Lesson 35 of 40 · Module 6 — Yachtmaster-level navigation

Advanced tidal height problems

Secondary port curves, interpolation and time-for-height calculations.

Yachtmaster30 minVideo · Notes · Interactive · Exercises

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0:00 / 4:54Chapter 1 of 9: Putting it all together

Transcript

At Yachtmaster level, a tidal height question rarely stops at one step. It starts in the Port Kerran tide table, carries the tides to Kerran Roads with the differences, and then reads the tidal curve. And it ends with a decision: when can we cross the bar, or how deep must we anchor? In this lesson we work one afternoon right through, then take on the classic problems.
On Thursday the third of June, the Port Kerran table gives low water at oh eight forty-six, high water at fourteen fifty-five and low water at twenty-one oh five, all in UT. Interpolate each Kerran Roads time difference using those UT times: plus nine, plus fifteen and plus eight minutes. Add them on, then add one hour for BST. Kerran Roads has low water at oh nine fifty-five, high water at sixteen ten and low water at twenty-two thirteen, BST.
Now the heights. High water at Port Kerran is four point seven metres, about six tenths of the way from neaps to springs, so the height difference is about minus nought point two six: call it minus nought point three. That gives Kerran Roads a high water of four point four metres, with low waters of nought point eight and nought point nine. So the range is three point six metres on the rising tide and three point five on the falling tide. Three point six is exactly halfway between the mean neap range of two point four and the spring range of four point eight, so read a curve halfway between the two.
To find the height of tide at thirteen hundred BST, count from high water at Kerran Roads, sixteen ten. Thirteen hundred is three hours ten minutes before high water, on the rising tide, so use the morning low water and the range of three point six. Go up from there to the day’s curve, halfway between springs and neaps, and read a factor of nought point five. Height equals low water plus factor times range: nought point eight plus nought point five times three point six, which is two point six metres.
Now a classic: a fictional bar near Kerran Roads dries nought point six metres, and you want half a metre under your one point eight metre keel. The height of tide you need is the draught, plus the clearance, plus the drying height: two point nine metres. On the rising tide that is two point nine minus nought point eight, divided by the range of three point six: a factor of nought point five eight. Read across to the rising side of the curve and down: two hours fifty-one minutes before high water, which is thirteen nineteen BST.
On the falling tide, use the evening low water and the range of three point five: a factor of nought point five seven, two hours fifty-five minutes after high water, at nineteen oh five BST. So the fictional bar can be crossed between thirteen nineteen and nineteen oh five BST. The curve is only a prediction, so start a little later, finish a little earlier, and watch the echo sounder.
At seventeen hundred you anchor in Kerran Roads for the night, and you want one metre under the keel at low water. The height of tide now is four point three metres, and low water at twenty-two thirteen is nought point nine, so the depth will fall by three point four metres. So anchor in at least one point eight plus one plus three point four: six point two metres on the echo sounder. Checking from the chart instead, you need a charted depth of at least one point eight plus one minus nought point nine: one point nine metres.
Over a drying feature, the depth is the height of tide minus the drying height. Mew Rock, off Port Kerran, dries one point two metres, so use the Port Kerran tides. At thirteen hundred BST the height of tide there is three point nought metres, leaving one point eight metres over the rock. With a draught of one point eight metres that is no clearance at all, so keep well clear, as its isolated danger mark tells you.
Finally, the mistakes that catch people out. Interpolating the time differences with BST instead of UT, or forgetting the hour altogether. Using the wrong low water for the range, or reading the wrong side of the curve. Interpolating from the wrong end of the printed values. And rounding too early, or the wrong way: round a height you need up, an earliest time later and a latest time earlier.

In this lesson you will learn

Work a Kerran Roads secondary-port problem in full for any table day: time differences in UT, then BST; height differences between neaps and springs
Read the Port Kerran curve, interpolated by the Kerran Roads range, for a height at a time and a time for a height on a rising or falling tide
Find the earliest and latest times to cross a bar or shallow patch with a chosen clearance under the keel
Work out the least depth to anchor in so you stay afloat with a margin at the next low water
Use drying heights in depth calculations, and avoid the common mistakes

One problem, several steps

Module 4 gave you every tool you need: the Port Kerran tide table in UT (Lesson 24), the tidal curve (Lesson 25), the rule of twelfths as a quick check (Lesson 26) and secondary ports (Lesson 27). At Yachtmaster level the tools are the same, but a single question strings them together, and it ends in a decision that matters on board: can we cross the bar, and when? How deep must we anchor so we are still afloat at low water?

