. Significant Coefficient B (-5.5°): There is strong permanent fore-and-aft magnetism. Action: Insert fore-and-aft corrector magnets.
2. Significant Coefficient C (-3.0°): There is moderate permanent athwartships magnetism. Action: Insert athwartships corrector magnets.
3. Moderate Coefficient D (-2.0°): There is a quadrantal error from horizontal soft iron. Action: Adjust the soft iron spheres.
4. Negligible Coefficient A (+0.125°): The constant error is minimal and likely requires no physical correction.

After placing the correctors, the adjuster would swing the ship again to create a new table of Residual Deviations. This new table is then used to create the final Deviation Card that the navigator uses for daily corrections.