10 techniques for determining a tidal window

Introduction

The Saint-Jean-Port-Joli nautical park is a superb place to spend a few days. The marina is close to the village center, the grocery store, the restaurants and a few boutiques. It is also close to a campground, making it easy to meet up with friends who prefer the road to the waterway. What’s more, there’s a very friendly Harbour Master!

But regulars also know that you need to choose your arrival window carefully, depending on the tide. If you arrive too close to low tide, you run the risk of grounding your sailboat.

A French tourist, whose yacht is pictured at the beginning of this text, serves as a warning. The photo shows his sailboat aground at the entrance to the nautical park. As the bottom is mud, the boat should have escaped with minimal damage. The state of the owner’s pride remains unknown!

The tides decide

Parc Nautique Saint-Jean-Port-Joli is inaccessible between one and two hours either side of low tide, depending on your draught and the height of the tide.

Parc Nautique de Saint-Jean-Port-Joli.

Saint-Jean-Port-Joli bears nothing special. As in many other places along the St-Lawrence river, it’s the tide that sets the windows for arrivals and departures. This is a must if you want to enter or leave the marina with sufficient depth, but also to make the best use of the tidal currents. To plan your arrival, you need to determine a time slot when you know the water is high enough for navigation. You then need to calculate your route backwards to determine a departure time consistent with this arrival window.

To each his own!

This text shows you how to identify tide windows, or to determine the water level at a given time. It details ten different techniques. Some are more useful in practice, others are more useful for exams. You should therefore read the parts of the text that are necessary, or that you consider useful, depending on your objectives. The table below is very helpful in determining which approaches to learn for which circumstances.

Electronic techniques

The preponderance of cellular and tablet devices for navigation purposes is the established norm for yachting. In doing so, the first four techniques explored in this text make use of electronic tools. Behind this diversity of applications, the source of tidal information is the same: the Department of Fisheries and Oceans Canada. The applications are all connected to the department’s public data interface.

The first technique explores the Federal Tides Application. It’s free, simple and accessible from any browser-enabled device. The site is part of the Government of Canada’s official publications.

The second technique explores the Boating application (navionics). The Boating application is popular for its simplicity and specialized navigation features (maps, signals, real-time data, etc.). Although it offers a 90-day trial period, you then have to pay a subscription fee to take advantage of the charts and other information.

The third technique explores the OpenCPN application. It’s a free navigation application, but requires the purchase of electronic charts.

The fourth technique explores the St. Lawrence Global Observatory. It’s similar to the federal application: free and accessible to anyone with a browser. It offers a wealth of information on currents, winds and tides. However, it is not possible to obtain tide data more than a week in advance.

Each of these techniques requires the ability to read a graph linking the height of the tide to the time of day. If you know how to read a graph, all you need to know is how to use the applications! You will be able to determine the height of the tide at any time and for any port where data is available. The techniques are simple, require no calculation and are very general. There’s a reason why it’s the standard for practical use!

As far as applications are concerned, readers should choose one that suits them. If you are just starting out, you can start with the first (free) application and then take time to explore the others. Of course, individual preferences play a big part in assessing the merits of each application. Personally, I use OpenCPN for planning and Boating for navigation. There are also other applications available (Savyy Navy, C-MAP, etc.).

Manual (or paper-based) techniques

While electronic techniques are the established practical standard, the Sailing Canada, Royal Yachting Association and Transport Canada exams still assess manual techniques. So, to pass the associated exams or certificates, you need to know the “paper” techniques. Depending on the type of certification you are considering, you will also need to familiarize yourself with the techniques associated with that particular certification.

The fifth technique is part of the requirements for Transport Canada’s Small Vessel Operator Certificate, Sailing Canada’s Basic Coastal Navigation Certificate and Sailing Canada’s Basic Keelboat Certificate. You will be able to determine high and low tides in reference ports, as well as the height of the water. You will be able to determine passage windows, such as those required to enter the Saint-Jean-Port-Joli marina.

The sixth technique is also part of the requirements for Transport Canada’s Charting and Piloting II exam, as well as for Sailing Canada’s Basic Coastal Navigation certification. You will be able to calculate the height of high and low tide at any port, whether primary or secondary, using the tools authorized for the Transport Canada or Sail Canada exams.

The seventh technique is part of the requirements for the Transport Canada Charting and Piloting II exam, as well as the Sailing Canada Intermediate Coastal Navigation Certificate. You will be able to calculate the height of high and low tide at any port, and at any time, whether reference or secondary, using the tools authorized for the Transport Canada or Sail Canada exams.

