Section D 4: Introduction to plotting

Transcription

1 Boating Course Student s Notes Section 4 Section 4: Introduction to plotting 4.1 General If a boat is being conned through a winding channel where there is a great deal of boat traffic, the helmsman is required to make frequent changes of course. As these are seldom entered in the log book, there is no record of exactly where the boat has been. To most boaters, this omission is not important. In contrast, if a boat must make a long passage over open water, where there are few aids to navigation, visibility is reduced, and land may be temporarily out of sight, the prudent boater makes sure a more permanent record exists. This can be provided by plotting, which consists of drawing a graphical representation of the boat s movements on a chart. Accurate plotting requires at least two qualified members in the crew one to navigate and keep the plot up to date, the other to steer and keep a good lookout. The navigator must constantly check the boat s position and determine the best course to steer, while the helmsman must accurately maintain the course, often over long periods of time. A well-kept plot can provide a very reliable record of where the boat has been, where it is now, and where it will be at a particular time in the future. 4.2 Area of uncertainty A boat s movement in relation to the earth s surface is a combination of its own movement through the water and the movement of that water in relation to the earth. The currents set up in the water by winds and gravitational forces are only partly predictable in speed and direction. Even when a boat is steered in a known direction at a known speed, these unpredictable factors combine to increase or decrease its rate of travel over the earth s surface and to push it to right or left of its intended path. Only when an accurate fix has been obtained is a boat s position known precisely. At other times, its position lies somewhere within an area of uncertainty. If a fix can be obtained at frequent intervals, the area of uncertainty remains quite small. But during a long run over open water, when there may be no way to obtain a fix, the area of uncertainty increases steadily as the boat moves away from its last known position. This is illustrated in Figure 4.1 where a boat is assumed to be travelling at 6.0 knots in a 1.0 knot current of unknown direction. After four hours, the area of uncertainty would cover an area of 50 square miles. This must be taken into account when navigating. 4.3 Time Navigators deal with various sorts of time, of which the most common are watch time and elapsed time. Watch time, as the name implies, is the time indicated by a watch. In order to avoid confusion between a.m. and p.m., it is normal practice on a boat to use the 24- hour clock for watch time and to express it as four digits, with the first two digits indicating the number of hours since midnight and the last two digits indicating the number of minutes past the hour. For example: 4:47 a.m. is expressed as :47 p.m. is expressed as 1647 Elapsed time is the time between two events, and is found by subtracting the earlier time from the later one. The calculation is slightly easier using a 24-hour clock, because a.m. and p.m. are not taken into account, but it must be remembered that the last two digits represent minutes and that there are 60 minutes in an hour, not 100. Elapsed time can be calculated very quickly by using a pocket calculator that automatically converts times expressed in hours, minutes, and seconds into hours expressed in decimal fractions. 33

2 Section 4 Boating Course Student s Notes Fix Calculated position Area of uncertainty C 090 S 6.0 Course line Miles Time Boat speed 6.0 kn Current 1.0 kn Current direction unknown Figure 4.1: iagrammatic illustration of the increase in a boat s area of uncertainty, at specific times, as it travels onwards from its last fix 4.4 efinitions There is little uniformity among authors when defining technical terms relating to plotting. The definitions used in this course have been adapted from The American Practical Navigator (Bowditch) and utton s Nautical Navigation, with modifications to make them more applicable to recreational boating An example Reference to Figures 4.2 to 4.7, which illustrate the situation outlined below, will help explain the meaning of some terms. A powerboat that cruises at 6.0 knots is to be taken, in poor visibility, from buoy X to buoy Y, which is 24 miles distant in the direction 080 (T) from buoy X. A third buoy, Z, lies 20 miles from buoy X in the direction 090 (T). A current of unknown strength flows towards the southwest. After undertaking some preliminary plotting, the navigator decides to steer 070 (T) to offset the effect of the current, and at 0736 passes buoy X close aboard (see Figure 4.2). Nothing more is seen until 1136, when buoy Z is passed close aboard and the 34 navigator realizes the current was much stronger than expected Speed The word speed (abbreviation: S) specifically refers to a boat s indicated speed through the water. A boat s speed is sometimes determined from the number of revolutions per minute (RPMs) of the engine. A series of timed runs is made over a measured distance, each run at a different RPM, to find the relationship of RPMs to speed. These are plotted as a graph to produce what is known as a speed curve. The relationship is assumed to be constant under all conditions, and when a boat s engine is set at a particular number of RPMs, its speed is assumed to be as indicated by the speed curve. The preparation and use of speed curves are covered in the CPS Advanced Piloting Course. Many recreational boats have a sensor fixed to the hull, which is connected to a speed and distance indicator in the cockpit. This permits the boat s speed, and the distance it has travelled, to be read directly from a dial. The accuracy of these instruments should not be taken for granted. Typically they are accurate at one particular speed but tend to under-read at lower (Revised 2006)

