Tides and Tidal Calculations

Causes of Tides

Read first: vertical datums on the chart and the publications you must carry. This topic turns those datums and books into real depths, times and stream rates.

In short: the tide is the regular rise and fall of the sea caused mainly by the Moon, helped or hindered by the Sun, as the Earth turns under them.

• The Moon’s gravity pulls the ocean towards it. On the far side of the Earth the water is “left behind”. Result: two bulges of water, one under the Moon and one on the opposite side.
• The Earth turns under the two bulges, so most places get two high waters (HW) and two low waters (LW) a day.
• The Moon moves on in its orbit, so a lunar day is about 24 h 50 min. HW comes about 50 min later each day, roughly every 12 h 25 min where the tide is semi-diurnal.
• The Sun raises a tide too, but it is only about half as strong as the Moon’s (NOAA, Tides and Water Levels tutorial).
• Types of tide:
  • Semi-diurnal: two HW and two LW a day, of similar height (UK and north-west Europe).
  • Diurnal: one HW and one LW a day. Some ports, for example in the Pacific, only have one HW/LW daily.
  • Mixed: two tides a day but of very different heights (diurnal inequality).
• Coastlines, sea basins and shallow water shape the real tide. Two ports a few miles apart can have very different times and ranges.
• Weather changes the tide. The predictions assume average weather:
  • High pressure lowers sea level, low pressure raises it: about 1 cm per 1 hPa away from average.
  • Strong onshore wind piles water up (storm surge); offshore wind can give a negative surge, with less water than predicted.
• On the bridge: in a deep low with an onshore gale, expect more water and earlier HW; in a big high with offshore wind, expect less water than charted plus predicted.

Spring and Neap Tides

In short: Sun and Moon in line = springs (big range). Sun and Moon at right angles = neaps (small range). The cycle repeats about every two weeks.

• Springs: at new moon and full moon. Sun, Moon and Earth are in line, so the two pulls add up. Higher HW, lower LW, bigger range, stronger streams.
• Neaps: at the Moon’s first and last quarter, about a week later. Sun and Moon pull at 90° and partly cancel. Lower HW, higher LW, smaller range, weaker streams.
• Two springs and two neaps every lunar month: springs about every 14–15 days, neaps half-way between.
• In many places the biggest springs come a day or two after new or full moon (the tide lags the Moon).
• Springs are larger near the equinoxes (March and September) and when the Moon is closest to the Earth (perigee).
• “Spring” has nothing to do with the season: it comes from the water “springing up”.
• Range = height of HW − height of LW. It is the number that tells you whether today is near springs or near neaps.

Tidal Levels and Chart Datum

In short: charted depths are measured down from chart datum (CD), normally LAT. Every tide height in the tables is a height above CD.

From the top down:

• Depth of water = charted depth + height of tide.
• Drying height (underlined figure on the chart) is above CD: water over it = height of tide − drying height.
• Because CD is LAT, the tide is almost never below it. It can be, though, in high pressure and offshore wind.
• Mean spring range = MHWS − MLWS. Mean neap range = MHWN − MLWN. ATT prints them for every standard port, so you can compare today’s range with them.
• The ATT gives these levels for each port, so you can find, for example, HAT − height of tide when you check a bridge clearance.

Admiralty Tide Tables and Tidal Stream Atlases

In short: the Admiralty Tide Tables (ATT, NP201–NP204) give daily HW/LW times and heights for standard ports, differences for secondary ports and harmonic constants. The Tidal Stream Atlases show the streams hour by hour as arrows.