The eighth technique is known as the sixths rule (or twelfths rule). It’s the most convenient technique for making quick calculations on deck. It is not required by any certificate, but it is well-established seamanship. Those who work in feet rather than meters will like the fact that it works with “twelfths”, as there are 12 inches in a foot. This makes it very easy to use when calculating in feet.

The ninth technique is mathematical and works directly with a sine curve equation. It allows you to identify the height of the tide at any given moment, but requires a calculator and an understanding of trigonometric functions. It may have the disadvantage of giving an impression of accuracy, as predictions are more precise than actual tidal behavior.

The tenth technique is the one taught in the Royal Yachting Association (RYA) Yachtmaster Offshore theory courses. It requires custom-made tidal curves. These are available in the UK, but not in Canada. Consequently, its only use is to pass the RYA exams.

A few definitions

In all the techniques described below, it is useful to be familiar with a minimum of concepts and definitions.

Tidal range is the difference between high and low tide. Tidal range is often expressed in meters and is specific to a given day and region. A tidal range of 3m in Saint-Jean-Port-Jolie, for example, means that the tide will vary by three meters. The context of the conversation or text will determine which tide is being referred to (morning? evening? which day?).

Chart datum is a convention. It’s the reference from which we measure the water level of the tide. This convention is established by the Canadian Hydrographic Service:

Chart datum is the low-water level to which are referred the depths of water covering permanently submerged features and the elevation of those that are periodically submerged. (Canadian Hydrographic Service)

A suitable approximate interpretation of chart datum is the “minimum level” of water under normal conditions. Thus, if a tide at a given hour is 2.0 meters and chart datum is 1.0 meter, the depth will be 2.0 1.0 = 3.0 meters. Tide level is always expressed from chart datum.

A tidal half-cycle is the time it takes to go from high tide to low tide (or vice versa). It’s usually around 6 hours and 12 minutes, or a quarter of the time required for the moon to make one complete revolution (24 h 48 minutes). The length of the half-cycle varies from place to place, depending on local hydrographic conditions.

A reference port is one which, in the eyes of Fisheries and Oceans Canada, is sufficiently important to justify its own tidal information.

On the other hand, a secondary port is one that, in the eyes of Fisheries and Oceans Canada, is not important enough to have its own tidal information. Corrections must be applied to the information from a reference port to obtain tide information for this secondary port.

Electronic techniques

Setting the scene

You wish to enter the Parc Nautique de Saint-Jean-Port-Joli on August 1, 2025. The harbor master’s office tells you to arrive two hours after low tide and two hours before the next low tide. What are the best times to arrive without running aground?

1st technique: federal tide application

The federal tide application is available at this address. Choose your language of use and then search for a “station” (image on the left, below). If required, you can click on the globe icon to identify one of the available stations (right-hand image, below). The Saint-Jean-Port-Joli station is one of them. You can then select it.

Once you have chosen the station you are interested in (below, Saint-Jean-Port-Joli), change the date to the one you are interested in (here, August 1, 2025).

Before reading the tides, pay attention to the time zone used by the application. Normally, the application automatically indicates daylight saving time (UTC-4) during the summer period. Otherwise, it will display Eastern Standard Time (UTC -5) and you will want to add an hour to obtain Daylight Saving Time. In the image below, the tides are shown in summer time, which corresponds directly to the times we normally use for our summer planning.

The application then graphically displays tide values at all times. It also displays high and low tide data. The first low tide is at 05:00 (summer time), the first high tide of the day is at 11:00 (summer time).

To obtain the time of the second low tide of the day, click on the appropriate point on the graph (image below). In this way, you can deduce that the second low tide of the day is at 5:00 p.m.

Based on the tide information and the local knowledge of the harbor master’s office, you’ll know that you should arrive between 7 a.m. (first low tide + 2) and 3 p.m. (second low tide – 2). That’s a lot of time!

Note that the application also allows you to deduce the tide level at any given moment, simply by clicking on the hour of interest.

In the image on the right, I’ve selected 13:30 (summer time). The application then displays a water level of 3.09 meters.

To interpret this water level correctly, you need to understand the Canadian Hydrographic Service convention, i.e. that 3.09 meters is above chart datum. So, if chart datum is 0.1 metres at Saint-Jean-Port-Joli, then the total depth is 3.1 metres.

2nd technique: Boating application

To use this approach, you need to have the Boating application installed on your tablet or phone. You will also need a subscription that includes canadian charts.

