The new and improved four bearings method

[Kuikueg]

I have completely rewritten my tutorial on finding position, speed and course of a target given four bearings to it, to include significant improvements in the procedures in terms of simplicity, some variations of the problem and, I hope, clearer explanations. This new version owes a lot to the kind comments and insight from many of you and I thank you all for it, specially Makman94.

You can find the tutorial here:
(http://lnpi.net/docs/the_four_bearings_method_v2.pdf) http://lnpi.net/docs/the_four_bearings_method_v2.pdf

[makman94]

you know Kuikueg, when i first saw your thread with the first version of ''Four Bearings Method'' ...i thought that the ''Four Bearings Method'' is one of the best (if ...not the BEST) thread that i have seen at Subsim the two years that i am here. Threads like this is the real power of Subsim

your method is really just a piece of art ...even the manuevering boards method demands some constant speeds(for our boat) and two sets of three bearings to have the results but yours...is just excellent,,,we have nothing to keep constant (only time intervals must be equals or analog) ..we can change speed and course anytime we want and repeat until we get to good positions...we are just absolutely free and this makes this method just...the best i have seen ! with four bearings ONLY ...we have true course ,range to target and speed of target ... what can i say?if you know a simplier method on manuevering board than Kuikueg's...please guys ...share it !

and now you are 'coming back' with this...version 2 !even simplier(i will say...a lot simplier !!)..is making this method even flexible than ever !your new discoveries for finding the 'red line' are making it a piece of cake on map drawings !
i am ...SPEECHLESS Kuikueg! the beauty of your thought is just amazes me !(you did it ones and you are doing it again!) .if i ever have voted for best threads...would,definetely, be yours !
my opinion is that you must be award not only by Subsim but from REAL NAVIES too(i am not joking) !i believe that this method(if we assume that doesn't exist allready) , surely ,deserves the best place in navies manuals for the situation: Chasing a target that is moving with a constant speed at a constant course (REALLY...i am wondering...are there such targets in real life?i mean targets that are moving at constant speed and course...)

Having said all these ...i only want to congratulate and say thank you for sharing this piece of art with us Kuikueg !


ps1: i had totally forgoten 'our' theme Kuikueg ! i promise to look at it and send you my thoughts !

ps2: to moderators : seriously,if there is a thread that must be sticked ...this is it ! it is just an ...'advertisment' for the high level of Subsim !

[Walle]

This is a very effective method! I tried it out yesterday, and it all worked out like a charm! Thank you for taking the time to share this!

Ps: And I concur, this thread should definitely be a sticky!

[irish1958]

Can somebody upload it to Subsim? Filefront doesn't appear to be working.

[Walle]

I could do it, but I'm sure Kuikueg would rather do it himself (so I don't get confused as the author).

[Harmsway!]

I concur. I only ran across the original method about a month ago. I was in the process of teaching my son geometry when I came across this. It fit right in what we were learning on the Theorems of congruent segments and congruent triangles.

Funny things is I spent 40 minutes watching someones video on this and was confused as heck. Luky I found your well written pdf and it all became clear as mud.

Thanks

Yes every skipper needs this in there hands.

[Zedi]

I linked the first one in the sticky tdc tutorial (http://www.subsim.com/radioroom//showpost.php?p=1503759&postcount=40). I edited the post now and added this one too for further reference.

[irish1958]

Kuikueg: Thanks.:salute: This is clear and easy to follow.:know: I'll give it a try when I can spare the time. :zzz:
I would think some computer whiz could write a small program to input the bearings and times and come out with the course, location and speed.

[Laconic]

Kuikueg: Thanks.:salute: This is clear and easy to follow.:know: I'll give it a try when I can spare the time. :zzz:
I would think some computer whiz could write a small program to input the bearings and times and come out with the course, location and speed.

Abracadabra (http://www.subsim.com/radioroom/downloads.php?do=file&id=1711)

(Not mine, credit to Gutted.)

[Kuikueg]

...even the manuevering boards method demands some constant speeds(for our boat) and two sets of three bearings to have the results but yours...


Thanks for your comments, Makman. It's not such a big deal.

