Chart work and tides

Ten questions with a minimum of 7. This is the hardest part of PY, and it includes tide calculations.

Practise this unit Print

Water under the keel

Water under the keel = charted sounding + nearest low water + additive correction − draught.

If you arrive exactly at high or low water, there is no correction: use that height.

Height at any time

Between two consecutive tides: h = mean + (first − second) / 2 × cos(180º × t / D). t is the time since the first tide and D the duration.

Always work in UTC: official time − clock advance = UTC. Sounding = charted sounding + h.

Pressure: each millibar below 1013 raises the sea one centimetre, and each millibar above lowers it.

Activities

• Tide tablesRead a tide table and the height table, and find the sounding.
• Tide trainerWork out soundings, water under the keel and tide times, step by step.
• Navigation calculationsTotal correction, courses, departure and dead reckoning, step by step.
• Chart plottingPlot positions, and measure courses and distances with ruler and dividers.

Questions in this unit

• At ship’s clock 1115 we take a GPS position at point A 36º 08'N – 005º 11'W and set course, with no wind or current, for point B 36º 29'N – 004º 57W. We calculate the rhumb line course in circular notation between them
• At ship’s clock 1700 at WPT 00 = 36º 10’N 005º 15’W they set course, with no wind or current, for WPT 01 = 36º 30'N – 003º 50'W and work out the direct true course and distance:
• They are at a point A on the way to the Strait of Gibraltar = 36º 31.2´N 006º 31.1´W and set course for another point in the Strait = 36º 14.2´N 006º 10.3´W and work out the rhumb line course
• At dead reckoning position l: 36º 17`N L: 007º 16`W we set course for point P at l: 36º 12`N L: 007º 24`W. Calculate analytically the direct course and distance run.
• On 27 January 2024 the yacht NOEGA leaves position l=39º 30` N L=000º 17`W for l: 39º 00`N L: 001º 15`E. Calculate the direct course and distance run to the final position.
• At l = 35º-40.0’ N, L = 005º-32.0’ W we head for a point at l = 36º-05.0´ N, L = 004º-44.0’ W. Calculate the distance between the two points.
• Rhumb line. At l=37º10’N and L=000º15’E, at speed v=12 knots, we set course for a point (P) at l=36º02’N and L=005º20’W. Total correction = + 5º. Calculate the compass course and distance to Point P:
• Calculate the direct course to sail from 29º 15' S, 179º 35' W to 25º 20' N, 178º 15' E.
• A ship at 15º 00' S, 178º 00' E wants to sail to 10º 00' S, 176º 00' W. Calculate the direct course.
• A ship at 12º 20'S, 177º 20' W wants to sail to 09º 10' S, 178º 15' E. Calculate the direct course (to the nearest half degree) and distance.
• At l= 10º 20’N and L= 100º 33’W, sailing on compass course 100º at 10 knots. Calculate the position 1h 48 min later, the total correction being +3º (solve analytically):
• On 27 January 2025 the yacht Noega leaves l=37º 32` N L=001º 06`W on true course 140º, total correction -5º, engine speed 12 knots. Calculate analytically the position and compass course after one hour’s sailing
• Rhumb line. At ship’s clock 0600, at l=37º10’N and L=000º15’E, we set true course 240º at 12 knots. Calculate the position at 0830
• On 27 January 2023, the yacht “La Savina” is at l: 36º 00.0’N and L: 005º 20.0’W on compass course 000º at 7 knots. Magnetic variation is 3º NW and deviation 10º NE. Affected by a current setting S 07º W at 7 knots. Calculate the course and speed made good:
• On 27 January 2025 on board the yacht La Savina the compass azimuth of Polaris is N 07º W (taken as at the Pole), sailing on true course 090º. Calculate the compass course.
• Bound for the Strait of Gibraltar, at ship’s clock 0600, at l: 35º10’N and L: 006º35’W, speed 12 knots, we set a rhumb line course for a point (P) at l: 35º50’N and L: 006º10’W, taking at the same time an azimuth of Polaris (taken as at the Pole) of -007º. Calculate the compass course and distance to Point P:
• At l= 35º-59.0´N L= 006º-15.0´W there is a current setting E at 3 knots, compass course 070º, speed 6 knots. Deviation= 5 NE, variation= 3 NW. Calculate the course and speed made good.
• At l= 36º-00.0´ N L= 006º-20.0´ W, speed 6 knots. At ship’s clock 19-00 we sail on true course 290º. At 23-00 we change to true course 260º until 04-00. Throughout, a current sets 080º at 4 knots. Calculate the position at 04-00.
• We sail at 8 knots on compass course 298º with no current, but with a SW wind giving 10º of leeway. Magnetic variation = 3º NW and compass deviation = –5º (minus). Calculate the course made over the ground.
• At l = 35º-50.0’ N, L = 006º-10.0’ W, we set course for a point at l = 34º-33.0´N, L = 009º-23.0’ W, speed 7 knots, with a current setting 090º at 3 knots. Calculate the course made good.
• On 10 July 2024 we are at 37° 30.0′ N, 002° 05.0′ E and set course for a point at 35º 39.0´ N and 002º 40.0´W. Calculate the true course to reach that point (to the nearest degree).
• We are at 36º 00.0′ N, 006º 00.0′ W, on compass course 138º. An easterly wind gives 12º of leeway. Calculate the course made by the boat under the wind, given magnetic variation = 3º NW and compass deviation = –9º (minus).
• At ship’s clock 06:00 we are at 35º 50.0′ N, 005º 50.0′ W, on compass course 350º. A westerly wind gives 20º of leeway. Calculate the course made by the boat under the wind, given magnetic variation = 5º NE and compass deviation = +10º (plus).
• From 34° 22.0′ N, 179° 45.0′ E we sail at 8 knots on these courses: True course 090º for 3 hours; True course 155º for 2 hours. Throughout, a current sets South at 3 miles an hour. Calculate the arrival position.
