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Old 02-16-2016, 12:38 PM   #1
palmic
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radar Real navigation target motion analysis cheatsheet

To those who likes real navigation mod in SH5 i can share my trigonometry cheatsheet.
You'll need also Sin/cosin + tan/cot tables to print! to conversion between angles and sin/cosin/tan/cot.

I always wanted to find how to calculate 4 bearings method by math, but always was too lazy to find out how
So i spent about a week by doing some research and found out many things about it.
The whole problematic is called bearings only target motion analysis.

While this document is very complex and you can find out how to detect target motion even if you are moving, i was focused only to replace tedious geometry work.
So i used just most simple equations from it.

Besides 4 bearings method i wanted to be able to solve any other situation while i was hunting some ship, so i found that everything between you and the target is triangle. So i started to learn old trigonometry again - you can find shortcuts how to calculate angles and sides of any triangle with some valid inputs also in that cheatsheet - its the law of sines and cosines.
With this you can find for example target distance in later stage of 4 bearings method, or which angle you should approach your target based on speeds.
Just try to write it again in geometry and see what triangle you have to solve.

Why you should want to use this?
Well if you are using geometry in silent hunter games, you should already know how tedious and often even inaccurate it is.
If you'll get used to this trigonometry work, you'll just write down a few equations which is much less work and its always 100% accurate no mater how rigorous you'll be.
And as an extra, you'll feel like ace

How you can use it if you never tried it, but you know how to use 4 bearings method by geometry?
- i recommend you to begin by using your well-known geometry 4 bearings method in conjunction with this - just write your sollution into the map just like before and together with it start to calculate it in this formula.
This is just to start with it - to get orientation in what exactly you are counting
- if you will not understand to some variables or what exactly you are calculating, go find out here: bearings only target motion analysis document.
You'll find out many answers if you solve it by geometry and compare angles and so with trigonometry results..

What if you dont know even 4 bearings method by geometry?
just learn it here:
and come back



EXAMPLE! :

Right now i had a convoy contact.
I measured all 3 bearings in constant timerange 10 minutes, so we dont have to calculate time ranges and we can use simplest equation:

My current course is Co (course own) = 255
B1 (bearing 1) - 71
B2 - 80
B3 - 87
(experienced wolves now already knows that the target is moving away of us for sure - thats the reason i would skip all targeting right now and let the target go, because i have different tasks)
You'll also realize how on your own when you started to use this technique, or geometry pretty soon..


Cot12 = (cotangent of angle between B1 & B2 which is 9) = 6.3138 (find it in the table from very beginning of this post)
Cot13 (cot of 16) = 3.4874

Sollution (from my cheatsheet):
1) Cot(DRM - B1) = 2*Cot13 - Cot12
2) Cot(DRM - B1) = 2*3.4874 - 6.3138
3) Cot(DRM - B1) = 6.9748 - 6.3138
4) Cot(DRM - B1) = 0.661
5) DRM - B1 = 56.4 degrees (here i got angle 56.4 from cotangent table - from that link at very beggining of this post - its cotanget 0.661 from 4) )
If you calculated negative cotangent value, go find angle in that table of the same absolute value and use the result angle as 90-angle+90.
This could be confusing from start, but if you look on linear scale of that values near to 90 degrees in cotangent table, it makes perfect sense. Contangent values dont finish by 90 degrees, but continues bellow zero behind 90 degrees!:
And this little hack makes exactly that.
6) DRM - 71 = 56.4 degrees
7) DRM = 56.4 + 71
8) DRM = 127.4 degrees
(Direction of relative motion)

Now whats DRM? in TMA document on figure 11.1 you can see DRM is the angle between your heading and target ship course. It means that if we will add DRM to our current course (Co), which is 255 we should get target ship course:
Ct (course target) = Co + 127.4
Ct = 255 + 127.4 = 382.4 (-360=22.4! )

It may seem pretty difficult and tedious, but its really not since you're getting used to it. This was pretty slow because of full description of the process.
Buy some good old analog notebook, ink pen and you'll be solving targets like real ace in one week.
Your homework now is to try it on your own and to find how to solve the spiess line (solution is in cheat sheet and all the input for it we already got here).
Spiess line is the fourth virtual bearing for next time period which you are solving in 4 bearings method to find out target real position.
You can find all complex description here in the document.


