Checking if your interception course is right
 

This aviation website might come in hand. Just ignore the wind page and insert the fields with the data you gathered from a convoy or a single ship. Just add some extra knots on ownship to arrive before and have time to setup your attack.

http://www.luizmonteiro.com/RA.aspx

You can do it even in old fashion way (like real sub captains did) with good ol' paper and pen like this:

As your approach to the ship is triangle (as basically everything what you will be solving in u-bote :/\\k:), you can describe it like triangle ABC where A is your position, B is collision point and C is current position of your target.
In this triangle opposite side to target position (C) is side c - your path to collision point (B).

Your task here is to solve angle at point A (your position) when you know target course and speed and you pretend you want to choose your speed.

In this example lets say target course is 100 and speed is 8kts

Your REAL bearing at which you hear it is 20. (real bearing means bearing at hydrophone + your current course)
The speed we want to maintain is 12kts (it means we want to flow at medium speed at surface).

So what we have here is triangle ABC with a=8, c=12. A=?, B=?, C=100-20=80 degrees

The law of sines says that we now have all mandatory input to find our desired A angle which solves our desired course to collision with the ship.
Its: "If you know either (1) or (2), you can use the law of sines to solve the triangle." We actually knows (1).

So: a/sin(a) = b/sin(b) = c/sin(c).
This means:
1) a/sin(A) = c/sin(C)
2) 8/sin(A) = 12/sin(80)
3) 8/sin(A) = 12/0.98
4) 8/sin(A) = 12.24
5) sin(A) = 8/12.24
5) sin(A) = 0.65
6) A angle is 40.6 degrees
7) our desired course has to be real target bearing + A angle => 20+40.6 = 60.6!

So if you have good target speed and course and you want to crash that ship directly to bow, order your navigator course 61 and wait few hours until you see the vessel! :rock:
If you want to be there in advance, just calculate with position of the target the same time in advance (when you'll get into this, you'll start to use trigonometry to find out at which bearing you'll here it next hour pretty simply)

HINT: If you want to re-orient the equation at 1) to solve the angle at once, its like that:
sin(A) = target_speed / your_desired_speed * sin(angle_on_bow (C) ) (which is basically equation to solve it all!!!)

Your task now her Kaleun is to solve the distance you will have to reach to collision point by the law of sines or law of cosines.
This means you'll have available even time to reach the target. And then you could start to grow your beard for sure :arrgh!: (and you can even stop to use navigator fixes, cuz you'll have better precision :03:)
For this, we need to have another input data and thats current distance to target at that bearing we hear it. Let's just say its 20.000 meters for now.
What will be distance to collision point? :salute:

BTW: As every inside angles of triangle summarized gives always 180 degrees, you can solve angle B pretty easily as 180-(60.6+80)=39.4

If you tried to attack ship in non-right angle by torpedo, you should already know, that its basically angle of track which could solve your torpedo solution if you are already in attack phase!
So this simple equation could literally gives you TDC inputs solution at max realism! :/\\k:

wow thanx palmic for such wonderful info. I was planning to ask the manual procedure in a sailing/navigation website but you were faster :salute:

I'll try it at home with very very enthusiasm...

But the challenge is how to know target course and speed from far far away

Scenario is, you get "smoke in the horizon" message: single ship or convoy it doesn't matter, you get heading to the target and you can additionally ask for a rough estimate of range; normally in the 9000 to 12000 range.

With target identification disabled, I can't even use the stadimeter. so my normal strategy would be to close at flank speed. Problem is that then by the time I am close enough to identify it and get a first course and speed estimate, I am actually too close now, so no longer "enough time to grow a beard" scenario. And being close means that there is a chance he will see me and in that case, he will change speed and heading again

Check my footer (Real navigation target motion analysis cheatsheet).
You can get bearings by hydrophone or visualy, doesn't matter

Wow! really impressive... I think I got the concept, although I still need to get the full idea. I mean I think I got to the point of being able to calculate the target course, which is what I need the most to plot an intercept

Thanks a lot :Kaleun_Salute:

This might be of interest: NIMA Maneuvering Board Manual

You really don't even need the fancy "Maneuvering Board" sheet. A ruler and protractor on a sheet of graph or even plain paper will do just fine.

