My other guide which explains how to use my calculator tool is published on Steam here:
https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=3321042803
Solutions from the four bearing method can be used as inputs on my calculator, if you want to solve things that way. Check it out! :)

• This method works when the contact remains at a constant speed and constant course.
  
• You must remain as stationary as possible for the initial bearing measurements.
  
• You must use a consistent time interval between bearing measurements.

Regarding time intervals - 10 minute intervals is usually too short, but can work in some circumstances if the contact is relatively close by. 15 to 20 should work pretty well. 30 minutes is even better.

If you are playing without using the pause button, you only have the duration of the interval to do your calculations in. So in that case, longer intervals make things easier.

The ships in this game do change course over time, depending on where they are headed. It is possible that you will get unlucky and they will change course in the middle of your calculations.

If you notice this, or something seems wrong, don't despair, just start over. There's plenty of time to spare when you're at sea.

You will need to use the map measurement tools to perform these calculations. Sometimes they can be a little tricky to control properly, but it is manageable. The ruler and the compass are all you need, but creating parallel lines in the game (at least for now) is bothersome. To make it a little easier, I strongly recommend using something like this mod:

https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=3270955106
Then you will see the course of every line drawn on the map and you can recreate it in parallel much more easily.

Also, the default map is 3D and if you have curvature enabled, it can skew things slightly. Overall it's manageable though. Otherwise you can try this mod (although it's outdated and doesn't work for me):

https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=2518835584
Alternatively, this mod does have a working 2D map, but if that's all you want you will need to disable all the other options. Instructions are provide on the mod page:

https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=3274920623

It can be from a radio message or from hydrophone. If you actually have visual contact this will still work but there are simpler methods available in that scenario.

You may be moving when you first detect the contact. That's ok. Just stop and take a new bearing when you are still.

Mark the timestamp of the bearing! Mathematically we will call this t = 0 and calculate from there.

Start the stopwatch! We want to take a new bearing after a specific time interval. 20 minutes is generally a reasonable duration. Don't wait too long in between recording the timestamp & starting the stopwatch.

You can just use the game clock and eyeball it if you don't want to use the stopwatch, but if you've come this far already, why would you take shortcuts?

Using the ruler, mark a line from your sub towards the bearing. Make it long enough that you have some room to work within later. Keep in mind that contacts could be 80km away or more, so make the lines relatively long.

Keep still and wait!

It's the same process as step one. After each time interval, mark the new bearing lines with the ruler.

Using 20 minutes as the interval (let's call it x), and looking at the stopwatch:

Bearing one is at t = 0
Bearing two is at t = 20 minutes (0 + x)
Bearing three is at t = 40 minutes (0 + 2x)

You should have something similar to this marked on your map:



Now we can start the fun stuff.

Select a point (let's call it R) anywhere on the line of bearing 2. It doesn't matter where R is at all, just give yourself some room to work and draw in.

Draw a line parallel to bearing 3 that runs through point R and intersects bearing 1.
Draw a line parallel to bearing 1 that runs through point R and intersects bearing 3.

It should look similar to this on the map:

Mark the intersection point on bearing 1 as i1.
Mark the intersection point on bearing 3 as i2.

Using the compass, from point i1 extend its radius until it touches bearing 2. Mark this point as d1.
It should look like this:

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Again using the compass, from point d1 extend the radius until it touches i2.

It should look like this:

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Drawing a line from i1 to i2 line gives you the course that the contact is steering towards. In this example it looks like it goes straight through d1 but this is coincidental. Sometimes it won't go anywhere near it. What is important is that you draw the line directly through i1 and i2.

However this does not tell us the actual speed of the ship, nor its actual location. Just the actual course. The ship could be anywhere parallel to line i1-i2. Remember, we picked point R at random and ended up with this particular result.

It should look like this:

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Measuring the distance of line i1-i2 will give you a "distance travelled" in 40 minutes (t = 2x) for calculation purposes which will be used in the next step, to predict the fourth bearing.

An example would look like this:

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Now that we know the "distance" between i1 and i2, and we know that it is after 40 minutes (time = 2x), we can work out the distance the contact will travel in the next 20 minute time interval.

Using the ruler, we need to extend line i1-i2 to point i3, which is positioned on the same course line and exactly half the distance of i1-i2 away.

You should have something like this:

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The hard work is done and we are nearly finished!

The most important part of this step is remembering that you must move!