The first step is to center the application on the port of interest. On the right, the image is centered on Saint-Jean-Port-Joli.

The application automatically displays the tide stations. These are small black rectangles, sometimes with a red gauge (as in the image), sometimes with a blue gauge (unillustrated). Choose the gauge closest to the point of interest.

The Boating application has no mouse, but rather a central cross-shaped cursor. Move the screen until the gauge is at the center of the cross. Then click on the question mark (at the eastern end of the cross) to display the dialog associated with this tide window.

Care must be taken to ensure that the cursor is on the gauge, and not on an adjacent object. Otherwise, you risk displaying information about another object of interest.

The image below (left) shows the tide cycle window when the gauge has been correctly clicked. Although the window is smaller than in other applications (it is compressed to the bottom of the screen), Boating nevertheless displays the actual water level (chart zero tide level) directly on the charts as long as you are in the tides context menu. This means you can identify the water level at any point in the tide cycle.

Choosing the right date is as simple as using the contextual menu at the bottom left of the screen (see image on right, below). By moving the wheels, you can identify the date you’re interested in, and the application will load the tide data for the day of interest.

To interpret the tide data, move the cursor at the bottom of the tide window. You can then find the time of low tide, high tide, or the water level at any time of day.

Please note that the times shown in Boating are necessarily those presented in the time zone of the tablet or cell phone you’re working with. In the images in this text, the tablet is in the Caribbean time zone (!), so the time is ahead of schedule. So, in the images below, you need to add an hour to find Quebec time. If your tablet or cell phone is on Quebec time, you won’t have this problem.

The first low tide of the day is at 4:51 a.m. (3:51 1 a.m. to take into account my tablet’s time difference) and the second low tide is at 5:01 p.m. (4:01 1 a.m. to take into account my tablet’s time difference). Taking into account the information from the marina, the window for arriving in Saint-Jean-Port-Joli is therefore between 6:51 am and 3:01 pm.

3rd technique: OpenCPN application

To use this technique, you need to have OpenCPN installed on your personal computer, and to have purchased Canadian charts. You then need to identify the region of interest (see image below).

In the display configuration menu (bottom right), click on the “Tide stations” option (see image below). Clicking on the option should then cause small yellow rectangles to appear, each indicating the water level at each tide station. As Open CPN derives its data from Fisheries and Oceans Canada, these are the same stations.

Once the stations are displayed, right-click on the station of interest (here, Saint-Jean-Port-Joli) to display the tides pop-up window. The software is quite temperamental: you may have to click more than once. You should then be able to see the window shown on the right. The look may vary from one brand of operating system to another. The image below is taken from an Apple. In any case, you should recognize the sine curve representing the tide level.

To move to the date of interest, use the “previous” and “next” buttons at the bottom of the window. If the date you’re interested in is fairly far in the future, you’ll need to be patient and click several times.

Once you’ve selected the day, the interpretation is the same as for the federal application. A small information box at top left gives the time and level of high tides (“pleine mer”: PM) and low tides (“basse mers”: BM). The same information is available as in the Federal Tides application. Note that by default, information is communicated in local mean time (LMT), i.e. the time determined by the longitude deviation from the Greenwhich Meridian. The times indicated will therefore not correspond exactly to those given by the federal tide application.

Once the low tides have been identified, the appropriate tidal window can be found by adding two hours to the first low tide (05:03 – 2 hours) and subtracting two hours from the second low tide (17:09 – 2 hours). The acceptable window for arrival is therefore between 07:03 in the morning and 15:09 in the afternoon (in ” local mean time “).

technique 4: St. Lawrence Global Observatory

From the St. Lawrence Global Observatory home page (below left), click on the “Navigation Tools” page and then the “Navigation” tab (below right). You will find a wealth of useful information for navigating the river. For the purposes of this text, the information we are interested in deals with tides.

Once in the navigation tab, the tool will show the default tidal currents (image below). However, there is a “tides” button at the bottom of the screen. Click on it. You will then be asked to choose a location on the map to identify a tide station (the data being the same, it is the same stations as the Federal application). In our case, we’ll choose “Saint-Jean-Port-Joli”.

The window will then show the tides for the current date (image below). And therein lies the biggest flaw in the OGSL tides application: to my knowledge, it is not possible to obtain tide forecasts more than a week in advance. Consequently, you have to use the tool when you’re close to planning your trip.

