Course to Steer Calculation - Tidal Navigation Guide

Prerequisites

• The Position Fixing lesson: lines of position, DR and EP, leeway, and True/Magnetic/Compass conversions (RYA Day Skipper Shorebased: chartwork and position fixing).
• Confidence with chart instruments: plotter or parallel rules, dividers, measuring distance on the latitude scale, and plotting and measuring True bearings.
• Access to an Admiralty tide table or a nautical almanac (Reeds) with standard port curves and secondary port differences, and a tidal stream atlas or chart with tidal diamonds. The RYA training chart (Portland Bill to Selsey, Chart Plotter exercise sheets) and almanac extracts are fine for practice.
• Day Skipper Practical candidates are expected to have tidal theory to Day Skipper Shorebased standard before the course. Shorebased students should be able to do every calculation in this lesson without electronic aids: the exam allows only the instruments listed above.

Learning Objectives

This lesson covers the tidal and course-plotting items of the RYA Day Skipper Shorebased syllabus (Tidal Knowledge, Course Shaping and Plotting, and the tidal part of Passage Planning) and the corresponding Day Skipper Practical items on tidal planning. By the end you will be able to:

• Explain the causes of tides, and the difference between springs and neaps (RYA syllabus: tidal definitions and theory).
• Define Chart Datum (LAT), HAT and the tidal levels MHWS, MHWN, MLWN and MLWS, and the terms range, rise, fall, stand and height of tide (RYA syllabus: tidal terms and chart datum).
• Convert between charted depth, drying height, height of tide and actual depth, and calculate clearance under bridges and cables (RYA syllabus: depth, drying heights, charted heights).
• Find the height of tide at a standard port at any time, and the time at which a given height occurs, using the tidal curve and the tide table (RYA syllabus: tidal curves for standard ports).
• Estimate heights quickly with the Rule of Twelfths, and know when not to (RYA syllabus: Rule of Twelfths and its limits).
• Work out times and heights of HW and LW at a secondary port, interpolating for springs, neaps and time (RYA syllabus: secondary port calculations).
• Allow for meteorological effects on tidal height: pressure, wind and storm surge.
• Calculate under-keel clearance and the earliest and latest time to cross a shoal, bar or sill, and choose a safe tidal window (RYA syllabus: clearance and tidal windows).
• Extract tidal stream direction and rate from tidal diamonds and a tidal stream atlas, interpolating between springs and neaps and between diamonds (RYA syllabus: tidal streams).
• Construct a course-to-steer vector triangle including leeway, and convert the result to a compass course (RYA syllabus: course to steer).
• Calculate an estimated position (EP) from a DR plot and the tidal streams experienced, and use it to monitor progress (RYA syllabus: EP and monitoring).

Finding Your Way Round the Almanac

Every calculation in this lesson starts with data from a nautical almanac (Reeds, or the Admiralty tide tables and the RYA Training Almanac used in the shorebased course). Knowing where each item lives saves minutes in the exam and avoids the commonest errors.

• Standard port pages give the times and heights of every HW and LW for the year, in the port's standard time, with the time zone and daylight-saving rules printed at the top; the tidal curve for that port, with the mean spring and neap ranges printed on it; and the mean tidal levels (MHWS, MHWN, MLWN, MLWS).
• Secondary port pages list the standard port to use and the differences: a line of standard-port times (for example "HW 0000 and 1200, 0600 and 1800; LW 0000 and 1200, 0600 and 1800") with the time difference under each, and height differences under MHWS, MHWN, MLWN and MLWS. Interpolate between the printed values for the actual standard-port time and height.
• Tidal levels table gathers the mean levels of all the ports in the area on one page. A note in the RYA Training Almanac reminds you that the HAT for a secondary port is found by extrapolating the differences beyond MHWS for a tide that reaches HAT at the standard port.
• Tidal stream atlas pages, one for each hour from six hours before to six hours after HW at the reference port (Victoria in the Training Almanac, Dover or Portsmouth in the Channel), with arrows and paired neap and spring rates in tenths of a knot.
• Computation of rates graph, which turns the spring and neap rates for the hour into today's rate.
• Reference pages: a distance, speed and time table; a compass deviation table; a table of lights' distance off when rising and dipping; the light characteristics and chart abbreviations; the International Port Traffic Signals; distress and life-saving signals.
• Port information and passage information for each stretch of coast, with VHF channels, approach waypoints, hazards and tidal notes, and the coastguard and weather broadcast schedules.

The RYA Training Almanac covers a fictitious area used with the RYA Training Charts, so that exam questions can be set without local knowledge: the Northern Territories (time zone UT, IALA Region A), the Southern Peninsula (zone minus 0100, Region A) and the Neptune Islands (zone minus 0100, IALA Region B). Read the time zone at the top of every tide table before you start, and convert to the zone the question uses.

