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Old 02-16-16, 12:38 PM   #1
palmic
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Join Date: Jan 2014
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radar Real navigation target motion analysis cheatsheet

Quote:
Update 2023-12-21: please download this archive and find all mentioned documents there: https://drive.google.com/drive/folde...yEpwpbPIPOCxtu

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; 12-21-23 at 08:13 AM. Reason: just some typo
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