You can go in any direction you like, but you need to change course and move somewhere before the next time interval finishes. I recommend moving roughly towards the contact (not away from it) and towards the course it is on. Move somewhere for a while, then stop, then wait to take the fourth bearing after the same time interval has passed.

Mark the intersection of the real fourth bearing on the predicted fourth bearing, call it i4.

You should end up with something like this:

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Congratulations, you now have triangulated the location of the contact and know exactly where it is positioned!

Draw a line parallel to i1-i3 through point i4. This is the actual course line the contact has been on the entire time.

It should look like this:

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On the actual course line, mark where it intersects the first bearing and call it i5.

Measure the distance between i5 to i4. This is how far it has travelled in three intervals of 20 minutes, which is 60 minutes (0 + 3x).

It should look like this:

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Speed = distance / time

Plug in your numbers and you will get the answer. Depending on which units you are using in the game for distance (km, nm) and speed (km/h, knots) you may need to do some conversions. I won't explain how to do that here (for now).

So, now we know:

• Contact's speed
  
• Contact's course
  
• Contact's location (aka its distance from us)

We can now plot our own intercept course based with this information. I also won't explain how to do that here (again, at least for now).

Happy hunting!

This method is based on the instructions from Rico Jansen, available here:
https://ricojansen.nl/downloads/four_bearings_method_v1%2CKuikueg.pdf

I always thought the steps in the PDF were a little too condensed, so have made a longer but (hopefully) easier to follow version.

The same rules apply with keeping the same time intervals between measurements.

Take the first three bearings from a stationary position. Now start moving somewhere else in preparation for taking the actual fourth bearing later.

Mark random point P1 on b1, and mark the midpoint between P1 and your Sub as G.

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Draw b3 parallel through G and mark intersection on b2 as P2.

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Draw a line through P1 and P2 and mark its intersection on b3 as P3. This is the course the contact is taking, but not the true one (because P1 was positioned randomly).

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Measure distance between P2 and P3, and extend it to mark P4. You can use a compass or you can use the ruler, as long as it stays on the course line and is the correct distance it will be ok. This will be used for the predicted fourth bearing.

Draw the predicted fourth bearing line from where your sub would be if it remained stationary, through P4.

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Since you should have been moving since taking b3, after repositioning the sub (and the same time interval has passed again) draw the fourth bearing line. Mark its intersection on the predicted fourth bearing and now you know the actual position of the contact after the third time interval.

Draw a line parallel to P1-P4 through Contact t3, this is the actual course the contact has been on the whole time.

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Mark the intersections of the true course line on b1 b2 and b3. Now you have all its position at t0, t1, t2 and t3 and can work out its speed to plot an intercept.

If you don't want to keep still for the first 3 bearings, but would rather continue on a rough course to get closer to your contact, you can apply this more advanced version of the four bearings method.

It's a lot messier and more complicated, but it does work.

Assumptions:

• For the first method, you maintain a constant course & speed for the first 3 bearings. It may work even if you change course & speed, but I have not tested it properly, so play safe.
  
• Contact maintains a constant course & speed for the process.

Note, for the second method you do NOT need to maintain constant course & speed.

The same suggestions apply with map tools, timing intervals, pausing, etc as in the Stationary method section at the top of this guide.

Mark your location and take the initial bearing of the contact (Sub.t0 and b1).
Maintain a constant speed & course.
After a specific time (eg 15, 20, or 30 minutes), mark your location and take a second bearing (Sub.t1 and b2). Let’s use 20 minute intervals for our example.

Draw 2 lines perpendicular to b2, through both bearings. Mark the points of intersection on b2 (A and B).

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Using the compass, extend the radius from point A to the intersection on b1 and mark the intersection of the other side of the circle on the first randomly drawn line (A1).
Repeat the same steps on the second line, drawing radius from B to b1, and mark intersection B1 on the other end of the circle.

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Draw lines parallel to b1 through points A1 and B1.
Continue on course until another standard time interval passes.

Things will get a little messier now.

At t2 (40 minutes, two 20 minute intervals) mark your own location and take a third bearing (b3). Now change either your course or your speed, or both!
In this example it looks b3 is intersecting through A1 and B1, but it’s not. It’s just a close coincidence.

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Mark the actual intersections of b3 and the two lines parallel to b1 (points C and D).

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Using the compass, draw a radius from point C on b3 to point A on b2, and from point D on b3 to point B on b2.

