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 Forum index » Archive » Archive: Perplex City » PXC: General/Updates
[UPDATE] - Operation Bayonet - Triangulating radio messages
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jonc
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Joined: 04 Jul 2006
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[UPDATE] - Operation Bayonet - Triangulating radio messages
Another Puzzle...

There has just been an update to the OB site:


Quote:
Identifying and triangulating radio messages (current)

We now know that the Third Power are based in Ascendancy Point, the city's tallest building with over 170 triple-height floors and tens of thousands of occupants, but we do not have access to their surveillance systems. Instead, we must pinpoint their location with Ascendancy Point by other means.

While Third Power messages from Earth to Ascendancy Point are being sent via Relaynet, the opposite is not true. Rather, Police have intercepted encrypted radio transmissions coming from within the Tower, presumably to the Centre for Reality Research. This is what we know:

1. Four receivers stationed on top of skyscrapers near Ascendancy Point have intercepted the radio transmissions. This diagram shows the exact altitude of each receiver as well as the distance between any pair of the receivers (straight-line distance in 3D-space).

2. Furthermore, using advanced ranging technology, we have determined the distance between each receiver and the originating source of the encrypted transmissions:




* Receiver 1: 646.12m from source
* Receiver 2: 1548.28m
* Receiver 3: 1249.19m
* Receiver 4: 1267.62m

We need to discover where in Ascendancy Point the Third Power is transmitting from. This should not be too difficult to calculate, but all members of Operation Bayonet are at full capacity. Again, we require your assistance to discover the source of the Third Power's radio transmissions. Please liaise with Kurt McAllister.


http://www.perplexcitypolice.com/case_notes.php?cid=PXC978C675&section=OB

PostPosted: Thu Jan 25, 2007 12:50 pm
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Scott
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I've got an exact location pinpointed. but the location is sort of an abstract set of coordinates, about 1050 meters off the ground. I'm putting together a nice set of diagrams showing the nature of the source.
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PostPosted: Thu Jan 25, 2007 2:24 pm
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jonc
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If anyone's interested:

https://addons.mozilla.org/firefox/920/

That's quite useful for checking pages, especially if they are pages without an associated RSS feed.

PostPosted: Thu Jan 25, 2007 2:31 pm
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Scott
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okay, I've got a diagram established, i'll send it off to kurt.

The signal might be be coming fFrom some sort of signalling dish or something, and is between 1010 meters and 1110 meters off the ground.
Drawing2-.8 x 11.jpg
 Description   operation bayonet signal
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Drawing2-.8 x 11.jpg

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PostPosted: Thu Jan 25, 2007 2:38 pm
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bit1313
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Scott - I have been working on this with my limited math skills.

Let me ask you a question.. are you assuming that the distance between rec 1 and 3 divided in half is the center of Ascendacy Point? (i.e. 1892.41/2 = 946.205)????

I have tried all sorts of triangle calc (even to the point of realizing that the distance between Rec1 and Rec3 at 1892.41 is based on the two altitudes and not a "straight shot".

Can help those of us that are math challenged understand?

Thanks!

bit1313

PostPosted: Thu Jan 25, 2007 3:06 pm
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Scott
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I did not assuming anything about the location of ascendancy point. I thought it would be a little more central to the receivers, but actually no, it is not at all. The lines drawn on the map do not represent the actual data in any way.

I started by setting rec1 at 0,0,1200 then worked out rec4 and rec2 in relation to that. easy enough, since i didn't need to know angles yet. Then I placed rec3 in relation to rec4. Again, easy enough. Next I needed to do the hard part. Rotate rec2 around an axis defined by rec1, so it meets the correct distance fFrom rec4. This involved 3 arcs which i'm not sure can be described easily. his gave me the correct locations of rec1, rec2, and rec4. I could then place rec3 using the same 3 arc technique. Lastly, I made 4 large spheres and determined where they meet.
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PostPosted: Thu Jan 25, 2007 3:17 pm
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xnbomb
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Cosines of the times

Scott wrote:
Lastly, I made 4 large spheres and determined where they meet.

