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2 – Nautical charts

Chart projections

Before working with electronic charts (C-MAP, Garmin, BA) it is essential to understand and work with paper charts. Both forms are 2-dimensional representations of a 3-dimensional world which will result in various distortions.

[画像:Mercator]

However, as long as two requirements are met we can use the 2-dimensional image for navigational purposes:

1. The angles between three objects in the chart should be the same as the angles between the real objects which they represent.
2. A straight course should appear as a straight line in the chart.

To fulfil these demands a nautical chart requires parallels and meridians that are both straight and parallel.
Moreover, the meridians will need to be perpendicular to the parallels.

Mercator projection

A well known method to create such a chart is named after Gerard Mercator Kremer – a Flemish scholar who studied in 's Hertogenbosch (the Netherlands) and Leuven (now Belgium) and who invented his famous projection in 1569.

The Mercator chart was designed for nautical navigators and can be constructed by wrapping a cylinder around the planet so that it touches the equator. On this cylinder the surface of the earth is projected and finally the cylinder is cut open to yield the 2-dimensional chart.

[画像:The construction of Mercator projection for nautical navigation.]

However, whereas the meridians converge on the globe they run parallel in the projection, indicating the distortion.

This is most prominent when we examine a high parallel. The length / circumference of such a parallel – a small circle – on the globe is much smaller than the equator. Yet, on the chart they have exactly the same length creating a misrepresentation which gets bigger nearer to the poles.

Mercator deformation and distortion

The extent of the distortions of the Mercator projection is highlighted in Figure 2.2 , confirming that only the vertical scale of the chart should be used for measuring distances.

Click on the world map to see the distortions of a Mercator projection. Each navy coloured circle / ellipse has a radius of 500 km.

Vertical scale

[画像:Vertical scale of the nautical chart]

The vertical scale of Figure 2.3 , depicted on the right, further demonstrates the distortion. The two little navy coloured markers have precisely the same size, the upper one measures only 0.64 degrees (= 38.4 NM) while the other measures 1.00 degrees (= 60 NM). So, distances – in degrees, or in miles and minutes – should not only be read on the vertical scale, but also at approximately the same height.

Horizontal scale

The horizontal scale is only valid for one latitude in the chart and can therefore only be used for the coordinates (a point, but not a line).

[画像:Mercator explained, projection distortions]

If you were to divide the surface of the earth in eight pieces and lift one out, as shown in Figure 2.4 (left) , its projection would result in Figure 2.4 (right) .
Now both A – A' and B – B' are as long as the bottom of the chart and are increasingly “too long”.

Additional projections

But there are of course other projections in use by yachtspersons. An important one is the stereographic projection, which is constructed by projecting the globe on a flat plane instead of a cylinder. On this chart parallels appear as slightly curved and also the meridians converge at high latitudes. So, strictly speaking, a straight course will not appear as a straight line in the chart, but the parallels remain perpendicular to the meridians. Most often, distortions are scarcely noticed when this projection is used to chart a small area. Like the Mercator projection, the vertical scale represents a meridian and should be used for measuring distances.

Furthermore there is the gnomonic projection on which the meridians are again converging. But most importantly, the parallels are arcs of a circle while great circles appear as straight lines. On a sphere the shortest route between A and B is not a straight line but an arc (part of a great circle). Though this is also true when you – for example – cross a little bay, we use for simplification a loxodrome (a handy straight line on your Mercator chart which does not reflect your shortest route). On a gnomonic chart this same loxodrome is an arc, while your shortest route (a great circle) ends up as a straight line. Hence, the gnomonic projection is particularly useful when sailing great circles – offshore and ocean distances – see celestial navigation course — zipped PDF .
The term "gnomonic" relates to a gnomon, a sundial or in particular the raised part of a sundial that casts the shadow; a style.

Organization of the chart: Marginalia

Maps have two basic components:

• the map / chart itself, customarily called the "face",
• information about the map, commonly called "marginalia", similar to my own use of marginalia .

The term marginalia comes from a convention that all additional information about the map was printed / drawn outside the edge of the map, i.e. in the margins. This convention has disappeared with time, but the term lives on.

The most important marginalia that should accompany a map are outlined below:

• Authority: the publisher responsible for the information in the chart, e.g. “British Admiralty Charts”.
• Title: the title gives a description of the area covered by the chart, e.g. “The east Mediterranean Sea”.
• Number: different chart types of the same area can be distinguished by the chart's number.
• Projection: most likely the Mercator projection as described above. Charts covering small areas can be constructed by stereographic projection.
• Scale: for example: 1:193 000. But since the chart is distorted this holds only for one specific latitude in the Mercator chart. The scale indicates how detailed the chart is (here 1 cm on the chart represents 193 thousand cm on the Earth).
• Horizontal geodetic datum: the definition of the relationship between the ellipsoid adopted as the model of the Earth's shape, and the Earth itself. Though there are hundreds of datums in use, most are only locally valid.
  Yet, the WGS-84 datum is global in scope and positions obtained by satellite navigation systems are usually referred to this datum. Therefore, a correction needs to be applied to a WGS-84 GPS position to agree with charts using other horizontal datums. For example to correct WGS-84 to the European datum, add e.g. 0,06' N 0,04' E (style guide ) to the WGS-84 position indicated by the GPS. Fortunately, most chart plotters may be set to display positions in several other datums besides WGS-84 and perform the calculations for you. Comparisons of WGS84, ETRS89 and ITRS .
• Chart sounding datum: the tidal datum to which soundings and drying heights on a chart are referred. Often shortened to “Chart Datum” when it is clear that reference is not being made to a horizontal datum. Chart sounding datums are also used as reference for heights (lighthouses, mountains, bridges). Multiple datums can be used in one chart: LAT for soundings and ML for heights; see Chapter 6 Chapter 6 .
• Soundings & height units: soundings and heights can be stated in – for example – metres, feet or fathoms. Today all charts worldwide should by now be metric, except for USA Hydrographic Office charts, which sometimes still use feet instead of the international standard.
• Horizontal scale: natural scale at for example 40° 15,3' S latitude where the horizontal scale can be used for measuring distances and where the chart scale is true.
• GPS compatibility: most charts neither have the precision nor the resolution to fully use the GPS / Galileo / GLONASS positioning potential. Moreover, still plenty of charts result from surveys done in the 19th century.
  Also, as mentioned above, GPS data often requires a correction for a local horizontal chart datum before it can be used in the chart.
• Corrections & edition: the chart is for example a 2019 edition but is – when properly corrected – still valid in 2028. Corrections are published continuously and the changes made should be mentioned in the bottom left corner of the chart.

Information in the chart

• Depths reduced to Chart Datum: a sounding like 3₅ indicates 31⁄2 metres of water under Lowest Astronomical Tide (LAT) – which is commonly the Chart Datum.
  An underlined sounding like 0₄ indicates a height of 40 cm above LAT. Heights above Chart Datum on drying areas are given in metres and decimetres. The metres figure is underlined.
  Depths are given from 0.1 to 20.9 in metres and decimetres, and from 21 to 31 in metres and half metres. Greater depths are rounded down to the nearest safest metre (for example, 32.7 metres is rounded down to 32 metres).
  The geographical position of a sounding is the centre of the depth figure.
• Isobaths or contours: lines connecting positions with the same depth.
• Heights reduced to chart datum: heights of for instance, lighthouses, mountains and cliffs are more often reduced to another datum such as Mean High Water (MHW) or Mean High Water Spring.
• Tidal information: details of both the vertical (see Chapter 7 see Chapter 7 ) and the horizontal (see Chapter 8 see Chapter 8 ) movement of the water is often included in the chart.
• Lighthouses, buoys & marks: characteristics of lights, buoys and marks, see Chapter 9 Chapter 9 .
• Seabed qualities: pebbles, seaweed, rocks, wrecks, pipelines, sand and other seabed characteristics for anchoring .
• Magnetic variation: angle between the "True North" and the "Magnetic North" varies in place and time. The local variation is indicated in the compass card / compass rose, see Chapter 3 Chapter 3 .
• Landmarks & conspicuous positions on the shore: churches, radio masts, mountain tops, etc. that can be used for compass bearings and other means of navigation, these will be put to good use in Chapter 4 Chapter 4 .

Coordinates and positions

A pair of nautical dividers (single handed dividers) is used to obtain precise coordinates from the chart.

This device enables you to take the distance between that particular position and the closest grid line, see Figure 2.5 below. You then place the dividers on the scale with one end on this grid line, leaving the other end precisely at your coordinate. Do this twice to get both latitude and longitude at the scale on the edge of the chart.

Following you will find some examples, an  excerpt from the PDFs  :

Plotting a position onto the chart is done by reversing this method.

Some chart symbols come with a line and circle precise location of chart symbol indicating the precise location, like the “Radio mast”, otherwise the center of the symbol, or its placeholder , is the precise location.

Another possible notation of
33° 28,5' E is
33° 28′ 30" E, which however doesn't easily allow for more precision like
33° 28,500' E does.

Also note that in most countries a comma – and not a period – is used as the decimal separator. Both 33° 28.500' E and 33° 28,500' E are valid notations.

Distances

To measure the distance between, for instance, the two oil rigs of Figure 2.6 , we will again need our dividers. Remember, we can only use the vertical scale.

[画像:Measure distances on the nautical chart]

We first take a convenient distance like 10' (10 nautical miles) on the vertical scale using the middle latitude. Then we start walking with the dividers from the southern oil rig to northern one. Finally, we adjust the dividers to measure the small remaining part at its own height, i.e. its own latitude; caution were you to measure it below 42°, you would read 6.8' instead of 7'.

The image shows that the total distance is 37 nautical miles, or 37 NM.

Courses

So, now we can measure distances and both plot and read out positions, but we also need directions. For example we need to find the course from safe-water buoy A to safe-water buoy B. To accomplish this we may use a parallel rule aka parallel ruler as shown in the chart of Figure 2.7 below:

[画像:Nautical course - parallel rulers]