• A ship at 26º 40' S, 177º 35' E wants to sail to 05º 15' S, 179º 28' W. Calculate the direct course (to the nearest half degree).
• At ship’s clock 09h 00m on 1 June 2025, we are at 15° 10.0′ N, 179° 22.0′ E. We sail at 10 knots: true course 135° for 4 hours, true course 090° for 3 hours. Throughout, a current sets SE at 3 miles an hour, constant to the end. Calculate the position at 16h 00m on 1 June 2025.
• At ship’s clock 08:00 on 21 March 2026, we are at 37° 34.0′ N, 000° 52.0′ E. We sail at 11 knots: true course 240° for 6 hours, true course 180° for 3 hours. Throughout, a current sets southwest (SW) at 3 miles an hour, constant to the end. Calculate the position at 17:00 on 21 March 2026.
• At ship’s clock 13:00 on 12 June 2026, we are at 28° 44.0′ N, 178° 52.0′ E. We sail at 10 knots: true course 280° for 7 hours, true course 360° for 3 hours. Throughout, a current sets NW at 3 miles an hour, constant to the end. Calculate the position at 23:00 on 12 June 2026.
• At ship’s clock 18:15 we are at 36º 05.0´ N, 006º 10.0´W. We sail at 6 knots on true course 160º, with an easterly wind giving 10º of leeway and a current setting SW at 3 miles an hour. Calculate the dead reckoning position at 20:45.
• With departure point A (l= 35º 45´N; L= 006º 30´W) and landfall point B (l= 36º 04’N; L= 004º 55’W), which answer is closest to the direct course and distance between them?
• At position A (35º55´N; 005º05´W) we head in a sailing boat at 5 knots for position B (36º10´N; 006º25´W). Which answer is closest to the course and distance from A to B?
• At l= 50º 30' N and L= 030º 50' W, we sail on true course 090º for 200 miles. Calculate the arrival position.
• Which answer is closest to the direct course and distance between A (l= 43º49´N; L= 007º54’W) and B (l= 43º40’N; L=001º55’W)?
• With departure at l= 36º 00’ N; L= 006º 10’ W, direct course 278º and distance run 40 miles. Find the arrival position.
• From l= 43º48.5´N; L= 007º43´W we head for l= 43º28´N; L= 002º45.5´W. What is the course and distance between them?
• What would be the course and distance between A (l= 35º40´N; L= 006º25W) and B (l= 34º40´N; L= 005º25´W), going from A to B?
• At ship’s clock 08:20 at l= 39º 22’ N; L= 003º 28’W we want to reach l= 40º 07’N; L= 003º 7’ W at 11:50. If the total correction is -9.3º, what course should we give the helmsman and what engine speed?
• For a passage from l= 44°05´N; L= 007°25´W to l= 43°45´N; L= 006° 30´W, find the closest direct course and distance.
• At ship’s clock 16:00 we are at 35º 50' N, 006º 10' W, sailing at 8 knots on compass course 060º. Variation = 5º NW. Deviation = +5º (plus). At 17:00 we turn to compass course 335º, a westerly starts to blow giving 10º of leeway, and we enter a current setting 090º at 3 miles an hour. On the new course, deviation is 0º. Calculate the position at 18:30.
• At ship’s clock 09:00 at latitude 35 50´N and longitude 006º 10´W we sail on compass course 060º at 6 knots with a NW wind giving 10º of leeway. Variation = 5º NE. Deviation +4º (plus). Calculate the position at 10:30.
• A ship at 13º N, 176º 30.0´E wants to sail to 11º S, 174º 50.0´E. Calculate the direct course (to the nearest half degree) and distance.
• At ship’s clock 13:00 we are at 35º 50.0′ N, 006º 20.0′ W. We sail at 6 knots on compass course 089º. There is a current setting SE at 3 miles an hour and a NW wind giving 10º of leeway. Variation = 3º NW and deviation = –6º (minus). Calculate the dead reckoning position at 14:30.
• From 38º 20′ N, 179º 05′ E, we set course for 35º 42′ N, 178º 38′ W. Calculate the direct course (to the nearest half degree).
• At ship’s clock 16:00 we are at 36º 04.0′ N, 006º 00.0′ W. We sail at 6 knots on compass course 240º. There is a current setting NW at 3 miles an hour and a SE wind giving 10º of leeway. Variation = 3º NW and deviation = +8º (plus). Calculate the dead reckoning position at 18:00.
• A ship at 15º 00.0′ N, 179º 15.0′ E sails at 10 knots: Course 120º for 3 hours. Course E (east) for 4 hours. Course 150º for 6 hours. Calculate the arrival position.
• What direct course must we sail to go from point A at l = 35º 46.8´N and L = 006º 00.2´W to point B at l = 35º 20.0´N and L = 006º 35.0´W?
• From 28º 10′ N, 179º 25′ W, we set course for 25º 55′ N, 178º 24′ E. Calculate the direct course.
• We sail at 7 knots on true course 160º. There is a current setting E at 3 miles an hour and a W wind giving 15º of leeway. At ship’s clock 12:00 we are at 36º 10.0′ N, 006º 10.0′ W. Calculate the dead reckoning position at 14:30.
• At ship’s clock 11:00 we are at 32º 15' N, 179º 40' E. We sail at 12 knots on true course 135º until 16:30, when we set course for 29º 37' N, 176º 21' W. Calculate the direct course (to the nearest degree).
• At ship’s clock 09:00 on 25 March 2023, from 35º 50.0′ N, 006º 10.0′ W we sail on true course 070º at 6 knots. A N wind gives 15º of leeway and a current sets SW at 3 miles an hour. Calculate the dead reckoning position at 10:30.
• On 25 March 2023, at ship’s clock 20:00, we are at 36º 00.0’ N, 006º 10.0′ W. We sail at 8 knots on true course 080º, with a current setting S at 3 miles an hour. Calculate the course the boat will make because of the current.
