Tidal height and stream

The tide is the slow rise and fall of sea level. The main cause is the gravitational pull of the Moon and, to a lesser extent, of the Sun. The figure shows the level over a day: in many seas, including those where the course is held, there are two high waters and two low waters a day, and about six hours pass from one low water to the next high water.

The Mediterranean and the Baltic are exceptions: tides there are almost negligible. In the waters of the course there are two high waters and two low waters a day, with exceptions such as the Solent, and the tables and calculations in the following parts are built on this rhythm.

When Sun and Moon are in line, at new moon and full moon, their pulls add together: high water is higher and low water lower. These are springs, with a large tidal range. When the pulls are at right angles, at first and last quarter, we have neaps, with a small range. The range is the difference between a high water and the next low water; the two steps of the figure show the two situations.

The biggest springs come about two days after new or full moon. The phases of the Moon repeat every lunar month: textbooks round it to 28 days, but it is really about 29.5. In a month there are therefore two periods of springs and two of neaps, about a week apart. In the almanac, springs have the date in red, neaps in blue.

High water is the highest level reached in a cycle, low water the lowest. The range is the difference between a high water and the next low water. In the figure, which uses the teaching data for Colville, low water is 0.8 m at 09:25 and high water 4.4 m at 15:31: the range is 4.4 − 0.8 = 3.6 m.

The range changes from day to day. For this reason the almanac also gives the averages: mean high water springs (MHWS) and neaps (MHWN), mean low water springs (MLWS) and neaps (MLWN). Highest astronomical tide (HAT) is the highest level the tide can reach, and is used to work out the clearance under a bridge.

The depths written on the chart are not measured from the sea level of the moment, but from Chart Datum (CD), the hydrographic zero, which corresponds roughly to the lowest tide predicted. The height of tide is the distance of sea level above Chart Datum at that moment; the charted depth is the depth below Chart Datum. The depth of water is how much water there really is under you.

In the figure the chart says 5 m and the tide is 4.6 m high: the water is 5 + 4.6 = 9.6 m deep. Here is the rule, as the manual gives it.

Depth of water = charted depth + height of tide. Where the seabed dries, subtract the drying height from the height of tide.

At some points the seabed uncovers at low water. In that case the chart gives not a depth but a drying height, measured above Chart Datum. The reasoning is turned upside down: to find how much water there is over the point you start from the height of tide and take away the drying height, because the seabed lies above zero.

In the figure the rock dries 0.5 m and the tide is 4.6 m: over it there are 4.6 − 0.5 = 4.1 m of water. If the result is negative, the point is out of the water. For a normal seabed you add, for a drying seabed you subtract: the sign reverses.

Daily tide tables exist only for standard ports: for each day they give the time and height of high and low waters. A secondary port has no tables: you take the times and heights of the linked standard port and apply the tidal differences from the almanac. The figure shows the example with the teaching data for Colville (standard) and Jackson Bay (secondary).

If the time or height of the standard port lies between two columns of the block of differences, you interpolate between the two values; you never extrapolate. On Monday 9 December high water at Colville is at 15:31, between 13:00 (difference −65 min) and 19:00 (−5 min): 151 minutes out of 360 give −40 minutes, so high water at Jackson Bay is at 14:51. For heights you interpolate in the same way between MHWN and MHWS: 4.4 m, difference +0.3 m, height 4.7 m. At the end, if needed, you correct for daylight saving time.

The rule of twelfths is a quick way to estimate the height of the tide at any hour. In a rise or fall of about six hours the tide moves by 1, 2, 3, 3, 2, 1 twelfths of the range, hour by hour. In the figure the bars show the twelfths of each hour.

After low water, in the 1st hour 1/12 of the range rises (total 1/12), in the 2nd 2/12 (total 3/12), in the 3rd 3/12 (total 6/12, that is half), in the 4th 3/12 (total 9/12), in the 5th 2/12 (total 11/12), in the 6th 1/12 (total 12/12). The rule is quick but approximate: it works only if the tide is regular and lasts about six hours, and it must not be used where the curve is irregular, such as the Solent with its double high water. There you need the tidal curve.

In the figure low water at Colville is at 09:25 (0.8 m) and high water at 15:31 (4.4 m). The range is 3.6 m, so one twelfth is 0.3 m. At 12:31 we are in the third hour after low water: about half of the range has risen.

The calculation is 0.8 + 0.5 × 3.6 = 2.6 m. For a more precise height the twelfths are not enough: you use the port's tidal curve, which we see in the next part.

The tidal curve gives a more precise height than the twelfths. You mark the day's high and low water heights on the scale and join them with a straight line; you enter with the time relative to high water, go up to the curve (between the springs curve and the neaps curve, according to the day's range), go across to the factor and apply it to the line. In the figure the horizontal axis shows the hours relative to high water and the vertical axis the factor, from 0 (low water) to 1 (high water).

At Colville, 12:31 is 3 hours before high water: factor 0.50, height 0.8 + 0.50 × 3.6 = 2.6 m. At 17:31, 2 hours after high water, the factor is 0.71: 1.3 + 0.71 × 3.1 = 3.5 m (the twelfths would give 3.6 m). For a secondary port you put the secondary port's time and height on the standard port's curve. In the exercises the tolerances are 0.1-0.15 m for heights and 8 to 18 minutes for times; at sea you leave a margin.

To enter you need enough water over every shallow point on the route. The water needed is the draught plus the clearance under the keel; the height of tide required is the water needed minus the charted depth of the critical point. In the first step: a draught of 1.8 m and a clearance of 0.5 m make 2.3 m of water; with a charted depth of 0.5 m you need a tide of 1.8 m. If the point dries, that is, it has a drying height instead of a depth, the sign reverses: water needed plus drying height.

In the second step you look for the time on the Colville curve. The rising factor is (1.8 − 0.8) ÷ 3.6 = 0.28, which gives about 11:38; falling, (1.8 − 1.3) ÷ 3.1 = 0.16, which gives about 20:06. The usable window is therefore from 11:38 to 20:06, with a margin at both ends. The same calculation, in reverse, tells you when a grounded boat floats again: you need a height of tide equal to the draught minus the charted depth. At sea strong wind and pressure change the real height: high pressure lowers it, low pressure raises it, by about 1 cm per hPa.

The tide also moves the water horizontally: this is the tidal stream. It is given by the set, the direction the water flows towards in degrees true, and by the drift or rate, the speed in knots. In the figure the set is 090°: the water flows towards the east, while a wind from 090° blows from the east. Confusing the two directions is a typical mistake.

The stream depends on the place, on the time relative to high water at the reference port and on whether the day is at springs or neaps. It is found in the tidal stream atlas, where the arrows carry two numbers in tenths of a knot: the first for neaps, the second for springs, or in a tidal diamond.

A cross-stream pushes the boat sideways: the ground track is not the same as the heading. To go from A to B you must work out how far to aim up-stream, that is, the course to steer. The four steps of the figure show the drawing on the chart: the track A-B, the stream vector for one hour, the arc of the boat's speed and the resulting course.

In the example the track is 186°T, the boat makes 9 knots and the stream is 033°T, 2.3 knots: the course to steer is 193°T, that is 200°M with variation 7°W. The speed over ground (SOG) is the length of the track covered in one hour and gives the time of arrival: 6.9 knots, so 6 miles in 52 minutes instead of 40. If the stream changes every hour, you draw one vector per hour, in a chain.

GPS does not allow for the tide: steering directly for the waypoint with a strong cross-stream lengthens the route. This is why you always draw the tidal stream triangle.