Gun ranging again...

[karch]

OK folks.

From the previous post, I am in the group that says that with only 2 microphones there is an infinite number of places a heard sound can come from knowing the speed of sound and the distance between listening posts.

I even drew graphs showing that there was a straight line from the enemy to your line, and that any where along the line the gun could be firing from and still give the identical sound delay between firing posts.

I drew this up with a CAD program to prove it.... and it is NOT TRUE. Somehow, instead of a straight line, it is a GIANT shallow curve. It almost looks straight.... look at my drawing:

The green concentric circles are 1 second sound intervals from listening post B

The orange circles are 1 second intervals from listening post A. When I marked the intersection of the appropriate circles and went to connect them with a straight line.... it didn't work. VERY STRANGE. Could someone tell me why.

Our theory is 99% right, and the line is close to straight, but it's not. I connected the 2 intersections from the outermost circles and extended them inwards and connected the 2 innermost intersections and extended the line outwards, you'll see the RED and BLUE lines definitely intersect, and the bullseyes marking the intersections look like they fit a radius.

Anyone have any idea why this would happen? And Booboo, look at all the numbers. This shows 4 points where a sound will arrive at A one second after B hears it and the listening posts and gun are NOT all in line.

EDIT: changed the location of my image file

[ February 18, 2002, 02:04 PM: Message edited by: karch ]

[Radar]

Hey, if you are using your math, there will be two solutions for each sounding... Determine a base bearing and throw out the other result. What your doing is nailing down a position by what is called distance-distance determining. There will be two angle solutions for each distance.

[karch]

I agree if you also know the angle TO the sound source from both listening posts, you can find it easily. You will only get 1 location, not 2.

BUT what if you can't find the direction the sound is coming from. Lower frequencies travel much further than high frequencies, but are much harder to get the direction of.

With a 3rd listening point, it would be easy to find the gun, there will be another line between B and the new C, where it intersects is where the gun will be.

I'm basing this experiment on the presumption that you can't get the angle of the gun from either microphone location and you ONLY have the sound delay to work from.

I work downtown in Chicago and sometimes with construction going on there is a HUGE low boom. It is louder than heck but you can't tell WHICH direction it is coming from. I'm guessing artillery is similar in being hard to get a good direction on.

[MajorBooBoo]

What is this? A Newbiewerfer thread? I cant see your pic by the way.

I am typing up a long text explanation now and will cut and paste it in later today. Its a holiday (pres day?) So I am off. See you in the other thread.

[Redwolf]

As posted in the other thread, you get two hyperbolas (english for hyperbel?) out of three sound-only observation points. The hyperbolas will cross and that's your battery position after kicking positions behind your lines out.

I am sure that's the end of the story. I can give you the raw formulas that you would have to resolve to X and Y coordinates, but I'm too lazy to do it myself (given that my equotations part of my brain is rusty and I probably need several attempts and hours).

[apex]

"The Schallmessverfahren (sound raning) utilizes the steady expansion of sound to all sides with constant speed to measure the time difference between different observation posts, in order to construct Richtungslinien (vectors, Hyperbolas) to the sound source. The intersection of two hyperbolas gives away the sound source, a third hyperbola is used for verification. The range of the measurements is 10 to 20 kilometers, 30 under good conditions. Influence from weather are adjusted for to 3.5 degrees and calm winds."

Engelmann/Scheibert, "Die deutsche Artillerie 1934-1945", translation by yours truly.

Definitely two sources needed, if you're in the group saying "infinite number of places", you are in the group that's wrong.

apex

[apex]

Addendum:

apex

[karch]

Originally posted by apex:

Definitely two sources needed, if you're in the group saying "infinite number of places", you are in the group that's wrong.

apex

Nope. You are wrong. Neener Neener Neener!

I am having massive DNS problems today. We moved our DNS servers over the weekend and everything isn't resolving correctly yet. Please let me know if anyone can see my chart above yet.