Manual techniques

The appeal of manual techniques varies greatly from one person to another. Advocates of manual techniques will argue that, should the on-board electronic systems fail, they have the undeniable advantage of being able to calculate tides by hand. But at a time when every person on board has their own cell phone, the risk of all electronic systems breaking down is relatively low. Still, knowing the “analog” methods of calculating tides is an added security.

For persons adept of the electronic view, you will have to resign yourself to the following statements: it is a requirement of the Sail Canada exams, the Transport Canada exams… and it requires a lot of small calculations. Knowing one or more of the techniques discussed below will help you pass your exams!

5th technique: Tide tables at a reference port

Setting the scene

(Note: this is the same situation as for the electronic applications)

You wish to enter the Parc Nautique de Saint-Jean-Port-Joli on August 1, 2025. The harbour master’s office tells you that you must arrive within the window starting two hours after low tide and ending two hours before the next low tide. Which tide windows will allow you to arrive?

Solution

You need to look up the documents entitled “Tide and Current Tables” on the Government of Canada website. These tables are produced by Fisheries and Oceans Canada.

Since we’re interested in Saint-Jean-Port-Joli, a water park along the St. Lawrence River, we’ll download volume 3, 2025 edition, which deals with the St. Lawrence River. The 2025 version is permanently stored on this site. In practice, we always try to take the most recent edition from the Government of Canada site.

Once you have downloaded the document, you will be able to find tide tables for all “reference” ports, i.e. those that Fisheries and Oceans Canada considers important enough to warrant a tide table. Saint-Jean-Port-Joli is a reference port.

The tide tables give you the predicted water levels for each high and low tide on each day of the year. For August, you should be able to find the equivalent page to the extract at the beginning of this section.

The page identifies the table to the right of this text. It shows the time for August 1, 2025, given in military time (0353 = 03 hours, 54 minutes). The water level at this time is 1.2 meters, i.e. low tide. At 09:54, the high tide is 4.0 meters, and so on.

For navigation purposes, two conventions are important. The first is that the time given is Quebec Standard Time (UTC-5), without taking daylight saving time into account. Consequently, since time is advanced by one hour during the summer, the low tide of 0354 is in fact 0454 in summer time. The second convention is that the water level given is the one above chart datum.

Our question can now be answered. Low tide is indicated at 0454 (summer time) and 1659 (summer time). A window to enter is therefore between 0654 and 1459 (two hours after the first low tide and two hours before the next low tide).

6th technique: Tide table at a secondary port

Setting the scene

You wish to dine at anchor on Île aux Grues on August 1, 2025. You need to know the depth of the water to determine the appropriate tow. What are the maximum and minimum depths?

Solution

Again, consult the tide table. However, Île aux Grues has no specific tide table. It’s a secondary port. Fisheries and Oceans only presents corrections to be made in relation to a reference port. To obtain tide levels, you need to

1. Identify the reference port on the date of interest;
2. Determine the tide level at the appropriate times;
3. Apply corrections to transform reference port predictions into secondary port predictions.

Each of these steps requires the identification of a table in the tide table. These can be found in the section of the document dealing with secondary ports, and are illustrated below.

While working out the solution, it’s very useful to work with a summary table that you fill in as you go along. This table is shown below, and can be used to develop any secondary port tidal exercise.

Summary table for identifying tides at a secondary port

Step 1: Identify the reference port

The first pages following the reference port tide tables detail which secondary port is associated with which reference port. In the case of Île aux Grues, page 56 indicates that the reference port is Saint-Jean-Port-Joli (image below). The reference port is indicated in bold, above the line describing the secondary port.

Step 2: Identify the tides at the reference port

Here we need to go to the tide table of the reference port and apply technique #5. Since we’ve already identified the tides at Saint-Jean-Port-Joli for August 1, 2025 (previous technique), we can copy them into the table (below). It’s a good idea to keep the times as they are in the table and convert to summer time only at the end.

Step 3: Identify whether each tide is a large tide or an average tide

A large tide is when the sun and moon work together to generate larger-than-average tides. This is normally the case when we’re close to a full or new moon. Otherwise, the sun and moon are out of phase (and this is not a great tide).

The corrections you need to make depend on the type of tide you’re facing. You need to identify whether it’s a large or medium tide by comparing the day’s water level (at the reference port) with the tables indicating the usual level of a large or medium tide.

The type of tide closest to the tide level of the day of interest (in this case, August 1st) is selected. If the high tide level is closer to a large tide, this tide is categorized as a large tide (otherwise, it’s an average tide).

