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During the Klingon Civil War Starfleet erected with 23 starships a tachyon detection grid at the Klingon-Romulan border, preventing a convoy of Romulan supply ships from sending further aid to the forces loyal to the House of Duras.
In the TNG episode "Preemptive Strike" Kalita explained to Ro Laren about the border at the Demilitarized Zone between the United Federation of Planets and the Cardassian Union: "There are sensor buoys all along the border. If we cross anywhere other than a checkpoint, Starfleet will send a ship to investigate."

And in the TNG episode "Redemption", a Romulan captain explained to Troi, disguised as a Tal Shiar agent: "The cloaking device does not always make us invulnerable, and you would know that if you had spent any time at all in the field. The Federation has littered it's borders with subspace listening posts, with gravitic sensors. They may even have a tachyon detection grid in operation, in which case they will know that we're there."

What would be necessary to litter the several light-years squared border at the Romulan Neutral Zone with subspace listening posts and sensor buoys to erect a grid dense enough that there is a high probability that a ship trying to cross the border gets detected?

How many buoys would be necessary?

And what do you think, are the "gravitic sensors" doing?

The issue I always had with the Tachyon detection grid was how two-dimensional it was. Why didn't the Romulans just go around it? To properly secure 3-dimensional space you would need lots of buoys, even if they had a range measured in lightyears.

That diagram of the grid shows a three-dimensional polyhedron. Does it only detect ships that fly through the grid? Because looking at a shape like that I'd expect it to be the equivalent of a 'very large array,' designed to watch effectively in all directions.

Also, the question of how many outposts are needed depends entirely on how long the detection range of the systems is. As a hypothetical...

If the buoy's sensor radius a light-day (~26 billion kilometers, able to detect objects four times as far away as the orbit of Pluto), then to cover one square light-year of border would require... Let's see, 365 light-days on a side, squared, is about 130 thousand square light-days; a sensor system one light-day in radius effect would cover 3.14 square light-days of that space, subtract a little for overlap at the fringes of sensor coverage and I'd figure on needing, oh, 44000 or 45000 sensor posts per square light-year, for a boarder that could easily be many thousands of square light-years.

Note that this 26 billion kilometer detection radius translates to about one minute's flying time at high warp.

Doubling the detection radius will reduce the required number of detectors by a factor of four- by a factor of eight if you have multiple layers of detectors stacked up 'in depth' for redundancy and to provide a longer window of detection.

Conversely, halving the detection radius will increase the required number of detectors by a factor of four (or eight). There's a square (or cube) law in effect.

Borgholio wrote:The issue I always had with the Tachyon detection grid was how two-dimensional it was. Why didn't the Romulans just go around it? To properly secure 3-dimensional space you would need lots of buoys, even if they had a range measured in lightyears.

I don't know how long the range is, but if it's long enough you'd get to the point where you could handwave this by saying they can detect ships at longer range above and below the galactic plane (since there is less interference from other phenomena), with each buoy covering a volume closer to a cylinder than a sphere.

Grumman wrote:

Borgholio wrote:The issue I always had with the Tachyon detection grid was how two-dimensional it was. Why didn't the Romulans just go around it? To properly secure 3-dimensional space you would need lots of buoys, even if they had a range measured in lightyears.

I don't know how long the range is, but if it's long enough you'd get to the point where you could handwave this by saying they can detect ships at longer range above and below the galactic plane (since there is less interference from other phenomena), with each buoy covering a volume closer to a cylinder than a sphere.

Oh indeed, but it would have to be an exceedingly long range. As Simon pointed out, you would need an absurd number of buoys or sensor platforms if the range was anything less than a full lightyear per device. It could very well be plausible to spend a week at warp going up and over the border detection grid if it means you can get a fleet of warbirds into Federation space without being detected.

Simon_Jester wrote:That diagram of the grid shows a three-dimensional polyhedron. Does it only detect ships that fly through the grid? Because looking at a shape like that I'd expect it to be the equivalent of a 'very large array,' designed to watch effectively in all directions.

Also, the question of how many outposts are needed depends entirely on how long the detection range of the systems is. As a hypothetical...

If the buoy's sensor radius a light-day (~26 billion kilometers, able to detect objects four times as far away as the orbit of Pluto), then to cover one square light-year of border would require... Let's see, 365 light-days on a side, squared, is about 130 thousand square light-days; a sensor system one light-day in radius effect would cover 3.14 square light-days of that space, subtract a little for overlap at the fringes of sensor coverage and I'd figure on needing, oh, 44000 or 45000 sensor posts per square light-year, for a boarder that could easily be many thousands of square light-years.

Note that this 26 billion kilometer detection radius translates to about one minute's flying time at high warp.

Doubling the detection radius will reduce the required number of detectors by a factor of four- by a factor of eight if you have multiple layers of detectors stacked up 'in depth' for redundancy and to provide a longer window of detection.

Conversely, halving the detection radius will increase the required number of detectors by a factor of four (or eight). There's a square (or cube) law in effect.

My impression was that it is not primarily a question of sensor range as there are needed two points (ship, post or buoy) between which a tachyon beam can be projected. A ship is detected when is crosses the tachyon beam projected between the two points (ship, post or buoy) as it interrupts the tachyon beam.

• • • • Or as Picard explained it: "My Chief Engineer has developed a system that should nullify that advantage. Each ship will send out an active tachyon beam to the other blockading ships. Now, in theory, any cloaked vessel that attempts to pass between our ships must cross that beam and be detected."

It seems necessary to have enough points (buoys) to have a grid with enough grid-lines evenly distributed that there aren't huge gaps between them.

