The four bearings method

[Jan Kyster]

Originally Posted by Kuikueg

http://www.filefront.com/17135612/fo...ngs_method.pdf

Much appreciated! Thanks!

[Kuikueg]

Originally Posted by makman94

hi Kuikueg,

no, no, i didn't meant at video that the technique has an acceptable 'error'.you see,english are not my language and many times don't help to express myself correct !

I know you didn't mean that. I just wanted to point it out for those not mathematically inclined, that might think there is an inherent error in the method. As your second video proves and you have explained, you can get really precise with it.

Thanks for the list and please check your PM's.

[makman94]

Originally Posted by Kuikueg

.....

Thanks for the list and please check your PM's.

ok Kuikueg ! i got it now

[karamazovnew]

Cool method... I only have one small problem with it that might not bother others. The GPS So I've just tried something cool and it worked.

I did all plotting far from my sub's icon, somewhere in the middle of the Atlantic. All plots were relative so I never had to convert stuff to true north. I never changed course, I'm not sure why Makman does it in his tutorial, as it's only necessary in the "sub stopped" technique. I only had to calculate how much "up" I went in the interval between readings, using the nomograph. After the 4'th bearing I had all data I needed. I then calculated a rough distance to get my eels into range. I had a sheet with turning radius of the boat and the time it took to complete a full 360 turn. I figured I only needed to change course and stop about 7 minutes later, at that speed. I did that, used the AOB technique to enter data into the TDC and get the 000 gyro bearing. To my horror I realized that I forgot to check where the target would be at that time, so it had already passed the sweat spot. Frantically, I did a quick check on the probable range when the target would be at bearing 340 and shot my eels when the target was at that bearing. 4 minutes later bum bum bum... I had never raised my periscope. Absolutely love it

[makman94]

Originally Posted by karamazovnew

Cool method... I only have one small problem with it that might not bother others. The GPS So I've just tried something cool and it worked.

I did all plotting far from my sub's icon, somewhere in the middle of the Atlantic. All plots were relative so I never had to convert stuff to true north. I never changed course, I'm not sure why Makman does it in his tutorial, as it's only necessary in the "sub stopped" technique. I only had to calculate how much "up" I went in the interval between readings, using the nomograph. After the 4'th bearing I had all data I needed. I then calculated a rough distance to get my eels into range. I had a sheet with turning radius of the boat and the time it took to complete a full 360 turn. I figured I only needed to change course and stop about 7 minutes later, at that speed. I did that, used the AOB technique to enter data into the TDC and get the 000 gyro bearing. To my horror I realized that I forgot to check where the target would be at that time, so it had already passed the sweat spot. Frantically, I did a quick check on the probable range when the target would be at bearing 340 and shot my eels when the target was at that bearing. 4 minutes later bum bum bum... I had never raised my periscope. Absolutely love it

hi Kara,

yea the gps(you mean the DIRECTIONS of hydro lines,right?) is annoying but i am afraid that is nessecery . the hydro station is totally unmodeled (another reason that i am saying that sh3 is not a sub simulator) and you can't get accurate (ok ...by 'accurate' i mean accurate to some level ,not exactly) hydro bearings. there are absolutely no tools that real station must had to measure the intensity of sound and narrow a little bit the peak of sound. also, there are other problems with the 'sonarman' . the moment he says 350 degrees the target is either to 349,5 or to 350,5 degrees(really....why devs have made simple things ..so complicated without a reason?). that's ok (can be overpassed) if the report happens to be asked exactly at the time he screams the new hydro bearing. but if the time is not at this moment then all you know is that target is somewhere between 349,5 and 350,5 .nothing can be done,afaik, to narrow this..so if you don't use the gps for hydro line you have to expect big inaccuracies ( as travelled distances getting bigger so inaccuracies getting bigger).

also there is one more (little this time) thing that annoyes me with sonarman . he doesn't answer immediatelly for reporting . sometimes he is quick and others not so we have some 'lose' from that too and if you add the inaccuraces becuase of the fact that drawings will take place at small zoom of navmap ....i think that all these will lead to a final solution which will be very off if not ...totally off !

so , at video ,i am pretending that sonarman has all these tools at his station for narrowing the peak of sound ( yea,i know ....now he 'narrows' it at a extreme level but do we have a better choice?) and giving me accurate directions for hydro lines.

would be nice, though, to know if there is a workaround for plotting accurate (as possiple) hydrolines without the gps.

