## Measuring a position

Take the compass and measure the distance from the object to a parallel and read the latiude at the vertical side of the chart.

Measure the distance from the object to a meridian and read the Longitude from the horizontal side.

## Measuring a Course

First estimate what you think the course will be. This is to prevent you from using the course plotter the wrong way around and thus reading 180 degrees incorrectly. This happens very often in the beginning.

Place side of the plotter from starting point to ending point

Turn the round disk to the north, the top of the map

Make sure that the north on the round disk really points to the north by making the lines on the round disk exactly parallel with the meridians and parallels on the map.

Read the course and check whether it matches the estimate you made in the first step.

Below is an example of measuring the course on the Zeebrugge lights line, which is 136 degrees. Make sure that the boat on the plotter points in the direction of the course. The lines on the round disk are parallel to the meridians and parallels.

## Estimated position

The compass course is given. We convert this to the true water track. Determine the distance traveled through the water. This can be calculated in two ways. Firstly, by keeping track of the log. Secondly, the average speed in knots, e.g. 5 knots, are given for, for example, 1 hour. In that case, the distance traveled is 5 x 1 = 5 Nm. Draw the true water track from the starting point and measure the distance. The point found would have been your position if there had been no current, called the dead reckoning. Now determine the current direction and current speed by looking it up in an almanac, chart or tidal atlas. Plot the current (downstream of the the dead reckoning) by drawing a line in the direction of the current with the length corresponding to the rate. Determine the estimated position. You can find the ground course by drawing a line from the starting point to the estimated position. The ground course can be measured with the plotter.

**Step by step with all details to take into account:**

For example, calculate the EP (estimated position):

1. Draw position of departure in the chart

2. Calculate the TWT (true water track). First write the formula down on a piece of paper.

CTS (C)

Dev ____________________+

CTS(M)

Leeway ____________________+

WT (M)

Var ____________________+

WT (T)

Tidal set ____________________+

COG

3. Plot the TWT on the chart and plot the distance on the TWT.

4. Find the DR.

5. Calculate how many hours before or after HW we are:

-6 | -5 | -4 | -3 | -2 | -1 | HW | +1 | +2 | +3 | +4 | +5 | +6

..:.. |..:.. |..:.. |..:.. |..:.. |..:.. |..:..|..:..|.. :.. |..:.. |..:.. |..:.. |..:.. |..:..

(Substract 1 hour in non-shaded areas.)

If necessary, connect current vectors (half-hour current HW+x and half-hour current HW+y.

7. Read the speed of the current at ST and DT.

9. Calculate the range in reference port for tidal diamonds (in the Reeds in Dover, see computation of rates)

10. Draw a diagonal line between current speed neap tide and spring tide (between Mean range at neaps and springs). Read the current rate.

11. Draw the current vector ->>>-, from the DR. (If necessary, connect current vectors )

12. Measure the EP.

## Course to steer

Plot the ground course on the map by drawing a line from your starting point to your destination. Determine the current direction and rate that you will experience during your trip by looking it up on a chart, almanac or tidal book. Draw the current on the chart from the starting point by drawing a line in the current direction and plotting the current rate on it. The end of the current vector is the position where you would be if you let the boat drift in the water at no speed for an hour with the current. Take the estimated speed of the boat through the water between the compass legs and circle this distance/speed from the end of the current vector through the ground track. Now you find the position on the ground track where you can be after an hour of sailing. The vector from the end of the current vector to the intersection of the circle with the course over ground is the true water track. Measure this with the plotter and then calculate the compass course to steer with the formula.

**Step by step with all details to take into account:**

For example, the question is: What is the CTS (M)?

1. Draw the departure and arrival positions.

2. Draw and measure the direction of the ground track ->>-

3. Write down the formula:

CTS (C)

Dev ____________________+

CTS(M)

Leeway ____________________+

WT (M)

Var ____________________+

WT (T)

Tidal set____________________+

COG

4. Look up the tidal set in the current diamond table or tidal atlas.

5. Determine HW in the standard port of the current atlas or current diamonds table.

6. Calculate how many hours before or after HW we are with a timeline like:

-6 | -5 | -4 | -3 | -2 | -1 | HW | +1 | +2 | +3 | +4 | +5 | +6 (These are the hours before and after HW)

..:.. |..:.. |..:.. |..:.. |..:.. |..:.. |..:.. |..:.. |.. :.. |..:.. | ..:.. |..:.. | ..:.. (Here we note the real times)

Calculate everything according to the time zone in the reference port from the tidal curve and table. (Subtract 1 hour DST in non-shaded areas.)

7. If necessary, connect current vectors, 2 half hour current vectors.

8. Read the speed of the current at ST and DT.

9. Calculate the range in the Standard port (in the Reeds in Dover, see computation of rates)

10. Draw a diagonal line between current speed neap tide and spring tide (between Mean range at neaps and springs). Read the current rate.