The computation of rates graph

Rather than interpolating stream rates by arithmetic, the almanac provides a graph. The Training Almanac's own instructions:

1. From the tide tables, calculate the range of the tide at the standard port for the day in question.
2. Note the neap and spring rates from the tidal stream atlas or tidal diamond for the required time and position.
3. On the graph, plot the neap rate on the dashed neap line and the spring rate on the dashed spring line, using the horizontal tidal stream rate scale.
4. With a pencil and a straightedge, join the two plotted points and extend the line to the edges of the graph.
5. Enter the vertical mean range scale with the range calculated in step 1 and draw a horizontal line to meet the pencil line.
6. From that intersection, draw a vertical line to the horizontal scale and read off the rate of the stream for today's range.

The graph is simply linear interpolation drawn out, so it gives the same answer as the formula below, but it is quicker and less error-prone under exam conditions, and it also works for ranges outside the neap-to-spring band.

Why Tides Matter

In UK waters the tide can rise and fall by anything from about 1 metre (parts of the Solent at neaps) to over 12 metres (the Bristol Channel at springs), and tidal streams commonly run at 2 to 4 knots, with 6 to 8 knots in some races. For a yacht making 5 or 6 knots, the tide can halve or double your speed over the ground, set you sideways onto danger, and decide whether there is water to enter a harbour at all. Tidal calculation is therefore not an exam exercise: it is the core of safe passage planning.

Two distinct things are both called "tide", and you must keep them apart in your head throughout this lesson:

• Tide (height of tide) is the vertical rise and fall of the sea surface. It decides how much water there is: for entering harbours, crossing bars, anchoring, passing under bridges and over shoals.
• Tidal stream is the horizontal movement of water. It decides where you go over the ground: your course to steer, your speed over the ground, and which direction is favourable at which time.

The two are related (the streams are caused by the same rise and fall) but their timing is not the same. In many places the stream is at its strongest at mid-tide and slack at HW and LW, but in estuaries, harbour mouths and round headlands the stream can still run for hours after HW or LW. Never assume that slack water coincides with high or low water: always use the stream data.

Causes of Tides: Springs and Neaps

Tides are caused mainly by the gravitational pull of the moon, and to a lesser extent the sun. Most UK ports have two high waters and two low waters each lunar day of about 24 hours 50 minutes, so HW is roughly 50 minutes later each day. This is called a semi-diurnal tide, and the interval from one HW to the next is about 12 hours 25 minutes.

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• Spring tides occur when the sun and moon are in line (new and full moon), so their pulls add together. The range is largest: higher high waters, lower low waters and the strongest streams. The name has nothing to do with the season.
• Neap tides occur when the sun and moon are at right angles (first and last quarter), so their pulls partly cancel. The range is smallest and the streams weakest.
• In UK waters, springs typically arrive one to two days after new or full moon, because the oceans respond with a delay. The cycle from springs to neaps to springs takes about 14.8 days, with neaps about 7 days after springs.
• Tide tables show whether a day is near springs or neaps by its range: compare the day's range with the mean spring and mean neap ranges printed for the standard port.
• The largest tides of the year (equinoctial springs) occur around the March and September equinoxes, when the sun and moon are over the equator and their effects are greatest. Perigean springs, when the moon is also at its closest to the Earth, are bigger still. Plan generous margins at these times.

Terms you must know

Chart Datum and Tidal Levels

All heights and depths on a chart are measured from a reference level called Chart Datum (CD). On UK Admiralty charts CD is approximately Lowest Astronomical Tide (LAT) — the lowest level the tide can be predicted to fall under average weather conditions. The water is therefore almost never below CD, so charted depths are a minimum and you normally have more water than is shown. The one exception is a large negative surge (a strong offshore wind with high pressure), which can take the water below LAT.

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Older charts and foreign charts may use a different datum, for example Mean Low Water Springs, in which case the tide can fall below CD. Always read the chart title block and the notes on datum before you rely on a charted depth.

The almanac lists the mean tidal levels for each standard port. The diagram below, from Wikimedia Commons, shows how the charted heights and depths relate to these levels: charted depth is measured down to chart datum, a drying height is measured up from it, the height of tide is the level of the sea surface above it, and the height of a light or bridge is measured above MHWS.

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Image: [Clubsail](https://commons.wikimedia.org/wiki/File:Definitions_of_Spring_and_Neap_tides.jpg), [CC BY 3.0](https://creativecommons.org/licenses/by/3.0/), via [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Definitions_of_Spring_and_Neap_tides.jpg)

Check the chart title block: the heights of lights are above MHWS on most Admiralty charts, but clearances under bridges and overhead cables on newer charts are above HAT. Using the wrong reference can cost you your masthead.