3 Boating Course Student s Notes Section 4 irection of current Speed unknown N 080 Y 24 Miles X 20 Miles 090 Z Figure 4.2: Relationship between buoys X, Y, and Z, and the direction of the current speeds and over-read at higher ones. Like a speed curve, they measure only the boat s forward movement through the water, not its speed and distance over the surface of the earth. A boat s movement in relation to the earth s surface can be obtained from instruments such as LORAN and GPS, which can also store the latitude and longitude of many different locations. These are then known as waypoints, about which more information is given in the CPS Piloting and Marine Electronics Courses. In areas where distances are measured in nautical miles, as on Canada s seacoasts, boat speeds are normally expressed in knots (abbreviation: kn), with a knot being defined as a nautical mile per hour. On the Great Lakes, however, distances may be measured in statute miles or kilometres, and in those cases speed may be expressed in statute miles per hour (mph) or in kilometres per hour (km/h). When used in conjunction with time, speed can be used to establish distance travelled Track A boat s intended path over the earth s surface is called its track (abbreviation: TR). At one time this was called the intended track, and it is important to note that the word track still implies a future intention. In the example described in subsection 4.4.1, the navigator plotted the boat s track on the chart as a straight line from buoy X to buoy Y and found the direction of the track to be 080 (T). The track was labelled TR 080, above the line (see Figure 4.3) Course A boat s course (abbreviation: C) is the horizontal direction in which a boat is to be steered, or is being steered. It is expressed in angular units from 000 clockwise through 360, using three digits. It may be designated as a true (T), magnetic (M), or compass (C) course, depending on whether the direction of the course line is measured from true north, magnetic north, or compass north. When determining the direction in which the boat is to be steered, the navigator must take into consideration any expected effects of (Revised 2006) 35

4 Section 4 Boating Course Student s Notes N Y TR 080 Cp 080 X Z Figure 4.3: The boat s track, in a direction of 080 (T) wind and current. As a result, the course is seldom exactly the same as the direction of the track. In the example described in subsection 4.4.1, the navigator was aware of a current flowing in a southwesterly direction and tried to offset its effect by steering a course of 070 (T) Course line The line that the navigator plots on the chart to give a graphic representation of the boat s course is called the course line. It is labelled with the true direction above (shown as the letter C and the true course in degrees, using three digits) and the speed below (shown as the letter S and the speed in knots). The course line drawn by the navigator in this example is shown in Figure Heading While the boat is under way, a helmsman must constantly correct steering errors that arise from the effect of wind, waves, and other factors. As these corrections often amount to several degrees on either side of the course, the direction in which the bow of the boat actually points is continually changing. The term heading (abbreviation: Hdg) is used to describe the horizontal direction in which a boat points (or heads) at any specific instant. It is expressed in angular units, clockwise from 000 through 360 from a reference direction. In the example described in subsection 4.4.1, although the boat s course remained constant at 070 (T), its heading was varying from 055 (T) to 085 (T) (see Figure 4.5). The heading is not plotted. C 070 S 6.0 TR Figure 4.4: The course line based on a course of 070 (T), added to the plot shown in Figure 4.3 (Revised 2006)

