Plotting and piloting

“Piloting” or “pilotage” is the art of wayfinding using visual fixed points with reference to a nautical chart or publication.

It is considered distinct from, or rather a part of, “navigating“ or “navigation”, which typically refers to wayfinding without frequent and continuous determination of position relative to observed fixed points.

Taking a compass bearing on this oil rig with a steering compass provides us with a “compass course” or “bearing”.
This course first needs correction for both the deviation – according to our current heading, see deviation card or graph – and the variation before plotting a Line of Position (LOP) on the chart as a true course.

 LOP  our position is somewhere on this line: 50° towards (or 180° + 50° = 230° eminating from) the oil rig.

Accuracy is enhanced by:

• more distance between the two landmarks.

• less distance between the vessel and the closest aid to navigation.

• One of these four ranges consists of two lights that are intentionally placed to provide an LOP. These pairs of lights are called leading lights producing a leading line: the recommended track.

In depth: ranges and leading lines.

In this case they indicate the safe approach towards the Wildrooz port by marking the channel between the dangerous rocks along a true course of 50°; often such a range LOP is labeled 50° 230° including the reverse direction.
When looking towards any leading lights, the nearest one will be lower as not to block the signal of the rear light, and in the middle of the channel both lights will appear vertically “in line".

Position fix

If two LOPs intersect we can construct a position fix  the ship's position on the earth.

Often, however, a triangle occurs when a third LOP is added in the construction. This indicates that there are errors involved in at least one of the bearings taken. In practice, we should consider each LOP as the average bearing in a wider sector of for instance 10°, with 5° on each side of the average bearing, like in the image below.

The optimum angular spread is 90° (two objects) or 120° (three objects).

Moreover, bearings on distant objects bring about more uncertainty in our position fix as the error sector widens.

Finally, if moving fast you should not put any time between the bearings

Without a third LOP – forming the dreaded triangle – there is the false suggestion of accuracy. Yet, instrument errors, erroneous identification of an aid to navigation, sloppy plotting, etc. can and will cause navigation errors.

Therefore, if in proximity to e.g. rocks Rocksyou should assume to be at the worst possible position, i.e. closest to the navigational hazard.

The lines plotted on the chart are always true courses and these are labeled with true courses by default, e.g. 168° T or simply 168° ; the “ T  ” is optional. If labeled with the corresponding magnetic course or compass course add an “M  ” or “C  ”, respectively.

A true course corrected for magnetic variation  magnetic course  use this for hand bearing compass.

A true course corrected for both magnetic variation and deviation  compass course  use this for the steering compass.

Dead reckoning

Dead reckoning (etymology: deduced reckoning, ded. reckoning) is a technique to determine a ship's approximate position by applying to the last established charted position a vector or series of vectors representing true courses and speed through the water. This means that if we have an earlier fix, we plot from that position our course and “distance travelled since then” and deduce our current position.

Vector labeling

S = Speed in knots

C as prefix = Course (default, so optional)

C as suffix = Compass course for steering compass (corrected for deviation)

M = Magnetic course for hand bearing compass (no deviation correction)

T = True course (default, so optional)

Mark with a middle arrowhead, a semi-circle (circular arc) and “DR  ”.

Speed and courses for DR plots are always through water and not over ground.  

Dead reckoning is also crucial since it provides an approximate position in the future. Each time a fix or running fix is plotted, a vector representing the ordered course and speed originate from it. The direction of this course line represents the ship's course, and the length represents the distance one would expect the ship to travel in a given time. This extrapolation is used as a safety precaution: so, when a predicted DR position places the ship in water 1 metre deep, it should raise an eyebrow…

In the example above the true courses are plotted on the chart, and to assist the helmsperson these course lines are labelled with the corresponding compass courses.

Guidelines for dead reckoning

Extrapolate your position in the future: plot a new course line from each new fix or running fix (single LOP).

Choose either a new DR track from an EP (single LOP), or continue along the original DR track.

Plot a DR position every time course or speed changes.