The scan you posted is fantastic, but I say it proved my point exactly. You NEED at least 3 listening posts to get the intersecting hyperbo-thingies REDWOLF mentioned. Otherwise you get a CURVED line that gives the same readings to the 2 listening posts. Withe 3, there are 2 Curved lines and they intersect where the gun is. I will draw this up tonight. I don't have the day off like you lucky sods. tppthbbbthbbbbbb (raspberry sound)

Redwolf, I agree with you. Let's find a way to prove it to them and make them kneel to our superior intelect!!!

Just kidding everyone, just kidding.

[Graaf Spee]

Originally posted by apex:

Definitely two sources needed, if you're in the group saying "infinite number of places", you are in the group that's wrong.

apex

Very nice pic But it actually proves that three sources are needed. With three sources you get three LINES. But with two sources you only get one line. If you instead had four sources (which seems to have been the case in the real world™) you would hav gotten six lines.

Here are two pictures two (hopefully) prove my point.

The circles represent the soundwave which in both cases arrives a little earlier at sorce B than A.

Trying to make it even more clear, this one showes the two cases overlapping each other.

The pictures are not that good but I hope they will make it clear that you would get exactly the same timedifference in both cases (and not only from these two, but from an infinit number of locations...). So where is the gun? If you had an observer that could tell exactly from which direction the sound came from it would of course be possible with only two sources. But I doubt that a human being would be able to determine it. Mayne give the general direction, but that would only narrow it down a little.

Can we all agree on this now? Two sorces is NOT enough. You need three and would like to have four.

/Kristian

[Tero]

Originally posted by Graaf Spee:

Very nice pic But it actually proves that three sources are needed. With three sources you get three LINES. But with two sources you only get one line. If you instead had four sources (which seems to have been the case in the real world™) you would hav gotten six lines.

Here are two pictures two (hopefully) prove my point.

One teeny-weeny fallacy in your train of thought : as it is not a table top we are talking about at (say) 10km's four gun shots tend to blend in as one, if they are fired as a salvo within one second of each other. A guy at LP may be able to make out four different reports but he will only be able to say the general direction of the shooting without any distiction between the individual shots. The guns are withing 25-50 meters of each other anyway so at 10km's they might well be next to each other.

If you had an observer that could tell exactly from which direction the sound came from it would of course be possible with only two sources. But I doubt that a human being would be able to determine it.

This is what they trained these people for. IIRC all were competent FO's to begin with and they specialized in this particular field. They may not be able to give the exact direction but at 10 km's I think the propability of only two LP's being able to get a close enough fix on the source is high.

Mayne give the general direction, but that would only narrow it down a little.

If the base (distance between the two LP's) is wide enough any high school student could figure out the approximate location of the source.

Can we all agree on this now? Two sorces is NOT enough. You need three and would like to have four.

Two LP's are enough

But the more the better.

BTW: what was the OOB of a sound/flash ranging unit anyway ? Did they have men to man more than the required two LP's ?

[Roborat]

Fascinating thread(s) all, lots of neat math stuff being thrown about, (starting to have flashbacks on my university math courses, not good). Just one question though, is anyone interested in how it is/was done in real life?? I am going from memory here, from some gunnery lectures, and I am not an arty officer, who are taught this stuff, but one of the officers in my unit has an interest in sound ranging tech and history, and I can check with him on particulars if desired.

What I remember is that about 6 to 12 microphones are used, and I think I remember something about them being placed in an arc, rather than a straight line. This technology was developed by us (Canadians) in WWI, and by WWII, the technique was fine tuned and quite accurate. We were, and apparently still are, leaders in this field. Someone posted something about solutions being good to 25 metres, I'm not sure on this, but it sounds about right. I know that in modern conditions, by the third round fired, the other side has the firing location of a gun pinpointed, hence the modern shoot and scoot doctrine. I also remember something about the process used to do the calculations being classified, but again I am going from memory.

