Plotting with Variation and Deviation (T-V-M-D-C)

TL;DR — When a magnetic compass is fitted, the person directing vessel movement must know and apply both variation and deviation to convert between true, magnetic, and compass courses. Failure to apply these corrections is a recognized source of navigational error that compounds over a voyage.

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What the Rule Says

The Regulatory Requirement

Federal regulations place a direct, affirmative duty on the person directing and controlling the movement of a towing vessel to know and apply variation and deviation. Specifically, that person must know and apply the variation and deviation, where a magnetic compass is fitted and where charts or maps have enough detail to enable this type of correction. 33 CFR §164.78

This is not a suggestion. It is a condition of lawful navigation. The same section requires that the person directing the vessel be able to fix the vessel's position using installed navigational equipment, aids to navigation, geographic reference points, and hydrographic contours — and that position-fixing depends on knowing the relationship between the compass course steered and the true course made good. 33 CFR §164.78

The Error Framework

Navigational errors arise from instrument error, observation error, plotting error, computation error, and the basic assumption that the vessel has held the planned course. Cumulative errors must be checked against fixes whenever possible. Bowditch Ch. 23 §2301 Failure to apply variation and deviation is a computation error that feeds directly into plotting error — the two categories that T-V-M-D-C is specifically designed to prevent.

Pre-Voyage Planning Context

Pre-voyage planning is the foundation of safe navigation. Plotting the intended track, identifying hazards, marking turn points, and calculating ETAs at each waypoint all depend on working in a consistent reference frame — true north — which requires converting the compass course to a true course before laying it on the chart. Bowditch Ch. 25 §2501 Voyage plans for towing vessels operating seaward of the U.S. territorial sea baseline must account for all pertinent information, including chart data, before departure. 33 CFR §164.80

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The T-V-M-D-C Framework Explained

The mnemonic T-V-M-D-C represents the ordered chain of corrections between True north and Compass north:

`` True → Variation → Magnetic → Deviation → Compass T V M D C ``

True (T): Direction referenced to geographic (true) north. Nautical charts are drawn on true north. All plotted courses and bearings on a chart are true. Bowditch Ch. 25 §2501

Variation (V): The angular difference between true north and magnetic north at a given geographic location. Variation is caused by the non-coincidence of the geographic and magnetic poles. It is printed on the compass rose of every nautical chart and changes slowly over time (annual rate of change is also noted on the rose). Variation is the same for every vessel at the same location regardless of the vessel's construction. 33 CFR §164.78

Magnetic (M): The direction referenced to magnetic north, after variation has been applied to a true direction (or before variation is applied when converting from compass to true).

Deviation (D): The angular difference between magnetic north and the direction the compass needle actually points, caused by the magnetic influence of the vessel's own structure, machinery, and cargo. Deviation varies with the vessel's heading and must be determined from a deviation table or deviation card specific to that compass on that vessel. 33 CFR §164.78

Compass (C): The direction actually read from the magnetic compass. This is what the helmsman steers.

The Sign Convention — East is Least, West is Best

This is the single most tested rule in compass correction problems:

• East variation or deviation is subtracted when converting True → Compass (or added when converting Compass → True).
• West variation or deviation is added when converting True → Compass (or subtracted when converting Compass → True).

The memory aid: "Correcting, add East" (going from Compass to True, add East errors). "Uncorrecting, add West" (going from True to Compass, add West errors).

Alternatively, the full mnemonic for converting Compass to True (correcting):

Can Dead Men Vote Twice — Compass, Deviation, Magnetic, Variation, True — add East, subtract West at each step.

Worked Example: True to Compass (Uncorrecting)

You plot a true course of 090°T on the chart. The chart compass rose shows variation 10°W. Your deviation table for that heading shows deviation 3°E. What compass course do you steer?

Step 1: T → M: Variation is 10°W. Going True to Compass, add West: 090° + 10° = 100°M. Step 2: M → C: Deviation is 3°E. Going True to Compass, subtract East: 100° − 3° = 097°C.

Steer 097°C.

Worked Example: Compass to True (Correcting)

The helmsman is steering 215°C. Deviation for that heading is 5°W. Variation is 12°E. What is the true course?

Step 1: C → M: Deviation is 5°W. Going Compass to True, subtract West: 215° − 5° = 210°M. Step 2: M → T: Variation is 12°E. Going Compass to True, add East: 210° + 12° = 222°T.

True course is 222°T.

Total Compass Error

When the exam gives you only a true course and a compass course (or asks you to find the combined error), the total compass error is the algebraic sum of variation and deviation. If variation is 10°W and deviation is 3°E, total error is 7°W. Apply it as a single correction between True and Compass.