Table 2 on page 54 shows the typical heights of medium and large tides for both high tide (upper high water) and low tide (lower high water). Thus, at Saint-Jean-Port-Joli, we note that high tides are 5.1 meters for the mean tide and 6.3 meters for a large tide. Low tides are 0.8 meters for mean tide and 0.2 meters for large tide.

On August 1, 2025, all the tide data for that day indicate an average tide. The high tide of 4.0 meters is closer to 5.1 meters than to 6.0 meters. Similarly, the low tides of 1.2 and 1.3 meters are closer to 0.8 meters than to 0.2 meters. All data indicate an average tide. We can therefore fill in the third column of our table accordingly (below).

Note that it’s not always the case that all tides on the same day are of the same type. It’s possible to have an average low tide followed by a large high tide (or other combination). It’s perfectly acceptable to have different values on the same day. On the other hand, it is possible for large low tides to show a negative value. This means that large low tides are lower than the chart datum at that point.

Step 4: Identify the corrections to be applied according to tide type

The corrections to be applied are shown in Table 3 (image below, page 56 of the document). The “differences” columns are those to be consulted in relation to the secondary port of interest. Note that there are a total of six difference columns: three for high tide (“upper high water”) and three for low tide (“lower low water”). One column gives the difference in terms of hours and minutes, while the other two columns indicate the height corrections to be made according to the type of tide (“medium tide” or “high tide”).

As the tide is mean throughout the day, mean tide corrections must be applied for both high and low tides (otherwise, the correction specific to the tide type would have to be applied). The following corrections are therefore applied:

• A 23-minute correction for high tides.
• A 0.1-meter correction for medium high tides.
• A 49-minute correction for low tides.
• A correction of -0.3 meters for low tides.

This information is noted for each entry in the calculation table (below). We can then move on to the next step.

Fifth step: add the corrections

Now it’s time to apply the time and water level corrections. The only subtlety to remember is that there are 60 minutes in an hour. The table below summarizes the arithmetic operations performed.

Sixth and final step: adapt to daylight saving time

Since it’s August, don’t forget to add the extra hour for daylight saving time. The table (below) is now complete.

Around lunchtime (1200), we can thus deduce that the water level will be around 4.1 meters (above chart datum). The tide will ebb in the afternoon, reaching 1.0 metre above chart datum. You then need to consult your nautical chart to identify the chart datum where you intend to anchor.

7th technique: Transport Canada sine tables

Setting the scene

You’re happy to know that the tide is high at 1117 on Île aux Grues on August 1, 2025, but you expect to arrive at 1228. You’d like to know what the water level will be at that time. Similarly, you’d like to know at what point in the afternoon the water level will fall below 2.5 meters above chart datum, giving you a good indication of when to leave.

Solution

This technique is the first of the manual approaches to calculating tide levels at “any” time, i.e. at times other than high or low tide. It requires access to Fisheries and Oceans Canada tide tables (and relevant extracts will be provided for review).

In most Canadian harbours, each succession of high and low tides follows roughly a sinusoidal curve. This sinusoidal curve must be adapted to the tidal half-cycle and its tidal range. Fisheries and Oceans Canada provides a generic sinusoidal table that must be adapted. These are tables 5 and 5A (pages 48 and 50 of the document).

Conceptually, Fisheries and Oceans cuts a sine curve into 10 parts of equal height (see left-hand image below). These sections are numbered from A to J. These sections are then divided into fractions of the time required for the water level to reach that section (image below, right).

The intervals associated with each category are then represented respectively in table 5 (duration, image below, left) and table 5A (height, image below, right).

In practice, the technique can be broken down into five calculation steps:

1. Identify the duration of the half-cycle of interest;
2. Identify the tidal range of interest;
3. Identify the time elapsed between the start of the half-cycle of interest and the time when the tide is desired;
4. Based on the times identified in steps 1 and 3, identify the column corresponding to the elapsed time in table 5.
5. Next, identify the column selected in step 4 in table 5A and select the data associated with the tidal range identified in step 2.

These steps are detailed below, to help you find the answer to the situation.

Steps 1, 2 and 3

We know from technique #5 that on August 1, 2025, high tide is 4.1 meters above chart datum at Île aux Grues (at 1117 summer time). Low tide ends at 1748, with a height of 1.0 metre (at chart datum). The tidal range is therefore 3.1 meters (4.1 – 1.0) and the duration of the half-cycle is 6h31 minutes (17h48 – 11h17).

The situation shows us that we want to know the water level at 12:28, i.e. 1h11 minutes after high tide (1228 – 1117).