Every such problem follows the same chain, and most mistakes happen at the joins:

Table: the Port Kerran high and low waters for the day, in UT.
Differences: carry them to Kerran Roads, interpolating in UT, then convert to BST.
Range and curve: the Kerran Roads range picks a curve between neaps and springs.
Height or time: read the curve forwards (height at a time) or backwards (time for a height).
Depth sum and decision: charted depth, drying height, draught and clearance.

Work slowly through the chain, write every step down, and check each answer makes sense before using it in the next.

The secondary port in full: Thu 3 Jun

Here is the afternoon of Thu 3 Jun from the table. You want the low water before the afternoon high water, the high water, and the low water after it, because a crossing or an anchoring problem can fall on either side of HW.

Port Kerran — times UT (add 1 hour for BST), heights in metres above chart datum
Day	Time	m	HW/LW
Thu 3 Jun	0237	4.9	HW
	0846	0.8	LW
	1455	4.7	HW
	2105	0.9	LW

Port	Times (UT)				Heights (metres)
Port	High Water		Low Water		MHWS	MHWN	MLWN	MLWS
Port Kerran	0000	0600	0100	0700	5.2	4.0	1.6	0.4
and	1200	1800	1300	1900
Differences Kerran Roads
	+0010	+0020	−0005	+0015	−0.3	−0.2	−0.1	0.0

Worked example

Kerran Roads, Thu 3 Jun: LW, HW and LW

1From the table, in UT: LW 0846 0.8 m, HW 1455 4.7 m, LW 2105 0.9 m. Don’t add the hour yet.
2Time differences, interpolated with the UT times. LW 0846 lies 106 of the 360 minutes from 0700 (+0015) towards 1300 (−0005): +15 + 0.29 × (−20) = +9.1 → +9 min. HW 1455 lies 175 of the 360 minutes from 1200 (+0010) towards 1800 (+0020): +10 + 0.49 × (+10) = +14.9 → +15 min. LW 2105 lies 125 of the 360 minutes from 1900 (+0015) towards 0100 (−0005): +15 + 0.35 × (−20) = +8.1 → +8 min.
3Add them, then the hour: LW 0855 UT = 0955 BST; HW 1510 UT = 1610 BST; LW 2113 UT = 2213 BST.
4Height differences, between the printed levels. LW 0.8 m is 0.33 of the way from MLWS to MLWN: −0.033 → 0.0 m. HW 4.7 m is 0.58 of the way from MHWN to MHWS: −0.258 → −0.3 m. LW 0.9 m is 0.42 of the way from MLWS to MLWN: −0.042 → 0.0 m.
5Kerran Roads heights: LW 0.8 m, HW 4.4 m, LW 0.9 m.
6Ranges: rising tide 4.4 − 0.8 = 3.6 m; falling tide 4.4 − 0.9 = 3.5 m. For the rising tide, read a curve 0.50 of the way from the neap curve to the spring curve: (3.6 − 2.4) ÷ (4.8 − 2.4) = 0.50.

LW 0955 BST 0.8 m · HW 1610 BST 4.4 m · LW 2213 BST 0.9 m

The last step matters more than it looks. The Port Kerran curve is printed for springs and neaps; on a day in between you read a curve in between, in proportion to the range. Use the Kerran Roads range for this, since that is the tide you are working, and the range on the correct side of HW: the rising tide uses the LW before it, the falling tide the LW after it. On Port Kerran’s gentle curve the difference is small, but at ports where the spring and neap curves differ a lot it decides the answer.

InteractiveSecondary port, step by step

Choose any high water in the table, then step through the working. The form fills in as you go; a time on a different date from the HW has its day added.

Tide (Port Kerran HW, from the table)

Secondary port form for Kerran Roads, Thu 3 Jun
Thu 3 Jun	LW	HW	LW
Port Kerran time (UT)	0846	1455	2105
Port Kerran height	0.8 m	4.7 m	0.9 m
Time difference	…	…	…
Kerran Roads (UT)	…	…	…
Kerran Roads (BST)	…	…	…
Height difference	…	…	…
Kerran Roads height	…	…	…

Step 1 of 6: From the table (UT)

Copy Port Kerran’s low water, high water and low water for Thu 3 Jun straight from the table, in UT. Don’t add the hour yet: the printed differences are referred to UT times.

Height at a time, time for a height

With the Kerran Roads times and heights on the form, the curve works exactly as in Lesson 25, with one change: the time axis counts from HW Kerran Roads. Write 1610 BST in the box under HW and the clock times of the hours either side.