Nice one, thank you, i never got how this board works :)
You can off course draw it to map, but i like more to write few equations on HW paper. Its just triangle with one side (target course with length of target speed, e.g. 6) and second our speed, all angles are already known in this situation (AoB, bearing of target from us, and the third is always 180-both others).
With this, you can simply find solution by the law of sines

And how do you work the stealth factor?
assuming day time, with good visibility, you can't just get into a perfect intercept, without being spotted. How far away can you remain without alerting the convoy escorts? how can you add that distance into the calculations?

I think I like the idea of plotting an intercept based on a slow speed (like convoy is doing 8 knots, so plot an intercept at 10 knots, but then run at flank speed to arrive much earlier), this way I am relatively far away until I reach intercept, then periscope depth for final adjustments... thoughts?

Here is the solution to your example problem on a maneuvering board.

The red line (em) is the target's true course and speed: 100°, 8 kts. (The speed scale used is 2:1, so the line is drawn to the 4 circle.) The blue circle is our desired speed to intercept: 12 kts. The dashed purple line is the target's bearing: 20°.

We want to move in the direction of the target, so we draw a line parallel to the dashed purple line from the end of the targets course and speed vector: this is the solid purple line (rm), which is the desired relative motion vector.

We then draw a line from the center (e) to where the rm line intersects our desired speed: this is the green line (er), which is our required course at 12 kts. As you can see, it is indeed 61°.

Now, if we measure the length of the relative motion line (rm), we can determine our relative speed. If you look at the bottom of the 2:1 scale on the far left, you will see that the relative speed is about 7.6 kts.

Supposing the target is 20,000 meters away, that equals about 21,800 yards. Using the nomogram at the bottom, we draw a line from the relative speed (7.6 kts.) through the distance to close (21,800 yds.) and arrive at a time of about 85 min., or 1 hour and 25 minutes.

The actual distance traveled can also be solved on the maneuvering board, but I didn't want to clutter it up too much.

You have more options, i would pick one of these:

1) if you want to be "scientificaly" set, you can check ingame speed table and check how far they will get after lets say 15 minutes which you want to have in advance for your final targeting from periscope depth...
Then you just recalculate the triangle with their current bearing from you moved from current to future-one (where they will be after 15 minutes), so your calculated solution will be with these 15 minutes in advance and you will be at collision point before them.

2) But i am rather much more lazy to calculate and rather follow the first calculation and i set a little quicker speed than i used in calculation. (You should not use flank speed if you want to be authentic, because flank speed in reality of ww2 overheated engines and they would require some maintenance then...)
- If i would get close enough to see the ships from distance i would just set the same course i know they have and move before them.
As you know their course, you know virtualy even their current angle on bow and of course the bearing which you see them at, so you know naturally even the third angle - the angle of tracks if you turn your boat to their course (to get closer).
This way i like to get lets say to move them to my bearing of about +- 120, or 240 - depends on if i have them at port or starboard.
So if i have them at 120, i am a lot before them to start to approach closing course - i order 30 degrees to starboard - and they move logically from bearing 120 to 90, because i turned by 30 degrees to the right..
So i know that our angle of tracks is 30 degree (because i had the same course and turned by 30 to closing them), bearing at which i see them is 90 so their current angle on bow has to be 180-90-30=60.

With intercept course set i just check if i keep them at my 90 or even moving them even more behind to 90+.... This way i know i am on my way to get to firing position in advance.

If you have distance from them you can even calculate how distant they would be before you in future if you would just stop and wait for them here - its current distance * sine(current AoB).
If their current AoB is 60, it means it would be current distance * sine(60) -> current distance * 0.9 (one decimal is enough in these equations...).
So - my task here would be just to lower their current AoB to me, which is automatically happening as i am closing to their track by angle of 30 degrees.