Step 4

Table 5 is consulted at line “6:30”, the line closest to the half-cycle time identified in step 1 (6:31). Each line in Table 5 corresponds to a given half-cycle time. By choosing the 6:30 line, we select the sine curve with the duration closest to the duration of our problem.

Then, in this line, we need to identify the column where the elapsed time is closest to the time elapsed since the start of the cycle (1h11). Column A is chosen, with an elapsed time of 56 minutes.

Step 5

Column A of Table 5A is then consulted, taking care to identify the line closest to the tidal range identified for the day of interest (3.1 meters). Each line modulates the intensity of the sine curve as a function of a given tidal range. Choosing the “3.0” line therefore selects the curve closest to the actual situation. Column A should read “0.15”, meaning a drop of 0.15 metres (15 centimetres).

Step 6

From this, we can deduce that at 12:28 pm, the tide level will be “roughly” 3.95 meters (4.1 -0.15) above chart datum.

What about the time of the 2.5-meter depth?

To identify when the depth will be 2.5 metres, we need to read the charts in reverse. The desired height is 1.5 metres above low tide. In table 5A, look for the column where the difference is closest to 1.5 metres for the tidal range line closest to the tidal range for that day (i.e. line “3.0”). The column identified is column “J”.

We then turn to table 5 to identify the elapsed time in column J for a time of 6.30 hours, i.e. 3 hours 15 minutes. As we analyzed the tidal difference from low tide, we need to start from the low tide time (17:48) and subtract the 3 hours, 15 minutes, to identify the start time. The result is 14h33 (1748 – 0315) at summer time. If you want to leave before the depth drops below 2.5 meters, this is the time you should leave.

8th technique: the sixths/twelfths rule

Scenario setting

From the scenario associated with technique #1, you know that on August 1, 2025, the arrival window at the Saint-Jean-Port-Joli nautical park is between 0654 and 1459 (summer time). What will the water level be at these times?

Solution

Most tidal half-cycles are about 6 hours long (more precisely, 6 hours, 12 minutes), the time it takes to go from high tide to low tide (or vice versa). The idea of the twelfths rule is to divide this half-cycle into six one-hour intervals and to calculate, for each sixth, the variations in water height by following a rule that gives roughly a sinusoidal curve.

This approximate rule is very simple to remember with the numerical sequence “1, 2, 3, 3, 2, 1”, which means:

• At the first hour, the water level will vary by one-twelfth of the tidal range.
• At the second hour, the water level will vary by two twelfths of the tidal range.
• At the third hour, the water level will vary by three twelfths of the tidal range.
• That at the fourth hour, the water level will vary by three twelfths of the tidal range.
• That at the fifth hour, the water level will vary by two twelfths of the tidal range.
• At the sixth hour, the water level will vary by one-twelfth of the tidal range.

Once you’ve understood this breakdown, you can simply make a table to calculate and add the variations. The table below calculates the water level at Saint-Jean-Port-Joli after low tide. Looking at the table for technique #5, we can identify a tidal range of 2.8 meters between morning low tide and afternoon high tide.

One twelfth of 2.8 metres corresponds to 0.23 metres (23 centimetres). The variation column then successively adds 0.23 (one twelfth), 0.47 (two twelfths) and so on to the water level of the previous hour. After six hours, we obtain the high tide value.

We can thus deduce that two hours after low tide, the water level will be approximately 1.9 meters above chart datum.

For the second part of the exercise, we can take the same approach, but working backwards in time from the afternoon low tide. The first two lines of the table have the following shape (tidal range 2.7 meters, starting at 1.3 meters).

So the water level will be about 2.0 meters (1.98) above chart datum two hours before low tide.

9th technique: sine equation

Setting the scene

What is the height of the tide at 0819 (summer time) in Saint-Jean-Port-Joli on August 1, 2025? At what time will the tide level be 3.31 meters?

Solution

The rule of twelfths and tables 5 and 5A are approximations of sine curves. Why not use such a curve directly? Any tidal cycle that approximates well with a sine curve can be modeled with the equation:

z = z_{\min} + \frac{\Delta z}{2}\left(1 \pm \cos\left(\pi\frac{t}{\Delta t}\right)\right),

where z is the water level above chart datum, z_{\min} is the low tide level of this half tidal cycle, \Delta z is the tidal range, \Delta t is the half-cycle in minutes and t is the elapsed time (in minutes) since the start of the half-cycle. The addition operation is used if the tide is falling, and the subtraction operation if the tide is rising. The above cosine function has its argument in radians (in degrees, replace \pi by 180).

