Lesson 26 of 40 · Module 4 — Tides and tidal streams

The rule of twelfths and clearance under the keel

A quick method for tidal height, and making sure you float.

Day Skipper20 minVideo · Notes · Interactive · Exercises

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0:00 / 4:51Chapter 1 of 9: A quicker estimate

Transcript

In the last lesson you used the Port Kerran tidal curve to find the height of tide at any time. That is accurate, but sometimes you want a quick answer in your head, at the helm, without the almanac. The rule of twelfths gives you one. Then you will use heights of tide to answer the question that matters most: will there be enough water under the keel?
Divide the range of the tide into twelve equal parts, called twelfths. In the first hour after low water, the tide rises one twelfth of the range. In the second hour it rises two twelfths. In the third and fourth hours it rises three twelfths each. Then two twelfths in the fifth hour, and one in the sixth, arriving at high water. One, two, three, three, two, one: and a falling tide works the same way, counting the hours after high water.
Here is a real day from the Port Kerran table: Wednesday the second of June. Converted to BST, low water is at zero nine zero nine, 0.6 metres, and high water at fifteen eighteen, 5.0 metres. The range is 4.4 metres, so one twelfth is about 0.37 metres. Three hours after low water, at twelve zero nine, the tide has risen six twelfths, which is half the range: 2.2 metres. Add that to the low water height, and the height of tide is 2.8 metres.
The rule assumes the tide rises steadily over six hours, in a neat, symmetrical curve. Port Kerran’s tide takes a little longer: on this morning, high water comes six hours and nine minutes after low water. So the rule is close, but not exact. At twelve zero nine the rule and the curve agree, but at thirteen zero nine the rule gives 3.9 metres and the curve 3.8. Where a port’s curve is irregular, with a long stand at high water or a double high water, the rule can be badly wrong, so use the port’s own curve.
Look at the steps again. Half of the whole range comes in the third and fourth hours, so the water rises and falls fastest around mid-tide, and changes very little near high and low water. On a mean spring tide at Port Kerran, with a range of 4.8 metres, that is 1.2 metres in each of those hours. So time a shallow crossing with care: at mid-tide the depth changes quickly, and touching the bottom on a falling tide can leave you stuck for hours. Tidal streams keep their own timetable: around Kerran the diamonds show the strongest streams near high and low water, so always check them separately.
Now the question that matters most: will we float? The depth of water is the charted depth plus the height of tide. Take away the yacht’s draught, 1.8 metres, and what is left is the clearance under the keel. Decide the smallest clearance you will accept, your safety margin, before you need it.
How much clearance is enough is the skipper’s choice, and it depends on the conditions. In waves the yacht rises and falls, so allow more. Allow more, too, where the chart’s survey is old or the bottom is rock, and where you trust the tidal prediction less. Weather moves the sea as well: as a rough guide, high pressure lowers it by about one centimetre for every hectopascal above average, and strong winds can push it up or hold it down. So the least depth you need is your draught plus your margin, and the height of tide you need is that, minus the charted depth.
Suppose you want to cross the drying patch in Kerran Bay, which dries 0.9 metres. The tide must first cover that drying height, then give you your draught and your margin on top. With a half-metre margin that is 1.8, plus 0.5, plus 0.9: you need 3.2 metres of tide. On Saturday the twelfth of June, the Port Kerran curve gives at least that from zero nine zero five until fourteen thirty-three BST.
When you anchor, the depth you see on arrival is not the depth you will have later. Say you anchor in Kerran Roads at fourteen thirty BST on Saturday the twelfth of June, and the sounder reads 4.6 metres. The height of tide there is 3.3 metres now, and low water at eighteen ten is 0.9 metres, so the tide will fall another 2.4 metres. That leaves 2.2 metres at low water: only 0.4 metres under the keel, less than a half-metre margin. Check this every time you anchor, and remember the yacht swings around her anchor, so the depth all around matters too.

In this lesson you will learn

Estimate the height of tide with the rule of twelfths, rising or falling
Judge when the rule is good enough and when to use the tidal curve
Explain why the height of tide changes fastest at mid-tide, and what that means for timing
Work out clearance under the keel, and choose a sensible safety margin
Find the height of tide needed to cross shallow or drying ground
Check that an anchored yacht will still float at low water

The rule of twelfths

In Lesson 25 you found the height of tide at any time from the Port Kerran tidal curve. That is the method to use at the chart table. But at the helm, or when you just want a quick check, it helps to have a method you can do in your head. The rule of twelfths is that method.