You are right about the maneouvrig board: the fact that you or your target become the center of coordinates limits somehow your maneouvres. Frequent changes of speed or course during the proccess at the very least will clutter the board so much as to make computation complex, ackward and confusing. But we have to acknowlege the need for it. In real life your own position is uncertain -without GPS, that is- and becoming the origin of coordinates simplifies the problem for that reason. Also, the scale of a real chart can be a limit to a direct method. The triangle might fall outside the chart, or be as little as to make accurate protracting of its distances imposible. There are very good reasons why navies use the maneovring board.

In the manual from the USN for the use of the MB, back in the forties, there is a case estated "given six bearings to contact establish its course, range and speed" or something like that. I have not gone through the proccess it describes, but I suspect that the doctrine for using six bearings instead of four, which would be enough, comes from the need to compensate for the uncertainty of your own position.

I would like to see a MB implemented in SH5. It really is simple, as much as including a nomograph, which is already done. We could use the real procedures manual in that case.

[Kuikueg]

:zzz:
I would think some computer whiz could write a small program to input the bearings and times and come out with the course, location and speed.
You would need to input the info about your own position too, somehow, if you are maneouvring, and you would lose the simplicity and the freedom of the method. But anyway, that's not the point. The point is doing it yourself, with ruler and compass. If you want to confront the problems a real captain and his officers faced while hunting, the stress of having to calculate with limited time, etc, a calculator is not the way to go. The experience that comes from drawing in the chart may increase your ability to assess a situation with limited information and help you taking the right decision, in short: it will increase your seamanship. Of course, this is a matter of personal taste. In my case, I have even built myself a slide rule to avoid the use of an electronic calculator.
That's the reason why I'm not interested in the MB program alluded to in this thread. It sure is a fine piece of software, but if I wanted electronic help I would just relax the realism settings in the sim.

[irish1958]

You would need to input the info about your own position too, somehow, if you are maneouvring, and you would lose the simplicity and the freedom of the method. But anyway, that's not the point. The point is doing it yourself, with ruler and compass. If you want to confront the problems a real captain and his officers faced while hunting, the stress of having to calculate with limited time, etc, a calculator is not the way to go. The experience that comes from drawing in the chart may increase your ability to assess a situation with limited information and help you taking the right decision, in short: it will increase your seamanship. Of course, this is a matter of personal taste. In my case, I have even built myself a slide rule to avoid the use of an electronic calculator.
That's the reason why I'm not interested in the MB program alluded to in this thread. It sure is a fine piece of software, but if I wanted electronic help I would just relax the realism settings in the sim.
Right on!
Again, thanks for the clear reasoning.:woot: I really intend to use this when I have time to do so.

[Pisces]

Damn Kuikeq, you did it again. That first drawing simplies things alot. Don't have time to read the rest of the document yet. Thumbs up!

[makman94]

.... There are very good reasons why navies use the maneovring board...

i have no doupt that there are very good reasons for navies using the manuevering board . in fact , i am sure that there are very good reasons .
i was talking for methods to use in our game ...comparing yours with mb's one.
for real maps ...yes,maybe triangle will become too small or too big, but if i was a navigator officer ,certainly, wouldn't ignore ''The Four Bearings Method'' (in case that triangle and drawings were 'in' my map)

... I have not gone through the proccess it describes, but I suspect that the doctrine for using six bearings instead of four, which would be enough, comes from the need to compensate for the uncertainty of your own position.

i have to 'dig' to find the manual for mb that describes the situation (find course-speed-range to target with bearings only) and i will sent it to you to have a look at it . you will see that it needs six bearings(with constant speeds and courses) for collecting only the target's data . it has nothing to do with the uncertainty of our own position.

[Pisces]

...
i have to 'dig' to find the manual for mb that describes the situation (find course-speed-range to target with bearings only) and i will sent it to you to have a look at it . you will see that it needs six bearings(with constant speeds and courses) for collecting only the target's data . it has nothing to do with the uncertainty of our own position.This is probably the part you mean. It's a 2 page excerpt of the MB manual:

http://www.filefront.com/13598315/bearingsonly_TMA.pdf

[makman94]

This is probably the part you mean. It's a 2 page excerpt of the MB manual:

http://www.filefront.com/13598315/bearingsonly_TMA.pdf

yes Pisces, thats it ! the original pages of manual containes another same example with it (but with different bearings ,speed and courses) .but it is the same example with this.

[Farinhir]

I had not noticed this one yet. I have been dealing with real life which prevents me from living my dream as a terror from the deep.

I am looking over the information now and I have to say that it is pretty good. I will continue to read through the information but it is pretty clear with what I have seen thus far.