One anecdotal story I got, modern times, (from the officer referenced above in his lecture) was him being out with a sound ranging unit on an arty range (in Gagetown,I think, may have been Wainwright). A US arty unit was up shooting and the ranging crew were practicing by tracking their shots. Anyway, they fired a winger, and the radiowaves were suddenly full of P.O.'ed officers yelling back and forth trying to determine who fired the errant round. The C.O. of the ranging unit came on, and informed them that it was the xth gun which had fired the bad round, and that it had fired yth in that barrage. (I can't remember the exact particulars, so I am not citing the exact sequence). Apparently they had this information almost simultaneously with the winger landing.

So if there is any interest, I can try and dig up more info on this, but it may take a while. I am sure, however, that there are others here who already have that this info and might chime in (hint, hint).

[karch]

At least we all now agree that you need either:

A) 3 listening points finding the enemy by sound delay between listening posts only.

2 listening posts finding the enemy by sound delay between listening posts AND direction of sound.

Is that correct?

You either need delay AND direction for 2 microphones, or 3 microphones to find the location without any direction finding.

Either would work, but I think getting the direction accurately is very difficult. If you were off by 10-30 degrees, your plot could be hundreds of yards off. I agree if you got very good direction finding, 2 points would work.

[JonS]

Ok. The assumption from Booboo now seems to be that there ARE in fact 3 sensors - 2 mikes and a listening station. Well. Excuse me. If you're just going to be slipping extra information in whenever it suits you, you won't mind if I think you're a supercilious twit. You obviously think you are being oh-so-clever with your pseudo-socratic method. I think you're just wasting our time.

As others have pointed out, if you have sensors that can measure delta(t) _and_ bearing, then using just two sensors is a trivial (relativly) problem. The reason is that you now have four pieces of information. If the sensors can _only_ measure delta(t) (which is the position I and others have contended all along), then I maintain that you need more than two (even neglecting for a 3D world).

Incidentally, for those who think that measuring the bearing of a sound is easy, calculate what effect on the target location a 1° error at 1000m, 2000m and 5000m has. Try again for 5° and 10°. Then, get out a compass or protractor and see how accurately you can determine the bearing to an unknown noise source.

Regards

JonS

[MajorBooBoo]

Originally posted by Roborat:

Fascinating thread(s) all, lots of neat math stuff being thrown about, (starting to have flashbacks on my university math courses, not good). Just one question though, is anyone interested in how it is/was done in real life??

So if there is any interest, I can try and dig up more info on this, but it may take a while. I am sure, however, that there are others here who already have that this info and might chime in (hint, hint).

I like to think it out first, then go on a research binge when I hit a good library. I can then compare what I come up with and the people of the day did.

Try to ignore JonS' importing his nastiness from the other thread. Is everyone from NZ like some of the characters that share themselves here? I think I am seeing a trend unfortunately.

[Asok]

following up from the old Nebelwerfer thread

Originally posted by MajorBooBoo:

What do you think of the Neanderthal like math demonstrated in this thread?

I would like to expand a little on the math and describe a technique. This technique would have revealed the “answer” they all sought easily. I will describe it and if needed will post a follow up to clear up any confusion. I am doing this in case there are silent followers of this thread that could learn something. The vociferous elements in this thread are clearly beyond learning anything.

(snip)

Here is the data:

The knowns are:

Speed of Sound 343 m/sec

1372 meters between recievers.

2 second time lag from sound (dr2)

r2=r1+686 meters

exact cartesian coords of recievers

taken as:

"left" reciever will be expressed as origin (0,0)

"right" reciever will be expressed as (1372,0)

(snip 'technique')

Anyone with any education beyond a high school level should have done this way back when Thomm posted the high school solutions. Anyone beyond a BS degree makes me wonder about the education institutions nowadays.