5 Boating Course Student s Notes Section 4 Figure 4.5: Changes in the heading of a boat as it is steered on a course of ead reckoning position A dead reckoning (R) position is based solely on the true course steered and the calculated distance travelled through the water, based on time and speed. All other factors are ignored, including the effects of wind and current. A R position is a poor indicator of a boat s position on the surface of the earth, but it is of fundamental importance as a base from which other types of position can be calculated. It is usually plotted from the most recent fix (although a running fix may be used, as explained in the CPS Piloting Course). A R position is marked on the chart as a dot and a semicircle (see subsection 5.5). It is always labelled with the time, which may be past, present, or future: in other words, a predicted R position may be plotted R plot A series of labelled R positions starting at a fix and showing the speed and distances travelled by a boat on each course line, together with LOPs and successive additional fixes, is known as a R plot. The R positions are plotted at regular intervals, usually every hour on the hour, although in tricky situations and with high-speed boats the R plot may be updated at intervals as brief as 10 minutes or less. (Revised 2006) A R position is also plotted every time there is a change of course or speed and whenever a bearing or a fix has been obtained. At each successive fix, the previous course line stops and a new course line is plotted starting at the new fix. More information on plotting is given in Section 5. For the example described in subsection 4.4.1, the R plot as it would be drawn by the navigator is shown in Figure Course made good A boat s course made good (abbreviation: CMG) is the direction in a straight line over the earth s surface from one fix to another. It is determined by drawing a line directly from a known point of departure to a subsequent known position. Intermediate courses are not taken into consideration. Whether the boat travelled in a direct line as a powerboat may do, or undertook a series of tacks as a sailboat may do, is of no consequence when determining the course made good. In this example, the boat s first fix was close aboard buoy X, at 0736, and the second fix was close aboard buoy Z at The course made good is therefore represented by the straight line from buoy X to buoy Z, which has a direction of 090 (T). It is labelled with the true direction above (shown as the abbreviation CMG and the number of degrees, using three digits) (see Figure 4.7). 37

6 Section 4 Boating Course Student s Notes C 070 S 6.0 TR 080 Y Z Figure 4.6: R plot starting at a fix and showing a series of R positions plotted along the course line, with the initial fix, the course line, and the R positions correctly labelled Speed made good The speed at which a boat covers the distance represented by the course made good is referred to as the speed made good (abbreviation: SMG). It is found by dividing the distance along the course made good by the time taken to travel from the first fix to the second fix. In this example, the distance was 20 miles, and it was covered in exactly 4 hours, so the speed made good was 20 divided by 4, or 5 knots. The line representing the course made good is labelled with the speed made good below the line, measured to the nearest tenth of a knot in this case, labelled as SMG 5.0 (see Figure 4.7). 4.5 Time, speed, and distance The relationship between time, speed, and distance is such that if two of them are known, the third can be calculated. Consider the following examples where T represents the elapsed time in hours, S represents the speed in knots, and represents the distance travelled in nautical miles: If a boat travels at a speed of 20 knots (i.e., 20 nautical miles per hour) for 2 hours, the distance it travels is equal to its speed (20) multiplied by the elapsed time (2). Thus, N Y CMG X 0736 SMG 5.0 Z 38 Figure 4.7: Example of course made good (Revised 2006)

7 Boating Course Student s Notes Section 4 = S T = 20 2 = 40 nautical miles If the boat travels a distance of 10 nautical miles in 2 hours, its speed is found by dividing the distance travelled (10) by the elapsed time (2). Thus, S = T S = = 5 knots Lastly, if the boat has to travel 30 nautical miles at 10 knots, the elapsed time will be the distance (30) divided by the speed (10). Thus, T = S T = = 3 hours A useful tool for remembering these relationships is the triangle shown in Figure 4.8. If the unknown value is covered up, the rest of the diagram shows the relationship between the other two values and hence the formula to be used to find the unknown value. S x T Figure 4.8: Aid for remembering the relationship between distance in nautical miles, speed in knots, and time interval in hours The foregoing examples are easy to solve because the distances, time intervals, and speeds are all expressed in comparable units, namely nautical miles, hours, and knots (bearing in mind that one knot means one nautical mile per hour ). When the time interval is expressed in minutes or hours and minutes, rather than in hours, the calculations become slightly more complicated. One way to deal with a time interval expressed in minutes or hours and minutes is to convert it to decimal hours with a pocket calculator and use the formulae illustrated above. Another method is to convert the time interval to minutes. Because there are 60 minutes in an hour, the number of whole hours is multiplied by 60 and then the number of additional minutes is added. For example, 2 hours and 47 minutes converts as follows: (2 60 minutes) + 47 minutes = 120 minutes + 47 minutes = 167 minutes. Because the formulae shown above apply where the time interval is expressed in hours, they must be adapted for use where the time interval is expressed in minutes; and so a factor of 60 is introduced to reflect the fact that there are 60 minutes in an hour. The basic formula becomes 60 = S t. (Note that the lowercase letter t denotes a time interval in minutes whereas the uppercase letter T denotes a time interval in hours.) If any two of the three values are known, the third value can be found by using the appropriate formula: To find the distance () in nautical miles, the formula is: = To find the speed (S) in knots, the formula is: S = To find the time interval (t) in minutes, the formula is: t = S t t 60 S A navigator uses these formulae constantly for inshore piloting, and should memorize them. The diagram in Figure 4.9 may be a useful memory aid. 39

