The new and improved four bearings method
 

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

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 !

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!

Upload to Subsim ?
 

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

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

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.

I linked the first one in the sticky tdc tutorial. I edited the post now and added this one too for further reference.

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

(Not mine, credit to Gutted.)

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.

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.

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!

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 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

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.

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.

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.por...2&pubCode=0008

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.