Weekly quiz: wet dock sill tide calculation

The English Channel port of Perros-Guirec (Brittany, NW France) just inaugurated the new gate-flap of its wet dock.

Let’s suppose you’re planning to go there for the July 14th fireworks. But will you make it in time?

Question of the day

🔹 Using the (manual) method of your choice, explain your calculation of the evening opening time, given a sill elevation at 7.5 meters above chart datum.

Here is the tide prediction :

And bonus questions

🔹 What time will the sill close at thereafter?
🔹 The timetables published by the harbor office most certainly differ slightly from those your calculated. For what reasons ?

👉 Reply on one of our social media below. We’ll post the solution right here next Sunday!

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Calculating the wet dock opening time

Apparently, not many of you were in for some bit of tide calculation. It looks as though apps have made it simple. Yet beware! Phones do fall overboard or run out of battery. So let’s go!

🔹 Arguably, the easiest method is to use the rule of twelfths. In mathematical terms, it makes the problem simpler by making it linear.

Let’s start by determining the tidal hours

Between low tide at 15:58 and high tide at 21:59, the interval is 6:01 long. We will split that into 6 periods (tidal hours), lasting each one hour.

Let’s now determine the rate at which the water will rise

The tidal range is 8.97 – 2.02 = 6.95 meters. During the first and last tidal hours, the water will rise one twelfth of that range, i.e. 0.58 m. During the second and fifth tidal hours, the water will rise two twelfths of that range, i.e. 1.16 m. And during the third and fourth tidal hours, the rise will be three twelfths, i.e. 1.74 m.

Starting from the high water mark, at 21:59 and 8.97 m, we first go one step back. One tidal hours before that, i.e. at 20:59, the water height will be 0.58 m less, i.e. 8.39 m. Let’s walk a further tidal hour back. At 19:59, the water will be 1.16 m less, i.e. 8.39 – 1.16 = 7.23 m.

We can now calculate the gate-flap opening time

We have now bracketed the desired water height: the wet dock will open when the water level reaches 7.5 m, so that will happen between 19:59 and 20:59. By interpolating, our predicted time will be approximately : 19:59 + (20:59 – 19:59) × (7.5 – 7.23) / (8.39 – 7.23) = 20:13

Calculating the wet dock closing time

🔹 The calculation for the closing time is similar. There are two differences, though. First, the water is now falling instead of rising. But most of all, the interval between high tide and low tide is now 6:22, which makes each of the 6 periods (tidal hours) 1:03 long instead of exactly one hour. Apart from that we once again bracket the sill height of 7.5 meters and find out it is reached during the second tidal hour, which begins at 23:02 and ends on the next day at 0:06. The water heights at both these times are 8.37 m and 7.17 m respectively. This makes for a calculated closing time at 23:48.

There are, of course, several other methods we could have used to calculate these times, some using trigonometry computations and several others being graphical, such as plotting on a circle or a tidal curve.

Why are the published times different from our predictions?

🔹 Now the published times of the gate-flap opening and closing times differ slightly from our calculated times. Of course, our calculations are approximate, because the rule of twelfths is a simplified method. Using other computation or graphical means could have led to better times.

In particular, being in the English Channel, the tide probably does not follow a perfect sine curve. A hint comes from the fact that the rising tide is shorter than the falling tide, and a tidal curve for this specific port would be more precise.

However, always bear in mind that in any case, these are but predictions, and the actual water height on the given day will be offset by some possible surge or decrease, due to a combination of atmospheric pressure, winds and coastal configuration.

We must, however, highlight that another offset might be at work.

Both opening and closing times are slightly early compared to the predictions : 20:05 vs. 20:13 and 23:27 vs. 23:48. Our best guess here is that this might be explained by possible leaking from the wet dock. Since this is not a simple sill, but rather a gate-flap closing the wet dock, it is most likely that the sealing can’t be perfect. Just like you would see on sluices, there might be some slight water loss, which could lead to the water level falling a fraction of a meter during the course of a tide. As a result, the wet dock is able to open earlier, but it also closes earlier in order to keep enough water in for the next tide.