The Port Kerran curve used for Kerran Roads on Thu 3 Jun: height of tide at 1300 BST (HW−3h10).

Worked example

Height of tide at Kerran Roads at 1300 BST

11300 is HW−3h10: before HW, so the tide is rising and the LW before HW goes with it (0.8 m).
2Range 3.6 m: read a curve 0.50 of the way from the neap curve to the spring curve: (3.6 − 2.4) ÷ (4.8 − 2.4) = 0.50.
3Up from HW−3h10 to that curve, across to the factor scale: about 0.50.
4Height = LW + factor × range = 0.8 + 0.50 × 3.6 = 2.6 m.

About 2.6 m above chart datum at 1300 BST

The time for a height runs the same construction backwards. Turn the height you need into a factor, find that factor on the correct side of the curve (left of HW when rising, right when falling), and drop down to the time axis. On the diagram, you go down from the height on the HW scale to the range line, across to the curve, then down.

factor = (height needed − LW) ÷ range

Then find this factor on the rising (before HW) or falling (after HW) side of the curve.

Crossing a bar or a shallow patch

The classic Yachtmaster question: when is there enough water to cross? Start by turning everything into a height of tide needed. Under the keel you want a clearance: the skipper’s choice, often 0.5 to 1.0 m in calm water and more in swell, when the boat heaves and pitches, or when the seabed is rock.

height needed = draught + clearance − charted depth

Over a drying feature the charted depth is negative, so you add the drying height instead.

Take a bar near Kerran Roads that dries 0.6 m. (The bar is fictional and is not drawn on the practice chart; we use it because bars are where this problem bites.) The course yacht draws 1.8 m and the skipper wants 0.5 m under the keel.

Time for a height: 2.9 m on the rising tide at Kerran Roads, Thu 3 Jun, for the fictional bar.

Worked example

Earliest and latest times over the fictional bar, Thu 3 Jun

1Height needed = 1.8 + 0.5 + 0.6 = 2.9 m.
2Rising tide, LW 0.8 m, range 3.6 m: factor = (2.9 − 0.8) ÷ 3.6 = 0.58. The rising side of the curve reaches it at HW−2h51: 1319 BST.
3Falling tide, LW 0.9 m, range 3.5 m: factor = (2.9 − 0.9) ÷ 3.5 = 0.57, reached at HW+2h55: 1905 BST.

Cross between about 1319 and 1905 BST, keeping clear of the edges of the window

The same method works for a shallow patch with a charted depth. Brennan Bank, south-east of the island, has a least charted depth of 2.1 m and uses the Port Kerran tides: with 1.8 m of draught and 1.0 m of clearance you need 0.7 m of tide, which is less than most low waters in the table. Raise the clearance for a swell and the window starts to matter.

InteractiveWhen can I cross?

Pick a tide, the fictional bar or Brennan Bank, and set the draught and clearance. The shaded band is the window; the dashed line is the height of tide you need.

Tide (Port Kerran HW, from the table)

Where

Draught

1.8 m

Clearance under the keel

0.5 m

A fictional bar drying 0.6 m, near Kerran Roads. It is not on the practice chart; use the Kerran Roads tides (secondary port).

Kerran Roads tides (BST): LW 0955 0.8 · HW 1610 4.4 · LW 2213 0.9
Height of tide needed: 1.8 (draught) + 0.5 (clearance) + 0.6 (drying height) = 2.9 m
Earliest (rising tide): 1319 BST (HW−2h51, factor 0.58)
Latest (falling tide): 1905 BST (HW+2h55, factor 0.57)
Window: 5h46, from 1319 to 1905 BST

Anchoring: allow for the fall

Anchor on a falling tide and the depth under you shrinks until low water. Whatever the echo sounder reads now, it will read less by the fall: the height of tide now minus the height at the next LW.

least depth now = draught + margin + fall

fall = height of tide now − height of the next LW. From the chart instead: least charted depth = draught + margin − height of the next LW.

Worked example

Anchoring in Kerran Roads at 1700 BST, Thu 3 Jun

11700 is HW+0h50, on the falling tide: range 3.5 m, factor 0.97, height now = 0.9 + 0.97 × 3.5 = 4.3 m.
2Next LW 2213 BST, 0.9 m. Fall = 4.3 − 0.9 = 3.4 m.
3You want 1.0 m under the keel at LW: least depth now = 1.8 + 1.0 + 3.4 = 6.2 m.
4Check from the chart: charted depth of at least 1.8 + 1.0 − 0.9 = 1.9 m.

