Latitude, Longitude, and Taking a Position Off the Chart

What the rule requires

The latitude border is the only mileage scale on the chart. One minute of latitude equals one nautical mile, so distance is always measured on the latitude scale alongside the vessel's own latitude, never on the longitude scale Bowditch Ch. 4 §405. That single sentence decides more Navigation General questions than anything else in this topic, and it decides them in both directions: it tells you where the miles come from, and it tells you that the graduation along the bottom of the sheet is not miles at all.

The two borders carry different quantities and are read in a fixed order. Latitude is measured 0 to 90 degrees north or south of the equator, longitude 0 to 180 degrees east or west of the Greenwich meridian, position is stated latitude first, and on a Mercator chart latitude is read from the side (left and right) scales and longitude from the top and bottom scales. A coordinate written without its hemisphere letter is not a position — 41°09.0' alone sits in two places on the earth.

The reason the latitude scale must be used at your latitude is the projection itself. The Mercator projection presents lines of latitude and longitude as straight lines crossing at right angles, with rhumb lines appearing as straight lines, and distances must be measured at the latitude of the line, since meridian length varies with latitude Bowditch Ch. 4 §402. Right-angle crossings and straight rhumb lines make the graticule look like an evenly ruled grid. It is not one. Step your dividers on the latitude border twenty minutes north of your working latitude and the spacing you are reading against is a different spacing.

The device most instructors use for which is which is the ladder: the flat rungs you could stand on are the parallels of latitude, the long sides running up and down are the meridians of longitude. Keep it, but know what it does not carry. It gives you orientation only — it says nothing about order of statement, and nothing about which border holds the miles. On a Mercator chart only the latitude border does.

Before you plot a coordinate someone else supplied

A position handed to you in a notice or a regulation carries a datum question with it, and the trigger is the label on the coordinate rather than anything about your chart. Geographic coordinates expressed in terms of latitude or longitude, or both, are not intended for plotting on maps or charts whose referenced horizontal datum is the North American Datum of 1983 (NAD 83), unless such geographic coordinates are expressly labeled NAD 83; geographic coordinates without the NAD 83 reference may be plotted on maps or charts referenced to NAD 83 only after application of the appropriate corrections that are published on the particular map or chart being used 33 CFR §100.01. Unlabelled coordinates are not unusable — they are usable after the correction printed on that sheet is applied. The regulation carrying that provision governs regattas and marine parades on the navigable waters of the United States, for the purpose of insuring safety of life in the regatta or marine parade area, which is exactly the situation in which a candidate is handed boundary coordinates and told to plot them.

A published notice gives the corner of a regatta area as 41°14.2'N, 072°06.8'W with no datum stated. Your chart is referenced to NAD 83. Do you plot it?

Not as given. Because the coordinates are not expressly labelled NAD 83, they may be plotted on a NAD 83 chart only after applying the appropriate corrections published on that particular chart, per 33 CFR §100.01. Find the correction note on the sheet, apply it, then plot.</details>

Dead reckoning is the determination of position by applying course steered and distance run from a known starting point Bowditch Ch. 1 §102, and that known starting point is a pair of readings taken off these two borders. An error of one minute in the latitude you enter is one mile of error carried forward through every leg after it.

Telling it apart

The criterion that separates the two borders is whether one minute of that scale equals one nautical mile. Only one of them does.

Latitude scale — the left and right edges, graduated 0 to 90 degrees north or south of the equator. One minute equals one nautical mile, so this is the scale dividers are set against. Read first when stating a position.
Longitude scale — the top and bottom edges, graduated 0 to 180 degrees east or west of the Greenwich meridian. Distance is never taken from it. Its minutes look identical to the minutes on the side border and are not miles.
The latitude scale, read at the wrong latitude — the right border, the wrong part of it. Meridian length varies with latitude, so the distance must be measured at the latitude of the line rather than wherever the border is convenient to reach.

Working a question

Departure 41°09.0'N, 072°18.0'W. Destination 41°02.0'N, 072°32.0'W. Required: true course and distance. The method is fixed Bowditch Ch. 4 §406 and the decision at each step is which scale you touch.