• At ship’s clock 19:00 on 20 March 2023, we are at 39° 33′ N, 000° 12′ W. We sail at 7 knots: true course 135° for 2 hours, 090° for 4 hours, 075° for 3 hours. From 22:00 on 20 March we enter a current setting SW at 3 miles an hour, constant to the end. Calculate the position at 04:00 on 21 March 2023.
• We sail on true course 260º at 8 knots. At ship’s clock 19:30 we are at 35º 55′ N and 005º 55′ W. A N wind gives 15º of leeway and a current sets NW at 3 miles an hour. Calculate the position at 21:00.
• We sail at 11 knots on compass course 270º, with a SW wind giving 15º of leeway and a current setting 050º at 4 miles an hour. Variation = 6º NE, deviation = +8º. Calculate the course made good.
• At ship’s clock 12:30 on 17 November 2023, we are at 26° 00.0′ S, 055° 00.0′ W. We sail at 10 knots on true course 135º. At 22:00 we set course for 26° 00.0′ S, 053° 00.0′ W. Calculate the true course to reach that point.
• On 5 April 2024, we are at 40° 00.0′ S, 178° 55.0′ E and set course for a point at 28º 40.0´ S and 177º 00.0´W. Calculate the true course to reach that point (to the nearest degree).
• On 6 June 2020 at ship’s clock 07:45 we are at true position 36°08.5´ N 006°12.0´ W, on Compass Course 100° at an Engine Speed of 8 knots, Deviation being 1.5° (+) and Magnetic Variation 2.5° (-). A north wind gives 10° of leeway and we are in a current setting South at 3 knots. Which position is closest to ours at 09:00?
• At 07:45, at l= 35º50´N; L= 006º 01´W we sail on Compass Course 080º at engine speed 5 knots. A northwesterly gives 5 degrees of leeway and a current sets 250º at 2.5 knots. Which answer is closest to our position at 09:15, given the total correction is 5º(+)?
• Which answer is closest to the rhumb line course and distance from l= 35º55´N; L= 006º10´W to l= 36º25´N; L= 007º10´W?
• A motor boat is at point A) 35º40´N; 007º15´W, and from there, at 6.5 knots, heads for point B) 35º41´N; 006º15´W. Which answer is closest to the course and distance from A) to B)?
• From l = 44°-36.5' N and L = 001°- 15.5' W, we sail on direct course 239° for 125 miles. Calculate the dead reckoning arrival position by rhumb line.
• With initial position l=36º05´N and L=006º15´W and final l=34º32´N and L=009º46´W, find the direct course and distance between them.
• Heading for the Strait in the Alboran Sea at 01:00 ship’s time in GPS position 35º 45.2' N – 004º 50.3' W, a vessel sets course for Punta Carbonera lighthouse (36º 14.7' N – 005º 18.1' W) under a steady fresh SE breeze at 6 knots. What is the direct rhumb-line course?
• At 11:00 ship’s time, 5 miles NW true of Cape Spartel in a current setting Rc = 045º at Ihc = 3 knots, you steer Ra = 060º at 12 knots engine speed (dm = 2º W, deviation = 2º E). What are the course and speed made good?
• On 13 March 2025 at 08:30 ship’s time, 4 miles N true of Punta Almina in a current setting Rc = N45ºE at Ih = 2 knots, you steer Ra = 275º (deviation 3º E, variation 1º W, speed 6 knots). What are the course and speed made good?
• Compute analytically the rhumb-line course and distance from initial position 36º 46' N, 010º 30' W to final position 33º 40' N, 008º 35' W:
• At 11:15 ship’s time in 36º 11' N, 005º 11' W, you steer Ra = 190º at 10 knots (Ct = −2.5º) with a SE wind giving 3º leeway and a SW current of 3 knots. What are the course and speed made good?
• Compute analytically the arrival longitude after sailing 300 miles on true course 154º from latitude 36º 50.2' N, longitude 123º 13.0' E:
• On 28 April 2024 the yacht PUNTA PRIMA departs from 38º 44' N, 001º 24' E on true course 310º at 10 knots for 2 hours without wind or current (Ct = −5º). What are her position after 2 hours and her compass course?
• Sailing from GPS 38º 20' N, 000º 22' W to 38º 38' N, 001º 21' E on 28 April 2024, the yacht PUNTA PRIMA computes analytically the direct course and distance:
• At 06:00 ship’s time, steering compass course Ra = 132º at 12 knots with no wind or current, you observe a compass azimuth of Polaris = 007º (and later bearings of Trafalgar at 06:10 and 06:30). What true course are you steering?
• At 07:00 ship’s time, while steering compass course Ra = 007º, you observe a compass azimuth of Polaris (assumed at the Pole) Za = 355º. What is the total compass error (CT)?
• Between point A (38º 10' N, 000º 27' W) and point B (38º 51' N, 001º 11' E), compute analytically the rhumb-line course and distance:
• Departing from a point near Isla Plana at 37º 34' N, 001º 12' W without wind or current on true course Rv = 220º at 10 knots, compute analytically the position 2 hours later:
• At 20:00 ship’s time you take a compass bearing of Punta Malabata lighthouse Da = 190º while observing Polaris at compass azimuth Za = 355º (assumed at the Pole). What is the true bearing (Dv) of Punta Malabata?
• Approaching the Strait making good surface course Rs = 070º with a SW wind causing 6º of leeway, you take a relative radar bearing of Cape Spartel = 45º (starboard). What is the true bearing (Dv) of Cape Spartel?
• Assuming Polaris coincides with the North Pole, you observe a compass azimuth of Polaris = 005º. Calculate the total compass error:
• At 19:00 ship’s time, 5 miles NW true of Punta Alcázar, you steer compass course Ra = 045º at 8 knots in a current setting South (180º) at 3 knots (variation = 4º NW, deviation = +8º). What is the course made good (Ref)?