Here's proof you're still as wrong as you've been for the whole time:

two different solutions using your technique

gun location candidate 1 = (1358,1000)

gun location candidate 2 = (1134, 500)

Getting to multiple solutions means that your technique can't find guns. If you want more proof than to different solutions, I'll be glad to supply some.

You would have been a little more convincing, if you had at least tried to take into account that extra LP you just invented. That would have allowed you to save at least some face.

regards,

Asok

[MajorBooBoo]

Originally posted by karch:

At least we all now agree that you need either:

A) 3 listening points finding the enemy by sound delay between listening posts only.

2 listening posts finding the enemy by sound delay between listening posts AND direction of sound.

Is that correct?

You either need delay AND direction for 2 microphones, or 3 microphones to find the location without any direction finding.

Either would work, but I think getting the direction accurately is very difficult. If you were off by 10-30 degrees, your plot could be hundreds of yards off. I agree if you got very good direction finding, 2 points would work.

A slight clarification; you need 3 mics AND a human first line of detection. He must be sufficiently in front of the MIC line to alert the CP to turn the whole deal on. It cannot be left on. If you read through the other thread, it is explained why. You also need some sort of talented computationists to figure out that math. The 2 MIC solution can be done by any high school grad I believe.

[MajorBooBoo]

Originally posted by Asok:

following up from the old Nebelwerfer thread

</font><blockquote>quote:</font><hr />Originally posted by MajorBooBoo:

What do you think of the Neanderthal like math demonstrated in this thread?

I would like to expand a little on the math and describe a technique. This technique would have revealed the “answer” they all sought easily. I will describe it and if needed will post a follow up to clear up any confusion. I am doing this in case there are silent followers of this thread that could learn something. The vociferous elements in this thread are clearly beyond learning anything.

(snip)

Here is the data:

The knowns are:

Speed of Sound 343 m/sec

1372 meters between recievers.

2 second time lag from sound (dr2)

r2=r1+686 meters

exact cartesian coords of recievers

taken as:

"left" reciever will be expressed as origin (0,0)

"right" reciever will be expressed as (1372,0)

(snip 'technique')

Anyone with any education beyond a high school level should have done this way back when Thomm posted the high school solutions. Anyone beyond a BS degree makes me wonder about the education institutions nowadays.

Here's proof you're still as wrong as you've been for the whole time:

two different solutions using your technique

gun location candidate 1 = (1358,1000)

gun location candidate 2 = (1134, 500)

Getting to multiple solutions means that your technique can't find guns. If you want more proof than to different solutions, I'll be glad to supply some.

You would have been a little more convincing, if you had at least tried to take into account that extra LP you just invented. That would have allowed you to save at least some face.

regards,

Asok</font>

[Asok]

Originally posted by MajorBooBoo:

A slight clarification; you need 3 mics AND a human first line of detection. He must be sufficiently in front of the MIC line to alert the CP to turn the whole deal on. It cannot be left on. If you read through the other thread, it is explained why. You also need some sort of talented computationists to figure out that math. The 2 MIC solution can be done by any high school grad I believe.

I have misjudged you; you are capable of learning. Offensive, and a little on the slow side, but capable of learning. Only a few days ago you presented a quite different position on the required CB assets.

Explain again, why I am "really wrong" with the infinite-solutions-to-two-mikes thing, please. I still didn't get your explanation, but that's quite understandable (with my limited English comprehension, not being a 'real' math teacher and all that), isn't it?

regards,

Asok

[Wolfe]

Originally posted by redwolf:

As posted in the other thread, you get two hyperbolas (english for hyperbel?) out of three sound-only observation points. The hyperbolas will cross and that's your battery position after kicking positions behind your lines out.

Sorry if I'm repeating anything from the previous thread. The following applies only to 2D space; for 3D space, I'm pretty sure you need 4 points.

So for 2D space: Don't you get 3 hyperbolas for 3 points (A, B, and C)? You have hyperbolas for A-B, B-C, and A-C. BTW, wouldn't there also be a fourth very complex formula involving A, B, and C simultaneously? But I do believe the 3 hyperbolas solve it for 2D space, regardless.