Anchor in at least 6.2 m now (charted depth 1.9 m or more)

The 6.5 m sounding just south of the anchor symbol easily passes: at LW it has 6.5 + 0.9 = 7.4 m. Two more checks before you settle down:

Know what your echo sounder shows. Many are set to read below the transducer or below the keel rather than from the surface. The formula above uses the total depth; correct the reading if yours is offset.
Staying longer? Check every LW you will be there for, not just the next: towards springs each one is lower. And work out the greatest depth, at HW, to decide how much cable to let out. On that sounding, the next HW (Fri 4 Jun, 0430 BST, 4.4 m) gives 10.9 m. As a rough guide only, many skippers let out at least four times the greatest depth when using all chain; more with rope, and more again in strong winds or poor holding.

InteractiveAnchoring as the tide falls

Choose a tide and the time you anchor in Kerran Roads, and set your margin. Then drag the second slider to watch the tide fall to low water.

Tide (Port Kerran HW, from the table)

Margin under the keel at LW

1.0 m

You anchor at 1700 BST (HW+0h50 Kerran Roads)

Height of tide at 1700: 4.3 m (factor 0.97, range 3.5 m)
Next LW, 2213 BST: 0.9 m
The depth will fall by: 4.3 − 0.9 = 3.4 m
Least depth to anchor in now: 1.8 + 1.0 + 3.4 = 6.2 m
Or, from the chart: least charted depth: 1.8 + 1.0 − 0.9 = 1.9 m
The 6.5 m sounding at LW: 6.5 + 0.9 = 7.4 m

Watch the tide to LW: 1700 BST (height of tide 4.3 m)

You anchored in exactly 6.2 m. Drag to low water at 2213.

Drying heights

A drying height (an underlined sounding, as in Lesson 8) is how far a feature stands above chart datum. The water over it is the height of tide minus the drying height; if that comes out negative, the feature is showing.

What the chart gives	Depth of water	Example
A charted depth (sounding)	charted depth + height of tide	6.5 m sounding at LW: 6.5 + 0.9 = 7.4 m
A drying height	height of tide − drying height	Mew Rock at 1300: 3.0 − 1.2 = 1.8 m
An echo sounder reading now	reading − (height now − height later)	6.2 m at 1700 becomes 2.8 m at LW

Worked example

Mew Rock at 1300 BST, Thu 3 Jun

1Mew Rock lies off Port Kerran, so use the Port Kerran tides: HW 1555 BST 4.7 m, LW before it 0946 BST 0.8 m.
21300 is HW−2h55; range 3.9 m, factor 0.56: height = 0.8 + 0.56 × 3.9 = 3.0 m.
3Depth over the rock = 3.0 − 1.2 = 1.8 m: no more than the yacht’s draught.

1.8 m over Mew Rock: keep clear, as its isolated danger mark says

Working backwards, the rock covers when the height of tide reaches 1.2 m: a factor of 0.10, at about 1056 BST. That factor is low on the curve, so the time is rough. The same sum tells you when a dinghy can land over the 0.8 m drying patch on the shore south-east of the Kerran Roads anchorage. No tidal data are given for that stretch of shore, so we assume the Kerran Roads tides apply there: it is only 1.6 M from the anchorage.

Common mistakes

These are the slips that most often turn a right method into a wrong answer. The numbers are from Thu 3 Jun.

Mistake	What it does here	How to avoid it
Interpolating the time difference with the BST time	HW difference +17 min instead of +15 min; forgetting the hour altogether puts every answer an hour out	Work in UT to the end of the differences; add the hour once.
Using the wrong LW, or the wrong side of the curve	A rising-tide time read on the falling side comes out after HW, around 1905 instead of 1319	Before HW: LW before and the left of the curve. After HW: LW after and the right.
Interpolating from the wrong end	Morning LW difference +1 min instead of +9 min; HW height 4.5 m instead of 4.4 m	Measure from the earlier printed time, and from MHWN or MLWS upwards.
Rounding too early, or the wrong way	Rounding the fictional bar’s factor 0.58 to 0.6 moves the earliest time by 4 minutes; a few such slips add up	Keep decimals until the end; round a height needed up, an earliest time later and a latest time earlier.