On August 1, 2025, the tide table gives us a tidal range of 2.8m between 0354 (UTC-5) and 0954 (UTC-5), which means a half-cycle of exactly 6 hours. We can revisit technique 5 to see how to obtain this information, but the table below summarizes the requirements.

We therefore deduce that z_{\min}=1.2, \Delta z = 2.8 and \Delta t = 360. As the tide is rising on this half-cycle, the sign of the sinusoidal equation is negative. So we have the expression:

z =1.2+1.4\left(1-\cos\left(\pi\frac{t}{360}\right)\right).

We’re looking for the tide level at 8:19 a.m. summer time, i.e. 07:19 a.m. Quebec standard time. The time difference is therefore 0719 – 0354 = 0325 , or 3 hours 25 minutes. In minutes, the difference is 205 minutes (or 3 x 60 25). We can therefore calculate from our equation:

\begin{align*}
z&= 1.2+ 1.4\left(1-\cos\left(\pi\frac{205}{360}\right)\right),\\
&=1.2+ 1.4\left(1-\cos\left(1.7890\right)\right),\\
&=1.2 +1.4\left(1- (-0.2164)\right),\\
&=1.2+ 1.4\left(1.2164\right),\\
&=1.2+ 1.703,\\
&=2.903
\end{align*}

The predicted water level is therefore 2.903 meters above chart datum at 8:19 am (summer time).

To determine the time at which the water level is 3.31 meters, we need to interrogate the equation in reverse. We set:

3.31 = 1.2+ 1.4\left(1-\cos\left(\pi\frac{t}{360}\right)\right),

and then isolate t. The result is:

\begin{align*}
3.31-1.2 &= 1.4\left(1-\cos\left(\pi \frac{t}{360}\right)\right),\\
\Rightarrow \frac{2.11}{1.4}&=1-\cos\left(\pi \frac{t}{360}\right),\\
\Rightarrow 1-\frac{2.11}{1.4}&=\cos\left(\pi \frac{t}{360}\right),\\
\Rightarrow \cos^{-1}\left(1-\frac{2.11}{1.4}\right)&=\pi \frac{t}{360},\\
\Rightarrow \frac{360}{\pi}\cos^{-1}\left(1-\frac{2.11}{1.4}\right)&=t,\\
\Rightarrow t &\approx 114.59\cos^{-1}\left(-0.5071\right),\\
&= 240.95.
\end{align*}

The tide is therefore at 3.21 meters 240.95 minutes after the start of the tidal half-cycle. We need to convert this answer into an intelligible time. 240.95 minutes corresponds to 4 hours 57 seconds, or 4 hours and one minute. Since the tidal cycle starts at 3:54 (UTC-5), the tide will be at 3.21 meters at 7:55 (UTC-5), or 8:55 in daylight saving time.

Note that the tide will also be at 3.31 meters on the downward half-cycle of the tide. To find the time, we need to model the other half-cycle. By analyzing the table for the day’s tide, we should deduce that z_{\min} = 1.3, \Delta z = 2.7 and \Delta t = 365. As the tidal half-cycle is descending, the sign of the equation is positive. So the expression describing the tide is:

z = 1.3+ 1.35\left(1 \cos\left(\pi\frac{t}{360}\right)\right).

From this expression, we should find t\approx 121.46, or about 2 hours 3 minutes. So the tide will be 3.21 metres at 12:57pm (summer time).

10th technique: RYA graphic analysis

English tide tables are similar to those in Canada. For each day, high and low tide times are shown for reference ports, along with the applicable corrections for secondary ports. Techniques 5 and 6 are therefore fully transposable to English tides.

However, the UK differs from Canada when it comes to calculating tides at intermediate times. This is because their tides are not well represented by sinusoidal curves, particularly for the southern ports of England.

On the left is a tidal curve for Portsmouth on March 14, 2025. Note the “double hump” reflecting a small high tide followed by a larger high tide (at 1133).

Because they are not well represented by sine curves, techniques 7, 8 and 9 are ill-suited to tidal calculations. Another approach is required.

The idea of the Reeds tide tables (a popular English supplier) is to provide a typical graph of the tidal curve for the region. This graph must then be calibrated according to the tidal range and the duration of the tidal cycle (as is done with Transport Canada’s Tables 5 and 5A). Once calibrated, the graph can be interrogated to deduce the information required for our tidal window. Below, I present an image of a typical chart for the city of Portsmouth.