Well done. I am also looking over the graphical proof you sent. I am still interested in trying to formulate the problem, but I can tell it will, most likely, not be general algebra.

[Pisces]

For those that are curious, you can find the full "Radar Navigation and Maneuvering Board Manual" package at this link:

http://msi.nga.mil/NGAPortal/MSI.portal?_nfpb=true&_pageLabel=msi_portal_page_62&pubCode=0008

[toniloCoyote]

Hello Kuikueg.

Firstly, congratulations for your work.

I have had to fight some time to understand the new method. I had big problems with the final step in section 4 (the four bearing), when you explain that we have to repeat what we have learned in section 2 for computing the actual course of the target.

At first I thought my head was hard and so I did not understand this step, but after reading the section 5, I realized that something was wrong (apart from the fact that my head is very hard).

In the last drawing of section 4 you say that the actual course of the target is the green line, and the only green line in the picture is one side of Triangle AEI, that is, the side A-I.

I spent an hour trying to understand how I could reach the result of that the actual course was the A-I line by using the method described in Section 2.
Now I believe have understood that the drawing does not agree with the explanation; that the actual course of the target is the P-R line, the point V is the "arbitrary point", the line is drawn between point P and V, the point C is the mirror of P, h is the line parallel to b3, and so we get the point R.

I think the confusion lies in two places. First in where the text says that the actual course of the target is the green line, and second, because in this drawing all the lines and procedures are posed in reverse order to those in section 2 (wherein there you use the lines b1 and b2, here you use lines b4 and b3) and this adds a bit of confusion.

If this is so, I believe that, in addition to fix the text where you say that the actual course of target is the green line (really, it's the black P-R), it can be much clearer if you explain that V is now the arbitrary point and C is the mirror of P through V.

If this is not so and I'm wrong, please excuse me. I have to study more.
Please, excuse any blunder due to my poor English / Mathematics.

Best regards.

[Kuikueg]

Hello Kuikueg.

Firstly, congratulations for your work.

I have had to fight some time to understand the new method. I had big problems with the final step in section 4 (the four bearing), when you explain that we have to repeat what we have learned in section 2 for computing the actual course of the target.

At first I thought my head was hard and so I did not understand this step, but after reading the section 5, I realized that something was wrong (apart from the fact that my head is very hard).

In the last drawing of section 4 you say that the actual course of the target is the green line, and the only green line in the picture is one side of Triangle AEI, that is, the side A-I.

I spent an hour trying to understand how I could reach the result of that the actual course was the A-I line by using the method described in Section 2.
Now I believe have understood that the drawing does not agree with the explanation; that the actual course of the target is the P-R line, the point V is the "arbitrary point", the line is drawn between point P and V, the point C is the mirror of P, h is the line parallel to b3, and so we get the point R.

I think the confusion lies in two places. First in where the text says that the actual course of the target is the green line, and second, because in this drawing all the lines and procedures are posed in reverse order to those in section 2 (wherein there you use the lines b1 and b2, here you use lines b4 and b3) and this adds a bit of confusion.

If this is so, I believe that, in addition to fix the text where you say that the actual course of target is the green line (really, it's the black P-R), it can be much clearer if you explain that V is now the arbitrary point and C is the mirror of P through V.

If this is not so and I'm wrong, please excuse me. I have to study more.
Please, excuse any blunder due to my poor English / Mathematics.

Best regards.

Hi, toniloCoyote, and thank you very much for your feedback.
The line P-R, which is the actual course of the target, is actually dark green, not black. At the time of writing I didn't realize I had already put a green line in the drawing and I understand the confusion that comes from it being there. Ironically, the (light) green line A-I is not part of the construction and was only there to make it clearer by adding symmetry and pointing out the geometrical nature of the rest of the lines, alluded to later (medians).

The construction of section 2 is done right to left, with the point P fixed and N (not V, but we are talking about the same point) as the arbitrary one, but there is no essential difference between what is done in section 2 and what needs to be done in the final step of section 4.

Anyway, you got everything right and I have corrected the document to avoid that confusion and updated the link in the first post. I hope nobody else will get lost with that again.

I am sorry for the trouble caused. I don't believe your head is hard, you have proved otherwise, and your English is clean and clear to me, though I suspect we are both spanish speakers.