Disclaimer: I found the TMA document at ricojansen.nl, i dont know who is author/owner.
If you know him, please let me know, ill gladly add his credits here



Gutte jagd Kaleunen!

Last edited by palmic; 01-06-2017 at 12:39 PM. Reason: just some typo
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Old 02-17-2016, 11:20 AM   #2
vdr1981
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Hardcore! Very useful thread!
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Old 02-17-2016, 03:03 PM   #3
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Real navigation and hardcore till end of time
nice job m8 keep it up
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Old 03-03-2016, 09:45 PM   #4
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Wow... I love the chart work and using various tools like the attack disk, but may have to add this to my repertoire. Now where did I lose my high school trig book.

Vielen Dank!
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Old 07-08-2016, 01:37 PM   #5
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This method is while being at full stop, correct? The problem is that even when I'm 0 kts I drift a few hundred meters, does it matter much?
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Old 07-12-2016, 09:57 AM   #6
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Quote:
Originally Posted by WildBlueYonder View Post
This method is while being at full stop, correct? The problem is that even when I'm 0 kts I drift a few hundred meters, does it matter much?
Yes it's while you are stationary.
Few hundreds meters does not matter same like +-1 minute interval inaccuracy, since you are unable to calculate with 0.1 degrees bearings anyway.

To be honest, you can calculate cotangents just with one decimal accuracy at all, its enough

You'll end up with 1-3 degrees target's course inaccuracy, which is ok i think, if you want real precise results, you should use longer period between bearings checks (20-30 minutes) and try to stay in around 100m from first bearing position..
Most of the time you dont need it, you can always confirm result next time around one hour after...
I always confirm it opticaly at firing position, where you need it accurate for your eels, but don't care much while i have it just for approach.
Since hydrophone can reach around 40km you cant lost contact if game dont despawn it..

Last edited by palmic; 07-13-2016 at 09:22 AM.
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Old 07-13-2016, 01:55 PM   #7
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Quote:
Originally Posted by palmic View Post
Yes it's while you are stationary.
Few hundreds meters does not matter same like +-1 minute interval inaccuracy, since you are unable to calculate with 0.1 degrees bearings anyway.

To be honest, you can calculate cotangents just with one decimal accuracy at all, its enough

You'll end up with 1-3 degrees target's course inaccuracy, which is ok i think, if you want real precise results, you should use longer period between bearings checks (20-30 minutes) and try to stay in around 100m from first bearing position..
Most of the time you dont need it, you can always confirm result next time around one hour after...
I always confirm it opticaly at firing position, where you need it accurate for your eels, but don't care much while i have it just for approach.
Since hydrophone can reach around 40km you cant lost contact if game dont despawn it..
Thanks for the reply!

For the Spiess line, I've seen your PDF, but I'm a bit confused on its application, do you have an example?
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Old 07-14-2016, 02:24 PM   #8
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Quote:
Originally Posted by WildBlueYonder View Post
Thanks for the reply!

For the Spiess line, I've seen your PDF, but I'm a bit confused on its application, do you have an example?
Ok let's calculate angle of spiess line from example from initial post.

So we have 3 bearings made with 10 minutes interval between
B1 - 71
B2 - 80
B3 - 87

What we get at example there is target course - 22 degrees. (its irrelevant here but just for clarification...)

--------

At my cheetsheet equation for spiess line is the second (Get 4 bearing method Spiess line)
So this is where we expect our sound contact sometimes at the future.

You have 2 options here - to calculate spiess line for moment of the same interval after (10 minutes here), or you can even calculate spiess line for other time, you just need to change the equation.
That's actually the reason for 2 equations in my cheetsheet (the first one is more simple, because you dont have to calculate different time interval than you used for getting first 3 bearings)
The second, allows you to calculate spiess line after 20 minutes, or 30 minutes here, its up to you how you plan your movement to get their real position.
(If you dont know what i am talking about, and you'll get it. - to get real position of target you need to move and cross 4.th bearing from another position with your calculated spiess line).

So - From my experience, 10 minutes is too short interval for moving to another position and get real 4th. bearing from there, you dont get far-enough from previous position, so lets calculate spiess line rather with 20 minutes interval.