Mean spring range = MHWS minus MLWS; mean neap range = MHWN minus MLWN. For example, at a port with MHWS 4.7 m, MHWN 3.8 m, MLWN 1.9 m and MLWS 0.8 m, the spring range is 3.9 m and the neap range is 1.9 m.

Depth, Drying Height and Height of Tide

Charted depth

A plain figure in the sea area is the charted depth (sounding) below CD. Add the height of tide to get the actual depth of water.

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Example: charted depth 2.5 m, height of tide 3.2 m. Actual depth = 2.5 + 3.2 = 5.7 m.

Drying heights

An underlined figure is a drying height: the height of the seabed above CD. It is uncovered at low tide. The depth of water over it is the height of tide minus the drying height.

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Example: a sandbank dries 1.2 m. With a height of tide of 2.0 m there is 2.0 minus 1.2 = 0.8 m of water over it. With a 1.5 m draught you cannot cross it until the height of tide exceeds 1.2 + 1.5 + safety margin, say 1.2 + 1.5 + 0.5 = 3.2 m.

Heights above the water

Heights of lights and of land features are given above MHWS (check your chart). Because the sea is below MHWS for most of the tide, you will normally see more of a lighthouse than charted at LW, and less at a high spring. The correction is the difference between MHWS and the present height of tide.

Clearance under bridges and cables

Charted clearances are measured from a high-water reference (MHWS or HAT) up to the underside of the bridge or cable. At any other time you have more headroom, equal to the difference between the reference level and the height of tide at that moment.

Worked example: A bridge has a charted clearance of 9.0 m above MHWS. At the port MHWS is 4.8 m. Your mast, including the VHF aerial and wind instruments, is 12.5 m above the waterline. You want a 0.5 m margin for wash and swell.

1. Height of the underside of the bridge above CD = 4.8 + 9.0 = 13.8 m.
2. Height required for the masthead above CD = height of tide + 12.5 + 0.5.
3. For this to clear: height of tide + 13.0 is less than 13.8, so the height of tide must be less than 0.8 m.

You can pass only within about an hour or so either side of LW on a spring tide, and on a neap tide (when LW may not drop below 1.9 m) you may not be able to pass at all. Always measure the true air draught of your boat, including the highest masthead fitting, and never trust a brochure figure.

Standard Ports and the Tidal Curve

Tide tables give predicted times and heights of HW and LW for standard ports (Dover, Portsmouth, Plymouth and so on). Each standard port also has a tidal curve diagram in the almanac, letting you find the height at any time between HW and LW. The curves are drawn for springs (solid line) and neaps (dashed line); interpolate between them according to the day's range. The shape of the curve is specific to each port: the Portsmouth curve shows the long stand at HW, and the Dover curve is a near-symmetrical sine shape.

Finding the height at a given time — step by step

1. From the tide table, extract the HW time and height, and the LW height, for the tide you need. Calculate the range (HW height minus LW height). Check whether the table is in UT, and convert to the time zone you are working in.
2. On the curve diagram, mark the HW height on the top scale and the LW height on the bottom scale, and join them with a straight diagonal line.
3. Fill in the time boxes under the curve: write the HW time in the HW box, then hours before and after HW in the boxes either side.
4. From the required time on the time axis, go vertically up to the curve. Use the spring or neap curve, or interpolate between them, according to the range.
5. From the curve, go horizontally across to the diagonal line.
6. From the diagonal, go vertically up (or down) to the height scale and read the height of tide.

Worked example — Portsmouth

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HW Portsmouth 1400, 4.8 m. LW 2012, 0.9 m. Required: height of tide at 1630.

1. Time from HW: 1630 minus 1400 = HW + 2 hours 30 minutes.
2. Range: 4.8 minus 0.9 = 3.9 m. Compare with the mean spring and neap ranges for Portsmouth: the range is near springs, so use the spring curve.
3. Plot 4.8 m and 0.9 m on the height scales and draw the diagonal.
4. Up from HW+2.5 to the spring curve, across to the diagonal, and up to the height scale: height of tide about 3.4 m.

Reading to the nearest 0.1 m is as good as the curve allows. In the exam, state your answer to one decimal place, and label each step of your working: the examiner marks the method as well as the answer.

Finding the time for a given height

Reverse the process. Start from the required height on the top scale, go down to the diagonal, across to the curve, then down to the time axis. This is how you find "the earliest time I can cross the bar" — see under-keel clearance below.

The Rule of Twelfths

When you need a quick mental estimate, the Rule of Twelfths assumes the tide rises (or falls) over about six hours in the proportions 1, 2, 3, 3, 2, 1 twelfths of the range.

Example: range 4.8 m, LW 0.9 m. Two hours after LW the tide has risen 3/12 of 4.8 = 1.2 m, so the height is 0.9 + 1.2 = 2.1 m.

The rule works from HW as well: for the fall, use the same fractions counting hours after HW. The rule is useful for estimating the half-tide level (halfway between HW and LW, three hours from either) and for a quick check on whether the tide is running too fast to cross a bar.