8 Section 4 Boating Course Student s Notes Figure 4.9: Aid for remembering the relationship between distance in nautical miles, speed in knots, and time interval in minutes To use the diagram: 1.Cover the value to be found. 2.Multiply together the values that are side by side. 3. ivide their product by the value that stands alone. Another way to come up with the three formulae is this: The basic formula 60 = S t is easy to remember because it looks like a street address 60 Street. After writing out that basic formula, identify the one value which is unknown, and therefore must be found, and circle it. Then move the partner of the circled value under the other two. In each case, start with the formula 60 = S t. To find the distance in nautical miles, circle the. Then move the 60 (which is its partner on the same side of the equals sign) under the S t: 60 = S t = To find the speed in knots, circle the S. Then move the t (which is its partner on the same side of the equals sign) under the 60 : 60 = S t S = S t t 60 S t To find the time interval in minutes, circle the t. Then move the S (which is its partner on the same side of the equals sign) under the 60 : 60 = S t t = 60 S 4.6 Rounding Under real conditions, speed can seldom be maintained accurately to better than the nearest half-knot, but time, speed, and distance problems often work out to answers with several decimal places. For the purposes of this course, the standards of accuracy are: For time: to the nearest whole minute; For speed: to the nearest tenth of a knot (0.1 knot); For distance: to the nearest tenth of a nautical mile (0.1 M). This means that the results of calculations must be rounded off. This is done at the end of the calculation by dropping the extra decimal places according to the following rules: If the decimal to be rounded off is 4 or lower, it is dropped. If the decimal to be rounded off is 5 or higher, the preceding digit is raised to the next higher value and the rounded digit is dropped. For example: Time is recorded to the nearest whole minute: minutes is rounded to 7 minutes; minutes is rounded to 3 minutes; minutes is rounded to 10 minutes; minutes is rounded to 6 minutes. 40

9 Boating Course Student s Notes Section 4 Speed is recorded to the nearest tenth of a knot: knots is rounded to 7.2 knots; knots is rounded to 3.3 knots; knots is rounded to 9.5 knots; knots is rounded to 5.8 knots. istance is recorded to the nearest tenth of a nautical mile: miles is rounded to 7.2 miles; miles is rounded to 3.3 miles; miles is rounded to 9.5 miles; miles is rounded to 5.8 miles. 41

10

11 Boating Course Student s Notes Section 5 Section 5: Plotting and labelling 5.1 General This section gives instruction in plotting and labelling on a marine chart. The knowledge gained in this section is then put to use in Section 6, which consists of a chartwork exercise to be completed in class. 5.2 Instruments The instruments required for plotting are: a pair of dividers for measuring distances; the CPS course plotter for plotting lines and measuring angles; several sharp pencils of medium hardness (grade F or No ); an eraser for making corrections and removing previous work. 5.3 Plotting The first step is to draw a line on the chart indicating where the navigator intends to go. This is the track (TR). A second line, the course line, is then drawn to indicate the course to steer (C). If no allowance is to be made for current, the track and the course line will coincide. If current is taken into account, they may differ by several degrees. While the vessel is under way, the R plot is updated with new information obtained from observations and calculations. This consists of drawing additional labelled lines that show LOPs, R positions, fixes, times, changes of speed, and so on. 5.4 The CPS course plotter (see Figure 5.1) This instrument was specifically designed by Canadian Power & Sail Squadrons to facilitate plotting both in the classroom and on board a boat. It has features which will make plotting both simpler and more easily understood. (Revised 2005) Main features The main features of the CPS plotter are: an etched, bevelled edge on which pencil markings can be made. istances can be marked on the edge and then transferred directly from the plot to the latitude scale of the chart to be measured which is a simpler method than transferring distances to the latitude scale using dividers; two boat outlines located at either end of the plotter, one red and the other blue, with an interior arrow. These help the user to choose the correct degree scale for measuring courses and bearings, and avoid using the reciprocal direction; a rotating disc inscribed with a north pointer and horizontal and vertical grid lines; two scales, in degrees one red, the other blue in a half-circle about the rotating disc. These are used to set a course or to read off a course by means of the north pointer. Note that the scales read counterclockwise; cut-out shapes that can be used as templates for drawing different position symbols; an etched area for entering the owner s name. The CPS plotter provides a means of measuring true directions anywhere on the chart. When the plotter is being used, the north pointer on the rotating disc must be pointing precisely north at all times. This is accomplished by aligning the vertical and horizontal grid lines inscribed on the disc with the meridians of longitude and parallels of latitude printed on the chart. Typically, there will be only one meridian or one parallel situated conveniently nearby to use for this alignment; but a single line is sufficient. Because meridians of longitude and parallels of latitude are precisely at right angles to each other on a Mercator chart, it does not matter whether a vertical line on the rotating disc is aligned with a meridian of longitude or a horizontal line is aligned with a parallel of latitude. 43