11. Draw the current vector ->>>-, from the starting position.

12. Circle the TWT ->- (log speed) through the ground track, from the end of the current vector and draw the TWT. Measure this and enter it in the table from COG to CCTS.

13. Look for variation. If necessary, calculate to the correct year. Find the MWT

14. Sketch to determine if the leeway is + or -. Calculate this to find the MCTS.

15. Find the deviation and calculate the CCTS.

## Cases

Download and print the __chart called “Examenkaart B voor de Vaarbewijzen__” on the website of the Dutch hydrographic service to practice.

### Case 1

You start at position 53° 00.0’N and 004° 50.0’E. You are sailing at 4 knots and a true course of 115°. The wind is north and the drift angle is 5°. The current speed is 1.6 knots and the direction is 345°.

Question 1a: What is your ground heading?

Question 1b: What is your latitude of your position after 1 hour of sailing?

Question 1c: What is the length of your position after 1 hour of sailing?

Question 1d: What was the ground speed?

Question 1e: What was the current angle?

### Answer case 1

Compass CTS = Compass Course to Steer / steered

Dev = Deviation** ________**+

Magnetic CTS = Magnetic Course to steer / steered

Leeway +5

**+**

*________*Magnetic WT = Magnetic Water Track = Magnetic Course Through Water

VAR = Variation

**+**

*________*True WT = True Water track = True Course through water = 120 –>–

Tidal set = -22 –>>>–

**+**

*________*COG = Course Over Ground = 98 –>>–

1a: 98°

1b: 52° 59,6′ N

1c: 004° 55,1′ E

1d: 3,1 knopen

1e: 120° – 98° = -22°

Case 2

You are planning to sail a trip from the T23 (top right of the map) to the T13. There is a current in the direction 95° with a speed of 1.8 knots. The log speed is 4.7 knots. There is a northwest wind and your drift is 5°.

Question 2a: What will be your true water track?

Question 2b: What will be your true course?

Question 2c: What will your ground speed be?

Question 2d: How long is the sailing?

### Answer case 2

2a: 244°

2b: 249°

Compass CTS = Compass Course to Steer / steered

Dev = Deviation** ________**+

Magnetic CTS = Magnetic Course to steer / steered

Leeway -5

**+**

*________*Magnetic WT = Magnetic Water Track = Magnetic Course Through Water

VAR = Variation

**+**

*________*True WT = True Water track = True Course through water 244 –>–

Tidal set = –>>>–

**+**

*________*COG = Course Over Ground –>>–

2c: 3,3 knots

2d: (distance 4,3 Nm / SOG 3,3 Kn) x 60 minutes = 1 hr 18 min

## Log speed and SOG

The log speed is measured by the log and thus indicates the boat’s speed through the water. This speed belongs to the true water track. Wind affects the log speed. SOG = speed over ground. This speed belongs to the ground course. Current affects ground speed.

## ETA

The estimated time of arrival (ETA) can be calculated by the following formula.

Travel time + departure time. Travel time is distance / ground speed (SOG).

Departure time is also called ETD or Estimated Time of Departure. For example, if the distance is 10 Nm and the speed is 5 knots and you depart at 12.00, the ETA is: 12.00 + 10/5 = 14.00. By the way, note that if the travel time is e.g. 2.1 hours, then it is not 2 hours and 10 minutes, but 2 hours and 6 minutes. To easily remember what to divide by what, there is the following mnemonic. The DST triangle. So that doesn’t stand for daylight saving time, but the D stands for distance, the S for speed over ground and the T for time.

D

S | T

(D/S) x 60 is thus the travel time T in minutes.

## Average current

We can also determine the average current over a number of hours in 1 construction. To do this, plot the different current vectors one after the other. Measure the average direction by measuring the direction from the starting point to the ending point. The average rate is the length of all vectors divided by the number of hours.

## Questions & Answers

Question 1: Approx. 2.5 Nm northwest of Schouwen there is the buoy BZ. What is the exact position of that buoy?

a: 51°41,5’N 003°37,5’E

b: 51°44.5’N 003°38.0’E

c: 51°44.0’N 003°38.6’E

Question 2: What is the course from that same buoy BZ to the buoy OG-WG (approx. 51 37.5 N; 3 24.0 E)?

a: 231

b: 225

c: 235

Question 3: From buoy OG-WG (approx. 51 37.5 N; 3 24.0 E) you will sail for an hour with a ground course of 170° and a ground course of 5 knots. What is your position after an hour?

a: 51°32.4’N 003°25.4’E

b: 51°32.2’N 003°25.0’E

c: 51°32.7’N 003°25.8’E

Question 4: What is the true course and distance from buoy OG-WG (approx. 51°37.5’N; 003°24.0’E) to VG1 (approx. 51°25.0’N and 002°49.0’E)?