But one thing that bothers me is if you have all 3 points in a straight line, can you still do it? Or would the hyperbolas overlap so much that you still get multiple possible points? And for 3D space, would all 4 points have to be in separate lines and planes to work?

[Edit: Ignore the rambling below; it's wrong.]

-----------

And one more thing, what if the point you're trying to find is further out than the distance between all of the other listening posts combined? Example: If you take the "easy" 2-listening post setup, you can actually have three different outcomes, depending on where the gun lies. If the sound is heard by both listening posts simultaneously, then the gun lies exactly between the two points, and all the possible locations form a line (in 2D space) or plane (in 3D space) of possibilities. If it's closer to one listening post than the other, but not further away than the distance between the two points, you get a hyperbolic line (2D) or hyperbolic plane (3D). If, however, the gun is further away than the distance between the two points, you actually get a hyperbolic area (2D) or hyperbolic volume (3D) of possibilities with its vertex at the nearer point, which adds an extra dimension of complexity (literally). So even with 4 listening posts in 3D space, you may still be screwed if the sound emanates from a location that is equal to or greater than the combined distances between the 4 listening posts.

Anybody got an aspirin?

- Chris

[ February 18, 2002, 10:02 PM: Message edited by: Wolfe ]

[MajorBooBoo]

Asok

I will make an attempt.. Here goes:

I was demonstrating how someone in the other thread SHOULD have deduced mathematically why I was "wrong". Get it? I was demonstrating a mathematical technique called iteration also. I used the iterative technique to show how I saw the math involved. The math does not converge. It diverges. Read my last Q&A post in the other thread very slowly and see this.

"Here we have the heart of the iterative technique:

1. Guess an R

2. Calculate a X that fits this R from the equation above C. to get a Y value

3. Use that X and Y to solve both of the equations A. and B.

4. Compare the R’s obtained. They will not be the same and a midpoint value chosen between them, Use that as a second guess and go back to step 1. Congrats, you are iterating.

5. If the R converges to a single value, you have a solution. If the R diverges, then the equations cannot be solved via this method. This is a very powerful technique in real world applications. Experience also could have told you that since X and Y are squared, there are a range of solutions. I knew this but wanted to see what discussion/proof would come up.

Anyone with any education beyond a high school level should have done this way back when Thomm posted the high school solutions. Anyone beyond a BS degree makes me wonder about the education institutions nowadays."

Do you see what I am saying? I am NOT saying that it converges and THAT is why it is obvious to me. The missing link is the human as explained also in that Q&A post! The combo of a human AND the easily produced hyperbolas for different time differentials (which are very good) makes the two MIC solution viable.

I also wanted to show that the math is not that involved as people were saying. Given this iterative technique, perhaps I can propose a challenge:

Can the very difficult math for the 3 sensor (one human, have to not forget him), be made easier with this iterative technique?

I cant explain it any more than that.

[ February 18, 2002, 07:33 PM: Message edited by: MajorBooBoo ]

[karch]

Originally posted by MajorBooBoo:

..... I was showing how to mathematically prove that JUST two MICs (without the LP) SHOULD be shown as NOT true and demonstrate a little higher math.

Over your head it would seem. You didnt get it. Someone once said:

It is better to hold ones tongue and be thought a fool then to open it and remove all doubt.[/QB]

You are confusing and more rude than the people you complain about.

Answer me this one question, as you seem to have changed your mind once cornered by facts.

DO YOU BELIEVE YOU CAN PINPOINT A FIRING GUN WITH 2 LISTENING POSTS KNOWING ONLY:

1) DISTANCE BETWEEN LISTENING POSTS

2) SPEED OF SOUND

Yes or No?

[MajorBooBoo]

Originally posted by karch:

Answer me this one question, as you seem to have changed your mind once cornered by facts.