12 Section 5 Boating Course Student s Notes RE N BLUE Figure 5.1: The CPS course plotter Note that the calibration is shown in 10-degree intervals in this illustration, whereas the calibration of the actual plotter is at 1-degree intervals. The following exercise illustrates the underlying principle of using the CPS plotter to draw a course line from a point of departure. Find the lighted fairway buoy situated on Training Chart IC/CA 9996 at L 'N, Lo 'W. Turn the rotating disc on the plotter so that the north pointer is set against the 000 mark on the scale. Lay the plotter on the chart so that the plotter s bevelled edge is against the lighted fairway buoy. Keeping that edge against the buoy, swivel the entire plotter until the north pointer on the disc is pointing straight up. The plotter s bevelled edge will now be vertical, and the blue boat/arrow on the plotter will be pointing towards the top of the chart. To fine-tune the alignment of the plotter, use a convenient meridian of longitude or parallel of latitude to align with one of the grid lines in the rotating disc. ouble-check that the 000 mark on the scale remains set against the north pointer and has not shifted. The result is that the bevelled edge is pointing due north from the buoy, or 000 (T). Note that the direction 000 is marked in blue on the plotter. This colour means that the direction from the buoy is indicated by the blue boat/arrow in this instance, upwards along the bevelled edge, not downwards. Now change to a new setting. Turn the rotating disc so that the north pointer is set against the 010 mark on the scale. Lay the plotter on the chart with the plotter s bevelled edge against the same buoy, and swivel the entire plotter to align one of the grid lines in the rotating disc against a convenient meridian of longitude or parallel of latitude. oublecheck that the 010 mark on the scale remains set against the north pointer. The result is that the bevelled edge is now pointing in a direction of 010 (T) from the buoy. Again, note that the direction 010 is marked in blue on the plotter, which means that the direction of 010 (T) is indicated by the blue boat/arrow. 44 (Revised 2005)

13 Boating Course Student s Notes Section 5 Set the north pointer against the 025 mark on the scale and go through the same procedure again. Repeat the procedure using gradually higher numbers such as 045, 060, 090, 135 and 150, right up to 180. It becomes evident that, as the number of degrees increases from 000 to 180, the bevelled edge of the plotter moves from being vertically aligned pointing upwards (north, or 000 (T)) to being horizontally aligned pointing towards the right (east, or 090 (T)) to being vertically aligned pointing downwards (south, or 180 (T)). Continue repeating the process with even higher numbers such as 190, 235, 270, 315, and 360. Note that these directions are all marked in red on the plotter, which means that the direction along the bevelled edge is indicated by the red boat/arrow. It becomes evident that, as the number of degrees increases from 180 to 360, the bevelled edge of the plotter moves from being vertically aligned pointing downwards (south, or 180 (T)) to being horizontally aligned pointing towards the left (west, or 270 (T)) to being vertically aligned pointing upwards (north, or 360 (T)) Finding the true course between two points (see Figure 5.2) Using a straight edge, draw a line from the point of departure to the destination. This line is the track, and if no allowance is being made for wind or current it is also the course line. C 300 S 10.0 RE BLUE N Figure 5.2: Finding the true course between two points (Revised 2005) 45