Take the range of the tide — the difference between the high water and the low water you are working between — and divide it into twelve equal parts, or twelfths. The rule says that, after low water, the tide rises by:

Hour after LW	Rises in that hour	Total risen by the end of it
1	1/12 of the range	1/12
2	2/12 of the range	3/12
3	3/12 of the range	6/12 (half)
4	3/12 of the range	9/12
5	2/12 of the range	11/12
6	1/12 of the range	12/12 (all: high water)

One, two, three, three, two, one: the twelfths of the range the tide rises (or falls) in each of the six hours.

A falling tide works the same way: count the hours after high water, and the tide falls by 1, 2, 3, 3, 2 and 1 twelfths. So:

Height = LW + (twelfths so far ÷ 12) × range

Rising tide, n hours after LW

Height = HW − (twelfths so far ÷ 12) × range

Falling tide, n hours after HW

Using the rule

Here is a real morning from the Port Kerran table. Remember the table is in UT: in June, add an hour for BST (Lesson 24).

Port Kerran — times UT (add 1 hour for BST), heights in metres above chart datum
Day	Time	m	HW/LW
Wed 2 Jun	0200	5.1	HW
	0809	0.6	LW
	1418	5.0	HW
	2027	0.7	LW

Worked example

Height of tide at 1209 BST on Wed 2 Jun, by the rule of twelfths

1Convert to BST: LW 0909 BST, 0.6 m; HW 1518 BST, 5.0 m. The tide is rising.
2Range = 5.0 − 0.6 = 4.4 m, so one twelfth = 4.4 ÷ 12 ≈ 0.37 m.
31209 is 3 hours after LW. Twelfths so far: 1 + 2 + 3 = 6, which is half the range: 6/12 × 4.4 = 2.2 m.
4Height = LW + rise = 0.6 + 2.2 = 2.8 m.

Height of tide at 1209 BST ≈ 2.8 m

On a falling tide, take the twelfths away from the HW height. That afternoon HW is 1518 BST, 5.0 m, and LW 2127 BST, 0.7 m (range 4.3 m). Two hours after HW, at 1718, the tide has fallen 1 + 2 = 3 twelfths: 5.0 − 3/12 × 4.3 = 3.93 m, about 3.9 m.

Between whole hours, go proportionally: 2.5 hours after LW is halfway between 3 and 6 twelfths, so about 4.5 twelfths. You can also run the rule backwards to estimate when a height will be reached — for example, that morning the tide reaches 2.8 m (LW plus half the range) about three hours after LW.

How good is the rule?

The rule is only an approximation. It assumes the tide rises (or falls) steadily over exactly six hours, in a regular, symmetrical curve. Port Kerran’s tides take a little longer — that morning, HW comes 6 h 9 min after LW — so the rule and the curve differ slightly:

Hours after LW	Time (BST)	Rule of twelfths	Port Kerran curve	Difference
1	1009	1.0 m	0.9 m	+0.1 m
2	1109	1.7 m	1.7 m	same
3	1209	2.8 m	2.8 m	same
4	1309	3.9 m	3.8 m	+0.1 m
5	1409	4.6 m	4.7 m	−0.1 m
6	1509	5.0 m	5.0 m	same

The curve for 1309 BST, 2 h 9 min before HW: factor × range + LW gives 3.8 m, against 3.9 m by the rule.

A tenth of a metre is a small error, and here the rule is good enough for a quick check. But many ports have irregular curves — a long stand at high water, a double high water, or a rise that is much quicker than the fall. There the rule can be badly wrong.

InteractiveBuild the twelfths, hour by hour

Pick any rise or fall from the Port Kerran table, then step through the six hours. The bars are the rule of twelfths; the orange line is the curve.

Tide (Port Kerran, times BST)

Range 5.0 − 0.6 = 4.4 m, so one twelfth is 0.37 m.

Start at LW, 0909 BST, 0.6 m. Press Next hour to add the first step.

The height changes fastest at mid-tide

Look at the steps again: half of the whole range comes in the third and fourth hours. The water rises and falls fastest around mid-tide, and hardly changes in the hour either side of high and low water. On a mean spring tide at Port Kerran (range 4.8 m) that is 1.2 m in each of the middle hours, against 0.4 m in the first and last. At neaps (range 2.4 m) it is half that.

Waiting for water. On a rising tide, the depth over a bar or a shallow patch comes quickly at mid-tide, slowly near HW.
Going aground. Touching the bottom on a rising tide near LW is the least-bad case: you soon float off. On a falling tide you must act at once: around mid-ebb the water leaves fast, and if you don’t get off straight away you may be stuck for hours, until the tide comes back.
Small timing errors matter most at mid-tide. At springs, half an hour there is worth about 0.6 m of height.