Worked example (tidal window): the Portsmouth tide above, LW 2012 at 0.9 m, range 3.9 m. You need a height of tide of 3.0 m at the bar. Rise required = 3.0 minus 0.9 = 2.1 m, which is 2.1 divided by 3.9 = 0.54 of the range. After 3 hours the rule gives 6/12 = 0.50; the fourth hour adds 3/12 (0.25), so 0.04 of the range further needs about a sixth of the fourth hour (10 minutes). The bar is passable about 3 hours 10 minutes after LW, around 2320. The tidal curve is more accurate; use this as a check.

Limitations: the rule assumes a symmetrical six-hour tide. It is badly wrong in places with unusual curves — the Solent (double high waters and a long stand), Poole, Swanage, Southampton and parts of the Channel. Use it for a quick check or in normal ports with ample margin; use the proper curve whenever clearance is tight. The RYA examiner expects you to say this unprompted.

Secondary Ports

Most harbours are secondary ports. The almanac gives their tidal predictions as differences from a nominated standard port: time differences for HW and LW, and height differences for MHWS, MHWN, MLWN and MLWS.

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Procedure

1. Look up the standard port's HW and LW times and heights for the day.
2. Look up the secondary port's time differences. These are given for two HW times and two LW times at the standard port (for example "HW 0000 and 1200: minus 0015; HW 0600 and 1800: minus 0005"). Interpolate according to the actual standard port time.
3. Look up the height differences for MHWS and MHWN (for HW heights) and MLWN and MLWS (for LW heights). Interpolate according to how the day's standard port heights compare with the mean levels.
4. Apply the differences. Remember to convert from UT to local time (add one hour for BST) — UK tables are printed in UT unless stated.
5. Use the standard port's tidal curve with the secondary port's corrected HW, LW and heights to find heights at intermediate times.

Worked example (springs)

Standard port Dover: HW 1200, 5.2 m (a spring tide, so use the spring differences). Folkestone differences at springs: time minus 0015, height minus 0.3 m. Folkestone HW = 1200 minus 0015 = 1145 UT; height = 5.2 minus 0.3 = 4.9 m. In summer, add one hour for BST: 1245 BST.

Worked example with full interpolation

The following figures for a hypothetical secondary port are chosen to show the method. Standard port Dover, mean levels MHWS 6.7 m, MHWN 5.3 m. Today's Dover HW is at 0900 UT, height 6.0 m.

Differences for the secondary port: time differences minus 0020 (HW at the standard port 0000 and 1200) and minus 0040 (HW at 0600 and 1800); height differences minus 0.4 m at MHWS and minus 0.2 m at MHWN.

1. Time. 0900 is halfway between 0600 and 1200, so the difference is halfway between minus 0040 and minus 0020: minus 0030. HW at the secondary port = 0900 minus 0030 = 0830 UT, which is 0930 BST.
2. Height. 6.0 m lies (6.0 minus 5.3) divided by (6.7 minus 5.3) = 0.7 divided by 1.4 = 0.5 of the way from neaps to springs. The difference is halfway between minus 0.2 and minus 0.4: minus 0.3 m. HW height = 6.0 minus 0.3 = 5.7 m.
3. Repeat for LW using the LW time differences and the MLWN and MLWS height differences.

Linear interpolation is accurate enough for Day Skipper work. Remember the secondary port may have a different shape of curve from its standard port; the almanac names the port whose curve to use, and the results at intermediate times are only as good as that assumption.

Meteorological effects

Predictions assume average weather. Real heights differ:

• Pressure: the sea surface rises about 1 cm for each millibar the pressure falls below 1013 mb, and falls about 1 cm for each millibar above. At 983 mb expect about 30 cm more water than predicted; at 1033 mb, about 20 cm less.
• Wind: a strong onshore wind piles water up, and a strong offshore wind pushes it away. Persistent winds in an enclosed sea such as the North Sea can change levels by a metre or more.
• Storm surge: a deep depression combined with strong onshore wind can raise levels by 2 m or more, which, if it coincides with a spring HW, causes flooding. A surge can also lower the sea below predicted LW.
• River flow: heavy rain upstream raises levels in estuaries and can delay or prevent the flood stream in a river.

The Admiralty and almanac sources warn that all these can happen. In your planning, never let a marginal under-keel clearance depend on a prediction to the last 10 cm.

Under-Keel Clearance

Under-keel clearance (UKC) is the water left under the keel.

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UKC = charted depth + height of tide minus draught.

Always add a safety margin on top of the bare UKC: at least 0.5 m in sheltered, smooth water and 1.0 m or more in an exposed entrance, in swell, over rock, or when the barometer is high (high pressure depresses the sea level by about 1 cm per millibar above 1013 mb). Remember also that a yacht heels and squats at speed, and that waves in a swell dip into troughs of a metre or more.