14 Section 5 Boating Course Student s Notes Lay the plotter edge against the course line, and hold it in place. Rotate the disc so that the north pointer indeed points north i.e., so that the north pointer or one of the other vertical lines on the disc is aligned with a meridian of longitude, or so that one of the horizontal lines on the disc is aligned with a parallel of latitude. It may be necessary to slide the plotter along the course line to do this, while ensuring that the plotter edge continues to lie precisely along the course line. Read the true course i.e., the direction of the course line against the north pointer, using the appropriate coloured degree marking depending on the direction of travel Plotting a course line from a point of departure in a given direction (see Figure 5.3) Rotate the disc so that the north pointer is set against the desired number of degrees (i.e., the desired course). Place the plotter edge against the point of departure and roughly in the required direction. Swivel the entire plotter until the north pointer on the disc is indeed pointing north: that is, swivel the plotter until the vertical or horizontal lines on the disc are aligned with the meridians of longitude or parallels of latitude on the chart. While swivelling the plotter, take care that the plotter edge continues to lie against the point of departure and that the C 040 S 10.0 RE BLUE N 46 Figure 5.3: Plotting a course line from a point of departure in a given direction

15 RE BLUE Boating Course Student s Notes Section 5 N Figure 5.4: Plotting LOPs based on bearings disc does not rotate within the plotter, so that the north pointer on the disc remains set against the desired number of degrees. raw the line in the direction indicated by the colour of the scale blue for directions between 000 (T) and 180 (T) and red for directions between 180 (T) and 360 (T) Plotting LOPs based on bearings (see Figure 5.4) Convert the compass bearing observed aboard the boat to a true bearing that can be used to plot an LOP on the chart. Rotate the disc so that the north pointer is set against the desired number of degrees (i.e., the true bearing). Place the plotter edge against the charted object on which the bearing was taken. Swivel the entire plotter until the north pointer on the disc is indeed pointing north: that is, swivel the plotter until the vertical or horizontal lines on the disc are aligned with the meridians of longitude or parallels of latitude on the chart. While swivelling the plotter, take care that the plotter edge continues to lie against the charted object and that the disc does not rotate within the plotter, so that the north pointer on the disc remains set against the desired number of degrees. 47

16 Red Blue Section 5 Boating Course Student s Notes raw the LOP along the bevelled edge of the plotter towards the observed object. If in doubt as to which side of the observed object the boat lies on, remember that the bearing is the direction from the boat to the charted object and draw the line as indicated by the colour on the scale: in other words, if a blue bearing is used (for directions between 000 (T) and 180 (T)), the LOP is drawn in the direction of the blue boat/arrow on the plotter, and if a red bearing is used (for directions between 180 (T) and 360 (T)), the LOP is drawn in the direction of the red boat/arrow on the plotter. Take care also to draw the LOP so that it ends at the observed object rather than extending through and beyond it, since the boat can be on only one side of the charted object at a given time. (An even better plotting technique is to draw the LOP so that it ends just short of the observed object, so there is no risk of losing the detail of the chart symbol through repeated erasures as new plots are drawn over the same area.) rawing parallel lines (see Figure 5.5) Place the plotter s bevelled edge against the first line. Rotate the disc so that the north pointer indeed points north i.e., so that the vertical and horizontal lines on the disc are aligned with the meridians of longitude and parallels of latitude on the chart; Move the plotter to the new position through which the parallel line is needed, and swivel it to align the grid lines on the disc again, with the north pointer pointing north. raw the new line along the bevelled edge of the plotter rawing position symbols The CPS plotter has cut-outs that the navigator can use as templates for drawing different position symbols. The ones used in this course are: a circle to indicate a fix; a half-circle to indicate a R position. In each case, a dot must be marked in the centre to indicate the exact position. (The other two cut-outs on the plotter are a triangle, which denotes a waypoint symbol, and a square, which denotes an estimated position. These are used in CPS advanced courses.) N Red Blue New line N Original line 48 Figure 5.5: rawing parallel lines