a: 24.8Nm and 238°

b: 25.4Nm and 243°

c: 25Nm and 240°

Question 5: From VG1 (approx. 51 25.0N and 002 49.0E) you sail a true water track of 30 degrees with a log speed of 5 knots. The direction of the current is 270°, 2.4 knots. What will be your ground course and ground speed?

a: GrK 359°, ground navigation 4.0 knots

b: GrK 5°, ground navigation 4.1 knots

c: GrK 2°, ground navigation 4.2 knots

Question 6: From position 51 45.0N and 002 45.0E you want to go to buoy Track Ferry (approx. 51 33.8N and 002 36.4E). The tidal current is 125 degrees and 2.9 knots. Your log speed is 5.5 knots. What is the True Water Track?

a: 230°

b: 240°

c: 237°

Question 7: In the previous question, what will be the SOG?

a: 5.2 knots

b: 4.8 knots

c: 5.5 knots

Question 8: At 12:00 you are at position 51°45.0’N and 003°00.0’E. your true water track is 330° and your log speed is 6 knots. The current is 180° and 2.2 knots. Where will you be at 13.00?

a: 51°47.0’N and 002° 55.0’E

b: 51°47.8’N and 002° 55.1’E

c: 51°47.5’N and 002° 55.5’E

Question 9: In the previous question, what was your ground speed and course?

a: 310° and 4.0 knots

b: 313° and 4.1 knots

c: 317° and 3.9 knots

Question 10: You are at position 52° 00.0’N 002° 30.0’E at 14.00 You are true water track of 42° with a logging speed of 7 knots. At 15:00 your GPS will show the next position. 52°07.2’N and 002°34.8’E. What was the current direction and speed between 14.00 and 15.00?

a: 319 degrees and 2.6 knots

b: 315 degrees and 2.5 knots

c: 325 degrees and 2.9 knots

Question 11: What is the average current direction for the next 3 hours? 1st hour 94°, 1.5 kn, 2nd hour 151°, 2.0 kn and the 3rd hour 228°, 0.7 kn.

a: 130°

b: 140°

c: 150°

Question 12: What is the average current rate in the next 3 hours? 1st hour 94°, 1.5 kn, 2nd hour 151°, 2.0 kn and 3rd hour 228°, 0.7 kn

a: 0.5 knot

b: 1 knot

c: 3 knots

Question 13: What is the average current direction in the next 3 hours? So from 1 hour before high tide to 1 hour after high tide? Current HW -1: 000° 0.3kts, Current HW 0: 022° 1.0kts, Current HW +1: 022° 1.4kts

a: 9

b: 19

c: 29

Question 14: What is the average current rate in the next 3 hours. So from 1 hour before high tide to 1 hour after high tide? Current HW -1: 000° 0.3kts, Current HW 0: 022° 1.0kts and Current HW +1: 022° 1.4kts

a: A: 2.7kn

b: 1.5 kn

c: 0.9 kN

Question 15: You are at buoy Schouwenbank (approx. 51°45.0’N and 003°14.3’E) and plan to sail towards the Noorderhoofd (north of Westkapelle). The current in the next 3 hours will be: 225° and 2 knots, 200° and 1.5 knots, 40° and 1.8 knots. What is the average flow direction and speed for the next 3 hours? What is the average flow direction and speed for the next 3 hours?

a: 208°, 0.5 knots

b: 206°, 1.5 knots

c: 207°, 1.6 knots

Question 16: You decide to calculate an average true water track from the position given in question 5 to West Kapelle (so you don’t necessarily have to stay on the light line). Which true water track should you use on average for the next 3 hours with the data from question 5, if your logging speed is 5 knots?

a: 134

b: 129

c: 144

Question 17: What will be the average ground speed in question 6?

a: 6.8kn

b: 5.2kn

c: 5.8kn

Question 18: To calculate the ETA, you need to add the travel time to the departure time. How do you calculate travel time?

a: Distance / Log speed

b: Distance / Ground speed

c: Ground speed / Distance

Question 19: You will be at buoy Schouwenbank at 14.00 (approx. 51°45.0’N and 003°14.3’E) and sail exactly on the light line towards the Noorderhoofd. Let’s say your ground speed is 6.5 knots for the next few hours. What is your ETA at buoy Middelbank?

a: 14.15

b: 15.11

c: 14.44

Question 20: At 14.00 you will be at buoy Schouwenbank (approx. 51°45.0’N and 003°14.3’E) and sail exactly on the light line towards the Noorderhoofd. Let’s say your ground speed is 6.5 knots for the next few hours. So, what is your ETA at buoy Kaloo?

a: 16.12

b: 15.22

c: 15.42