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Worked example — when can I cross the bar?

Your draught is 1.8 m. The bar has a charted depth of 0.4 m (or dries 0.4 m — be careful which!). You want a 1.0 m safety margin because there is swell.

• If charted depth is 0.4 m: required height of tide = 1.8 + 1.0 minus 0.4 = 2.4 m.
• If it dries 0.4 m: required height of tide = 1.8 + 1.0 + 0.4 = 3.2 m.

Now use the tidal curve in reverse: plot the day's HW and LW, enter at 2.4 m (or 3.2 m) on the height scale, go down to the diagonal, across to the curve on the rising side, and down to read the earliest time. Do the same on the falling side for the latest time. That gives your tidal window.

Planning with a tidal window

A tidal window is a block of time during which an event is possible: crossing a bar, leaving a drying berth, rounding a headland with a fair tide, or passing under a bridge. Building the window is a skippering skill the Day Skipper examiner will ask about:

1. Calculate the earliest and latest times from the tide curve.
2. Decide how long the passage to the gate takes, using your realistic speed over the ground, not your best speed.
3. Add a buffer of at least 30 minutes at the early end for delays.
4. Decide the alternative if you miss it: wait offshore, anchor, or go to a second port that is accessible at all states of tide.

Tidal Streams

Height of tide is vertical movement; tidal stream is the horizontal flow. Streams are referenced to HW at a standard port (often Dover for the Channel, or the local standard port) and given hourly from HW minus 6 to HW plus 6.

Tidal diamonds

On the chart, a lettered diamond marks a position for which stream data are tabulated on the same chart. The table is headed by the diamond letter and position, and gives, for each hour from six hours before to six hours after HW at the reference port, the direction of the stream and its rate at springs and at neaps. The real example below shows how a chart prints it: the three diamonds A, B and C are listed side by side, and a rate of "Slack" appears where the stream turns.

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Image: Mark.murphy, public domain, via [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Nautical_chart_tidal_diamond.PNG)

For each hour the table gives the direction the stream flows towards (degrees True — streams "set" towards, whereas winds blow from), the spring rate (Sp) and the neap rate (Np) in knots. To use it:

1. Find the HW time at the reference port for your day and time zone.
2. Work out which hour relative to HW you need: if HW is 1400 and you want the stream at 1630, that is HW plus 2.
3. Read the line for HW plus 2: direction and the spring and neap rates.
4. Interpolate between spring and neap rates for today's range (see below).

Example from the table above: at diamond B, three hours before HW the stream sets 213 degrees at 0.9 knots (springs) or 0.5 knots (neaps), and at HW plus 1 it sets 031 degrees at 1.9 knots (springs) or 1.1 knots (neaps). Note that the set changes by almost 180 degrees as the stream turns, and passes through slack water in between.

Tidal stream atlases

A tidal stream atlas shows the same information pictorially: one page per hour, with arrows for direction and figures for rates. The page below is from a historical Admiralty Thames Estuary atlas. It is headed by the hour in relation to HW at a reference port; each arrow shows the direction of flow, and a pair of figures such as 10,15 means 1.0 knot at neaps and 1.5 knots at springs.

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Image: Hydrographic Office of the Admiralty, public domain, via [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Thames_estuary_tidal_streams_Page010_at_high_water_Sheerness.jpg). Reduced in size.

Admiralty atlases print the rates as two figures separated by a comma, neap rate first, with the decimal point omitted: 12,25 means 1.2 knots at neaps and 2.5 knots at springs. Some almanac extracts print the same information as spring rate with the neap rate in brackets, for example 2.5 (1.2). Always read the key on the page. Each atlas page is drawn for a stated hour before or after HW at a reference port (such as Dover or Portsmouth), and the key tells you which.

Atlases also show areas of eddies, overfalls and races, and the stream in places where no diamond exists. They give a better overall picture for planning; diamonds give precise figures at one point.

Interpolating between springs and neaps

On a day between springs and neaps, the rate lies between the two figures.

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The diagram shows a simple linear method based on days from springs. The standard RYA and almanac method is more precise: use the day's range at the standard port. If the mean spring range is 4.2 m and the mean neap range is 2.0 m and today's range is 3.1 m, today is halfway between neaps and springs, so a spring rate of 3.0 knots and neap rate of 1.5 knots gives about 2.25 knots. Most almanacs include a computation-of-rates graph for doing this quickly. In practice, if in doubt, use the spring rate — it is the safe, conservative assumption.

Interpolating by the proportion of the range between neap and spring, in formula form: today's rate = neap rate + (spring rate minus neap rate) x (today's range minus neap range) divided by (spring range minus neap range). For the figures above, 1.5 + 1.5 x (1.1 divided by 2.2) = 1.5 + 0.75 = 2.25 knots.