17 Boating Course Student s Notes Section Labelling Standardized labelling is used on plots, so that others who look at the chart can follow the boat s progress. The most important piece of information is always marked above the plotted line, while information of lesser importance is marked below the line. Labels describing a line are written parallel to the line, while labels describing a point are written at an angle to any nearby lines Course line A course line is labelled with the true direction above the line (marked as the letter C and the true course in degrees, using three digits) and the speed below the line (marked as the letter S and the speed in knots, to the nearest tenth of a knot). Note that all directions marked on the chart are understood to be true directions measured in degrees, and that all speeds marked on the chart are understood to be in knots. Consequently, when the course line is labelled, the course is shown without the degree symbol or the indication (T) (e.g., as C 070 ) and the speed is shown without the word knots or the abbreviation kn (e.g., as S 6.0 ) LOPs An LOP associated with a fix is labelled with the bearing on the south side of the line (in degrees, written as three digits). An isolated LOP is labelled with the time on the north side of the line and the bearing on the south side of the line. In the case of a long LOP to a distant charted object, where it is obvious what object was used to take the bearing, such as a major lightstation, it may be possible to reduce clutter on the chart by drawing only the sportion of the LOP in the vicinity of the boat s position, making it at least long enough that it can be labelled. If it is essential to draw a long line for clarity, then the LOP should be drawn as a solid line only in the vicinity of the boat s position and extended as a broken line to the distant charted object. (Revised 2006) R positions R positions are plotted on the course line: at least every hour on the hour; whenever there is a change in course or speed; whenever a bearing is taken or a fix is obtained. A R position is indicated by a dot enclosed within a semicircle and labelled with the time. R positions are usually carried at least one hour ahead of the boat s current position Fixes A fix is indicated by a dot enclosed within a circle with the time marked against it. If it is a two-bearing fix, the LOPs are plotted and labelled as described above. If the fix is close aboard a charted aid, this is obvious from the chart. Figure 5.6 illustrates how the sequence of events described below would be shown on the chart according to standard labelling conventions. You are navigator on a boat coming into port at dusk on a wet and very windy evening. It is a difficult approach, and you draw your track in a direction of 054 (T) from the previous fix to the green buoy CS 47 which lies close to shore. There is no current, and the wind was dead ahead at your last fix, so you decide to steer a course that is the same as the direction of your track. You label the course line accordingly and plot the R positions every hour. At 1835 you spot a buoy dead ahead and believe you are right on track, but at 1843 you get a bearing of 347 (T) on a television tower, and another of 091 (T) on a chimney. It takes you a few minutes to plot the resulting LOPs and obtain a fix. You then realize that the wind has shifted, you are several miles SSW of your R position, and the buoy you can see dead ahead is CS 48, which marks an area of foul ground. At 1852 you alter course to 023 (T), and at 2034 pass green buoy CS 47 close aboard before altering course to 119 (T) to follow the range into harbour. 49

18 Section 5 Boating Course Student s Notes TV Tr N CS 47 G C 119 S C 023 S 6.0 R CS S Chy Figure 5.6: An example of a labelled R plot 5.6 Standards of accuracy for chartwork In the real world, when a boat is under way, the wind, waves, and current make it difficult to keep a boat s heading to within 5 degrees of the desired course, and its speed may fluctuate over a range of several knots. This is particularly true of sailboats. In the classroom, none of these influences exists, and much greater accuracy can be achieved in chartwork exercises. The following standards of accuracy are expected in classroom and examination chartwork: For directions (courses, bearings, and the direction of tracks): to the nearest degree; For distances: to the nearest tenth of a nautical mile (0.1 M); For positions expressed as latitude and longitude coordinates: to the nearest tenth of a minute (0.1'); 50 For time: to the nearest minute; For speed: to the nearest tenth of a knot (0.1 knot). In practice, if a run is made at high speed over a short distance, the rounding of decimals to the standards indicated above will create a significant error if the results of that initial run are then used as a basis for calculating subsequent time intervals, speeds, or distances over longer journeys. 5.7 Planning a cruise The type of planning depends on whether there is a crew of two, or whether the helmsman is solo. In this section, it is assumed that a navigator is present who can devote full time to navigation Establishing a point of departure This must be done at the start of the cruise to establish the first fix. If that first fix is uncertain, or is (Revised 2006)