• On 1 April 2021 at 02:20 in 36º 03.0' N, 006º 05.7' W on Ra = 134º (deviation –7.5º, variation –3.5º) at 10 knots, you enter an unknown current; at 03:35 Da Spartel = 222º and Da Malabata = 163º. Find the current's set and drift:
• At 15:00 steering Ra = 245º at 5 knots (Ct = 0º), Punta Carnero bears Da = 023º at 4.1 miles. With a North wind giving 4º leeway and a current setting 230º at 2 knots, calculate your position at 17:00:
• At 1100 in 36º 10' N, 006º 10' W you steer true course 152º at 8 knots. At 1232 Cape Spartel bears 127º true and Punta Malabata is at 19.4 miles. What are the set and drift of the current?
• Steering true course 283º, you take a 029º Starboard relative bearing to Punta Europa lighthouse at the moment Punta Almina lighthouse is abeam to port. Calculate your position:
• In the Strait of Gibraltar at 4 knots on Rv = 320º, radar distance to Punta Paloma is 9 miles at 14:30, and at 16:30 true bearing to Punta de Gracia is 021º. Calculate your position at 16:30:
• You observe the leading line of Punta Carnero lighthouse with Punta Europa lighthouse at a compass bearing of 242º. Calculate the total compass error:
• Find your simultaneous position when on the opposition line of Cape Trafalgar and Cape Spartel lighthouses while the end of Barbate port breakwater bears 040º true:
• On Ra = 251º at 12 knots (deviation 2.0º E, variation 1.0º W), Da Punta Cires = 159º at 11:00 and radar distance to Isla de Tarifa = 3 miles at 11:20. Find your true position at 11:20:
• At 15:00, 5 miles SE true of Punta Europa at Vm = 8 knots in a current Rc = N39E at Ihc = 2 knots (variation 3º W, deviation 2º E), find the compass course to pass 4 miles off Punta Cires and your speed made good:
• While on the leading line of Punta Carnero and Punta Europa lighthouses with Punta Almina lighthouse bearing 194º true, find your simultaneous position:
• Steering Rv = 072º at 8 knots, you observe Punta Europa lighthouse at Dv = 020º at 16:06, and maintaining course and speed you observe Punta Almina lighthouse at Dv = 175º at 16:36. Find your 16:36 running fix:
• On the opposition line of Punta de Gracia lighthouse and Tangier port north breakwater head while observing Punta Paloma lighthouse at Dv = 070º, find your simultaneous position:
• On 15 November 2025 steering Ra = 151º at 8 knots (deviation 1.5º E), Da Cabo Roche = 034º at 10:30 and radar distance to Cape Trafalgar = 7 miles at 10:50. Find your true position at 10:50:
• At 12:00, 2' W of Cabo Roche at 10 knots, you steer Ra = 230º (dm 2º W, dev 3º W, N wind 8º leeway) to 13:00; then head for Spartel (Rc = 090º, Ihc = 2 kn, dev 1º W, W wind 10º leeway) to 15:00; then Ra = 082º (dev 10º E) to 16:00. Find 13:00 Ra and 16:00 position:
• At 5.5 miles from Tangier port breakwater head on the opposition line of Punta Paloma and Punta Malabata lighthouses, find your simultaneous position:
• Located 4 miles from Punta de Gracia lighthouse on the opposition line of Cape Trafalgar lighthouse and Punta de Gracia lighthouse, find your simultaneous position:
• At a distance of 2 miles from Cape Trafalgar lighthouse while Cape Spartel lighthouse bears 170º true, find your simultaneous position:
• On 15 August 2024 steering Ra = 185° at 6 knots (deviation 2° W), you take Da Punta Carnero = 310° at 07:45 and Da Punta Almina = 195° at 08:15. Determine your position at 08:15:
• On 13 March 2023 at 14:15 in 36° 13.0' N, 005° 13.0' W in a current setting N20W at 2.4 knots with a South wind causing 2° leeway (Ra = 215°, dev +1°, dm 1° W), find the engine speed needed to reach Punta Europa at 14:45:
• On 4 March 2023 at 10:15 in 36° 05.6' N, 006° 09.0' W in a current setting S45E at 4 knots, you steer Ra = 115° (deviation –3°, variation for 2023) at 6 knots. Find your effective course and speed:
• Located on the leading line of Punta Paloma lighthouse and Isla de Tarifa lighthouse while observing Punta Cires lighthouse at a distance of 3 miles, find your position:
• On 1 February 2023 at 04:45 in 35° 51.0' N, 006° 11.0' W steering Ra = 083° (dev +2°, dm 1° W) at 4.5 knots in an unknown current, at 07:05 Da Punta de Gracia = 035° and Da Spartel = 150°. Find the current's set and drift:
• At a distance of 7.6 miles from Ras El Aswad (Cabo Negro) lighthouse on the leading line of Punta Europa lighthouse with Punta Almina lighthouse, find your position:
• On the Isla de Tarifa–Punta Cires opposition at 3 miles from Punta Cires, you head for Cape Trafalgar in a SSW current of 3.5 knots and a South wind giving 3º leeway (Vm = 9 knots, CT = +1º). Find Ra and Vef:
• At HRB 0605 in DR position 36º 10' N – 005º 14' W, you observe Polaris at compass azimuth 354º and head for Ceuta (green entrance light) at 8 knots in a current Rc = N76E at Ihc = 3 knots. Calculate the compass course to Ceuta:
• At HRB 1345 outside the TSS, you simultaneously take compass bearings Da Punta Paloma = 061º, Da Punta de Gracia = 018º and Da Trafalgar = 325º with Ct = 6º NW. Plot your position:
• At HRB 1445 you steer Rv = 280º at 8 knots in fog, observing radar true bearing Dv Trafalgar = 015º; maintaining course and speed, at HRB 1515 you observe Dv Trafalgar = 060º. Calculate your position at HRB 1445:
• At HRB 1800, 15' due South true of Trafalgar lighthouse, you set course for Tangier (breakwater end light) under sail at 8 knots with a fresh NE wind causing 5º leeway (variation 2º W, deviation +6º). Calculate the compass course:
• At HRB 0310 on Ra = 132º at 12 knots (Ct = 7º W), you take a compass bearing of Trafalgar Da = 037º in fog; maintaining course and speed, at HRB 0330 you take a second bearing Da = 337º. Calculate your position at HRB 0330:
• At HRB 0700 with Punta Europa bearing due North true at 9.3 miles, you steer Ra = 249º (Ct = 6º E) at 8 knots with a North wind causing 5º leeway. Calculate the HRB when Punta Malabata bears due South true:
• At HRB 1009, radar simultaneously indicates a distance of 5 miles to Cape Spartel lighthouse and 4 miles to Tangier port breakwater head lighthouse. Plot your position:
• At HRB 1124 you fix your position with Dv Punta de Gracia = N49ºE at 10.8 miles, then lose engine power in calm wind and drift for 2 hours in a current setting 112º at 2 knots. Calculate your position at HRB 1324:
• At HRB 1424 steaming into the current (Rc = 112º, Ihc = 2 knots) at 8 knots log speed, radar shows Cape Spartel lighthouse at true bearing Dv = 160º and distance 12.2 miles. Plot your position at 1424:
• At HRB 1524 in GPS position 36º 00.6' N – 006º 05.1' W, you set course for Barbate port (red breakwater light) at 8 knots in a current setting Rc = 112º at Ihc = 2 knots. Calculate your HRB of arrival at Barbate:
• At HRB 1030 steering Ra = 140º (variation 2º W, deviation –4º) at 8 knots without wind or current, you take Da Trafalgar = 026º; at HRB 1115 you take Da Trafalgar = 340º. Calculate your position at 1115:
• At HRB 1320 in GPS position 35º 57.4' N, 005º 50.7' W at 6 knots, you set course for Tangier port breakwater light in a current setting Rc = 114º at Ihc = 2 knots (Ct = –8º). Calculate your compass course to Tangier:
• From 35º 57.4' N, 005º 50.7' W at HRB 1320 heading for Tangier breakwater light at 6 knots log speed in a current setting Rc = 114º at Ihc = 2 knots, find your HRB of arrival at Tangier:
• Observing Da = 235º at 5 miles from Punta Cires on the Punta Cires–Punta Alcázar leading line, you steer Ra = 038º at Vb = 8 knots in a current setting 075º at 3 knots. Calculate your effective course:
• At HRB 1000 you observe Punta de Gracia lighthouse dead ahead while Cape Trafalgar lighthouse is 90º abeam to port. From this fix, what is your distance to Barbate port red breakwater light?
• At HRB 1200 radar gives simultaneous distances of 7 miles to Punta Paloma and 10 miles to Punta Alcázar; from this fix you head for Tangier port light (Ct = 6º NE) with a West wind causing 5º leeway. Find Ra:
• At HRB 0900 steering Ra = 246º at 8 knots without wind or current (Ct = 6º NW), you take Da Punta Europa = 286º; at HRB 0930 you take Da Punta Europa = 356º. Calculate your position at HRB 0930:
• At HRB 15:30 in GPS position l: 36º 03' N, L: 005º 13' W with a West wind causing 10º leeway, you set course for Ceuta port green light (Ct = –5.5º). Calculate your compass course to Ceuta:
• At HRB 04:35 in GPS position l: 35º 58.0' N, L: 006º 00.00' W you head for Tangier port light at 7 knots engine speed in a current setting 110º at Ihc = 2 knots. Calculate your time of arrival at Tangier:
• Find your position when located on the leading line of Cabo Roche and Cape Trafalgar lighthouses while observing Punta de Gracia lighthouse at a true bearing of 026º:
• At HRB 12:00 you take simultaneous distances of 7 miles to Punta Paloma lighthouse and 10 miles to Punta Alcázar lighthouse. Find your position at HRB 12:00:
• In position l: 36º 03' N, L: 005º 50' W you set course for Tangier port breakwater light at 10 knots (Ct = 6º NE) in a current setting N80E at Ihc = 2 knots. Calculate the compass course to steer:
• At HRB 05:30 you take a compass azimuth of Polaris = 352º while simultaneously taking compass bearings Da Spartel = 128º and Da Trafalgar = 022º. Find your position at HRB 05:30:
• Steering Rv = 046º at 12 knots, you take Dv Cape Spartel = 078º at Hrb 00:00 and Dv Cape Spartel = 150º at Hrb 00:20. What is your position at Hrb 00:20?
• At Hrb 12:00 in GPS position l: 35º 57.4' N, L: 005º 50.7' W you head for Tangier port breakwater light at 6 knots engine speed in a current setting Rc = 114º at Ihc = 2 knots (Ct = –8º). Find Ra:
• At Hrb 09:50 on the Isla Tarifa–Punta Cires opposition with Da Punta Alcázar = 174º (CT = 6º NE), you head for point P (5' due South of Punta de Gracia) at 10 knots with a N wind (5º leeway) and new CT = 4º NE. Find Ra:
• At HRB 0830 in position l: 35º 50' N and L: 006º 10' W at 12 knots, you set true course directly for Tarifa lighthouse. Calculate your position at 0930:
• At HRB 0900 steering Ra = 041º (Ct = 06º NW, speed 07 knots) you take Da Cape Spartel = 076º; maintaining course and speed, at HRB 1000 you take Da Cape Spartel = 196º. Plot your position at HRB 1000:
• At Hrb 18-24 a yacht in l = 36º 11.0' N and L = 005º 13.0' W sets course for Ceuta port green light at 5 knots with a West wind causing 5º leeway and Ct = 8º NW. Find Ra and arrival time:
• A yacht wishes to sail from point A (l = 35º 53.4' N, L = 006° 10.0' W) to point B (10 miles due North true of Punta Malabata lighthouse) with variation 2° NW and deviation 12° NW. What compass course must be steered?
