Chart Work UNIT 12 CHART WORK EXERCISES Exercises Structure 12.1 Introduction Objectives 12.2 Finding the Distance that the Ship will Pass off a given Point When Abeam 12.3 Course and Distance 12.3.1 To Find Course and Distance Between Two Position 12.3.2 Find the Distance Between Two Positions 12.3.3 Calculating the Speed Between Two Positions 12.4 Set and Drift due to Current and Leeway due to Wind 12.4.1 Leeway 12.4.2 Set and Drift of the Current 12.5 Ship’s Speed, Course and Speed Made Good 12.6 Finding the Course and Distance Made Good with a Tidal Stream or Current 12.7 Finding the Course to Steer Allowing for Tidal Stream or Current and Leeway 12.8 Finding the Direction and Strength of Tidal Stream or Current from Charts or Tables 12.9 Running Fix and How to Use it to Plot a Position 12.10 Finding Positions by Running Fix in a Tidal Stream or Current 12.11 Calculating the Actual Set Rate of Tidal Stream or Current from DR and Fixed Positions 12.12 Summary 12.13 Key Words 12.14 Answers to SAQs 12.1 INTRODUCTION Chart work is all about laying off courses through safe waters and sailing from one port to another in minimum possible time. Knowledge of the currents along the route and direction in which they set will certainly help the navigator in achieving this goal. In this unit, we will carryout chart work exercises in laying off courses, finding distances and calculating speed between two positions with and without current. Objectives After studying this unit, you should be able to • find the course and distance made good by the ship with the tidal stream or current, • course to steer to allow for a current, • obtain a running fix with or without a current, and • calculate the set and drift when the DR and fixed positions are given. 37 Practical Navigation 12.2 FINDING THE DISTANCE THAT THE SHIP WILL PASS OFF A GIVEN POINT WHEN ABEAM A landmark or lighthouse is said to be abeam of the ship, when it comes in line with perpendicular to the ship’s fore and aft centreline on any side of the vessel. Bearing of that lighthouse when abeam will be either 90° to the portside or 90° to the starboard side of ship’s heading (ship’s course) at that moment. The distance of that lighthouse at this moment (when abeam) is called beam distance and bearing is known as ‘beam bearing’. Note Beam bearing is always on course being steered or one can say ship’s heading at that moment. Example 12.1 (a) From a vessel steering 270° (T), at 1830 hrs. Royal Sovereign Lt. Vessel bore 044° (T) and Beachy Head Light bore 337° (T). Find the ship’s position. (b) From the position obtained at 1830 hrs, from this position vessel steered a course of 259°(T). Find distance when St. Catherine Pt. will be beam if ship’s speed was 12 knots? Solution (a) To find ship’s position at 1830 hrs. Draw a line with Royal Sovereign Lt. Vessel Bearing 044°(T) and Beachy Head light bearing 337°(T) and where the two bearings intersect is the position of the ship at 1830 hrs. Ship’s position at 1830 hrs: Lat 50°38´ N Long 00°19´ E (b) From this position lay course of 259°(T) and extend this line beyond St. Catherine Pt. From chart, it is clear that this point will be abeam on stbd. Side. Beam bearing of this lighthouse will be 259 + 90 = 349°(T). From St. Catherine Pt. lay off the reverse of this bearing, i.e. 169°(T). Wherever this bearing line intersects the laid course line of 259°(T) is the point where lighthouse will be abeam. From this point, measure the distance on chart to the St. Catherine Pt. This distance is the beam distance which is : 8 miles. Beachy Head Royal Sovereign Catherines Pt 3370 (T) 1830 0440 (T) 0 8m 69 1 Figure 12.1 38 Chart Work 12.3 COURSE AND DISTANCE Exercises We have learnt in Unit 10, that true course is the angle between true north and ship’s head measured clockwise from true north and expressed in 360° notation. Distance is expressed in nautical miles and is the length of arc of meridian subtending an angle of one minute at the centre of its curvature. You are reminded that on mercator chart, a nautical mile is equal to 1´ of d´lat and that is why distance is always measured along latitude scale on a chart. 