19 Boating Course Student s Notes Section 5 missed, further errors will arise until a new fix can be established. The point of departure should be a very accurate fix such as close aboard a marked aid, or at the intersection of two ranges. For plotting purposes, having an aid close aboard is taken to mean that the boat is actually at the aid, so plotting is done from the dot or circle in the base of the chart symbol which indicates the aid s position. Even if the boat is in fact 50 metres away from the aid, this amounts to less than three one-hundredths of a nautical mile (0.03 M), a distance so small it cannot be plotted on a relatively small-scale chart such as Training Chart IC/CA Establishing a destination The last part of any cruise will probably consist of conning the boat into a harbour or quiet anchorage, and will be undertaken at very reduced speed. Prior to that, the boat will probably maintain normal speed until a predetermined destination is reached. This must be a clearly identifiable location outside the anchorage, marked on the chart and easily recognized from the boat as it approaches on the final leg Plotting and labelling the track and the course line The direct route from the point of departure to the destination is first inspected carefully to ensure that it is clear of hazards. If it is clear, the track is plotted on the chart as a straight line between the two points. If hazards are present, the track must be plotted as a series of two or more legs that bypass the danger spots. The course line will be the same as the track unless allowance is to be made for the effect of wind and current. For most chartwork exercises in this course, it is assumed there is no wind or current. On the course line, measure the direction of each leg and label it to indicate the direction (i.e., the course) and expected speed. The labelling consists of the letter C and the course expressed as three digits above the line, and the letter S and the speed in knots below the line (see subsection 5.5.1). If the cruise includes more than one leg, the procedure must be repeated for each leg Finding the expected duration Measure along the course line from the point of departure to the destination to find the total distance. For powerboats, assume the most economical cruising speed. For sailboats, estimate the speed from the strength and direction of the wind and anticipate changes. To calculate the duration of the cruise, the formula t = is used, or the formula T = S 60 S if long distances are involved etermining the compass course to steer The magnetic variation is read from the chart and applied to the true course to give the magnetic course (see Section 2). eviation may then be applied to the magnetic course to obtain the compass course to steer. For the purposes of the Boating Course, the variation on Training Chart IC/CA 9996 is taken to be 20 E in all chartwork exercises unless otherwise stated. As well and again, only for the purposes of this Boating Course since the deviation is taken to be 0 on all headings, the compass course is always the same as the magnetic course Selecting aids to navigation and landmarks Study the chart carefully, and observe the aids and landmarks that might be used on each leg of the cruise. Greater accuracy will be achieved by selecting those close to the track. 51

20 Section 5 Boating Course Student s Notes Identifying possible LOPs These can be obtained from ranges, lights in line, steep coasts in line, points of land in line, etc. LOPs can also be obtained from bearings taken on lights (their characteristics should be noted), hills, water towers, church steeples, and similar features that have a distinctive shape. If the boat has a depth finder, sharp changes in depth as indicated by closely spaced depth contours, can give a fairly reliable LOP in lakes, but where tidal movements cause large changes of depth, they may be more difficult to interpret. Using LOPs The information obtained from LOPs can be used in a number of ways. An LOP that is almost parallel with the track can give an indication of cross-track error i.e., the boat s distance to right or left of the track. A back bearing on the point of departure, or on a conspicuous object very close to it, will give an early indication of whether the boat is on track. If the back bearing is approximately equal to the reciprocal of the direction of the track, the boat is on track; if the bearing is less than the reciprocal, the boat is to the left of the track; if it is greater, the boat is to the right of the track (Less is Left). An LOP that cuts the track at right angles can give an estimate of the distance travelled from the last known position. By taking time into account, the boat s speed made good can be estimated, and the estimated time of arrival (ETA) at the destination can be updated. If a conspicuous object lies at or very close to the destination, it can be used to detect cross-track error near the end of the leg, and may be used as a leading mark towards which the boat can be steered. Identifying possible fixes These are most useful if they can be found towards the end of each leg, or where a change in course must 52 be made, or near the destination, especially if the entrance to the anchorage is hard to find. They can be obtained from: buoys and other marked aids that will be passed close aboard or whose distance off can be easily estimated; two LOPs that intersect nearly at right angles Plotting R positions R positions should be recorded at least every hour on the hour, but until the actual time of departure is known, they cannot be plotted, nor the times marked against them. When visibility is reduced, R positions may be the only indicator of the boat s position, and they should be marked at regular intervals along the course line. On a very long cruise in a slow boat, the distance travelled in an hour should be sufficient. uring particularly difficult periods, or on fast boats, which can go a long way off course in an hour, it is more appropriate to calculate the distance travelled in a shorter time, such as 10 minutes. 5.8 Keeping a log To maintain a permanent record of the cruise, the most important pieces of navigational information should be entered in the log. This need not be a complicated document, but times, courses steered, bearings, fixes, ETAs, etc. should be entered in it. Log books can be purchased at most marine supply stores. An example of a simple log is provided and should be completed as part of the cruise which is the homework for this section. It may be started in class under the guidance of the instructor, and completed at home as time permits. 5.9 Summary of labelling conventions and standards of accuracy For a complete summary of the labelling conventions and the standards of accuracy for chartwork and piloting exercises used in this course, see the Supplementary Material included as part of these Student s Notes.

21 Boating Course Student s Notes Section 5 Boating Course eck Log Form ECK LOG VESSEL: NAVIGATOR: ate/ Obser- Latitude Longitude T V M C Speed ist. ETA Remarks time vation (Use two lines if necessary) 53

22