Determine your current position: plot a corrected DR position if the predicted course line proofed wrong (e.g. a change in wind meant you sailed less distance and in a different direction), and continue from there.

Running fix

Under certain circumstances – such as low visibility – only one line of position can be obtained at a time. In this event, a line of position obtained at an earlier time may be advanced to the time of the later LOP.

These two LOPs should not be parallel to each other; remember that the optimal angular spread is 90°. The position obtained is termed a running fix because the ship has “run” a certain distance during the time interval between the two LOPs.

Guidelines for advancing a LOP

• The distance from EP: equal to the distance between the two corresponding DR positions.

• The direction from EP: equal to the direction between the two corresponding DR positions.

• Draw the advanced LOP with a dotted line and notate both times.

• Label the Running Fix position with an ellipse and "RFix" without underlining.

Turn bearing

Similar to the danger bearing and dead reckoning, the turn bearing is constructed on the chart in advance and should likewise be used as a means of anticipation for sailing out of safe waters. The turn bearing is plotted on an appropriate aid to navigation and is marked “TB”. As you pass the object its bearing will slowly change and only when it reaches the turn bearing turn the vessel on her new course.

This type of bearing is also used for selecting an anchorage position or diving position.

Snellius construction

Willebrord Snellius – a 16th century mathematician from Leiden, the Netherlands – became famous for implementing and co-inventing the loxodrome / rhumb line and his method of triangulation.

The Snellius construction was first used to obtain the length of the meridian, and thus the earth's circumference, through measuring the distance between two Dutch cities by famously taking the angles from and to church towers of villages in between.

Nowadays we use the Snellius method to derive our position from three bearings without the use of LOPs, so that deviation and variation are left out → simplifying things.

On top of that, since only relative angles are needed, a sextant can be used to determine the angles between navigation aids at greater distances. Closer in, a compass will suffice as well.

Construction

First steps, see Figure 4.11

• compass bearings are 320° on A;   360° on B;   050° on object C.

• the angle between A and B = 40°.

• the angle between B and C = 50°.

• draw lines from A to B and from B to C.

• add the two light-blue perpendicular bisectors of lines AB and BC.

• draw at object A a construction line 40° inland of line AB.

• draw at object C a second construction line 50° inland of line CB.

Final steps, see Figure 4.12

• at object A: draw a line perpendicular to the construction line.

• at object C: draw another line perpendicular to the construction line.

• the two intersections with the light-blue lines indicate the centres of two circles.

• finally, draw the first circle using A and B and the second circle using B and C.

• the offshore intersection of the two circle gives us our position fix.

The two advantages:

1. both deviation and variation can be left out since the angles (here 40° and 50°) are relative ones.

2. a sextant can be used to obtain high precision angles between objects at greater distances, where it would be less precise with compass bearings.

Fix by depth soundings

A series of depth soundings – in this example every 10 minutes – can greatly improve your DR fix, and works best with an irregular or steeply inclined seabed.

Guidelines

• Correct your soundings for tidal height, see chapters 6, 7 and 8. Also note that the depth sounder measures sideways when heeled.

• Copy the DR course line on a transparent sheet, and notate the depths adjacent according to the times of the soundings.

• Move the sheet over the chart to find its best location, and mark as EP.

Due to leeway, currents or other factors the two course lines need not be parallel to or of same length as each other.

Line Of Position (LOP): the locus of points along which a ship's position must lie. A minimum of two LOPs are necessary to establish a fix. It is standard practice to use at least three LOPs when obtaining a fix, to guard against the false security, and add accuracy.

Leading lights or range lights are a pair of light beacons, forming a leading line, indicating a safe passage for vessels entering a shallow or dangerous channel; and may also be used for position fixing. The beacons consist of two lights that are separated in distance and elevation, so that when they are aligned, with one above the other, they provide a bearing. Leading lights are often illuminated day and night.

If unlit, the beacons are known as a range or a transit.

Transit bearing / range: the method of lining up charted objects to obtain an LOP.

Position fix: the intersection of various LOPs, labeled as Fix or Fix.