[toniloCoyote]

Sorry, In my old LCD the line shows black, and N looks like a V :damn:
(Pedí por Navidades un monitor nuevo, pero la crisis, ya sabes ...)

Thank you, and best regards.

[toniloCoyote]

Hi again, Kuikueg.

I think you have changed the link's text but not the href.
It could be matter about my computer's cache, but I had to copy/paste the text for downloading the new file.

Cheers.

[Kuikueg]

Hi again, Kuikueg.

I think you have changed the link's text but not the href.
It could be matter about my computer's cache, but I had to copy/paste the text for downloading the new file.

Cheers.

You are right. Link corrected.

¡Sabía que hablabas español! :DL
Saludos

[Trevally.]

Thanks Kuikueg for this new improved method:up:

I have written an ingame tutorial based on this method
for use with TDWs UI (Real Nav). See here
http://www.subsim.com/radioroom/showthread.php?t=177725

[musides]

Excellent work and great descriptions!

[BigBANGtheory]

Its good work dude, plus a Trevally tutorial this is turning out to be a good and shiny day. :sunny:

[gi_dan2987]

You are right. Link corrected.

¡Sabía que hablabas español! :DL
Saludos

I use Nefelodamon's method, if that was originally based on your idea then thank you for coming up with such a helpful formula. I must say, your math skills are outstanding, and if the Germans didn't use this historically than I don't know what they were thinking. My question is, this method is only true assuming that all variables remain the same correct? I've had ships change course and speed on me, throwing all my calculations out the window. But of course it's hard to tell if they've changed course or speed until all your fish miss the target. Also, how can you effectively attack a convoy at night when it's pitch black out so UZO's unusable, and with 100% realism??

[Snotface]

Hi,

it looks like FileFront has removed the file. Does anyone else have a link, please?

Thanks

[Buccaneer]

@ Kuikueg
Excelent tutorial to track contacts while manouvering :up:
To test this method in SH3 i created small mission with big randomizing zones for spawn and waypoint (for greater target course deviation). Before running the mission i enabled marks on map (for later periscope check). Crawling around for ~2 hrs collecting bearings i finally made the target true course line. Now the moment of truth - periscope up - visual check (mark appeares on the map) - zoom in map... :o... ship travels along the estimated course with ~20m offset to the side(in map scale). Precision was amazing:D

Thanks for sharing

Hi,

it looks like FileFront has removed the file. Does anyone else have a link, please?

Thanks
I found the document here - www.gamefront.com (http://www.gamefront.com/files/17879977)

[kylania]

So I've been really disappointed with this recently and turns out it's all my fault! I've been trying to use it with Real Navigation and every time I did I got totally incorrect and nonsensical results. I watched videos for hours, I read PDFs for hours, I tried practice results, I wrote down all the steps one at a time. Nothing worked.

Then today I realized that in step 27 of 31 steps I was making a mark on the WRONG LINE the whole time. :O: Hopefully it'll work next time I find a target. heh

[potus]

Link doesn't work? :hmmm:

[Kuikueg]

Get it from here http://lnpi.net/docs/the_four_bearings_method_v2.pdf

I'm going to update the first post.

[TaTi94]

@KUIKUEG
I've just installed SH4 and I'm studying your method, and it's awesome! there's just one thing, I can't get right!
I started out facing north and there was a merchant northeast from me some 15 km away, heading west. this was a training mission I created so I can practice your method in it. Anyway I got my first bearing and started cruising and changing course. In 15 minute intervals I took 3 reading and draw them as b1, b2 and b3. While I took these 3 readings I was always moving a bit towards the merchant(NNE, E, NEE) I calculated the estimated fourth bearing and I turned away from him (I was moving west just like him). What I want to ask: was this a mistake? because when I took the real fourth bearing and calculated his position and course, it was really off! like almost 90 degrees off! I know this because I created the mission! :D So what kind of freedom of movement do I have? Changing course 180 degrees, I was moving away from him and I suspect that was my mistake, but the sonarman still said the merchant was CLOSING!

[Fish In The Water]

@KUIKUEG...

It looks like Kuikueg hasn't been active in a couple months, but until he gets back, welcome to Subsim and have fun! :sunny:

[Shkval]

Few things about this method... it doesn't work on "moving away" and "constant distance" contact's courses, (or very close to "constant distance")... if you are moving, you should move in opposite direction of a contact, i.e. if he is moving SW you should move NE (you MUST get crossing of bearings) if you are getting parallel bearings it is impossible to get contact's course... time between bearings is also very important, the longer the better! Usually 10 minutes is enough for merchants, 5 - 7 for warships... good luck.