Between diamonds, and tidal gates

Where your route lies between two diamonds, take the stream from the nearer or average the two according to distance. Near headlands, in races and in channels, streams change over short distances, and the nearest diamond may not represent the stream at your position: use the atlas and a wide safety margin.

Some places act as tidal gates: a point where the stream is so strong or the passage so constricted that you must arrive at the right time to get a fair tide. Examples are Portland Bill, the Needles Channel, Hurst Narrows, the Alderney Race and the Raz de Sein. Plan to arrive at the gate with the stream in your favour and as close to slack water as the design of the plan allows. Allow for the fact that a boat that is late loses twice: it loses time and meets the contrary stream.

Course to Steer Allowing for Tidal Stream

The course to steer (CTS) is the heading that, combined with the tidal stream, will carry the boat along the desired ground track.

Construction — step by step

1. Draw the ground track from the start (A) to the destination (B) and extend it beyond B. Mark it with two arrowheads.
2. Decide on a time interval, usually one hour (or the whole leg if it is under about three hours, using the summed tidal vectors).
3. From A, lay off the tidal stream vector for that period: direction and distance. Call its end C. Mark it with three arrowheads.
4. Set the dividers to the distance the boat will travel through the water in the same period (boat speed multiplied by time).
5. With one point on C, swing an arc to cut the ground track. Call that point D.
6. The line C to D is the water track. Measure its direction: that is the course to steer in True. Mark it with one arrowhead.
7. A to D is the speed (or distance) made good over the ground — use it to calculate the ETA.
8. Correct for leeway by steering up into the wind, then convert True to Magnetic (variation) and Magnetic to Compass (deviation).

The arrowhead convention (one for water track, two for ground track, three for tide) is the standard RYA convention. Examiners expect it, and it makes your plot readable by anyone.

Worked example

From A to B is 8 miles on 270 degrees T. Boat speed is 5 knots. The stream for the next hour sets 180 degrees T at 2 knots. Variation 3 degrees W, deviation 2 degrees E, and no leeway (motoring).

1. Draw A to B on 270 degrees T.
2. From A lay off 2 miles on 180 degrees T to C.
3. From C, swing a 5 mile arc to cut the ground track at D.
4. Geometry: the sideways component of the tide (2 miles) must be cancelled, so the angle between water track and ground track has a sine of 2 divided by 5 = 0.4, about 24 degrees. The water track is 270 + 24 = 294 degrees T (steer north of the track to counter a southgoing stream).
5. A to D measures about 4.6 miles: speed made good 4.6 knots. The 8 mile leg takes about 1 hour 45 minutes — and over that time the stream will change, so a longer leg should be worked using the tidal vectors for each hour, added end to end.
6. Variation 3 degrees W: 294 + 3 = 297 degrees M. Deviation 2 degrees E: 297 minus 2 = 295 degrees C.

Steer 295 degrees C. Notice that steering straight at the destination (270 degrees) would have let the stream carry you nearly 2 miles south in the first hour.

The conversion rule: going from True to Magnetic, add West variation and subtract East; going from Magnetic to Compass, add West deviation and subtract East. Going the other way (Compass to True) the signs reverse: add East, subtract West. The memory aid is "Can Dead Men Vote Twice" for the order Compass, Deviation, Magnetic, Variation, True, with "West is best, East is least" meaning that going from True towards Compass you add West. Always say which direction you are converting.

Allowing for leeway

Leeway is the sideways slip of the boat caused by wind on the hull and rig. It acts to leeward, so to counter it you steer up into the wind. Leeway is applied to the water track after the vector triangle is solved, and it is applied before variation and deviation.

Typical values for a cruising yacht: close-hauled in a moderate breeze 5 to 10 degrees; reaching 0 to 5 degrees; running and motoring in light wind, none. In heavy conditions with a short-keeled boat it may be more. The best estimate comes from your own observation of the wake angle relative to the fore-and-aft line.

Example: the water track is 294 degrees T and the wind is from the north-west (wind on the starboard bow, boat close-hauled), leeway 6 degrees. The boat slips to leeward, to the south, so you must steer 6 degrees further to windward: the heading is 294 + 6 = 300 degrees T. Check by asking: "which side is the wind on, and which way will I be pushed?" Steer towards the wind side of the water track.

Multi-hour legs

For a leg of several hours, do not draw a new triangle each hour (which would make you follow a curved path). Instead, lay off all the hourly tidal vectors end to end from A, then swing an arc of boat speed multiplied by the total time from the end of the last vector. One heading held for the whole passage gives the shortest time — the tides largely cancel out if the passage spans a full flood and ebb.

The Day Skipper exam often asks you to find the CTS for a leg of two or three hours with different hourly streams. Use the correct hour for each vector, and use spring or neap or interpolated rates as asked. Pay attention to the start time relative to HW: the first vector is for the hour in which you depart.