What i mean here is we want to know, where we would hear our contact after 20 minutes from this position, while we will be already somewhere else to hear it from another position and by this situation we will actually create 2d raster to get real position of our target (spiess line is something like our ghost would stay at our previous position and get 4th. bearing from here, while we'll get it from another position and cross of this lines will give us real position of our target).
So lets do it!

Example to get bearing of spiess line after 20 minutes:

legend:
B4 - spiess line
t12 - time interval between B1 - B2 (first 2 bearings from first example in initial post) - 10 minutes = 10
t13 - time interval between B1 - B3 - 20 minutes = 20
t34 - time interval between B3 - B4(spiess line) - 20 minutes = 20 (yes, this is our decided time interval between B3 and spiess line)
t23 - time interval between B2 - B3 - 10
t24 - time interval between B2 - B4 - 10+20=30
t14 - time interval between B1 - B4 - 10+10+20=40
b12 - angle between B1 and B2 - 80-71=9
b13 - angle between B1 and B3 - 87-71=16

real calculation:
B4 = B1+arccot( ( t13*t24*cot(b13) - t12*t34*cot(b12) ) / t23*t14)
B4 = 71+arccot( ( 20*30*cot(16) - 10*20*cot(9) ) / 10*40)
B4 = 71+arccot( ( 2*3*cot(16) - 1*2*cot(9) ) / 1*4)
B4 = 71+arccot( ( 6*cot(16) - 2*cot(9) ) / 4)
B4 = 71+arccot( ( 6*3.5 - 2*6.3 ) / 4)
B4 = 71+arccot( ( 21 - 12.6 ) / 4)
B4 = 71+arccot( 2.1)
B4 = 71+25.4
B4 = 96.4

So after 20 minutes, we should here our contact from this position at bearing 96-97, we can move now and hear it from another position to get their distance as well...
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Old 07-15-2016, 09:34 AM   #9
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Quote:
Originally Posted by palmic View Post
Ok let's calculate angle of spiess line from example from initial post.

So we have 3 bearings made with 10 minutes interval between
B1 - 71
B2 - 80
B3 - 87

What we get at example there is target course - 22 degrees. (its irrelevant here but just for clarification...)

--------

At my cheetsheet equation for spiess line is the second (Get 4 bearing method Spiess line)
So this is where we expect our sound contact sometimes at the future.

You have 2 options here - to calculate spiess line for moment of the same interval after (10 minutes here), or you can even calculate spiess line for other time, you just need to change the equation.
That's actually the reason for 2 equations in my cheetsheet (the first one is more simple, because you dont have to calculate different time interval than you used for getting first 3 bearings)
The second, allows you to calculate spiess line after 20 minutes, or 30 minutes here, its up to you how you plan your movement to get their real position.
(If you dont know what i am talking about, and you'll get it. - to get real position of target you need to move and cross 4.th bearing from another position with your calculated spiess line).

So - From my experience, 10 minutes is too short interval for moving to another position and get real 4th. bearing from there, you dont get far-enough from previous position, so lets calculate spiess line rather with 20 minutes interval.

What i mean here is we want to know, where we would hear our contact after 20 minutes from this position, while we will be already somewhere else to hear it from another position and by this situation we will actually create 2d raster to get real position of our target (spiess line is something like our ghost would stay at our previous position and get 4th. bearing from here, while we'll get it from another position and cross of this lines will give us real position of our target).
So lets do it!

Example to get bearing of spiess line after 20 minutes:

legend:
B4 - spiess line
t12 - time interval between B1 - B2 (first 2 bearings from first example in initial post) - 10 minutes = 10
t13 - time interval between B1 - B3 - 20 minutes = 20
t34 - time interval between B3 - B4(spiess line) - 20 minutes = 20 (yes, this is our decided time interval between B3 and spiess line)
t23 - time interval between B2 - B3 - 10
t24 - time interval between B2 - B4 - 10+20=30
t14 - time interval between B1 - B4 - 10+10+20=40
b12 - angle between B1 and B2 - 80-71=9
b13 - angle between B1 and B3 - 87-71=16

real calculation:
B4 = B1+arccot( ( t13*t24*cot(b13) - t12*t34*cot(b12) ) / t23*t14)
B4 = 71+arccot( ( 20*30*cot(16) - 10*20*cot(9) ) / 10*40)
B4 = 71+arccot( ( 2*3*cot(16) - 1*2*cot(9) ) / 1*4)
B4 = 71+arccot( ( 6*cot(16) - 2*cot(9) ) / 4)
B4 = 71+arccot( ( 6*3.5 - 2*6.3 ) / 4)
B4 = 71+arccot( ( 21 - 12.6 ) / 4)
B4 = 71+arccot( 2.1)
B4 = 71+25.4
B4 = 96.4

So after 20 minutes, we should here our contact from this position at bearing 96-97, we can move now and hear it from another position to get their distance as well...
Thanks for the explanation, I'm working on a mathematical proof to see if this is always applicable, it should though!