If i am quick enough, i will eventually see them at 120 again and this means - if i still have that 30 angle of tracks (closing to them by 30 degrees at collision point), that current AoB is 180-30-120=30 - AND THAT MEANS - current distance * 0.5. (sine of 30 is 0.5)
SO! If they are about 15km out of me, they will be just 7500m away if i will stop here!

And so on. Just keep in mind this very simple triangle and you will always have situation under control, because this is what ultimately is happening in this approach situation.

Just check where you have limit of bearing where you see your target because you can of course get behind their track if you will not stop in time...
In this situation - 30 degress angle of tracks, if i would get them to 150, i would be actually inside their track (150+30=180 - there is not even one degree remaining for AoB -> this means current AoB is exactly 0! - they are just moving directly on me..)

In nature its very simple and you can even calculate this things in head just in few seconds, you just have to get used to it. Forget map, forget geometry and just remember all angles in the triangle gives sum 180, thats all... :salute:

Always get course of your target from distance if you can, and you have practically everything..
By the course you can even very effectively get their speed visually, just get close enough to see at least their smoke, set the same course, and change speed to fix the bearing which you are seeing them - if you manage to keep them at the same bearing for 2-3 minutes, you have the same speed :salute:

... and maybe check even "How to prepare torpedo Attack with basic trigonometry" in my footer, there's more uses for these rules which will help you to realise how this works.

These problems can also be solved on a maneuvering board, if you're interested in that method. The link I provided above to the manual explains it all, but I'd be happy to help if you have any questions.

My first question is:
Do you use the board in game? I opened "toggle chart visibility", then looked for plotting tools, maneuvering boards
Then I centered it in my last know position

Challenge is: I cannot write on top of it, is this something that can be done? it was not too difficult to replicate the circles and protractor to get the 61 degree heading, and there is a nomograph just in the right side of the map, but I still don't know how to get the 7.6 relative speed using map tools

EDIT: I just noticed it is a given; I thought you had to graph it, but I can see now that it is actually just a matter of counting the 4 lines

EDIT2: Wrong again!, the line you need to draw to get 7.6 is from m to r... I now get it... however, with the drawing tools and really small maneuver board available in game, it might be challenging to get anything accurate.. Can you attach a "clean" maneuver board file? I like the high resolution of your example... worst case I can still print and draw manually

TBH, I've never played any version of SH, so I can't answer that.

Just use "E" key to toggle the chart. Toggle off to pick first point of line, then toggle chart on, move cursor to desired position, you know... :salute:

No worries, still any chance you can post a clean version of the board?

Also, if you have time, would you solve the following scenario in the maneuver board:
same idea as before, the contact is at 20 degrees heading, 20K meters away, course is 100 and the speed is 8
your maximum speed is 15 knots, your cruise speed is 12 knots

how would you intercept it, optimally, if you want to be at least 8km away until you reach your desired periscope position (this so that it won't spot you during your cruise?

thanks again!!

When you already see your target and you know their course, you dont need to calculating anything.
Just set the same course with higher speed and put him behind enough to have time to prepare and then set course to get closer and closer to his track.
When you think its close enough, turn the sub to have perpendicular course to its course to prepare sub to best firing position and tune distance from periscope depth as he is closing..
(for instance if their course is 100, you'll have to prepare sub to course 10 and wait until he will be before you)



Until you see your target
So here you have this triangle:
AoB (angle C) = 100 degrees (angle between his course and the bearing of 20)
his speed (side b) = 8
your speed (side c) = 12
https://image.prntscr.com/image/egwp...sGvFKKlJJw.png

What you want here is the angle between the bearing which you see the target and your desired course (angle B)
The law of sines for angle B here is that:
b/sin(B) = c/sin(C)
8/sin(B) = 12/sin(100)
8/sin(B) = 12/1
8/sin(B) = 12
sin(B) = 8/12
sin(B) = 0.7
B = 45 degrees

So your desired course to meet your target by the speed of 12 kts is the current absolute bearing + 45 => 20 + 45 = 65.