Cross bearing: LOPs on several navigational aids will obtain a position fix. Remember to use an optimal angular spread: 90° for 2 LOPs or 120° for 3 LOPs.

Running fix: advancing an earlier LOP to combine it with a current LOP. Make sure to use only the corresponding DR positions; RFix.

Dead reckoning: determining a position by plotting courses and speeds from a known position – this is good seamanship – will keep the vessel out of harm's way; labeled as DR. It is also used to predict when lights become visible or to determine the set and rate of a current.

Simply put: dead reckoning provides us insight in our present position or our future position.

Estimated position, LOP + DR: combining a corresponding DR position with a single LOP will give an EP position; Single LOP + DR EP.

This is an improved position based on a DR position.

Estimated position, tide applied: Dead Reckoning with horizontal tidal movement (SET and DFT) applied will give an EP position; Estimated position with tide applied EP.

Snellius construction: a cunning and convenient way to use the angles (via compass or / and ideally by sextant) between three aids to navigation to obtain a position fix. The advantage over a cross bearing is that both magnetic variation and deviation don't need to be taken into account. Furthermore, with a sextant, even at distances beyond 15 NM this method is precise.

Course versus Track: (C) the term “course" was originally restricted to directions steered or intended to be steered through the water, while the term “track” is a path over ground.

Course Made Good: (CMG) the resultant direction – a straight line – between any two points on the vessel's track. For instance: 4 NM east and 4 NM north, would lead to CMG of 045° T.

This is a misnomer in that "courses" are directions steered or intended to be steered through the water. Therefore the term “Track Made Good” (TMG) is more precise and proper.

Track Made Good: (TMG) the single resultant direction from the point of departure to point of arrival at any given time. The use of this term is preferred to the use of the misnomer “Course Made Good.”

CMG versus COG: CMG (resultant direction) should be distinguished from Course over Ground (COG), which is a dynamic real- time value obtained from satellite navigation.

Course over Ground (COG) or Track is the direction of the parth over the ground actually followed by a vessel. The preferred term is Track (TR). It is normally a somewhat irregular line.

Speed Made Good: (SMG) the speed of the vessel achieved over the CMG line / TMG track.

Speed: (S) the speed of the vessel through the water, in contrast to Speed Over Ground ( SOG ).

Set: (SET) the direction in which the current is flowing (see chapters 6,7 and 8), current is always expressed in degrees true and always expressed in the direction it is flowing, whereas wind is expressed as where it comes from. 

Drift / Rate: (DFT) the speed (in knots) of the current (see chapters 6,7 and 8).

Heading: (HDG) the direction in which a vessel is pointing at any given moment. It is expressed as the angular distance relative to north, usually 000° at north, clockwise through 359°, in degrees of either true, magnetic, or compass direction. It is a constantly changing value as a vessel yaws back and forth across the course due to the combined effects of sea, wind, and steering error.

For example, on a sailing yacht the helmsperson may be trying to steer a course of 180°, but the heading one moment is 188° and the next moment it is 074°. The Course remains 180°, which is the intended direction of movement through the water.

Leeway (angle): the leeward motion of a vessel due to wind (and not due water movement); the leeway angle is the angular difference between a vessel's course and the Track (COG) due to the effect of wind in moving a vessel bodily to leeward.

Course to Steer: CTS is the course to steer to counteract (current and) leeway.

In other words: the course that a vessel should steer in order to arrive at a waypoint, bearing in mind the effects of wind and tide.

Course through Water / Water Track: CTW is the direction of the yacht through the water derived from combining heading and leeway. Water Track = HDG ± leeway.

Bearing: the direction from one place to another, measured in degrees of angle. When using compass bearings, the reference line is north, so “the lighthouse is on a bearing of 270°” means “the lighthouse is to the west of us.” When using relative bearings, the reference line is the vessel’s centerline. So, dead ahead is 000° and a buoy abeam to starboard (which is nautical terminology for “at 90° to the right when you are facing forward”) bears 090°. Electronic chart plotters provide a continuously updated bearing to an active waypoint.

Default time: is the 24 hour clock “ship time”, otherwise UTC.