Plotting with Variation and Deviation: Working T-V-M-D-C

What the rule requires

Every question on this topic is decided before you touch the arithmetic, at the moment you work out which way along the sequence you are travelling. The chain is fixed: True, Variation, Magnetic, Deviation, Compass. Variation moves between true and magnetic; deviation moves between magnetic and compass. Bowditch Ch. 6 §602

Two directions of travel, and each has its own sign rule.

• Correcting is compass toward true, working up the chain from C to T. Add east, subtract west.
• Uncorrecting is true toward compass, working down from T to C. Add west, subtract east.

The trigger is the product the question wants. If it wants a value for the chart, you are correcting. If it wants a value for the helmsman, you are uncorrecting. A question that gives you a course plotted between two charted points and asks what to steer is an uncorrecting problem every time, because the plot yields a true course: you read it where the parallel rulers cross the outer (true) ring of the compass rose. Bowditch Ch. 4 §406

The two errors come from different places and you cannot substitute one for the other.

• Variation is the angle between true north and magnetic north at a place. It is printed inside the chart's compass rose, and it changes with position and slowly over time. Bowditch Ch. 6 §601
• Deviation is the angle between magnetic north and the vessel's own compass north, caused by the vessel's own magnetism. It changes with the vessel's heading and is read from the deviation card.

Each is labelled east or west, and that label is the only thing the sign rule cares about once you have settled your direction of travel.

The mnemonics in circulation are worth using because they are the ones the rest of the trade uses. Going down the chain, True Virgins Make Dull Companions, Add Whiskey — T-V-M-D-C, add west. Going up, Can Dead Men Vote Twice, At Elections — C-D-M-V-T, add east. Both are sound as far as they go, and what they do not carry is where the two figures come from: the jingle will happily let you apply a single deviation figure to a whole voyage, when the card gives a different value for each heading. Read the card for the heading you are actually on.

Your plotted true course is 118°T. Variation at the rose is 9°E. Before you look at the deviation card, what is the magnetic course, and why?

109°M. You are uncorrecting, true toward compass, so easterly errors are subtracted: 118 − 9 = 109. The trap is the reflex "east is least, west is best" learned only in the correcting direction, which would give 127. Variation is the T-to-M step, so the deviation card has no part in this figure yet.

Telling it apart: variation against deviation

One criterion separates them: which pair of norths the angle lies between. Get that right and you can never apply the wrong figure at the wrong step. Bowditch Ch. 6 §601

• Variation — true north to magnetic north. A property of the place, so every vessel in that patch of water has the same value, and a vessel that comes about on a reciprocal heading still has it. Source: the compass rose. Most often misfiled by a candidate who applies it at the M-to-C step, which produces a plausible number and a wrong answer.
• Deviation — magnetic north to the vessel's compass north. A property of this vessel on this heading, from her own magnetism, so it changes as she alters course. Source: the deviation card. Most often misfiled by taking one row of the card and using it for both legs of a two-leg problem.

Because deviation is indexed to the vessel's head, the value you draw from the card is the one for the heading being steered. That matters on a problem giving you several headings and a single card: there is a correct row for each, and the exam distractors are usually built from the neighbouring rows.

Working a question

You are bound from a departure point to a charted buoy. The line joining them, walked to the nearest rose with the parallel rulers, crosses the outer ring at 047°. The rose shows variation 14°W. The deviation card shows 3°E on headings around 060, and 2°W on headings around 300. Give the course to steer per steering compass.

1. Fix the direction of travel. The figure in hand came off the chart's true ring, and the answer is going to the helm. True toward compass, so you are uncorrecting: add west, subtract east. Bowditch Ch. 6 §602
2. Take the variation from the rose, not from anywhere else. 14°W, and it belongs to the T-to-M step only. Bowditch Ch. 6 §601
3. Apply it. Westerly, and you are uncorrecting, so add: 047 + 14 = 061°M.
4. Enter the deviation card with the heading you will be steering, roughly 060, not with 047 and not with the reciprocal. That row gives 3°E.
5. Apply it. Easterly, uncorrecting, so subtract: 061 − 3 = 058° psc. That is the answer to the question as asked.
6. Label the plot. The line carries C above and S below. The direction the plot produced is true, so 058 is a helm order and stays off the chart. Bowditch Ch. 4 §406

Run it back to check, which takes ten seconds and catches a reversed sign every time. From 058° psc, correcting: deviation 3°E added gives 061°M, variation 14°W subtracted gives 047°T. You are back on the number the chart gave you. If the return trip does not land on your starting value, you have applied a sign in the wrong direction, not made an arithmetic slip.