DO YOU BELIEVE YOU CAN PINPOINT A FIRING GUN WITH 2 LISTENING POSTS KNOWING ONLY:

1) DISTANCE BETWEEN LISTENING POSTS

2) SPEED OF SOUND

Yes or No?

You are forgetting the human again. You are calling the sensor points (mics) listening points. How big is a pinpoint? Think about it. How much time to find the pinpoint? Do I want to bombard a pinpoint or a real target full of enemy and weapons?

Do you believe in Fuzzy Logic? yes or No?

[karch]

Yes I believe in fuzzy logic, but you are not answering my question.

You used do believe all you needed was the distance between 2 listening points and the speed of sound...

Originally posted by MajorBooBoo:

.....This person is throwing out the important piece of information about the seperation of the surveyed receptors. This constrainment is vital. Without using it you fall into teh pitfalls that others have been doing here.

use this:

If you have two mikes (x1,y1) and (x2,y2) and a time=distance difference dr12 then you have three equations

r1^2 = (x-x1)^2 + (y-y1)^2

r2^2 = (x-x2)^2 + (y-y2)^2

r2 = r1 + dr12

Use this:

The knowns are:

Speed of Sound

1000 meters between recievers.

404.74 time lag from sound (dr2)

R1=R2-404.74 (or however you make your R's)

exact cartesian coords of recievers

The real starting point is to make a correct diagram.[/QB]

Where is your 3rd reading coming from there.

I will ask this again.

DO YOU BELIEVE YOU CAN -FIND- A FIRING GUN WITH 2 LISTENING POSTS KNOWING ONLY:

1) DISTANCE BETWEEN LISTENING POSTS

2) SPEED OF SOUND

I'll give you a plus or minus 400 yards to find the gun.

Answer my question, I answered yours. And your descriptions are too confusing for me. Make a drawing of the concentric circles you have been talking about. I can't picture them.

[JonS]

Originally posted by karch:

snip: useful diagram

...When I marked the intersection of the appropriate circles and went to connect them with a straight line.... it didn't work. VERY STRANGE. Could someone tell me why.

....

As the distance from the sensors to the target increases, the difference between G-S1 and G-S2 becomes insignificant.

In your diagram you have the following ratios:

700:350 = 2:1

1050:700 = 1.5:1

1400:1050 = 1.333:1

1750:1400 = 1.25:1

As you extend the overall range from the sensors to the gun, the ratio approaches (but doesn't quite reach) 1:1 , in other words, the difference between the lengths becomes negiligable. For example, at 3500:3150 the ratio is 1.111:1 , while at 10350:10000 the ratio is down to 1.035:1

This is why the line segments are not straight lines.

Regards

JonS

aka The Nasty Kiwi

[karch]

Thanks for the answer JonS. I'll take your word for it that that's why it's a curve instead of a line. Still, very interesting.

I think I found the main source of conflict between Major Booboo and Me (and others)

KARCH

You can't find a gun if all you have are 2 listening points, the distance between them and the speed of sound.

BooBoo

Yes you can, (as long as you have angular data).

That is where the argument goes wrong. He did put that third listening point for the person to turn on the recorder and guess the gun's direction. Why not use the same 3rd point and measure the sound difference from there, OR just have one person getting direction from either listening point A or B. It will give you the same result. It will be horribly innacurate because of the difficulty in gauging direction, but it will be the same with 2 points or 3.

Once you put in the third person, you seem to have changed your argument. I've been saying for pages you can locate a gun with 2 listening points and a direction... one or two. My point that you seem to keep arguing against is that you can't find the location knowing only the distance between listening points, the sound deleay of the report between them, and the speed of sound.

All you have EVER had to do is AGREE that is true. You need more information, either angular or another microphone.

Did you misunderstand all of our drawings or did you change your answer mid-arguement.

And for someone harping on graphs and charts, you haven't posted one yourself yet.

And would you lay off the rude remarks. Stick to descriptions and drawings.