• In position l = 36º 15' N, L = 006º 15' W you set course to pass 5 miles SW true of Cape Trafalgar lighthouse with a North wind causing 5º leeway and Ct = –7º. Find the compass course Ra:
• At Hrb 1600 off Isla de Tarifa lighthouse you want to reach Tangier port breakwater light at Hrb 1800 in a current setting Rc = 075º at Ihc = 3 knots (Ct = –5º). Find the compass course Ra:
• On the leading line of Punta Carnero and Punta Europa lighthouses while observing Punta Almina lighthouse due South true, what is your position?
• In position l = 35º 46.0' N, L = 006º 19.0' W you set course to pass 3 miles off Cape Spartel lighthouse with a NW wind causing 6º leeway once on course. Calculate the true course Rv:
• At HRB 11-30 on Ra = 086º at Vhb = 6 knots (deviation 3º NW, variation 3º NW), you take Da Punta Alcázar = 136º; at HRB 12-00 you take Da Punta Alcázar = 176º. Calculate your position at HRB 12-00:
• At HRB 20-00 while on the opposition line between Punta Europa and Punta Almina, you take a compass bearing of Punta Europa Da = 338º. Find the total compass error:
• Steering Ra = 041º with Ct = –6º at speed v = 12 knots, you take Da Cape Spartel = 076º at Hrb 0900 and Da Cape Spartel = 196º at Hrb 0930. Find your position at Hrb 0930:
• In the Strait of Gibraltar on Ra = 270º at v = 12 knots (deviation –2º, variation 3º NW), you take Da Isla de Tarifa = 065º at Hrb 1000 and Da Punta de Gracia = 345º at Hrb 1030. Find your position at Hrb 1030:
• At HRB 17-00 in true position l = 36º-07.0' N, L = 005º-57.4' W you head for Cape Spartel lighthouse at Vhb = 7 knots; at HRB 19-00 you take Dv Punta Malabata = 138º and Dv Cape Spartel = 210º. Calculate Rc and Ihc:
• At HRB 21-45 on the Isla Tarifa–Punta Alcázar opposition at 5 miles from Punta Alcázar, you steer Rv = 070º at Vhb = 6 knots in a current setting Rc = 095º at Ihc = 3 knots. Find your distance off Punta Europa when crossing the Punta Europa–Punta Almina opposition:
• Steaming at 8 knots on true course 060º, at 11:00 Cape Spartel lighthouse bears 123º at 4 miles, and at 12:30 you are 5 miles due North true of Punta Malabata lighthouse. Calculate the set and drift of the current:
• On 9 April 2016 on the Punta Alcázar–Punta Cires leading line and due East true of Punta Carnero, you head to pass 3 miles off Isla de Tarifa at 8 knots in a current Rc = SE, Ihc = 3 knots (chart dm 05º 00' W 2006 (6' E), dev –8º). Find Ra:
• On 9 June 2016 on the Cape Spartel–Punta Malabata leading line at 5.4 miles from Cape Spartel, you head to pass 5 miles off Punta Malabata with a SE wind (8º leeway), chart dm 6º NW 2006 (6' E) and deviation –5º. Calculate Ra:
• Steaming on Rv = 227º at 5.1 knots, at HRB 14:00 you are on the Punta Europa–Punta Carnero leading line at 6 miles from Punta Europa, and at HRB 16:00 you are due South of Punta Europa and due East of Isla de Tarifa. Find Rc and Ihc:
• At HRB 19:00 you are 6 miles due East true of Punta Europa lighthouse and head for Ceuta (green entrance light) in a current setting Rc = E at Ihc = 2 knots. Calculate the true course and speed needed to arrive at HRB 21:00:
• While on the opposition line of Cape Spartel and Punta Malabata lighthouses, you observe Punta Malabata lighthouse at a compass bearing of 071º. Calculate the total compass error:
• At HRB 12:00 you take Dv Isla de Tarifa = 110º and Dv Punta Alcázar = 145º, then head for Tangier port breakwater light at 8 knots in a current setting West at Ihc = 3 knots (variation 8º NE, deviation +4º). Find Ra to Tangier:
• At HRB 15:00 on the Isla de Tarifa–Punta Cires opposition with Dv Punta Carnero = 032º, you steer Rv = 070º at 8 knots with a North wind causing 15º leeway. Calculate your position when abeam of Punta Almina lighthouse:
• At HRB 10:00 while on the opposition line of Isla de Tarifa and Punta Malabata lighthouses, you observe Isla de Tarifa lighthouse at a compass bearing of 041º. Calculate the total compass error:
• At HRB 12:00 on the Cape Trafalgar–Cabo Roche leading line and due West true of Punta Camarinal lighthouse, you set course to pass 5 miles off Cabo Roche lighthouse with a SW wind causing 20º leeway. Find the true course Rv:
• At HRB 14:00, 5 miles due North true of Punta Malabata lighthouse at 5 knots, you head to pass 2 miles off Punta Cires with a North wind causing 15º leeway (variation 4º NW, deviation +12º). Calculate the compass course Ra:
• At HRB 15:00 steering Rv = 075º at 7 knots you cross due North true of Cape Spartel lighthouse, and at HRB 16:00 you take true bearing Dv Punta Malabata = 160º. Calculate your position at HRB 16:00:
• On the Isla de Tarifa–Punta Alcázar opposition and due West true of Punta Cires lighthouse, you head to pass 5 miles off Punta Almina with a SE wind causing 15º leeway (variation 5º NW, deviation +10º). Calculate Ra:
• At HRB 16:00, 3 miles due East true of Punta Almina lighthouse, you set course for Algeciras port (red entrance light) in a current setting SW at Ihc = 3 knots (variation 3º NW, deviation –5º) to arrive at HRB 20:00. Find Ra:
• Steaming on true course 332º at 8 knots, you cross the opposition line of Punta Almina and Punta Europa lighthouses and observe Punta Europa lighthouse at compass bearing Da = 338º. Calculate the total compass error:
• On 25 July 2020 when due South true of Punta Paloma lighthouse and SW true of Isla de Tarifa lighthouse, you head to pass 3 miles off Punta Cires at 6 knots with a NW wind (15º leeway), chart dm 5.5º E 2015 (6' W) and dev +6º. Find Ra:
• At HRB 15:00 when due South true of Punta Camarinal and due West true of Punta Paloma, you head for Tangier breakwater light in a West current of Ihc = 3 knots (dm 3º NE, dev –3º) to arrive at HRB 18:00. Find Ra and Vb:
• On 10 December 2021 at 02:20 steering Ra = 142º at 12 knots (deviation –6º, NE wind causing 6º leeway), Cape Trafalgar bears 052º Port relative, and at 02:50 it bears 122º Port relative. Find your position at 02:20:
• While crossing the opposition line of Punta Alcázar and Isla de Tarifa lighthouses, you take a compass bearing of Punta Alcázar Da = 173º. What is the total compass error?