12.3.1 To Find Course and Distance between Two Positions Let us take an example and see if we can find course and distance between two given points on the chart. Example 12.2 Find the true course and distance from position (A) Lat. 49º 05´ N Long. 03º 40´ W to a position (B) Lat. 49o 33´ N Long. 03º 09´W. Solution (a) Plot the two positions on the chart. (b) Join the two positions by a straight line; the direction of this line represents the course, and the length of the line is the distance between positions. (c) To find the true course: First Method Set the edge of the parallel ruler along the course line and carefully transfer them to the nearest compass rose, placing one edge through the exact centre of the rose. Read off the true direction from the compass rose, taking care not to read off the reciprocal course (i.e. 180º away). (True direction of the course being from starting position towards the destination.) Second Method The course can also be found by transferring the parallel ruler to the nearest meridian on the chart. The angle that the course line makes with the meridian, measured in a clockwise direction from north and given in the three figure notation, is the true course, i.e. 035º (T). If the true course was required from position (B) to (A), it would be 215º (T). (d) To Find the Distance One nautical mile is equal to one minute of the arc on the latitude scale. Using the dividers and the scale of the latitude between two positions, measures the distance, i.e. 34.2 miles. You are once again reminded that the distance between any two positions must be measured in the region of the mean latitude between these positions. When large distances are involved, set the dividers to a convenient distance, e.g. 10 miles, or 20 miles along the mean Latitude; step off along the course line making a note of the number of steps taken, measuring the final portion of a step separately. Ans : True Course 035º (T) Distance 34.2 Miles. 12.3.2 Finding the Distance Between Two Positions One nautical mile is equal to one minute of the arc on the latitude scale. Using the dividers and the scale of the latitude between two positions, one can measure the distance. In Figure 12.2, distance can be measured by putting two ends of dividers on “A” and “B” and measuring on the latitude scale. 39 Practical Navigation In Figure 12.2, distance from “A” to “B” is 9 NM (nautical miles). A B 0 337 ( T Figure 12.2 12.3.3 Calculating the Speed Between Two Positions Speed of any ship is the distance travelled in one hour expressed in Nautical miles/hour or Knots. So 10 knots means ship is travelling at 10 nm in one hour. In Figure 12.2, as we saw distance from “A” to “B” is 9NM and if a vessel takes 30 minutes to sail from “A” to “B”, the speed of this vessel can be calculated by dividing the distance (NM) by time (HRS). In this case, speed of this vessel is 9/0.5 = 18 kts. 12.4 SET AND DRIFT DUE TO CURRENT AND LEEWAY DUE TO WIND 12.4.1 Leeway The effect of wind on the course steered is called the “Leeway”. Leeway is the angle between the ship’s fore and aft line and the line of the wake left behind her. In other words, it is the angle between the course steered and the course made good. It is estimated approximately in number of degrees to the leeward side, according to the direction and the force of the prevailing wind. In practice, the leeway is estimated by the navigator as so many degrees to port or starboard and necessary allowance made for it in computing the course to steer. Explanation If the ship steers a course of 086º (T) and the wind is from North (force 5) and she experiences a leeway of say 6° then the course made good (after allowing for leeway) is ascertained as follows : Wind “N”ly B 086º(T) Leeway 6º A 092º (T) C Figure 12.3 40 In Figure 12.3, AB is the course steered viz. 086°(T), wind is from North, then ∠ BAC Chart Work will be the leeway, i.e. 6° (or 6° to stbd.) and the course made good after leeway will be Exercises 092°(T). Note In all questions dealing with leeway, it is advisable to draw a rough sketch. 12.4.2 Set and Drift of the Current The course and the distance between the DR Position and the observed position is the set and the drift of the current during the period under reference.