Two arithmetic points that account for a fair share of lost marks. Any result over 360 has 360 taken off it, so a true course of 355 with 12°W variation uncorrected gives 367, which is 007°M. Any result below zero has 360 added: 006 with 11°W corrected gives −005, which is 355. Write the intermediate magnetic value down rather than holding it in your head, because the second step depends on it and an exam distractor is usually sitting on the magnetic figure.

Returning on the reciprocal, you take a bearing of a light with the steering compass while heading about 300. Variation is still 14°W and the card shows 2°W on that head. What is the true direction?

286°T. You are correcting, compass toward true, so westerly errors are subtracted at both steps: 302 − 2 = 300°M, then 300 − 14 = 286°T. The deviation is the one for the vessel's head, since that is what the card is indexed to. A candidate who carries the outbound 3°E across to this leg gets 291 and picks a wrong option that looks arithmetically clean.

Where candidates lose the point

Applying "east is least, west is best" to a course-to-steer question. The device is the correcting rule with the labels stripped off, and it is right only when you are going compass toward true. Asked to steer, the candidate with variation 14°W subtracts it, reaches 033, and finds that number among the options because the examiner put it there. The direction of travel sets the sign; the E/W label alone does not. Bowditch Ch. 6 §602

Stopping at magnetic. Both steps get applied correctly, then the candidate selects 061 when the question says per steering compass. Read the units in the stem before the options: psc means the answer sits at the C end of the chain, and °M means it stops one step short.

Pulling deviation off the compass rose. The rose carries variation. Deviation exists only on the vessel's own card, because it is caused by that vessel's magnetism. A question giving you a rose and no card is asking for a magnetic answer. Bowditch Ch. 6 §601

Entering the deviation card with the wrong number. Candidates index it against the true course, or against a bearing they have just taken, instead of against the vessel's head. On a card that changes several degrees between adjacent rows, that alone moves the answer into a distractor.

Reading the rose off the wrong ring. The true course is what the ruler cuts on the outer ring. A figure taken anywhere else on the rose is not the true course, and the whole T-V-M-D-C run built on it will be wrong by the variation even though every sign was applied correctly. Bowditch Ch. 4 §406

Using a stale variation. Variation changes with position and slowly with time. On a large chart, the rose nearest your working area is the one to read, not the one nearest the title block.

Check yourself

Your true course from the plot is 214°T. Variation is 7°E, deviation 2°E on that head. What do you steer?

205° psc. Uncorrecting, so easterly errors are subtracted at both steps: 214 − 7 = 207°M, 207 − 2 = 205° psc. A candidate adding both reaches 223, which is the reciprocal-sign error the examiner expects. Bowditch Ch. 6 §602

You are steering 178° psc. The card shows 4°W. Variation is 11°E. What is your true course?

185°T. Correcting: subtract the westerly deviation, 178 − 4 = 174°M, then add the easterly variation, 174 + 11 = 185°T. Mixing the two labels in one problem is where the sign rule earns its keep — the direction of travel, not the label, decides the operation.

A question gives you a chart with the compass rose and no deviation card, and asks for the course to steer. What is wrong with the question as you read it?

Nothing is wrong; the answer stops at magnetic. Deviation is the vessel's own error and comes from her card, so with no card supplied the only conversion available is true to magnetic using the variation in the rose. Bowditch Ch. 6 §601

Your plotted true course is 352°T, variation 15°W, deviation 1°E. Course to steer?

006° psc. Uncorrecting: 352 + 15 = 367, which is 007°M after taking off 360, then subtract the easterly degree for 006° psc. Candidates who carry 367 forward and answer 366 have done the navigation right and the arithmetic short.

Two legs: the first steered around 090, the second around 200. Your card shows 5°E at 090 and 6°W at 200. A candidate applies 5°E to both. What has gone wrong, and how much is the second leg out?

Deviation changes with the vessel's heading, so each leg takes its own row from the card. Using 5°E on the second leg instead of 6°W puts that course 11° in error, enough to make every subsequent position wrong.

You have converted 062°T to 071° psc. Without redoing the plot, how do you satisfy yourself the signs went the right way?

Run the chain back the other way. Correcting from 071° psc with the same two figures must return exactly 062°T. Landing anywhere else means a sign was applied in the uncorrecting sense when it should have been correcting, or the reverse.

Variation at your working position is 9°W. A vessel a mile off your beam is steering the reciprocal of your course. What variation applies to her, and what deviation?

The same 9°W, because variation belongs to the place and both vessels are in it. Her deviation is her own, from her own card and for her own head, and nothing about your card tells you what it is.