4.6 Compass Error & TVMDC Conversions

The Conversion Ladder

Once variation and deviation are defined, every exam problem is just careful bookkeeping on the ladder:

T → V → M → D → C (TVMDC)

• T True
• V Variation
• M Magnetic
• D Deviation
• C Compass

Going T → C is converting a chart (true) direction into what you steer or what a compass bearing should read. Going C → T is converting a compass observation into a true direction for plotting.

The reverse mnemonic is CDMVT (Compass–Deviation–Magnetic–Variation–True). Same ladder, opposite direction. Write the five letters every time until the process is automatic; partial mental math is how candidates drop 5° and fail a Chart Plot module that only allows one miss at 90%.

“East Is Least, West Is Best” — When Uncorrecting

When converting from true toward compass (uncorrecting / “applying errors to get compass”), the classic rule is:

East is least, West is best.

Meaning:

• Easterly variation or deviation is subtracted
• Westerly variation or deviation is added

Apply variation first (T → M), then deviation (M → C), each with the same east/west rule when uncorrecting.

Uncorrecting examples (True → Compass)

Example A — westerly variation, zero deviation

Desired true course 100°T. Variation 12°W. Deviation 0°.

T → M: West is best → add 12° → magnetic = 100 + 12 = 112°M
M → C: Dev 0 → compass course = 112°C

You must steer 112° by compass to make good 100° true (still ignoring set/drift; that is a later plot topic).

Example B — easterly variation

True course 050°T. Variation 8°E. Deviation 0°.

T → M: East is least → subtract 8° → 042°M = 042°C

Example C — both variation and deviation

True course 220°T. Variation 14°W. On the magnetic/compass head you will steer, deviation table gives 3°E (for exam problems, you may need one iteration if the table is entered by compass heading—see below).

T → M: add 14°W → 220 + 14 = 234°M
M → C: East is least → subtract 3°E → 231°C

Example D — magnetic to true with west variation (correcting preview)

A problem states magnetic course 090°M, variation 10°W, and asks for true.

Now you are going M → T (up the ladder). Reverse the uncorrecting rule: for correcting, add east, subtract west (or: west is no longer “best” when climbing to true).

M → T: subtract 10°W → true = 090 − 10 = 080°T

This is the classic “mag to true with W variation → subtract” pattern the exam loves.

Correcting: Compass → True

When converting from compass toward true (correcting a compass bearing or course to true):

Reverse “East is least, West is best.”
Add easterly errors, subtract westerly errors.

Some instructors teach “correcting, add east” as the only phrase they need and then reverse for uncorrecting. Either system works if you are consistent and always note the direction of conversion.

Correcting examples (Compass → True)

Example E

Compass bearing 315°C. Deviation on the ship’s head 2°W. Variation 11°E.

C → M: correcting, subtract west → 315 − 2 = 313°M
M → T: correcting, add east → 313 + 11 = 324°T

Example F

Compass course 000°C. Dev 4°E. Var 6°W.

C → M: add east → 000 + 4 = 004°M
M → T: subtract west → 004 − 6 = 358°T (wrap past 360 as needed: 4 − 6 = −2 → 358°)

Entering the Deviation Table Correctly

Deviation is tabulated against ship’s head, often compass heading. When a problem gives a true course to convert to compass, you may not know the exact compass head until you convert—but deviation depends on that head. Exam practice:

1. Convert T → M with variation.
2. Enter the table with magnetic heading if the table is magnetic-based, or estimate compass head, apply deviation, and recheck if the table is compass-based and your first guess was off by many degrees.
3. For multiple-choice Master questions, tabulated heads usually match cleanly so one pass is enough.

Mini table drill

Convert true course 075°T, variation 9°W, to compass course.

T → M: 075 + 9 = 084°M. Nearest table head ~090° → Dev 0° → 084°C.
(If forced to interpolate between 060° and 090°, deviation is a fraction of a degree—usually the exam keeps it simple.)

Compass Error Applied as a Single Step

If variation and deviation have already been combined into compass error (CE):

• Uncorrecting (T → C): East least / West best using the single CE
• Correcting (C → T): reverse

Example G. True course 140°T, CE 7°W → compass = 140 + 7 = 147°C.
Example H. Compass bearing 020°C, CE 5°E → true = 020 + 5 = 025°T (correcting adds east).

Master Exam Arithmetic Practice Set

Work these exactly as you would under a REC clock. Answers follow the steps.

Solutions:

1. T→M: 090+15=105°M=105°C
2. T→M: 200−10=190°M; M→C: 190+2=192°C
3. C→M: 270+3=273°M; M→T: 273−12=261°T
4. M→T: 135−8=127°T
5. T→M: 000−6=354°M; M→C: 354−4=350°C
6. Correcting with CE 9°W: 045−9=036°T

Sign discipline and 360° wrap

Courses live on a 0–360° circle. If subtraction goes negative, add 360. If addition exceeds 360, subtract 360. Write intermediate magnetic values; skipping straight from T to C without M is fine only when you use combined CE correctly—otherwise show V and D separately.

Operational Notes for Master LT 100

On a near-coastal small passenger run you will often:

1. Lay a true track on the chart for the next leg.
2. Apply set and drift to get a true course to steer (Chart Plot chapter).
3. Convert that true CTS through TVMDC to a compass course to steer.
4. Brief the helm: “Steer 231 by compass,” not “about southwest.”

GPS course-over-ground is not a substitute for understanding TVMDC on the exam, and it is not a substitute for a cross-checked compass when electronics glitch in rain and spray.

Common scoring mistakes

• Applying deviation before variation when using the ladder (order is T-V-M-D-C).
• Using “east is least” while correcting instead of uncorrecting.
• Taking variation from the wrong rose or ignoring a given annual change.
• Entering the deviation table with true heading by mistake.
• Forgetting to normalize angles into 000–360°.

Drill until each conversion is under thirty seconds. Q162 is a 70% module, but the same skill must be flawless when only one Chart Plot error is allowed on Q163.