• Both are among the compulsory publications on the bridge, in the “5 A’s” (the Admiralty books) of the publications list, next to the Sailing Directions and the List of Lights.
• ATT volumes (published every year): NP201 United Kingdom and Ireland (now in two parts, NP201A and NP201B); NP202 to NP204 cover other sea areas, including the Indian Ocean and South China Sea (NP203) and the Pacific Ocean (NP204). Together about 500 standard and 5,700 secondary ports (UKHO).
• What is inside each volume:
  • Part I — standard ports: daily times and heights of HW and LW, and the tidal curves (spring and neap) for each standard port, with its mean ranges.
  • Part II — secondary ports: time and height differences to apply to a named standard port.
  • Part III — harmonic constants, for the Simplified Harmonic Method (used where the curves do not describe the tide well, such as ports with a large diurnal inequality).
  • Notes on prediction methods, weather effects and, in some volumes, tidal stream tables.
• Time zone: each page states the zone of its times. UK ports are in UT (GMT): add 1 h in summer (BST).
• Digital: ADMIRALTY TotalTide gives the same predictions for over 7,000 ports. ADMIRALTY EasyTide (free, 7 days) must not be used for navigation.
• Tidal Stream Atlases (for north-west European waters, for example NP233 Dover Strait, NP337 The Solent):
  • 12–13 chartlets, one for each hour from HW −6 to HW +6 at a reference port (often Dover).
  • Arrows give the direction; thicker arrows = stronger stream.
  • Rates in tenths of a knot, as two figures: “12,23” = 1.2 kn at mean neaps, 2.3 kn at mean springs. The comma marks the spot where the stream was measured.
  • A computation of rates diagram in the atlas helps you find today’s rate between neaps and springs.

Height of Tide at a Standard Port

In short: take HW and LW from ATT, work out the range, choose the curve, and read the height for your time (or the time for your height) off the standard port curve.

Height at a given time

1. From Part I, write down the HW and LW times and heights either side of your time. Correct the time zone (BST +1 h).
2. Range = HW height − LW height. Compare it with the mean spring and neap ranges printed on the curve page.
3. Pick the curve: spring curve, neap curve, or interpolate by eye between them. If the range is bigger than springs, use the spring curve.
4. Mark HW height on the top scale and LW height on the bottom scale of the curve diagram and join them with a straight line.
5. Put the HW time in the box under the curve and find your time as hours before or after HW.
6. Go up from your time to the curve, across to the HW–LW line, then up (or down) to the height scale. That is the height of tide above CD.

The curve really gives a factor (0 at LW, 1 at HW). Same result by sum: height = LW + factor × range.

Example (illustrative figures): HW 0630 5.8 m, LW 1245 0.9 m. Range 4.9 m, near springs. At 0930 (HW +3) the curve gives a factor of about 0.55: height ≈ 0.9 + 0.55 × 4.9 ≈ 3.6 m.

Time for a given height

• Work backwards: factor = (required height − LW) ÷ range.
• Enter the curve from the height side, go across to the curve on the correct side (rising or falling), then down to read the time from HW.
• Example: you need 3.0 m. Factor = (3.0 − 0.9) ÷ 4.9 ≈ 0.43. Read the falling side of the curve and add the interval to the HW time.
• Typical use: “What is the latest time I can cross the bar?” or “When is there enough water to leave the berth?”

Quick check: rule of twelfths

• Over a 6-hour rise or fall, the tide changes by about 1/12, 2/12, 3/12, 3/12, 2/12, 1/12 of the range in each hour.
• Half the range goes in the middle two hours; the streams are strongest then too.
• It assumes a regular 6-hour tide. Use it as a sanity check, not as the exam method, and never in places with odd tide curves.

Secondary Ports

In short: a secondary port has no daily predictions. Take the day’s figures for its standard port, apply the time and height differences from Part II, then use the standard port curve.

1. In Part II, find the secondary port and the standard port it is linked to. That is not always the nearest port: it is the one with a similar tide.
2. From Part I, take the standard port’s HW and LW times and heights for the day.
3. Time differences: Part II gives HW and LW differences for two standard-port times (for example 0000 and 0600, repeated at 1200 and 1800). Interpolate for today’s time. HW differences go on HW, LW differences on LW: never mix them.
4. Height differences: given at MHWS, MHWN, MLWN and MLWS. Interpolate for today’s HW height between the MHWS and MHWN differences, and for today’s LW height between the MLWN and MLWS differences.
5. Apply the seasonal change in mean level if one is given (usually a few cm).
6. You now have the secondary port’s HW and LW. Use the standard port’s curve with these figures, timed from the secondary port’s HW.

Example (illustrative figures): standard port HW 0600 5.8 m. Time difference at 0600 = −0040, so secondary HW = 0520. Height differences: −0.4 m at MHWS 6.0 m, −0.2 m at MHWN 4.8 m. 5.8 m is most of the way to springs, so the difference ≈ −0.4 m: secondary HW ≈ 5.4 m.