[Kuikueg]

Few things about this method... it doesn't work on "moving away" and "constant distance" contact's courses, (or very close to "constant distance")... if you are moving, you should move in opposite direction of a contact, i.e. if he is moving SW you should move NE (you MUST get crossing of bearings) if you are getting parallel bearings it is impossible to get contact's course... time between bearings is also very important, the longer the better! Usually 10 minutes is enough for merchants, 5 - 7 for warships... good luck.

To the things pointed out by Shkval I have to add:


There always are two solutions, each to each side of the triangle defined by the first three bearings, with respect to your own position. Only one of them is reasonable (normally). Be sure you compute the right one.
You can move freely as long as you keep your bearings crossing, the higher the angle the better, and you end up far from the computed fourth bearing, so your last bearing crosses the computed one on a fairly open angle.
Don't rule out that you made a mistake in the procedure. I used to make them, and I know the method inside out. It's easy to get confused when plotting inside the game.

Solve first the inconsistency between your assumed position and the sonar man report.

[Pisces]

Kuikeg's link is dead. I uploaded version 2 to my own website:

version 1 of the method:
http://ricojansen.nl/downloads/four_bearings_method.pdf

version 2 of his methods:
http://ricojansen.nl/downloads/the_four_bearings_method_v2,%20Kuikueg.pdf

[pythos]

Doing the four bearing method, and having no luck.
The point of failure seems to be at the point when the parallels are moved to intersect Bearing 2.
Having had numerous failures in acquiring contact course I decided to try this with map contacts on and was using the TDC historical mission (one ship on a east to west coast, and the U- boat on a northerly heading.)
I used the periscope for the bearing info, and found that when I drew out the parallels on bearing 1 and 3, that the course was nearly perpendicular to the actual contact course.
Then I looked at how to acquire a predicted course line that would match the contacts East to West course, and honestly I could find none.
I have done the tutorial included in Steel Wolves for the four bearings several times, and encountered that although the tutorial is saying "we have acquired a bearing of (place bearing here), that when I clicked on the sonar operator I get "no sound contact".
In actual practice I find the sonar bearings useless (even when tracking a single contact, as the operator only reports the closest contact, and in a shipping lane that can be many instances of the closest changing during the course of acquiring four bearings over 20 minutes.
I sure wish I could get this method to work, cause if this works this will make this sim really immersive.

[DieReeperbahn]

I've had mixed results as well. I find that you must use the highest magnification when making a plot or too much error will creep into the solution. But I just play on and assume the target changed course or speed or my WO is tired...:zzz:

[MCM]

Is there a new download link for the improved fast method? THX!

[Sjizzle]

Is there a new download link for the improved fast method? THX!


u can train this method in game u need to have TDW's UI or TWos mega mod ....in main menu section tutorials and from there select four bearing

[MCM]

WOW didn't know that. This is great!!! THX very much :salute:

[THEBERBSTER]

This is a useful alternative method.
Pause your game and then use the Alt + Tab Keys.
You can enter 1 bearing at a time or best to put 3 bearings in at the same time before moving the sub.
Hydrophone Tracker For Four Bearings (Sits On Your Desktop) (http://www.subsim.com/radioroom/showpost.php?p=1347786&postcount=1)

Peter

[WildBlueYonder]

One disadvantage of the method taught by TWoS is that you have to be stationary for the first three bearings. Is there a way to apply the method while moving the entire time?

[alboverburn]

Here is my quick utility made in geogebra for the 4 bearing method.
Requires geogebra, obviously.
http://www.filedropper.com/4bearingsv5 (http://www.filedropper.com/4bearingsv4)

In the near future I'll add an intercept point as well, so that you don't have to draw anything on the in-game map.
If you don't use km as an unit of measure, just modify the variable "Speed" and instead of "0.53996", put in whatever is necessary to convert from your preferred unit to knots. 1 km/h is 0.53996 knots.

Attention, sometimes the indicated target course is opposite of what it is, so you may need to add or subtract 180°.