or even better (just for me is this ) : can we tweak somehow the sonarman's reports and gives an output with the 'half' first demical ?? something like ''bearing: 340,5 degrees'' when target is between 340 and 340,5 degrees or 'bearing: 341 degrees'' when target is between 340,5 and 341 degrees.
then gps will not be needed and accuracy will not be 100% which ,i think , is 'closing' to reality.

about no course's changes : no ,this is wrong Kara.if we assume that you don't change course and speed (in order to be able to make the 'up going' plotting ) from the start of the procedure ,then the fourth bearing is ,in fact, the 'red line' (if we assume that you did all correct).so you will have 'problem' there as both lines(fourth bearing and 'red line') will be the same line. the goal is to avoid parallel hydro lines ...each other or with the 'red line' .thats why i changed course .or you can change speed (instead of course) between time intervals.(but whatever you do ....something must be changed either course or speed or...both).

sure it is not nessecery to use your scope ! i used it only to get an accurate speed for target . but if you don't use it you have to be based on your map plotting for getting the target's speed and becuase it will be a little off (target's course 'error' is causing this) you must use a greater angle at your 'salvo' shooting in order to get him for sure .
also , as you are going to shoot from hydrophone i want just to point out that we fire at target when we start 'hearing' him ...10 degrees in FRONT of the decided shooting bearing.

[karamazovnew]

Actually by GPS I meant the position of our sub. Changing your course and speed wildly would make normal plotting impossible. Take the first example (Static sub for the first three bearings): at your fourth bearing you'd probably just start engines as acceleration/distance charts are available for a ship, but protracting a turn in which you accelerate is... HARD

Now are you sure what you said about the Red Line? As I understood it, using just 3 points will give you an infinite number of possible courses. By projecting the "future" position on all these probable courses (protracting them), you end up with the red line which is basically the Geometric Place (no ideea how to translate Locul Geometric from romanian to english) of all possible locations (not bearings) of your target at your next reading. It's not a bearing, but a bearing+range, if you will. By intersecting that with the actual 4'th bearing, you get the position. Or did I misunderstand the whole concept? So far, I've never had it overlapping the 4'th bearing. It did come close on some tries, but still far enough to allow a good solution.

Here's an example:
I loaded up just before firing eels at a Light Cruiser. Previously I had already calculated everything through normal plotting and he was going at 13.5 knots and a course of around 250, the solution was perfect and the PK updated it like clockwork. The problem was that he was extremely near, so I took bearings at 1minute intervals.

Uploaded with ImageShack.us

You won't see my sub anywhere on the map, I was going on a 133 course at 3 knots. I had to protract my position. As you can see, I drew up circles at 100 yards intervals (1 minute at 3 knots means 100 yards). All bearing were relative to my bow (325,333,350,31,75). I ended up with a solution of 14 knots (950 yards in 2 minutes, between the 3'd and 5'th bearings) and a relative course of 115 degrees. Added to my course of 133, it gave a nice 248 true course for my target. The actual Range at the 4'th bearing was off by less than 50 yards (around 500 on the map, 550 on the sonar), but it took me a couple of seconds to use the sonar so... considering that SH has that line 0.5 problem, I'd say the solution was PERFECT. I don't need to convince anyone that I didn't change speed or course, since my bearings were plotted starting from theoretical linear and equally spaced protracted positions

Try this for yourself, using my bearings. Heck, you can even do this while in port

EDIT: About a year ago I desperately tried to solve this problem. I failed miserably so, Kuikueg, you have my deepest respect. I wanted to create a method of simply keeping your periscope on the target and ending up with a perfect solution after a short while. This method is so simple that it proves it can work. I can't wait to figure out the formula.

[makman94]

Originally Posted by karamazovnew

.........
Now are you sure what you said about the Red Line? As I understood it, using just 3 points will give you an infinite number of possible courses. By projecting the "future" position on all these probable courses (protracting them), you end up with the red line which is basically the Geometric Place (no ideea how to translate Locul Geometric from romanian to english) of all possible locations (not bearings) of your target at your next reading. It's not a bearing, but a bearing+range, if you will. By intersecting that with the actual 4'th bearing, you get the position. Or did I misunderstand the whole concept? So far, I've never had it overlapping the 4'th bearing. It did come close on some tries, but still far enough to allow a good solution.
.......

yes Kara ,i am sure ! in fact it is... proved ! yes ,'red line' is a geometrical locul and this geometrical locul is (as Kuikueg showed) a straight line. now, your fourth bearing is a straight line also and i am telling you that if you don't change course and speed during your time intervals these two lines will be the SAME line.
i will send you the prove of this at your pms.
if not...then it is a fault at your map drawings or caused becuased of inaccuracies of silent hunter.
send me the mission you played to give it a try and i will tell you my results