Calculating the ground track and speed made good

Sometimes the question is reversed: "I steer 090 degrees T at 5 knots for the next 3 hours, what will my ground track be?" This is the EP problem, and uses the same triangle in the other direction.

Estimated Position (EP)

An estimated position is your best estimate of where you are, formed from the DR (course steered and distance through the water, corrected for leeway) and the tidal stream experienced. It is plotted with a triangle, and each EP is labelled with the time. Unlike a fix, an EP is only as good as the estimates in it; it is used to monitor progress, to decide whether you are on track, and to plan the next leg when no fix is available.

Procedure

1. Plot the DR from the last known position: the course steered (True, after removing compass error and leeway) and the distance run through the water (log reading or speed multiplied by time).
2. From the end of the DR, plot the tidal vector for the period: direction and distance (rate multiplied by time) using the appropriate hours.
3. The end of the tidal vector is the EP. Draw a triangle around it, label it with the time, and mark the ground track from the start through it.
4. Update at least hourly and at every alteration of course. Replace it with a fix whenever one is available.

Plotting it with a plotter and dividers

Set the course on the dial, square the plotter to the meridians and slide its edge through the start position, then pencil the water track. Open the dividers to the distance run on the latitude scale, level with where you are, and step it along the line. Do the same for the tidal vector from the end of the water track. Practise on the digital Portland plotter; the exercises at the end of this lesson include a DR and an EP to plot.

Worked example

You are at a fix at 1000. You steer 090 degrees T at 5 knots for 2 hours. The stream for the first hour sets 180 degrees T at 1.5 knots, and for the second hour 180 degrees T at 2.5 knots.

1. DR: 090 degrees T for 10 miles.
2. Tide: 180 degrees T for 1.5 + 2.5 = 4 miles (the two vectors are in the same direction, so they simply add; if the directions differed you would plot them end to end).
3. The EP lies 10 miles east and 4 miles south of the start. The ground track is the angle whose tangent is 4 divided by 10, which is 22 degrees south of east, so about 112 degrees T. The distance made good is the square root of (100 + 16) = 10.8 miles in 2 hours, speed over ground 5.4 knots.

Notice the ground track is nowhere near the course steered: if you had plotted only the DR you would believe you were 4 miles north of where you are, and that is exactly how yachts end up on rocks.

Cross-checks

A GPS shows speed over ground (SOG) and course over ground (COG), which already contain the tide. Use them to check your EP and to measure the actual stream: if your log shows 5 knots through the water and GPS shows 6.2 knots along a track, the fair component is 1.2 knots. The RYA expects you to keep the paper plot going even when GPS is working.

Common Mistakes

Click to zoom

• Adding a drying height instead of subtracting it. Underlined figures are above CD.
• Using the Rule of Twelfths where clearance is tight, or in ports with irregular tides.
• Forgetting BST. Tide tables are usually in UT; add one hour in summer.
• Not interpolating secondary port differences for springs and neaps, or for time of HW.
• Using the wrong tidal hour. Streams are referenced to HW at a specific standard port — check which one.
• Drawing the tidal vector the wrong way. Streams are given as the direction they flow towards.
• Measuring the CTS from A to D (that is the ground track) instead of from C to D.
• Steering a new course every hour on a long leg instead of summing the vectors.
• Leaving no safety margin in UKC — swell, high pressure and squat all reduce real clearance.
• Not updating EPs hourly with the current hour's stream.
• Applying leeway the wrong way, or applying it before the vector triangle instead of after.
• Confusing the datum for bridge heights. Check whether the chart gives clearance above MHWS or HAT.
• Mixing up the neap and spring figures in an atlas, or forgetting to read the key.
• Assuming slack water at HW or LW. The streams turn at different times from the heights.

Worked Example: Planning a Tidal Passage

You plan to leave a harbour entrance at 1000 and sail 12 miles on a ground track of 090 degrees T to a headland where the stream runs hard. Your boat averages 5 knots through the water. HW at the standard port is 1030. Streams at the nearest diamond: at HW, set 090 degrees T at 1.0 knot (neaps) and 1.8 knots (springs); at HW plus 1, set 090 degrees T at 0.4 and 0.8 knots. Today's range is exactly halfway between neaps and springs. Each table row is used for the hour centred on that time, so the first hour (1000 to 1100) uses the HW row and the second hour (1100 to 1200) uses the HW plus 1 row.

