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Lesson 9 Tide Calculations

Rule of sevenths

In the tabel with Tidal level squares in the nautical chart the height of tide is given at springs and at neaps. However if we need to know the height of tide on a day between springs and neaps, we will need to calculate it with the 1/7th rule. The 1/7 rule can be used for interpolation between mean high water springs (MHWS) and mean high water neaps (MLWN) like in the following 3 examples:

  1. Height of tide at high water
  2. Height of tide at low water
  3. Tidal current rate.

Height of tide at high water:

A.) Height of tide at HW = MHWN + (number of days till Neaps / 7) x difference between MHWS and MHWN

B.) Height of tide at HW = MHWS - (number of days till springs / 7) x difference between MHWS and MHWN

Height of tide at low water:

A.) Height of tide at LW = MLWS + (number of days till springs / 7) x difference between MLWS and MLWN

B.) Height of tide at LW = MLWN - (number of days till neaps / 7) x difference between MLWS and MLWN

Tidal rate:

In the tidal current table the rate is given at springs and neaps, so not for the days in between. Also this we can calculate with the 1/7e rule:

A.) Rate = Rate at springs + (number of days till Neaps / 7) x difference in the rate at springs and the rate at neaps.

B.) Rate = Rate at springs - (number of days till Springs / 7) x difference in the rate at springs and the rate at neaps

Rule of twelfths

The water rises in 6 hours from low- to high tide. In the first hour the water rises 1/12th of the total range, in the second hour 2/12th, in the third hour 3/12th, in the fourth hour 3/12th, in the fifth hour 2/12th and in the last hour 1/12th. In total 12/12th is 100%. In tide tables there are sometimes only the height of tide at high and low water on that day. If we want to calculate the height of tide at a moment in between, for example x hours before or after HW, we need to do that as follows:

  1. Calculate the range.
  2. Calculate how many hours before or after HW or LW we need to know the height of tide.
  3. Multiply the number of 12th with the range.
  4. Calculate:

High water - (../12 x range) = height of tide

Or

Low water + (../12 x raneg) = height of tide

1-12-regel

Graphic method

It is also possible to read the height of tide using a graph. For example: What will be the height of tide on 19 April (is printed red so it is springs) at 14.45 UT?
In the nautical almanac we can read:

HW Dover (6,6 m) at 11.41 UT
LW Dover (0,8 m) at 19.10 UT

1. 14.45 ut is between HW Dover at 11.41 UT and LW Dover 19.10 UT.
2. Fil in the relevant times after HW on the x-axis.
3. Draw a line from HW 6.6 to LW 0.8 left of the graph.
4. Draw a line vertical line from 14.45 to the graph of springs, the red one.
5. Draw a horizontal line to the diagonal line left of the graph.
6. Draw a vertical line to determine the height of tide: 4,3 meter.

Grafische methode 

Note that the springtij-graph is always under the neaps graph.

Passing a sill or shoal

The graphic method is very suitable to determine the time window to pass a sill or shoal. In many ports with a large range like in Normany or Britany, there is a sill to prevent the harbour to dry at low water.

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  1. Calculate how much height of tide is needed, counting in that the sill often dries at LAT and also the draft of the ship and the minimal under keel clearance (UKC).
  2. Draw 2 diagonal lines in the graph. 1 diagonal for the periode between low and the next high tide and 1 for the period between high and the next low water. The height of tide of the 2 low water moments can differ.
  3. Then draw a vertical line of the horizontal axis from the minimum required height of tide to the 1st diagonal and read from what time you can sail over the sill or shoal.
  4. Then draw a vertical line of the horizontal axis from the minimum required height of tide to the 2nd diagonal and read until what time you can sail over the sill.
  5. This is how you can find the time window in which you can cross the sill. A number of hours before HW till a number of hours after HW.

Crossing a shoal with the HP33

Using the HP33, we can also calculate in which time frame we can sail over a shoal. Imagine that we want to sail over shoal with a flat bottom boat with a draft of 60cm and that we want to maintain an under keel clearance of 40cm. The shallowest point is 40 cm above LAT, as there is a underlined value 0 4 on the nautical chart (green colored area). That means that we need 60cm + 40cm + 40cm = 1.40cm height of tide.