Check the datum question first. Both coordinates here are your own, lifted from a NAD 83 chart, so no correction applies. Had either come from an outside source without a NAD 83 label, the correction published on the sheet would go on before the pencil does.
Lay off the departure latitude. Find 41°09.0'N on the side border, on both left and right edges, and align a straight edge between them. Latitude comes off the side scales only.
Lay off the departure longitude. Find 072°18.0'W on the top and bottom borders and align between them. The intersection is the departure position.
Repeat for 41°02.0'N, 072°32.0'W. Both positions are now pricked.
Draw the straight line joining them. On a Mercator chart that straight line is the rhumb line — a constant true course.
Read the course. Walk a set of parallel rulers from the line to the nearest compass rose and read the true course where the ruler crosses the outer (true) ring — approximately 236°T here, running southwest, which agrees with a position that is both south and west of the departure. If the ruler slips against the graduated edge, the reading is discarded and the walk repeated.
Measure the distance. Span the dividers to the line's full length, carry them to the side border, and read against the graduation at about 41°06' — between the two latitudes worked, not at the top or bottom corner of the sheet. The span reads roughly 12.7 minutes of latitude, which is 12.7 nautical miles.
Sanity-check the answer against the latitude difference. 41°09.0' to 41°02.0' is 7.0 minutes, so the run cannot be less than 7.0 miles. A measured answer of 6 miles means the dividers went to the longitude border.
Label the line. C (course) above and S (speed) below — C 236 over the line, S 8.0 under it.

Step 8 is the one that saves the point under time pressure. The difference of latitude is free, it needs no dividers, and it puts a hard floor under any distance you report.

Where candidates lose the point

Spanning the dividers on the bottom border because it is closer to the line. The bottom border is graduated in minutes of longitude, which is why the mistake survives a glance — the numbers are minutes and the marks look the same as the side scale. Distance is never measured on the longitude scale, and on a chart in the forties the error runs about a quarter short.

Using the latitude scale, but reading it at the corner of the sheet. This one is harder to catch because the candidate did reach for the correct border. Meridian length varies with latitude, so the graduation must be read at the latitude of the line being measured.

Treating the graticule as a uniform grid because the rhumb line came out straight. The Mercator presents parallels and meridians as straight lines crossing at right angles, and that regularity is what invites the conclusion that either border will serve for distance. The projection buys straight rhumb lines by varying the latitude scale across the sheet.

Transposing the coordinate pair. Position is stated latitude first. On a distractor built as 072°18.0'N, 041°09.0'W, a candidate who is working fast selects it because both numbers are correct.

Plotting an unlabelled coordinate straight onto a NAD 83 chart. The attraction is that nothing appears wrong: the coordinate is well formed, the chart is current, the position falls in plausible water. Coordinates without the NAD 83 reference require the corrections published on that particular chart before plotting.

Check yourself

You are measuring the distance of a course line that runs between 39°50'N and 40°04'N. Your chart's latitude border extends from 39°30'N to 41°00'N. Where on the border do you set the dividers?

Against the graduation at about 39°57'N — the latitude of the line being measured. Distance must be measured at the latitude of the line, because meridian length varies with latitude (Bowditch Ch. 4 §402). Reading up at 40°50' introduces a scale error even though you are on the correct border.</details>

A course line measures 9.4 minutes of arc when spanned against the bottom border of the chart. What is the distance run?

Unknown from that measurement — it must be re-measured. One minute of latitude equals one nautical mile; the bottom border is graduated in longitude and distance is never taken from it (Bowditch Ch. 4 §405). Re-span the line and read it on the side scale at the working latitude.</details>

Which of these is a properly stated position: 073°42.5'W, 40°28.0'N — or 40°28.0'N, 073°42.5'W?

The second. Position is stated latitude first, latitude 0 to 90 degrees north or south of the equator and longitude 0 to 180 degrees east or west of the Greenwich meridian (Bowditch Ch. 4 §405). Both forms contain the same two numbers, which is why the reversed option is a standing distractor.</details>

Your departure is 42°15.0'N and your destination 42°06.0'N. Before touching the dividers, what is the least possible distance between them?

9.0 nautical miles. The difference of latitude is 9.0 minutes and one minute of latitude is one nautical mile, so the rhumb line cannot be shorter than that — it is shorter only if the two positions share a longitude, in which case it equals 9.0. Any measured answer below 9.0 miles was taken off the wrong scale.</details>

You are plotting the boundary of a marine parade area from coordinates in a notice. No datum is stated. What is required before the position goes on your NAD 83 chart?

Application of the appropriate corrections published on that particular chart. Coordinates not expressly labelled NAD 83 are not intended for plotting on a chart referenced to NAD 83 and may be plotted only after those corrections are applied (33 CFR §100.01). The trigger is the absence of the NAD 83 label on the coordinate.</details>

You have joined two charted points with a straight line and walked the parallel rulers to the compass rose. Which ring do you read, and what do you write on the line?

The outer ring, which is the true ring, giving true course. Label the line with C (course) above and S (speed) below (Bowditch Ch. 4 §406). If the rulers slipped during the walk, discard the reading and repeat it rather than adjusting the number.</details>

On a Mercator chart, why does a straight pencil line give you a single course to steer?

Because the Mercator projection presents rhumb lines — lines of constant bearing — as straight lines, with the parallels and meridians crossing at right angles (Bowditch Ch. 4 §402). That same property is why the latitude scale is not constant down the sheet, so the straight line does not license measuring its length wherever it is convenient.</details>