1. Interpolate each rate: HW row, 1.4 knots; HW plus 1 row, 0.6 knots.
2. The tide is fair (it runs east, the way you are going), so speed over the ground is 5 + 1.4 = 6.4 knots in the first hour and 5 + 0.6 = 5.6 knots in the second. Distance covered: 6.4 + 5.6 = 12.0 miles in 2 hours.
3. You reach the headland at about 1200, which is HW plus 1.5, with the stream already fading and about to turn against you.
4. The margin is therefore thin. If you leave an hour late, you arrive at HW plus 2.5 with the stream turning foul at a headland where it runs hard. The sensible plan is to leave no later than 1000, brief the crew on a point of no return, and name an alternative (an anchorage or harbour short of the headland) in the log.
5. Fix every 30 minutes and update the EP hourly, comparing the actual speed over the ground with 6.4 and 5.6 knots. If you are well behind, divert early.

This is the kind of reasoning the examiner expects at Day Skipper level: a fair tide where it matters, an arrival at the gate with a margin, a fallback, and the figures to back them up.

Summary

• Charted depths and drying heights are measured from Chart Datum (approximately LAT). Actual depth = charted depth + height of tide; depth over a drying feature = height of tide minus drying height.
• Springs (new and full moon) give the biggest range and strongest streams; neaps the smallest. The cycle is about 14.8 days.
• Use the standard port tidal curve for accurate heights at any time; the Rule of Twelfths only for quick estimates in normal ports.
• Secondary port times and heights come from interpolated differences applied to the standard port, then converted to local time.
• Pressure, wind and surge move the real tide away from the prediction: about 1 cm per millibar.
• UKC = charted depth + tide minus draught; always add a safety margin. For bridges, the clearance equals the charted clearance plus the difference between the reference level and the present height of tide.
• Tidal streams come from diamonds or atlases, referenced to standard port HW; interpolate between spring and neap rates by the day's range.
• Course to steer: tidal vector first, then boat speed arc, then measure the water track, apply leeway, and convert to compass.
• An EP is the DR plus the tidal vectors for the period. Update it hourly and replace it with a fix as soon as one is available.

Check Your Understanding

1. Why do charted depths represent a minimum depth in almost all conditions?

Answer: They are measured below Chart Datum, which is approximately Lowest Astronomical Tide — the lowest predictable tide level — so the tide is almost always above it.

1. A rock dries 1.6 m. The height of tide is 3.4 m. How much water is over it?

Answer: 3.4 minus 1.6 = 1.8 m.

1. Charted depth is 1.2 m, height of tide 2.3 m, draught 1.5 m. What is the UKC, and is it enough in sheltered water?

Answer: 1.2 + 2.3 minus 1.5 = 2.0 m. Yes — well above a 0.5 m margin.

1. Range 3.6 m, LW 1.0 m. Using the Rule of Twelfths, what is the height 3 hours after LW?

Answer: Cumulative rise after 3 hours is 6/12 of 3.6 = 1.8 m. Height = 1.0 + 1.8 = 2.8 m.

1. When should you not rely on the Rule of Twelfths?

Answer: When clearance is tight, and in ports with irregular tidal curves such as the Solent, Poole or Swanage.

1. Dover HW is 0930 UT, 6.4 m (springs). A secondary port has differences of minus 0020 and minus 0.4 m at springs. What are HW time (in BST) and height?

Answer: 0930 minus 0020 = 0910 UT, 1010 BST. Height 6.4 minus 0.4 = 6.0 m.

1. A diamond shows 045 degrees T, 2.4 knots springs, 1.2 knots neaps. Today is exactly midway between springs and neaps. What stream do you use?

Answer: 045 degrees T at about 1.8 knots.

1. In the course-to-steer triangle, which line gives the course to steer and which the speed over the ground?

Answer: The water track (from the end of the tidal vector to where the boat-speed arc cuts the ground track) gives the course to steer. The distance along the ground track from the start to that point gives the speed made good.

1. You need a 2.0 m height of tide to enter a marina. How do you find the earliest time?

Answer: On the tidal curve, draw the day's diagonal, enter at 2.0 m on the height scale, go to the diagonal, across to the rising side of the curve, and down to the time scale.

1. Why should you add tidal vectors end to end for a four-hour leg rather than steering a new course each hour?

Answer: Summing the vectors and steering a single heading gives the shortest path through the water; correcting hour by hour makes the boat follow a longer curved track.

1. A bridge has a charted clearance of 10.0 m above MHWS (4.6 m at the port). The height of tide is 2.1 m. What is the clearance now, and can a yacht of air draught 12.0 m pass with a 0.5 m margin?

Answer: Clearance = 10.0 + (4.6 minus 2.1) = 12.5 m. The yacht needs 12.0 + 0.5 = 12.5 m, so it just passes with no spare margin; wait for a lower tide or choose another route if there is any doubt.

1. You steer 090 degrees T at 5 knots for 2 hours while the stream sets 180 degrees T for 4 miles in total. Where is your EP relative to the start, and what is your ground track and speed over ground?

Answer: 10 miles east and 4 miles south, a ground track of about 112 degrees T over about 10.8 miles, so a speed over ground of about 5.4 knots.