The Bearing Rate Course Finding method

[Nisgeis]

First, apologies if this has been discussed before, I don't recall ever seeing it, but who knows.

Right, so, we know about TMA, where you take a bearing reading at a fixed time interval, but what happens if we take a time reading at a fixed bearing interval?

When thinking about turning so your bow was on the target in order to determine whether the AoB was port or starbaord, I wondered whether that's the point at which when the highest bearing rate change would occur and quickly decided it wasn't, as exactly like the doppler effect and a siren, the sound is at the highest pitch when the siren is closest to you. In that way, the pitch of the siren can tell you when the siren is closest (if the pitch doesn't drop then the siren will collide with you).

When stationary and tracking a target, the point it will be closest to you will be when the target's AoB is 90 (port or starboard) as that is the point at which its position on the track is the closest to your position.

So, now we know that, we can measure and record the time it takes for the bearing to change a fixed interval (say five degrees) and then use that to determine whether target's bearing rate has decreased, which means that the target has passes an AoB of 90. When we have the relative bearing at which the target's AoB was 90 (within a maximum error of two and a half degrees), we can then use our own course to determine tha target's course.

When we have the target's course we can the match that course and use speed matching to hold the target on a constant bearing to determine the target's speed.

So there you have it, a simple method that needs no plotting and no range finding in order to determine target course and speed. It will work for sonar bearings, but to speed match you will need to have an optical bearing if the target is travelling faster than seven knots. If you have radar, this will also work, but you might as well plot.

The disadvantage to this method is that you will always have to surrender a position ahead in order to determine when you are behind the target's beam, but you shouldn't be too far behind and if you aren't fast enough to catch, then you won't intercept.

Anyone see any holes? Apart from not being able to determine range?

[Diopos]

Is the sub stationary when you collect the data or is it moving?


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[Nisgeis]

Stationary.

[Diopos]

You can use a 3 -bearings only method to get a course. The time intervals of observation are included in the calc. In the 8010 thread I had a link to the 1943 official maneuvering board manual (US NAVY). You should give it a try! (I think Case X is the relavent one). I think that you or on veeery sound basis! :up:


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[Diopos]

Coming to think of it, it should be more useful in situations where the bearing change rate is "appreciable" (whatever that means). With "Slow movers" over the horizon at small AoBs, collecting the data would be ...tiresome (low bearing per time change).


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[Nisgeis]

You can use TC to avoid the delay, as long as you note down the start time and slow to 1x when you are approaching an interval. I think the lower rate of change will lead to better accuracy of course, as the time interval will be larger and therefore easier to measure when they are at AoB of 90. Higher speed targets at close range = less difference and rougher estimate of the course. I think that will work that way.

[Munchausen]

When stationary and tracking a target, the point it will be closest to you will be when the target's AoB is 90 (port or starboard) as that is the point at which its position on the track is the closest to your position.

:hmmm: Not always. Say the target cuts across your bow at about a 45 degree angle. It will be closest when on (or near) the bow and will be further away when AOB reaches 90.

[Diopos]

:hmmm: Not always. Say the target cuts across your bow at about a 45 degree angle. It will be closest when on (or near) the bow and will be further away when AOB reaches 90.

The minimum distance between a point A and a line is AB, B being the point where a Vertical -passing through A- cuts the line.


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[Pisces]

Well, you wanted an equal-bearing interval method, so this one is not what you want. It's a slide-rule for the 3-bearing equal time interval method. You can still do the same, but it's just a different variable you are measuring. I'm not sure if you were allready aware of it. I think you do. Oh well,

http://www.subsim.com/radioroom/showthread.php?t=147719

(This is the SH3 thread, I also made one in the SH4 section back then, but it's all the same ofcourse)

The formula for the calculation is explained and proven in this document, around page 4.

http://www.filefront.com/17237360/NOE_-_Bearings_Only_TMA.pdf

It certainly seems to lend itself for a fixed bearing interval approach, but only with a digital calculator I fear. Making a sliderule for it would require another extra scale independant from the 2 that the fixed-time interval requires. The fixed bearing interval would require independant scales for both time periods, as wel as one for the size of the bearing interval (which I expect one would not like that to be built-in value). Or reducing the 2 'time' disks to one 'ratio of times'-disk wouldn't help in practice. You'd still have to do the division manually.

I haven't figured out how to construct such a thing. But after I finished working on the above slide-rule I definately thought about trying to implement it too. However the complexity of the formula got the better of me. Maybe it's time to pick up the attempt again. (it certainly beats wasting braincells on 8010)

[Rockin Robbins]

:hmmm: Not always. Say the target cuts across your bow at about a 45 degree angle. It will be closest when on (or near) the bow and will be further away when AOB reaches 90.
The angles between the two courses don't matter. The point where a line drawn at right angles to the target course bisects your submarine is the closest approach. At that point the Angle on the Bow is 90º.

As I see it, Nisgeis has covered all the bases. The only problem is the reality that stopping a real submarine just can't happen unless you are on the surface. But that won't stop us from playing with the concept in the game.

[Rockin Robbins]

The minimum distance between a point A and a line is AB, B being the point where a Vertical -passing through A- cuts the line.


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Minor correction, not a vertical but a perpendicular.

[Nisgeis]

As I see it, Nisgeis has covered all the bases. The only problem is the reality that stopping a real submarine just can't happen unless you are on the surface. But that won't stop us from playing with the concept in the game.

It can be used with optical bearings as well when stationary. I don't think a minor creep speed to stay buoyant would affect the outcome too badly. You wouldn't get exactly the right course, but you'd get something in the right ball park.

[Diopos]

Minor correction, not a vertical but a perpendicular.

:oops::oops::oops:.



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[Munchausen]

The angles between the two courses don't matter. The point where a line drawn at right angles to the target course bisects your submarine is the closest approach. At that point the Angle on the Bow is 90º.

:cool: The concept should work ... but it's the observer or the sonar head or the radar ... not the submarine ... that's the center point. In fact, I tried for a long time to use sonar, thinking that the tangent would be when the sonar operator said, "constant distance" ... except he kept saying it ... on average, for about forty degrees of bearing.

[Rockin Robbins]

:cool: The concept should work ... but it's the observer or the sonar head or the radar ... not the submarine ... that's the center point. In fact, I tried for a long time to use sonar, thinking that the tangent would be when the sonar operator said, "constant distance" ... except he kept saying it ... on average, for about forty degrees of bearing.
All measurements from your sub are standardized to be from a single point on the submarine, the center. So although sonar measurements are taken dozens of feet ahead of periscope measurements, the outputs are all normalized so that when the crew looks at a sonar bearing they can point the scope at that bearing and see the object. So radar, sonar, both periscopes all return the same bearings. This is true both in the game and on a real sub.

[Nisgeis]

Having another think about this. Once you have the target's course and you have obtained the speed by holding it at a contant bearing on a parallel course, you can find the range. You can work it out with some trig, using the right angled triangle between where the AoB was 90 and your earliest recorded time when the bearing was at a five degree interval. Using the distance travelled at that speed in that time elapsed with the formula Opposite = Adjacent * Tan(Angle) to fine the distance to track. Or you can simply draw out the distance travelled and find where that distance fits in the triangle and that will give you the range.

Assuming that you can speed match of course, but if you can't, then you will have trouble intercepting the faster target.

It's getting slightly more complicated now though. :hmmm:.

[Munchausen]

:hmmm: Why do you need the range if you already have track and speed?

[Nisgeis]

You have course and speed, but have no idea where the intercept point is unless you have range, so you'd have to approach purely on a constant bearing to guarantee an intercept, which is less than optimal.