I like this puzzle a lot, particularly because this is exactly how the global positioning system determines the location of a receiver. There is a goodly amount of trigonometry involved, and it hardly ever gets done by hand in operational contexts. You only absolutely need three spheres to get an intersection at a point (when all else is working perfectly, which is to say that the length of time the signal takes to get from the transmitter to receiver is not modified by atmospheric interference, reflections etc.), and the fourth is really there for insurance. I'm hoping that given the very short distances and advanced technology involved that this is an ideal case, and the solution is at a point Very Happy .

EDIT: Hmm, what I stated above is not quite true. Three spheres intersect at two points. This is usually sufficient for a solution in the context of using a consumer GPS because only one those points is typically anywhere near where the surface of the Earth is known to be located. You do need four spheres to intersect at a single point.
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PostPosted: Thu Jan 25, 2007 3:52 pm
Last edited by xnbomb on Thu Jan 25, 2007 4:42 pm; edited 1 time in total
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Scott
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Re: Cosines of the times

xnbomb wrote:
I'm hoping that given the very short distances and advanced technology involved that this is an ideal case, and the solution is at a point Very Happy .
That would be cool, wouldn't it? Sadly, no, the volume of the source is 8277.6 cubic meters. The good news is, we mainly need a height, so we can mostly discard the width and depth of the area. We know the fFloors of the building are "triple-height", whatever that means. So we simply have to narrow the point down to a dozen meters or so. But the height I've come up with is about 100 meters tall. I've checked and rechecked my measurements, and my diagram is exactly right given the dimensions we have. So taking the middle of the area, (which looks rather waferish) I come up with about 1065 meters off the ground.
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PostPosted: Thu Jan 25, 2007 4:14 pm
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DarkHuman
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a floor is 10feet. triple that is 30 feet (10 meters) you got 1065 M. and the building has 170 floors. so the 106th and 1/2 floor Very Happy
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PostPosted: Thu Jan 25, 2007 4:25 pm
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Macavity
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So, has anyone emailed Kurt yet?

If not, I'll do it.
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PostPosted: Thu Jan 25, 2007 4:46 pm
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jonc
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Just trying to understand the "volume" that you've generated.

How did you generate the volume? Are you presuming that there is some error +/- 0.01

Otherwise, surely with 4 spheres we would get a plane or a point, not a volume.

(gets out pen and paper + SOH CAH TOA Smile )


jonc

PostPosted: Thu Jan 25, 2007 4:54 pm
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Scott
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if you look at my attachment above, in the upper left hand corner of the diagram is the shape of 4 spheres intersecting, labeled "Signal Shape". it is a 4 sided object in which each side and each edges curves. some more than others. it is a very thin wafer of space. it would be a much smaller location area if Rec1's distance were something slightly less than 646.12.
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PostPosted: Thu Jan 25, 2007 5:20 pm
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Mikeyj
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DarkHuman wrote:
a floor is 10feet. triple that is 30 feet (10 meters) you got 1065 M. and the building has 170 floors. so the 106th and 1/2 floor Very Happy


Does the half floor make sense? At first I thought it did, being on a table or a wall, but as these are triple-height 15 foot is quite a big table. I'm imagining a Tintin-esque Eiffel Tower-alike transmitter...but maybe that's just me. That should be quite easy to spot, right?

Why is maths so effortlessly impressive to those of us who have no idea? Congratulations Scott Smile I don't know why it's right, but your diagrams are lovely. They'd make a nice geeky T-shirt. Smile
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PostPosted: Fri Jan 26, 2007 5:13 am
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cjr22
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Exact answer?

I've gone through the maths myself, and I get an exact point rather than a area, at a height of 1111 meters.

I used 0,0,600 as the location of rec4, and then used the rec3-rec4 line as the y axis (putting rec3 at 0,1269,800), this game me a location of

1000,588,1111

for the transmitter. I've sent an email to Kurt. I can attach the python code I used if anyone is interested.

PostPosted: Fri Jan 26, 2007 7:48 am
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Scott
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hm, interesting. Well I'm completely certain my rec points are right. I'm supposing my method of fFinding the intersection of spheres is insufficient. I'll take my humility and contemplate the matter.
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Balance of Powers is a game whose only rule is: There must be a political party.


PostPosted: Fri Jan 26, 2007 12:31 pm
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