Key terms

Height of tide: Height of the sea surface above chart datum at a given time.
Factor: Fraction of the range the tide has risen above LW (0 at LW, 1 at HW), read from the curve.
Interpolated curve: A curve read between the spring and neap curves, in proportion to where the day’s range lies between the mean ranges.
Clearance under the keel: Depth of water minus draught; the margin the skipper chooses for safety.
Height of tide needed: Draught + clearance − charted depth (adding the drying height over a drying feature).
Crossing window: The time between the earliest (rising tide) and latest (falling tide) times with enough water.
Fall: Height of tide now minus the height at the next LW: how much the depth will drop.
Drying height: Height of a feature above chart datum (an underlined sounding); depth over it = height of tide − drying height.
Secondary port form: A grid for working secondary-port times and heights step by step, standard port to BST.

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.

Sun 13 Jun: Port Kerran HW is 1132 UT, 4.9 m. Using the Kerran Roads differences, at what time is HW at Kerran Roads? Give the time in BST, on the 24-hour clock.

Port Kerran — times UT (add 1 hour for BST), heights in metres above chart datum
Day	Time	m	HW/LW
Sun 13 Jun	0522	0.8	LW
	1132	4.9	HW
	1742	0.6	LW
	2352	5.0	HW

Port	Times (UT)				Heights (metres)
Port	High Water		Low Water		MHWS	MHWN	MLWN	MLWS
Port Kerran	0000	0600	0100	0700	5.2	4.0	1.6	0.4
and	1200	1800	1300	1900
Differences Kerran Roads
	+0010	+0020	−0005	+0015	−0.3	−0.2	−0.1	0.0

Same day: Port Kerran HW 4.9 m and the LW after it, 1742 UT, 0.6 m. What is the range at Kerran Roads for the falling tide?

Port	Times (UT)				Heights (metres)
Port	High Water		Low Water		MHWS	MHWN	MLWN	MLWS
Port Kerran	0000	0600	0100	0700	5.2	4.0	1.6	0.4
and	1200	1800	1300	1900
Differences Kerran Roads
	+0010	+0020	−0005	+0015	−0.3	−0.2	−0.1	0.0

The Kerran Roads range for the falling tide is 4.0 m (mean ranges at Port Kerran: springs 4.8 m, neaps 2.4 m). Which curve do you read?

Sun 13 Jun, Kerran Roads (from the secondary-port form): LW 0632 BST 0.8 m, HW 1243 BST 4.6 m, LW 1853 BST 0.6 m. Using the Port Kerran curve, what is the height of tide at Kerran Roads at 1600 BST?

Wed 2 Jun, Kerran Roads: LW 0920 BST 0.6 m, HW 1532 BST 4.7 m, LW 2137 BST 0.7 m. A bar near Kerran Roads dries 0.6 m (the bar is fictional and not on the practice chart; use the Kerran Roads tides). The course yacht draws 1.8 m and you want 0.5 m under the keel. What is the earliest time you can cross before the afternoon HW? Give the time in BST, on the 24-hour clock.

Mon 14 Jun, Port Kerran (from the table): LW 0601 UT 0.5 m, HW 1211 UT 5.1 m, LW 1821 UT 0.4 m. With a swell running, you want 2.0 m under the keel to cross Brennan Bank (least charted depth 2.1 m), draught 1.8 m. What is the latest time you can cross after the midday HW? Give the time in BST, on the 24-hour clock.

Sun 13 Jun, Kerran Roads: LW 0632 BST 0.8 m, HW 1243 BST 4.6 m, LW 1853 BST 0.6 m. You arrive at 1400 BST and want to stay at anchor through the evening LW with 1.0 m under the keel (draught 1.8 m). What is the least depth you can anchor in now? (Your echo sounder shows the depth below the surface.)

The circled sounding on the shore south-east of the Kerran Roads anchorage is a drying height: it dries 0.8 m. Assume the Kerran Roads tides apply there. On Sun 13 Jun (Kerran Roads: LW 0632 BST 0.8 m, HW 1243 BST 4.6 m, LW 1853 BST 0.6 m), how much water is there over it at 1100 BST?

Kerran Roads, Sun 13 Jun: LW 0632 BST 0.8 m, HW 1243 BST 4.6 m, LW 1853 BST 0.6 m. You want the earliest time to cross a shallow patch on the rising tide before the 1243 HW. Which range do you use?

Your working for the fictional bar on Thu 3 Jun gives an earliest time of 1319 BST and a latest time of 1905 BST. How should you use them?

0 of 10 answered · 0 correct

Yachtmaster tidal height practice

Fresh problems from the Port Kerran table (1–14 June): Kerran Roads times, heights from the curve, crossing windows on rising and falling tides, anchoring depths and drying heights.