• On 22 May 2021 (dm 1º NW) at HRB 06:00, due N true of Tangier breakwater light and due W true of Punta Cires in a current Rc = E, Ihc = 3 knots with a W wind (4º leeway, dev 2º NE), find Ra and Vb to reach 2' N of Tangier light at 06:30:
• A yacht located 7 miles due North true of Punta Cires lighthouse steers compass course Ra = S65W (deviation 8º NW, variation 4º NW) at 12 knots. What is its position after steaming for 1 hour 15 minutes?
• Steaming on true course 242º at 6 knots, you cross the leading line of Punta Alcázar and Punta Cires lighthouses and observe Punta Cires at compass bearing Da = 238º. Calculate the total compass error:
• On 5 November 2022 in position 36º 10.0' N, 005º 10.0' W you set course to pass 4 miles off Punta Carnero lighthouse with a NW wind causing 12º leeway (variation 1º NW, deviation –4º). Calculate the compass course Ra:
• At HRB 11:00 in position 36º 05' N, 006º 00' W steering true course 110º at 8 knots with a NE wind causing 20º leeway, calculate your DR position when Punta Camarinal lighthouse is abeam:
• While crossing the leading line of Cabo Roche and Cape Trafalgar lighthouses, you observe it at a compass bearing of 316º (variation 2º W). Calculate the total compass error:
• Steaming at 8 knots in a current setting West at Ihc = 3 knots, when 3 miles due East true of Punta Almina lighthouse you head for Algeciras port red entrance light (variation 7º NE, deviation +5º). Find Ra:
• At HRB 08:15 when due South true of Punta Paloma lighthouse and due West true of Isla de Tarifa lighthouse, you steer Rv = 290º at 8 knots in a SW current of Ihc = 3 knots. Find the true bearing to Trafalgar at HRB 09:45:
• At HRB 09:00 on the Isla de Tarifa–Punta Cires opposition and due North true of Punta Alcázar, you steer Rv = 270º at 8 knots; at HRB 10:31 Dv Camarinal = 343º and Dv Cires = 091º. Find Rc and Ihc:
• At HRB 08:15 in position 35º 50.0' N, 005º 10.0' W you set course for Algeciras (red breakwater light) with an East wind causing 12º leeway (variation 2º NW, deviation –8º). Calculate the compass course Ra:
• In position 36º 00.0' N, 005º 40.0' W you set course to pass 5 miles off Cape Trafalgar lighthouse with a NE wind causing 12º leeway (variation 4º W, deviation –6º). Calculate the compass course Ra:
• At HRB 15h 00m you simultaneously obtain Dv Punta Paloma = 340º and Dv Punta Cires = 120º, then head for Tangier port breakwater light with an East wind causing 20º leeway (variation 4º NE, deviation –4º). Find Ra:
• At HRB 12h 12m when due South true of Punta Europa and due East true of Punta Carnero, you head for Ceuta green entrance light at 6 knots in a SW current of Ihc = 2 knots (variation 3º NE, deviation –9º). Find Ra and arrival HRB:
• At 11h 00m in position 36º 15.0' N, 005º 15.0' W you steer compass course 173º with a West wind causing 15º leeway (variation 3º NE, deviation +8º). Calculate your position when Punta Europa lighthouse is abeam:
• At HRB 11:00 when 5 miles SW true of Punta Paloma lighthouse, you set course to pass 5 miles off Cape Trafalgar lighthouse with a NE wind causing 15º leeway (variation 3º NW, deviation +3º). Calculate the compass course Ra:
• At HRB 08:00 steering compass course Ra = 296º, you cross the opposition line of Cape Trafalgar and Punta Camarinal lighthouses and observe Cape Trafalgar at compass bearing Da = 303º. Calculate the total compass error:
• Steaming on true course 070º at 6 knots in an unknown current, at HRB 09:00 Punta Carnero bears 090º Port at 6 miles, and at HRB 10:30 Punta Almina bears Dv = 183º at 5.2 miles. Calculate Rc and Ihc:
• Determine the compass course (Ra) to sail from Algeciras port breakwater red light to Punta Almina lighthouse with an easterly wind causing 4° leeway (deviation –5° and chart variation for the year 2020):
• Steaming on true course 258° at 10 knots, you take true bearing Dv Punta Carnero = 321° at 02h 30m and Dv Punta Carnero = 020° at 03h 00m. Calculate your position at 03h 00m:
• At Hrb 17:42, 7 miles due West true of Cape Spartel lighthouse, a vessel steers Ra = 030º at 12 knots (Ct = –5º); at Hrb 19:02 it fixes its position on the Punta de Gracia–Spartel opposition at 9.4 miles from Punta Paloma. Find Rc and Ihc:
• Steering compass course Ra = 250° while on the opposition line of Punta Carnero and Punta Cires lighthouses, you take a relative bearing (M) of 049° to Punta Cires lighthouse. Calculate the total compass error (Ct):
• In a current setting 200º at 3.5 knots, from the Punta Paloma–Punta Malabata opposition at 6.4 miles from Punta Paloma you head to pass 7.1' off Cape Spartel (Ct = +3.5º, engine speed 11.2 knots). Find Ra and Vef:
• At HRB 0300 steering compass course Ra = 132º at 12 knots without wind or current, you take a compass azimuth of Polaris (assumed at the Pole) = 007º. Calculate your true course (Rv):
• In GPS position l: 36º 00.00' N, L: 005º 50.00' W you head for Barbate breakwater red light at 9 knots engine speed (Ct = 4º NW) in a current setting 110º at 2 knots. Calculate the compass course to Barbate:
• When due South true of Punta Camarinal lighthouse with Isla de Tarifa lighthouse bearing Dv = 070º, you head for Barbate landfall light at 7 knots in a SW current of Ihc = 3 knots (variation 4º NE, deviation +8º). Find Ra:
• On 10 July 2024 departing Barbate port entrance light with an East wind causing 15º leeway, calculate the compass course to pass 5 miles off Punta Paloma lighthouse (chart dm 4º W 2012 (5' E), deviation +9º):