I still have a few questions if you don't mind:
1) What is distance float? And the "Get spiess line distance" part allows us to calculate how many meters the contact has moved during the measurements? So that dividing by time we get speed?
2) What does the "Target distance float" part accomplish?
3) Are A and B input variables or things which need to be calculated? I'm a bit confused. Yes, I know how to apply Carnot's theorem or the sine one, it's just that I don't understand what A and B refer to, I've read it to no avail.
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Old 07-15-2016, 11:08 AM   #10
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Quote:
Originally Posted by WildBlueYonder View Post
Thanks for the explanation, I'm working on a mathematical proof to see if this is always applicable, it should though!

I still have a few questions if you don't mind:
1) What is distance float? And the "Get spiess line distance" part allows us to calculate how many meters the contact has moved during the measurements? So that dividing by time we get speed?
2) What does the "Target distance float" part accomplish?
3) Are A and B input variables or things which need to be calculated? I'm a bit confused. Yes, I know how to apply Carnot's theorem or the sine one, it's just that I don't understand what A and B refer to, I've read it to no avail.
With "distance float" i mean distance you float from position of first 3 bearings to new position to get 4th. bearing from there.
Relatively distance target float is the same in relevance to target.

The other quetstions are pure simple trigonometry, just draw the bearings, target course and even your course to new position to map, 4th. bearing from there and try to understand what side or angle of triangle you need to solve.

The law of sine is ultimate solution for every sides and angles in that triangles..
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Old 07-16-2016, 08:35 AM   #11
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Quote:
Originally Posted by palmic View Post
With "distance float" i mean distance you float from position of first 3 bearings to new position to get 4th. bearing from there.
Relatively distance target float is the same in relevance to target.

The other quetstions are pure simple trigonometry, just draw the bearings, target course and even your course to new position to map, 4th. bearing from there and try to understand what side or angle of triangle you need to solve.

The law of sine is ultimate solution for every sides and angles in that triangles..
So after I calculate the 4 bearings, I have do draw them on the map? Yes, I know how to solve it, but my question is, to get angle A and B, do I get them from the map or calculate them with a formula?
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Old 07-16-2016, 10:07 AM   #12
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Default Real navigation target motion analysis cheatsheet

It's up to you, you can get it from map.
I prefer calculation.

Just draw it if you need to imagine the triangles, then solve them mathematically.
It's more simple and geometry is not as accurate as math


Sent from phone

Last edited by palmic; 07-17-2016 at 05:05 AM.
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Old 04-05-2017, 07:01 AM   #13
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I not understand that so step

"5) DRM - B1 = 56.4 degrees (here i got angle 56.4 from cotangent table - from that link at very beggining of this post - its cotanget 0.661 from 4) )"

how to get 56.4?....
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Old 04-05-2017, 11:25 AM   #14
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Quote:
Originally Posted by hauangua View Post
I not understand that so step

"5) DRM - B1 = 56.4 degrees (here i got angle 56.4 from cotangent table - from that link at very beggining of this post - its cotanget 0.661 from 4) )"

how to get 56.4?....
In 4) you can see:
4) Cot(DRM - B1) = 0.661

0.661 is cotangent of angle 56.4 degrees
Download sin/cosin tangent/cotanget tables from beginning of this thread and print it
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Old 04-06-2017, 12:56 AM   #15
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Quote:
Originally Posted by palmic View Post
In 4) you can see:
4) Cot(DRM - B1) = 0.661

0.661 is cotangent of angle 56.4 degrees
Download sin/cosin tangent/cotanget tables from beginning of this thread and print it
I download your tables... but no see 0.661 ...Ctg of 56.4...!!
this I no understand
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