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Draw a line through points A & C in the first circle, and mark the intersection on the other side of the circle (C1).

Do the same on the second circle, drawing a line from point B through point D and marking intersection D1.

Draw a line through D1 and C1 all the way back towards your sub. This line is the predicted 4th bearing, if you maintained your course and speed. Remember, in reality we changed course and/or speed after taking the third bearing.

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I’ve zoomed in to show how it would intersect to prove it’s accurate :)

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But in reality, we changed course and/or speed and ended up over here instead.

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After t3 (60 minutes, or three 20 minute intervals) mark your location and the fourth bearing b4.

Mark the intersection of b4 and the predicted b4, now we know the actual position of the contact.

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Draw a line perpendicular to b4 from Contact t3. Mark its intersection on b3 (E)

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Using the compass, draw a circle from E with the radius to point Contact t3. Mark the intersection of the circle with the perpendicular line you drew in the previous step (E1).

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Draw a line parallel to b3 (shown in red) through point E1, and mark where it intersects b2. This is where the Contact was at t1, or after 20 minutes.

Draw a line from Contact Position t1 through the Contact Position on b4. This is the course the contact has been on the entire time.

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Where it intersects each bearing is where it was at each time interval.

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Your map should look something like this once it is all done.

Now using the map tools you can calculate the distance the contact has travelled over the 60 minutes, and determine the speed from that.

Similar to stationary method 2, this is my version of the steps outlined by Rico Jansen from his guide here: https://ricojansen.nl/downloads/four_bearings_method_v1%2CKuikueg.pdf

I again found the steps a bit hard to follow as there were some labelling issues on the diagrams and I found some instructions confusing. I also found the final steps in the PDF on how to determine actual course and speed too vague and it didn't make a lot of sense to me, so I switch back to the same process used in the In Motion Method 1 guide above.

The big advantage to this method is that you do not need to maintain a constant course and speed for it to work. Feel free to move around at your leisure.

Take the first three bearings and mark your position, you can change course and speed as you go along, if you like.

Mark a random point P2 on b2, and draw a line perpendicular to b2 through it.Mark the intersection on b1 as A.

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Using the compass, draw a circle from point P2 with radius A, and mark point B on the intersection of the perpendicular line you drew earlier.

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Draw a line parallel to b1 through point B, and mark its intersection on b3 as P3.

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Draw a line through P2 and P3, and mark its intersection on b1 as P1. This is one potential solution, but remember P2 was placed at random.

Pick another random point on b2, marked as Q2. Again draw a line perpendicular to b2 through it. We will repeat the same process we applied on P2.

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Mark intersection of perpendicular line on b1 as C, and use the compass with radius Q2-C to find D on the same line.

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Draw a new parallel of b1 through D, and mark its intersection on b3 as Q3.

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Draw a line through Q2 and Q3 and mark its intersection on b1 as Q1. This is another potential solution.

As you can see, the potential solutions dramatically vary. There are infinite solutions, depending on where we place P2 and Q2. Next we will solve the predicted 4th bearing line and start trying to triangulate the position of the contact.

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Using the compass, draw a circle from point P3 with radius to P2. Mark its intersection on the potential course line as P4.

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Repeat the process from Q3. Using the compass, draw a circle from Q3 to Q2 and mark Q4 intersection on the potential course line.

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Draw a line through P4 and Q4. This is the predicted 4th bearing line.We now need to take the actual 4th bearing.

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From the sub’s new position at t3, plot b4 and mark its intersection on the predicted 4th bearing. This is where the contact was at t3.

Now I will deviate from the steps in the PDF for reasons stated above. We will follow the same steps in the other motion guide to solve the course and speed of the contact.

Draw a line perpendicular to b4 through Contact.t3 and mark its intersection on b3 as E.

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Using the compass, draw a circle from E with radius to Contact.t3, and mark its symmetrical position as E1 on the perpendicular line you drew.

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Draw a line parallel to b3 through E1 and mark its intersection with b2. This is the contact position at t1.

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Draw a line through Contact.t1 and Contact.t3 and mark the intersections on b3 and b1. You now have the true course and the position of the contact at each time interval. You can now calculate speed and start plotting an intercept.

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Zooming out to show how it looks. Yes, it’s still a messy process.
You can delete some items as you go, but I have left them all in for this guide so you can see how everything has unfolded.