[Kuikueg]

Originally Posted by makman94

yes Kara ,i am sure ! in fact it is... proved ! yes ,'red line' is a geometrical locul and this geometrical locul is (as Kuikueg showed) a straight line. now, your fourth bearing is a straight line also and i am telling you that if you don't change course and speed during your time intervals these two lines will be the SAME line.
i will send you the prove of this at your pms.
if not...then it is a fault at your map drawings or caused becuased of inaccuracies of silent hunter.
send me the mission you played to give it a try and i will tell you my results

I don't know if you are not understanding each other but I'll try to clarify.
The need for changing course, either for the fourth bearing or for any other depends only on the circumstances. The fourth bearing won't be in general equal or parallel to the red line even though you don't change course. Actually, in my explanation of the method, you could draw a straight line in the diagrams representing submarine's course and the solution holds, because it does not depend even on the location of the submarine. But in certain circumstances, such as those in Makman's video, you may need to change course in order to obtain a non parallel bearing and increase accuracy of the solution. I insist: is circumstantial.

Something that catches my attention is that, if I understand well, Karamazov is not taking a fifth bearing to calculate course and speed of target. Four bearings is enough to know that, but it implies repeating the calculations backwards through the bearings and finding an initial red line through which to find the initial position of target via first bearing. Is that what you are doing, Karamazov? Are you maybe estimating true course by sight from those used in the construction? Are you doing anything else I can't think of?

Edit: sorry Karamazov, your picture made things really clear for me. You take a fifth bearing. Silly me. Thanks for your comments.

[makman94]

Originally Posted by Kuikueg

......
The need for changing course, either for the fourth bearing or for any other depends only on the circumstances. The fourth bearing won't be in general equal or parallel to the red line even though you don't change course. Actually, in my explanation of the method, you could draw a straight line in the diagrams representing submarine's course and the solution holds, because it does not depend even on the location of the submarine. But in certain circumstances, such as those in Makman's video, you may need to change course in order to obtain a non parallel bearing and increase accuracy of the solution. I insist: is circumstantial.......

.....

Kuikueg , check your pm

i insist that if you DON'T CHANGE COURSE AND SPEED the fourth bearing will be ALWAYS the red line !
all these only at the situation that you haven't change COURSE AND SPEED

you say: ''Actually, in my explanation of the method, you could draw a straight line in the diagrams representing submarine's course and the solution holds...''
this point is not correct,imo, Kuikueg. if you draw a straight line for your course then the spaces between the time intervals will not be equal (which can be 'translated' as a 'speed' change)

[Kuikueg]

Makman is right!!!

Not absolutely, but right.

If you keep speed and course through all the process this is what happens:

The construction of a possible solution course (among the infinite existent) implies choosing a point along the second bearing. What if you choose your own second position as a starting point? you will end up with your own fourth position as the protracted one for your target. Therefore, the red line always goes through your fourth position. So if you don't change speed or course along the process, your fourth bearing will be meaningless. In the document that explains the method, I had considered meaningless the submarine position, so I put on some arbitrary ones and all went well, because it seems that slight variations on speed or course result in wide variations in the red line, under feasible circumstances, which is enough to provide an accurate solution.

I was quite perplex when I realized that, after Karamazov's statement that he had not changed course. After reviewing his snapshot, I notice that he had at least changed speed between his first and third bearing. That's enough. I have yet to assess to what amount the direction vector of the red line is sensible to those changes, but I can assure you that you need at least one change in speed or course anywhere along the construction to make your fourth bearing meaningful, (not necessarily right before the fourth bearing, and that's the only reason I said not absolutely right at the beginning, but he is essentially right: it is not that your bearing will coincide with the red line, but that it will cut it through your own position, a point that we mathematicians call a singular point -and we sailors call collision point- where information has vanished. That is, roughly: the bearing to a ship in your own position is any).

I will rewrite the document posted in this thread to reflect those facts and post it here.

Thank you, Makman. Well seen. This is collaboration at its best.