 

Imaging it is 1 March 2011. You could cross the shoal from 05.00 till 09.00 and again from 17.00 till 23.00.

Using Navionics

Nowadays, more and more use is made of navigation App's like Navionics. With this, we can also quickly read the time window in which we can sail over the surface. We use the same boat data as in the previous case. Depth of 60cm. Under keel clearance of 40cm. So 14dm is needed to be added. Furthermore, it is 21 June 2018.

What you can do in the Navionics App is to put the cross at the nearest "tide station". Kornwerderzand in this example. Then the tide graph with timeline appears below the map. You can slide that timeline so that the height of tide indicates at least 1.4m. That is therefore from 02.01u see below.

And it will be until 05.19, see below. After that time there is not enough height of tide to cross the shoal.

Powerpoints

PowerPoints

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Questions & explanations

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For the following questions you need these data. Print this PDF file first.

Question 1: In the tide table you see that the height of tide at high water is 2,4m, and at low water 0,5m. What is the dept at HW at a shoal area where the charted depth is: 0,6 meter? (Note: underlined means dying height.)

Answer:

a: 3,00

b: 1,60

c: 1,80

Question 2: In the nautical chart we find 1,5m (underlined, so a drying height). The height of tide at HW is 3,2 meter; the range is 1,2 meter. What observed depth could we expect with LW?

Answer:

a: 1 meter

b: 0,5 meter

c: 1,5 meter

Question 3: The height of tide on a certain place at HW Springs is 5 meter. The height of tide at HW neaps is 2,9 meter. What will be the height of tide at HW, 3 days after springs?

Answer:

a: 2,9 meter

b: 3,9 meter

c: 4,1 meter 

Question 4: Tide table for Flushing:
HW 04.55 4,9 m
LW 11.18 0,5 m
What will be the height of tide at 06.55?

Answer:

a: 4,0 meter

b: 3,8 meter

c: 3,3 meter

Question 5: If the height of tide at HW is 4 meter and 1,6 meter at LW. What will be the height of tide 2 hours after HW?

Answer:

a: 3,4 meter

b: 2,4 meter

c: 2,0 meter

Question 6: What is the height of tide at Westkapelle 4 days after full moon (=2 days after springs) 2 hours before HW? (Use the 1/7th rule and the rule of the 12th.) In the nautical chart you find tidal squares with these details:
MHWS 4,2
MHWN 3,4
MLWN 0,8
MLWS 0,3

Answer:

a: 3,9 meter

b: 4,1 meter

c: 3,1 meter

Question 7: According to your GPS you are sailing at 11.00 on a 10 meter depth line. At 08.00 it was low water (height of tide was 0,4m) and at 14.00 it will be High water (height of tide 4,7m). The time between HW and LW is 6 hours. What will be the observed depth at 11.00?

Answer:

a: 11,10 meter

b: 12,55 meter

c: 13,20 meter

Question 8: Use the PDF with information. What will be the height of tide on 10 December at 09.00 in Flushing?

Answer:

a: 17 dm

b: 31 dm

c: 8 dm

Question 9: To pass a shoal area close to Flushing, you will need 2,5 meter height of tide minimum. When are you able to cross that shoal on 9 December?

Answer:

a: van 07.00 tot 16.00

b: van 13.00 tot 16.00

c: van 07.00 tot 13.00

Question 10: What time it is exactly Low water in Flushing in the afternoon of 21 December?

Answer:

a: 14.14

b: 01.36

c: 20.40

About Elmar Teeuwen

Elmar is a CWO sailing instructor and RYA Yachtmaster® Offshore, Commercial Endorsement with STCW95 and certified coastal navigation teacher.
He has more than a decade of experience with teaching sailors on the North Sea, Atlantic, Med and Caribbean from beginners to instructor level, as well as regatta teams.
In addition to his native language Dutch, Elmar speaks English, German and Italian.
His knowledge and teaching skills could be off great value to anyone who wants to realise his sailing dreams.