Note that the scale below the curve is empty, leaving it up to the user to enter the appropriate times between high water (h.w) and low water (l.w). This is how you enter the tidal cycle data. Similarly, the scale for high and low tide is left blank. This information must be entered on the upper left (high tide) and lower left (low tide) graduations to draw an interpolation line between high and low tide.

A complete graph would thus take the form of the image below. We can deduce that at 1105 (halfway between 1035 and 1135), the water level is about 2.8 meters. To understand the construction, we should also see from the graph that high tide is 3.9 meters, low tide is 1.5 meters and that at 1235, the tide will be about 3.35 meters.

The Free Sailing Tutorials center offers a comprehensive video illustrating the standard chart calculation technique (below).

Some concluding remarks

The usual electronic applications are extremely easy to use. All you have to do is read a graph! However, not all of them offer the same advantages, or have the same disadvantages.

First and foremost, the time required for each application is not the same. The Federal Tides application uses the time applicable to the place of navigation (in Canada, this is usually summer time). The OpenCPN application uses local meantime.

It is also possible to display times in Universal Time Coordinated at Greenwich (UTC 0). This allows tides to be displayed in daylight saving time if you’re ready to make the conversion calculations. Finally, the Boating application uses the time set in the tablet or cell phone’s operating system. If you’re in Quebec, this will be either Eastern Standard Time (UTC-5) or Daylight Saving Time (UTC-4). It’s important to understand these small differences to avoid misinterpretation!

It should also be noted that the St. Lawrence Global Observatory does not (to my knowledge) provide tide forecasts more than a week in advance. So it’s not a suitable tool for long-term planning.

In terms of paper techniques, the fifth, sixth and seventh techniques are the bare minimum required to pass Transport Canada (or Sail Canada) exams. You may want to acquire an additional technique to check your answers. If, on the other hand, you’re a math whiz, it may be quicker to work straight through the 9th technique.

For those with a knack for math, we may want to learn more about tidal prediction techniques. We might be interested in how Fisheries and Oceans makes its tide forecasts. We might also be interested in the relative performance of different techniques.

If we’re calculating tide windows for the first time, learning these techniques will take some effort. Take the ones you need and go one step at a time. Over time, the techniques become second nature. Then you can concentrate on what matters most: the pleasure of sailing… without running aground.

References

Camping au Bonnet rouge (n.d.). Camping au Bonnet rouge, document retrieved online in March 2025 from this address.

Cégep de Rimouski (n.d.). Usage des cartes et pilotage 2 – Préparation à l’examen, document retrieved online in March 2025 from this address.

C-MAP (n.d.). Worldwide nautical charts backed by C-MAP expertise, document retrieved online in March 2025 from this address.

Google Play (n.d.). Navionics Boating, document retrieved online in March 2025 from this address.

St. Lawrence Global Observatory (n.d.). Navigation, document retrieved online in March 2025 from this address.

O-Charts (n.d.). Charts for Open CPN, document retrieved online in March 2025 from this address.

OpenCPN.org (n.d.). Open CPN official site, document retrieved online in March 2025 from this address.

Parc Nautique de Saint-Jean-Port-Joli (n.d.). Parc Nautique, document retrieved online in March 2025 from this address.

Fisheries and Oceans Canada (2024). Tables des marées et des courants (Volume 3), document retrieved online in March 2025 from this address.

Fisheries and Oceans Canada (2025-a). Pêches et Océans Canada, document retrieved online in March 2025 from this address.

Fisheries and Oceans Canada (2025-b). Saint-Jean-Port-Joli, document retrieved online in March 2025 from this address.

Royal Yachting Association (n.d.). Royal Yachting Association, document retrieved online in March 2025 from this address.

Savyy Navy (n.d.). Navigation application for boats, GPS and nautical charts, document retrieved online in March 2025 from this address.

Transport Canada (2025). Small craft training course, document retrieved online in March 2025 from this address.

Tide-forecast.com (n.d.). Tide Times for Portsmouth, document retrieved online in March 2025 from this address.

Voile Canada (n.d.). Voile Canada, document retrieved online in March 2025 from this address.

Voile Canada (2024). Brevet de croisière élémentaire, document retrieved online in March 2025 from this address.

Voile Canada (2021-a). Brevet de navigation côtière élémentaire, document retrieved online in March 2025 from this address.

Voile Canada (2021-b). Brevet de navigation côtière intermédiaire, document retrieved online in March 2025 from this address.

Wikipedia (n.d.-a). Rule of twelfth, document retrieved online in March 2025 from this address.

Wikipedia (n.d.-b). Calcul de marée, document retrieved online in March 2025 from this address.