[karamazovnew]

I've played around with that GeoGebra program you sent me, what an amazing tool, I'll always keep this installed. I used my previous bearings for practice. I didn't even need to use my sub's position on the second bearing, somehow the red line always coincides with the fourth bearing. I have to admit, I feel stupid right now. Not because I was wrong before, but because I must've done SOMETHING wrong to end up with good solutions and now, for the love of God, I can't remember WHAT . The picture I sent before was not a fake, yet time and time again I can't get that red line anymore . It wasn't from plotting mistakes, although drawing circles so small I could've actually fulfilled the rule to change speed because of the silly 0.5 error in the SH ruler

So Makman, you have my apologies for not initially believing you. So.. on the move, after 3 bearings, we can can the 4'th. I still can't shake the feeling that knowing what distance we've traveled between readings, we could somehow protract the bearings back to our original position. That would solve this problem .

Wait, I've just thought about a counterexample to what I've just said. Imagine moving along at a constant speed and course and all first 3 bearings are 90 degrees. This means that the 4'th will also be 90, this can either be a ship moving parallel to you at the same speed as you, or at any angle to your course but at a greater speed. Yeap, this problem is unsolvable...

[Kuikueg]

Originally Posted by karamazovnew

I've played around with that GeoGebra program you sent me, what an amazing tool, I'll always keep this installed. I used my previous bearings for practice. I didn't even need to use my sub's position on the second bearing, somehow the red line always coincides with the fourth bearing. I have to admit, I feel stupid right now. Not because I was wrong before, but because I must've done SOMETHING wrong to end up with good solutions and now, for the love of God, I can't remember WHAT . The picture I sent before was not a fake, yet time and time again I can't get that red line anymore . It wasn't from plotting mistakes, although drawing circles so small I could've actually fulfilled the rule to change speed because of the silly 0.5 error in the SH ruler

So Makman, you have my apologies for not initially believing you. So.. on the move, after 3 bearings, we can can the 4'th. I still can't shake the feeling that knowing what distance we've traveled between readings, we could somehow protract the bearings back to our original position. That would solve this problem .

Wait, I've just thought about a counterexample to what I've just said. Imagine moving along at a constant speed and course and all first 3 bearings are 90 degrees. This means that the 4'th will also be 90, this can either be a ship moving parallel to you at the same speed as you, or at any angle to your course but at a greater speed. Yeap, this problem is unsolvable...

The problem is solvable. I think you did not read my last post.

[karamazovnew]

Originally Posted by Kuikueg

The problem is solvable. I think you did not read my last post.

I did, I meant that the problem of 4 bearings while your sub is holding a steady course and speed is unsolvable.

And I managed to figure out why my solutions were correct. Because of the 0.5 ruler round-up, I ended up with errors in my position which translated into differences in my sub's speed. Since the distances and ranges were very small, this was enough to give me a workable solution. At longer distances (>10km), I would've ended up with the redline overlapping my 4'th bearing. So when I scaled up my plot, making my sub travel 1000 yards instead of 100, the error went down by a factor of 10 and I immediately ended up with all protracted points on the 4'th bearing

[Kuikueg]

Originally Posted by karamazovnew

I did, I meant that the problem of 4 bearings while your sub is holding a steady course and speed is unsolvable.

And I managed to figure out why my solutions were correct. Because of the 0.5 ruler round-up, I ended up with errors in my position which translated into differences in my sub's speed. Since the distances and ranges were very small, this was enough to give me a workable solution. At longer distances (>10km), I would've ended up with the redline overlapping my 4'th bearing. So when I scaled up my plot, making my sub travel 1000 yards instead of 100, the error went down by a factor of 10 and I immediately ended up with all protracted points on the 4'th bearing

Right on!

[makman94]

only good things can comes over due these thoughts Kuikueg and Kara !

an idea came to me after all this discussion...i am thinking that the procedure can be a little ( ok ... a little) simplified like this :
we will take advantage of the fact that we always know one point of red line .this point is a point ON our course(imagine a straight course) after exactly a distance that is 3 times the distance that we travelled during the first interval.
so here is a simplified procedure:

1.for the FIRST interval we DON'T change speed and course and we mark our starting and ending point . (for the other interval we are doing whatever we want...changing courses or speeds or...both)

2. extending(at a straight line) the distance between these two points that way that it will end to a point that the distance from the start point to this point to be equal with 3 times the first distance.

this point is, for sure , one point of red line.

3. the other point of the red line will be found as we allready know from Kuikueg's tutorial and we are ready to draw the red line .
the rest procedure is as shown at Kuikueg's tutorial.


the 'winning' is that we are avoiding some drawings on navmap (circles...extensions...etc) in order to find a second point for the red line.
i know... not big 'winning' ! but we are getting a ...little faster with less drawing ,right ?

ps: yea Kara, this programme is just a piece of art ...and really powerfull !

ps: Kuikueg you have a pm