• At HRB 10h 20m in position 35º 55.0' N, 005º 50.0' W you head for Barbate landfall light in a current setting Rc = 110º at Ihc = 2 knots (variation 1.5º NE, deviation –11.5º) to arrive at HRB 13h 08m. Find Ra and Vb:
• On arrival at the port of Barbate, they berth in the Marina with a charted sounding = 2 metres, the yacht’s maximum draught being 2 metres, and obtain from the Tide Tables: height of nearest low water = 0.54 metres, additive correction for the arrival interval = 0.36 metres, and work out the water under the keel at that moment:
• On arrival at Ceuta, they berth at the Club Náutico CAS with a charted sounding = 2 metres, the yacht’s maximum draught being 2 metres. From the Tide Tables: height of nearest low water = 0.29 metres and additive correction for the arrival interval = 0.33 metres. They work out the water under the keel at that moment:
• At ship’s clock 0404 on 28 March (matching UTC in the 2020 Tide Tables), they arrive at Barbate and berth in the Marina with a charted sounding = 2 metres, at the time of the first high water of the day, whose height in the Tide Tables is 2.10 metres, the yacht’s maximum draught being 2 metres. They work out the water under the keel at that moment:
• At ship’s clock 17:10 after entering Barbate they tie up at the Marina waiting quay and are given a berth with a charted sounding = 2.50 m, the yacht’s draught being 2.50 m, and obtain from the current Tide Tables: nearest low water height = 0.87 m; additive correction for the arrival interval = 0.01 m. With this data they work out the water under the keel at the berth:
• On arrival at Tangier, they are given a berth in the Marina of the Real Club Náutico with a charted sounding = 2.05 metres, the yacht’s maximum draught being 2.10 metres, and obtain from the current Tide Tables: nearest low water height = 0.54 metres; additive correction for the time interval = 1.00 metres. And they work out the water under the keel:
• They arrive at Barbate and after clearing in at the Marina at ship’s clock 1230 are given a berth with a charted sounding = 2 metres, the yacht’s draught being 1.50 metres, and obtain from the current Tide Tables: nearest low water height = 0.37 metres; additive correction for the arrival time interval = 1.20 metres. They work out the water under the keel at that moment:
• At ship’s clock 0745 we arrive at the port of Barbate at the time of the first high water of the day, height = 2.30 m, and berth in the marina with a charted sounding = 2.5 m. The boat has a maximum draught of 2.20 m. Calculate the water under the keel:
• At ship’s clock 10:30 we enter Tangier with a maximum draught of 2.40 m and are given a berth in the marina with a charted sounding of 2.50 m. From the current tide tables: nearest low water height 0.35, additive correction for the arrival interval 0.15 m. Calculate the water under the keel:
• We enter Barbate at the time of the second low water of the day with a maximum draught of 1.66 m and berth at a charted sounding of 2.20 m, the Tide Tables giving a second low water height of 0.76 m. Calculate the water under the keel at the moment of berthing:
• At ship’s clock 2300, we enter the marina at Mazagón with a maximum draught of 1.80 m and tie up at a berth with charted sounding Sc = 1.60 metres. The Tide Tables give: additive correction for the arrival interval, ca = 0.30 metres, and nearest low water height abjp = 0.65 metres. Find the water under the yacht’s keel at that moment.
• We enter the port of Barbate at the time of the 2nd High Water of the day, height 1.80 metres, and berth at a charted sounding of 2 metres, our maximum draught being 1.20 metres. Calculate the water under the keel at the moment of berthing:
• Sailing at a point with a charted sounding of 5 metres (San Ciprián) and reading from the tide tables: High water time = 08:30, height 5.55 m; Low water time = 14:45, height 2.05 m. Which answer is closest to the sounding at 11:25?
• Sailing at a point with a charted sounding of 12 metres, which answer is closest to the sounding at 10:40? We have: High water time = 06:34, height 1.75 m. Low water time = 12:40, height 0.25 m.
• Sailing at a point with a charted sounding of 6 metres, and reading from the tide tables: High water 06:10, height 5.65 m. Low water 12:29, height 2.15 m. Which answer is closest to the sounding at 09:09?
• At a point with a charted sounding of 6 metres, we read from the tide tables: High water = 12:10, height 3.3 metres. Low water = 18:20, height 0.40 metres. Which answer is closest to the sounding at 12:30?
• Port of Cádiz. Tide Tables for 7 June 2016: Time Height 03:48 3.34 09:44 0.56 16:08 3.47 22:19 0.47. Calculate the official time between the first low water and the second high water of 7 June 2016 at which we will have at least a sounding of 2.8 metres, on a shoal charted at 1.7 metres. Clock advance: +2 hours.
• 04:10 3.05 18 10:08 0.77 18 16:23 2.99 18 22:24 0.81 18. Calculate the official time between the first high water and the first low water of 18 March 2025 at which we will have a sounding of 3.95 metres on a shoal charted at 1.63 metres. Clock advance: +1 hour.
• Calculate the distance run and the direct course to sail from 43° 50.5´N; 005° 45.0´W to 44° 02.8´N; 005° 38.6´W.
• At l= 36º 00' N; L= 005º 30' W, we sail on true course 090º for a distance of 100'. Calculate the arrival position.