Clearance under the keel

The heights of tide you have worked out answer the question that matters most: will we float? Building on Lesson 8 and Lesson 24:

Depth = charted depth + height of tide

Over drying ground: depth = height of tide − drying height

Clearance under the keel = depth − draught

The water left between the bottom of the keel and the seabed

The draught is how far the boat reaches below the waterline: for the course yacht, 1.8 m. Clearance under the keel is often called under-keel clearance (UKC).

Brennan Bank at 1009 BST on Wed 2 Jun, with 0.9 m of tide (from the curve).

Worked example

Clearance over Brennan Bank at 1009 BST

1Charted least depth (from the chart): 2.1 m. Height of tide from the curve: 0.9 m.
2Depth = 2.1 + 0.9 = 3.0 m.
3Clearance = 3.0 − 1.8 = 1.2 m.

1.2 m under the keel

Choosing a safety margin

You never plan for the keel to just skim the bottom. Before you need it, decide the least clearance you will accept: your safety margin. It is the skipper’s choice — commonly somewhere around 0.5 to 1.0 m for a yacht, more when the conditions call for it. Then work backwards:

Least depth needed = draught + margin

Height of tide needed = draught + margin − charted depth

Over drying ground the drying height adds: draught + margin + drying height

Allow more margin when…	Why
There are waves or swell	The boat rises and falls, so the keel comes lower in the troughs.
The survey is old or sparse, or the bottom is rock	There may be less water than charted, and touching rock does real damage. Soft mud is more forgiving.
You trust the prediction less	Times and heights are predictions for average weather, and interpolating (or using a secondary port) adds small errors.
The weather is unusual	See below: pressure and wind move the sea level.

Weather. As a rough guide, sea level changes by about 1 cm for each hectopascal (hPa) of difference from average pressure (about 1013 hPa): high pressure pushes the sea down, low pressure lets it rise. A high of 1033 hPa can leave about 0.2 m less water than predicted. Strong winds blowing onshore can raise the level, and offshore winds lower it; a storm surge can change it by much more. These are approximate — another reason to keep a margin.

Crossing a shallow patch or drying ground

To cross shallow water, work out the height of tide you need, then use the curve (Lesson 25) to find when you have it. On a rising tide the window opens; on a falling tide it closes — so plan to be across with time to spare.

Worked example

Crossing the drying patch in Kerran Bay on Sat 12 Jun

1The chart shows an underlined 0.9: the ground dries 0.9 m above chart datum.
2Margin chosen: 0.5 m (calm day). Height of tide needed = draught + margin + drying height = 1.8 + 0.5 + 0.9 = 3.2 m.
3That morning (BST): LW 0541 1.1 m, HW 1152 4.6 m. From the curve, the height reaches 3.2 m at 0905 on the flood and drops below it at 1433 on the ebb.

Cross between about 0905 and 1433 BST — and the nearer HW, the more water to spare.

InteractiveGo or no-go?

Choose a shallow place on the practice chart, a day, a time and your margin. The checker works out the depth, the clearance and the times you can cross that day.

It dries, so the tide must first cover the drying height before there is any water over it at all.

Day

Time (BST): 1000

Safety margin: 0.5 m

Draught 1.8 m. Heights from the Port Kerran curve.

At 1000 BST
Height of tide 3.9 m
Depth 3.9 − 0.9 = 3.0 m
Under the keel 3.0 − 1.8 = 1.2 m

Height of tide needed
1.8 + 0.5 + 0.9 (drying) = 3.2 m
Enough tide on this day: until 0214, 0905–1433, from 2124 BST

Go: 3.9 m of tide is at least the 3.2 m you need, leaving 1.2 m under the keel.

Height of tide (m) against time (BST). Green: at least the height you need.

Anchoring: will you still float at low water?

When you anchor, the depth on the sounder is the depth now. If the tide is going to fall, there will be less water later. The question is: how much more will it fall before low water, and will you still have your margin then?

Worked example

Anchoring in Kerran Roads at 1430 BST on Sat 12 Jun

1The sounder reads 4.6 m. (This course assumes it is set to show the depth from the surface; many are set to show depth below the transducer or below the keel — know which yours shows.)
2Height of tide now at Kerran Roads: 3.3 m. Next LW: 1810 BST, 0.9 m. Still to fall: 3.3 − 0.9 = 2.4 m.
3Depth at LW = 4.6 − 2.4 = 2.2 m. Clearance at LW = 2.2 − 1.8 = 0.4 m.
4With a 0.5 m margin you need at least 1.8 + 0.5 + 2.4 = 4.7 m on the sounder now.