• A small error in time matters less than a small error in height: 0.3 m can decide whether you clear a sill.
• Some shallow-water ports with unusual tides (for example the Solent area, Swanage to Selsey) have their own curves, often timed from LW. Follow the instructions in ATT for them.

Depth, Under-Keel Clearance and Air Draught

In short: add the tide to the chart for depth; subtract it from HAT for clearance under a bridge. Then take your draught or air draught off and keep a margin.

• Depth = charted depth + height of tide.
• Under-keel clearance (UKC) = depth − draught. Then allow for squat, swell, weather and poor survey data.
  • Example: charted 2.4 m + tide 3.6 m = 6.0 m of water. Draught 4.5 m → UKC 1.5 m before squat.
• Over a drying bank: water = height of tide − drying height.
  • Example: drying height 1.2 m, tide 3.6 m → 2.4 m of water.
• Clearance under a bridge or power cable = charted clearance (above HAT) + (HAT − height of tide) − air draught.
  • Example: charted 18.0 m, HAT 6.2 m, tide 3.6 m → 18.0 + 2.6 = 20.6 m under the bridge. Air draught 19.0 m → margin 1.6 m.
  • Least clearance is at HAT. Check the chart notes: older or foreign charts may use MHWS.
• Remember the weather: high pressure and offshore wind can take water away from the prediction.

Tidal Streams: Tidal Diamonds and Atlases

In short: a tidal diamond on the chart points to a table with the stream’s direction and spring/neap rates for each hour from HW −6 to HW +6 at a standard port. Interpolate the rate for today’s range.

• Tidal diamond: a letter in a diamond, printed in magenta, at the spot where the stream was measured. Letters run A, B, C… on each chart.
• The table on the chart has 13 rows (HW −6 … HW … HW +6) at a named standard port. For each diamond: direction (°T), spring rate and neap rate in knots.
• Each row covers half an hour either side: the HW +3 row is good from HW +2½ to HW +3½.
• Direction is the way the stream sets towards. A stream of 045° flows to the north-east (the opposite of wind, which is named for where it comes from).
• Rate for today: work out today’s range at the standard port, then
  • rate = neap rate + (spring rate − neap rate) × (today’s range − mean neap range) ÷ (mean spring range − mean neap range);
  • or use the computation of rates diagram. Rough guide: the neap rate is about half the spring rate.
• Example (illustrative figures): diamond C at HW +2: 045°, springs 2.4 kn, neaps 1.2 kn. Today’s range 4.4 m; mean ranges springs 6.0 m, neaps 3.2 m. Rate = 1.2 + 1.2 × (1.2 ÷ 2.8) ≈ 1.7 kn. In one hour the ship is set 1.7 NM towards 045°.
• Use the set and drift for your EP and course to steer: see position fixing and set and drift.
• Tidal stream = horizontal flow caused by the tide; it reverses with the tide. Current = non-tidal flow (ocean currents, wind drift, river outflow).
• The atlas and the diamonds give the same kind of data. The atlas shows the whole area at a glance; a diamond gives the figure at one spot.

Tides on the Bridge: Planning, Fixing and Grounding

In short: tides decide when you can go, how much water you have, where the stream sets you and what you do if you touch bottom.

• Passage planning (appraisal): tide tables and tidal stream atlases are on the list of sources. Before departure, check the critical points for tidal heights and flow: bars, sills, shallow channels, low bridges, tidal gates where a fair stream saves hours.
• ECDIS: if the ETA in the route is wrong, the tidal data applied to the route is wrong too. Apply tidal and current data only if integrated and up to date.
• Fixing by soundings: to compare a line of soundings with the chart, first take off the height of tide (and check the echo sounder, for example with a lead line).
• Vertical sextant angle: the height of a light or landmark on the chart is above MHWS; the elevation in a light description is above MHWS too.
• Aground: find the state of the tide when you grounded and the times and heights of the next HW and LW. A rising tide may lift you off; on a falling tide you may sit harder and the hull may be stressed. See actions after grounding.
• At anchor: allow for the range when choosing depth and scope; the ship swings when the stream turns.