[THEBERBSTER]

A Warm Welcome To The Subsim Community > alboverburn
Subsim <> How To Donate <> See The Benefits <> Support The Community (http://www.subsim.com/radioroom/showthread.php?p=2033119%23post2033119)
If you are new to SH5 look > > HERE (http://www.subsim.com/radioroom/showpost.php?p=2391239&postcount=1) <<
Highly Recommended SH5 > The Wolves Of Steel Mega Mod (http://www.subsim.com/radioroom/showpost.php?p=2165720&postcount=1)

[Ashikaga]

Hello ! love the tutorial ! However.

I have a problem with the sextant in the game. When I try to measure altitude it does not work the way a sextant should work. Ie, I cannot reach the sun's border. The sextant does not move that high or the sun seems to near.

Difficult to explain really.

Any info on that ?

Ashikaga.

[JAFO-]

Kuikeg's link is dead. I uploaded version 2 to my own website:

version 1 of the method:
http://ricojansen.nl/downloads/four_bearings_method.pdf

version 2 of his methods:
http://ricojansen.nl/downloads/the_four_bearings_method_v2,%20Kuikueg.pdf

Thanks for these, I was going nuts trying to track them down.. but I noticed that both these links are slightly broken.. some poking around found that the correct links are:

Version 1:
http://ricojansen.nl/downloads/four_bearings_method_v1,Kuikueg.pdf

Version 2:
http://ricojansen.nl/downloads/the_four_bearings_method_v2,Kuikueg.pdf

[THEBERBSTER]

Hi J
Might be of interest to you.
Post #21 4 Bearing Method By Kuikueg > 4 YouTube Tutorials + Instructions (http://www.subsim.com/radioroom/showpost.php?p=2184956&postcount=22)
Peter

[JAFO-]

Hi J
Might be of interest to you.

Hey.. thanks! :Kaleun_Cheers:

[nazaka]

HELLO!

I often use the 4 bearing method static version.

I have try to understand the moving version but I'm having some trouble.

Does anyone have a tuto video ingame?
It's often more easy to learn one method when someone do it ingame :yep:

[JAFO-]

I have try to understand the moving version but I'm having some trouble.

Does anyone have a tuto video ingame?
It's often more easy to learn one method when someone do it ingame :yep:

The only one I'm aware of is makman94's series of 3 videos, titled "The Art of Hydrophone Hunting". You can see them here:

https://www.youtube.com/channel/UCyOe9eC8PU-hr7dRwegMseQ

[nazaka]

Thank you!! :Kaleun_Cheers:

I just have one question: on SH5, you can follow a target with a hydro when you are immersed, moving with the batteries?
Seems to me we have a lot of noise in the compartment

[JAFO-]

I just have one question: on SH5, you can follow a target with a hydro when you are immersed, moving with the batteries?
Seems to me we have a lot of noise in the compartment

I'm not a SH5 player (SH3 is my preference) but it seems to me that's why the sonarman has headphones on.. :03:

If the noise bothers you, maybe there are mods that can turn down the noise levels, like there are for SH3.

Other than that, I wouldn't worry too much about it.. moving at speed degrades the signal more than the crew being their usual boisterous selves. Just slow down when you want to take a bearing, if you find it's having an adverse effect.

[JAFO-]

Does anyone have a tuto video ingame?
It's often more easy to learn one method when someone do it ingame :yep:

Ok.. I also have another video for you.. makman94's original video. The series I linked to you earlier is an improved do-over of the original, but you may want to watch it anyway.

It's titled "The Ultimate Hydrohunt Video", and can be found at Plissken_04's massive collection, here:
ftp://Maik:Woelfe@hartmuthaas.no-ip.org/Public/Sharing/SH3COMMUNITYMODS/MAKMAN94/The%20Ultimate%20Hydrohunt%20Video%20%21.rar

Alternatively, it can be found at YouTube, where OrthokentroN has broken it up into 5 sections and posted it on his channel here:
https://www.youtube.com/channel/UChO4zDw04Pr2b2QKQWccSUA


Also, I highly recommend jerm138's PDF titled "Sonar_Tracking", which is the best and clearest explanation of the principles behind both the stationary and moving 4 bearing methods that I've ever seen. The illustrations are clear and simple, as are the explanations.

It can be found here:
http://ricojansen.nl/downloads/Sonar_Tracking.pdf

The thread where he released the document is also well worth a read:
http://www.subsim.com/radioroom/showthread.php?t=160817

[nazaka]

Wow! Thanks! :Kaleun_Salute:

If i don't understand with all of that, it's i'm an incompetent :D