Not enough: only 0.4 m under the keel at LW — move into deeper water

Kerran Roads is a secondary port, so its heights differ a little from Port Kerran’s. The heights above have been worked out for you; Lesson 27 shows how.

InteractiveWill we float at low water?

Set the day, your arrival time and the sounder reading at Kerran Roads anchorage. Staying overnight? Check the following low water too.

Day

Arrive (BST): 1430

Sounder reads (depth from the surface)

Margin at low water: 0.5 m

Height of tide now (1430 BST): 3.3 m
Next low water: 1810 BST, 0.9 m
Still to fall: 3.3 − 0.9 = 2.4 m
Depth at low water: 4.6 − 2.4 = 2.2 m
Under the keel at low water: 2.2 − 1.8 = 0.4 m

Not enough: only 0.4 m under the keel at low water. Find a spot where the sounder reads at least 4.7 m now.

Kerran Roads heights: Port Kerran’s high and low waters converted with the Kerran Roads differences, then the Port Kerran curve (Lesson 27 shows how). Draught 1.8 m.

Two more things to check. First, the yacht swings around her anchor with the wind and the stream, so the depth all around the circle she can swing through matters, not just where you dropped the anchor. Second, if you are staying overnight, work out the clearance for the lowest low water of your stay.

Putting it together

Find HW and LW for the day, in BST, and the range.
Quick estimate: the rule of twelfths (1, 2, 3, 3, 2, 1). For planning: the port’s curve.
Decide your margin from the sea state, the chart, the bottom and how far you trust the prediction.
Height of tide needed = draught + margin − charted depth (+ drying height over drying ground).
When anchoring, take off the fall still to come before LW.
Keep watching the sounder: it tells you what the sums can’t.

Key terms

Rule of twelfths: A quick estimate: the tide rises or falls 1, 2, 3, 3, 2, 1 twelfths of the range in the six hours after LW or HW.
Range: The difference in height between a high water and the low water next to it.
Mid-tide: About halfway between HW and LW, when the height changes fastest.
Draught: How far the boat reaches below the waterline (the course yacht: 1.8 m).
Depth: Charted depth plus height of tide; over drying ground, height of tide minus drying height.
Clearance under the keel (UKC): Depth minus draught: the water between the keel and the seabed.
Safety margin: The least clearance under the keel the skipper will accept, chosen for the conditions.
Height of tide needed: Draught + margin − charted depth (plus the drying height over drying ground).
Fall to come: How much further the tide will drop before low water: the height now minus the LW height.
Surge: A change in sea level caused by weather (pressure and wind), on top of the predicted tide.

Exercises

Check your understanding. You get a second try at each question, then the worked answer. Score 70% or more to complete the lesson — your progress is saved in this browser.

Port Kerran, Fri 11 Jun: LW 0456 BST 1.3 m, HW 1108 BST 4.3 m. Using the rule of twelfths, what is the height of tide at 0856 BST?

Port Kerran, Wed 2 Jun: HW 1518 BST 5.0 m, LW 2127 BST 0.7 m. Using the rule of twelfths, what is the height of tide at 1718 BST?

According to the rule of twelfths, when is the height of tide changing fastest?

On Wed 2 Jun (Port Kerran LW 0909 BST 0.6 m, HW 1518 BST 5.0 m), the rule of twelfths gives 3.9 m at 1309 BST, but the Port Kerran curve (below) gives 3.8 m. Which statement is right?

You plan to cross Brennan Bank at 1009 BST on Wed 2 Jun, when the curve gives a height of tide of 0.9 m. Read the bank’s least depth from the chart (the ringed sounding). What will the clearance under the keel be, for a draught of 1.8 m?

You want to cross the drying patch in Kerran Bay (the ringed, underlined sounding: it dries 0.9 m). Your draught is 1.8 m and you want a safety margin of 0.5 m. What height of tide do you need?

Mew Rock dries 1.2 m. How much water covers it at high water on Wed 2 Jun, 1518 BST, 5.0 m?

You anchor in Kerran Roads at 1430 BST on Sat 12 Jun. The sounder (set to show depth from the surface) reads 4.6 m. The height of tide there is 3.3 m now, and the next low water, at 1810 BST, is 0.9 m. How much water will there be under your 1.8 m keel at low water?

A big high-pressure system gives 1033 hPa, about 20 hPa above average. Roughly how will the sea level compare with the predicted height of tide?

Which of these crossings calls for the biggest safety margin under the keel?

0 of 10 answered · 0 correct

Tidal heights and clearance

Fresh questions from the Port Kerran table and the practice chart: rule-of-twelfths heights, clearance under the keel, crossing heights and anchoring. Times are BST.