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Why It Matters on the Exam

Direct Regulatory Hook

The OUPV and Master 100 GT written exams test compass correction problems extensively because the underlying regulatory duty is explicit. The person directing a vessel with a magnetic compass must know and apply variation and deviation. 33 CFR §164.78 Exam questions will present a true course and ask for the compass course, or present a compass bearing and ask for the true bearing, or ask you to identify the total compass error.

Position Fixing Dependency

A vessel's position cannot be correctly fixed from a magnetic compass bearing unless that bearing is converted to a true bearing before it is plotted on the chart. The requirement to fix position using navigational equipment, aids to navigation, and geographic reference points is meaningless if the operator cannot convert compass bearings to true. 33 CFR §164.78 Buoys alone cannot fix a position; they can only corroborate a position fixed by other means. 33 CFR §164.78 This reinforces that accurate compass correction is essential to any reliable fix.

Cumulative Error Risk

Navigational errors — including computation errors — accumulate over a voyage and must be checked against fixes whenever possible. Bowditch Ch. 23 §2301 A consistent error in compass correction (for example, always adding deviation when it should be subtracted) will produce a systematic track error that grows with distance. On a coastal passage, this can place the vessel in shoal water or on a hazard that the voyage plan was designed to avoid. Bowditch Ch. 25 §2501

Voyage Planning Integration

Towing vessel voyage plans seaward of the territorial sea baseline must account for proximity to hazards and must be checked before departure. 33 CFR §164.80 A voyage plan built on uncorrected compass courses will have waypoints and ETAs that do not correspond to the vessel's actual track over ground.

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Common Pitfalls

1. Reversing the sign when switching direction of conversion. The most frequent error. Remember: the same variation or deviation that you add going one direction, you subtract going the other. Write out T-V-M-D-C in order and label each step before calculating.

2. Applying variation to the wrong location. Variation is read from the compass rose on the chart for the area of operation. Using the variation from a different chart or a rose that has not been updated for annual change will introduce error. 33 CFR §164.78

3. Using a deviation value for the wrong heading. Deviation changes with the vessel's heading. The deviation table must be entered with the compass heading being steered, not the true course. Using the deviation for 000°C when the vessel is steering 090°C is a common exam trap.

4. Confusing variation with deviation. Variation is a property of the geographic location; deviation is a property of the vessel and its heading. They are separate corrections applied in sequence, not interchangeable.

5. Forgetting that buoys do not fix position. Exam questions sometimes present a scenario where a mariner uses a buoy bearing as a sole position fix. Buoys are placed in approximate positions and may not maintain exact charted positions due to current, ice, or collision. They cannot fix a position; they can only establish an estimated position if no other aids are available. 33 CFR §164.78

6. Skipping the correction entirely on electronic charts. Electronic chart systems display true courses. If the helmsman is steering by magnetic compass and the OOW reads the compass course directly onto the chart without correction, the plotted track will be wrong. The regulatory duty to apply variation and deviation applies regardless of what other navigation systems are in use. 33 CFR §164.78

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Quick Check

Q1 — You plot a true course of 045°T. Variation is 15°W. Deviation for that heading is 4°E. What compass course do you order the helmsman to steer?

T → M: Add West variation (going T to C): 045° + 15° = 060°M. M → C: Subtract East deviation (going T to C): 060° − 4° = 056°C. Answer: Steer 056°C.

Q2 — The helmsman reports steering 270°C. Deviation is 6°W. Variation is 8°E. What true course do you plot on the chart?

C → M: Subtract West deviation (going C to T): 270° − 6° = 264°M. M → T: Add East variation (going C to T): 264° + 8° = 272°T. Answer: Plot 272°T.

Q3 — What is the total compass error when variation is 12°E and deviation is 5°W?

Total error = 12°E − 5°W = 7°E. Answer: 7°E total compass error.

Q4 — Under 33 CFR §164.78, may a person directing a towing vessel fix the vessel's position using a buoy bearing alone?

No. Buoys are placed in approximate positions and may not maintain exact charted positions. They cannot fix a position; they may only establish an estimated position if no other aids are available. 33 CFR §164.78

Q5 — You observe a lighthouse bearing 135°C. Deviation for your current heading is 3°E. Variation is 10°W. What true bearing do you plot from the lighthouse?

C → M: Subtract East deviation: 135° − 3° = 132°M. M → T: Subtract West variation (going C to T, subtract West): 132° − 10° = 122°T. Answer: Plot a bearing line of 122°T from the lighthouse.

Q6 — Which type of navigational error does failure to apply compass corrections represent, according to Bowditch?

Computation error, which contributes to cumulative navigational error that must be checked against fixes whenever possible. Bowditch Ch. 23 §2301