You can see here that since you have your target with AoB about 80-100 degrees, you can calculate the sine of angle between the bearing and desired course simply as his speed / your speed.
Its about 10 seconds to get your desired course..
You can round sines to whole numbers, theres no need to be very precise since your input data are also rough. Try it and youll see it works.

Sorry for the late response, I've been busy. Anyway, here is a solution on a maneuvering board:

Example 2

A few things to note first:

• There are two different plots here: one consisting of the "speed triangles" (emr and emr') and another consisting of relative positions (R ["reference" ship, or our own ship] and M ["maneuvering" ship, or the ship we are tracking])
• This assumes we want to arrive ahead of ship M and will be traveling at max speed (15 kts.)
• This assumes ship M does not change course or speed
• Speed scale is 2:1 and distance scale is 3:1
• All distances are in yards (20km ≈ 22,000yds.; 8km ≈ 8,750yds.)

Now, here are the steps for plotting this solution:

1. Plot the position of M at 22,000yds, 20°.
2. Draw a circle around own ship (R) with radius 8,750yds., the distance we want to keep from M
3. Draw a line from M, tangent to the 8,750yd circle (note that if we drew the tangent to the other side, we would end up behind ship M). This is the desired relative movement line. By inspection, we see that the direction of relative movement (DRM) is 223.6°
4. Draw a line (em) representing M's course and speed (100°, 8 kts.)
5. From the end of em, draw a line (rm) parallel to the DRM which stops at our desired speed of 15 kts. (the 7.5 circle at 2:1 scale)
6. Draw line er to find the required course at 15 kts. of 70°. The length of rm is the speed of relative movement (SRM): ≈9.2 kts.
7. Draw a perpendicular to the DRM which intersects R at the center. The point where this line intersects the 8750yd circle is the closest point of approach (CPA): 8750yds. @ bearing 314°
8. Using the 3:1 scale, measure the distance from M to the CPA: 20,000yds.
9. On the nomogram, draw a line from 9.2 kts. through 20,000yds. to find the time to CPA: ≈66 minutes

Now, if (for example) we then want to turn to intercept M at a speed of 12 kts., we can do the following:

1. Draw a line (r'm) parallel to M's bearing at the CPA (314°) which stops at the 12 kt. circle (6 at 2:1 scale)
2. Draw line er' to determine the required course at 12 kts.: 335.5°
3. The length of r'm is the SRM: ≈18.0 kts.
4. On the nomogram, draw a line from 18.0 kts. through 8,750yds to find the time to intercept: ≈15 minutes

But, as you asked earlier, how did we determine that M's true course and speed was 100° @ 8 kts. in the first place? Take a look at this example:


Example 3


Suppose we first spotted M (by radar or other method) at 1600hrs., bearing 05.8°, range 26,100 yds. Six minutes later, we spot M at 12.2°, 23,900 yds. Another six minutes go by and we spot M at 20°, 22,000 yds.


We plot these positions on the maneuvering board, draw a line through them and find that M has a DRM of 136.5°. In six minutes time (one tenth of an hour), M has moved about 3,500 yds., so we draw a line on the nomogram from 6 minutes through 3,500 yds. to find that M has an SRM of 17.6kts.


Now, our own ship is moving on a course of 340° at 12kts., so we draw line er to represent that. We then draw line rm parallel to the DRM with a length matching 17.6kts. And finally, we draw line em and find M's true couse and speed of 100°, 8 kts.


Pretty much any maneuvering problem can be solved quickly and intuitively on a maneuvering board, once you become familiar with how it works. The manual I linked to earlier even shows how to solve complex problems, such as maneuvers involving multiple ships at one time with different speeds and distance constraints.

Nathaniel B.: I belive you did something wrong.
If the target is at 20° (NNE) and its course is 100 (EES). approach course could never be 314° (WWN), its just opposite..

314° is not an approach course in my example. It is what the bearing of the target will be when we reach the closest point of approach while keeping 8km distant.