If you take a square-light-year and distribute buoys with a distance of a light-day from each other (365 x 365 = 133.225 buoys) and connect each buoy with a tachyon beam with each other buoy, you get a nice tachyon grid. But would it be dense enough that it is improbably that a ship can slip through it without interrupting such a tachyon beam?

If it is 1.000 square-lights, the amount of buoys - each still with a distance of a light-day from each other - would be greater (365.000 x 365.000 = 133.225.000.000 buoys), the beams that are connecting each buoy with all other buoys would increase accordingly. But would the grid be dense enough that it is improbably that a ship can slip through it without interrupting such a tachyon beam?

With that it isn't even considered that each buoy would need as many tachyon emitters and tachyon receivers as there are other bouys. As this seems impossible as the surface of each bouy is limited, it has to be impossible that each bouy can be connected with each other buoy. This reduces the amount of grid lines. To compensate for this, one would need more buoys to increase the density of the grid again to a level that it is improbably that a ship can slip through the grid without interrupting a tachyon beam.

It may be that tachyon emitters are like phased array radars- which can emit numerous beams from a single antenna. And tachyon detectors may be like cosmic ray particle detectors- which do not need to be specifically aimed at their target; one detector can spot numerous kinds of particles hitting from numerous directions and accurately track which way each particle came in.
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Replying to some of the others...

Ahem: note that you do NOT distribute buoys on a square grid, because space does not consist of 'tiles' from an RTS game. If buoys are spaced in a square grid and their sensor coverage only reaches halfway to the next buoy along a direct line, there's a big gap in the center of each 'square' of buoys. You can of course cover that gap with another buoy, but at that point you have effectively doubled the total number of buoys required in your network, and that may not be the most efficient arrangement.

So you actually want to arrange the buoys so that the spheres of detection they support will form a packing something like this. Unfortunately I'm having trouble researching "what is the smallest number of circles you can use to do this." As a question it seems to be less popular than the question "what is the most non-overlapping circles you can fit in a rectangle," which in our case would be useless because we want NO gaps and therefore must accept overlap.

Above I estimated needing ~45000 buoys to provide sufficient overlap (each buoy having a detection radius of one light-day, and thus covering a circle one light-day in radius and pi square light-days in area). It might be more like 50000 or even 55000, again assuming detection radius, not spacing of one light-day.

Given roughly fifty thousand buoys, even if you arranged the buoys over a one square light year area chaotically so that every buoy had direct line of sight to every other buoy and there were beams connecting all of them, there would be roughly the square of the total number of buoys, divided by two- about 1.25 billion beams. If each beam is, say, a kilometer wide, then the total cross-sectional area of an average beam from the point of view of a passing Romulan ship is... one kilometer, times the average length of the beam. The average length of a beam between two random points on a square one unit in side length is about 0.52 units, as proven here (yay calculus!)

Therefore you have 1.25 billion beams, 0.52 light-days long on average (that is, about 13.5 billion kilometers long), and one kilometer wide. Total beam area is about 1.6*10^19 square kilometers. From the point of view of a cloaked Romulan warbird, this grid of Federation buoys covers the light-year of area with 16 billion billions square kilometers of beams that have to be avoided. The problem is that a square light-year covers roughly 90 million billion billions of square kilometers of emptiness... space is, to quote the great man, big.

So your chances of being detected by flying through the beams is roughly 16 out of 90 million.

Note that this probability is VASTLY reduced if the Federation spaces their buoys in a regular geometric grid, because then you have multiple beams between multiple buoys that follow the same path, while leaving larger amounts of empty space.

It is also VASTLY reduced if a Federation sensor buoy is not capable of maintaining tachyon beam locks on, oh, 37000 of its nearest neighbors within a light-year, and has to settle for smaller numbers of beams. Then you get a much sparser and more threadbare grid... and the existing grid had about a one in six million chance of working as it was.

It is VASTLY increased, though, if the tachyon beam is sensitive to ships passing near the beam (in cosmic terms), rather than being like one of those laser tripwires you have to cross directly. For example, if each beam is interrupted whenever a cloaked vessel passes within a million kilometers, each beam is effectively two million kilometers 'wide' rather than one kilometer 'wide.' The probability of detection for the Romulan ship stops being a lousy 16 out of 90000000, and becomes an actually rather respectable 16000000 out of 90000000

[If anyone has any questions about any of the math I just did, I have just gotten on spring break and there is almost nothing I would enjoy more on this website than to explain myself. Everything I did personally is within reach of any middle school graduate who paid attention; the calculus proof on the site I linked is harder but still doable with sufficient explanation]

Simon_Jester wrote:It may be that tachyon emitters are like phased array radars- which can emit numerous beams from a single antenna. And tachyon detectors may be like cosmic ray particle detectors- which do not need to be specifically aimed at their target; one detector can spot numerous kinds of particles hitting from numerous directions and accurately track which way each particle came in.

That sounds plausible.

Simon_Jester wrote:[...]It is VASTLY increased, though, if the tachyon beam is sensitive to ships passing near the beam (in cosmic terms), rather than being like one of those laser tripwires you have to cross directly. For example, if each beam is interrupted whenever a cloaked vessel passes within a million kilometers, each beam is effectively two million kilometers 'wide' rather than one kilometer 'wide.' The probability of detection for the Romulan ship stops being a lousy 16 out of 90000000, and becomes an actually rather respectable 16000000 out of 90000000

How could that work?

How could the tachyon receiver on a buoy notice that a ship merely flies in the vicinity of a beam projected at it if the beam is not interrupted by the ship?

WATCH-MAN wrote:How could the tachyon receiver on a buoy notice that a ship merely flies in the vicinity of a beam projected at it if the beam is not interrupted by the ship?

If the beam acts as an "antenna" sensitive to the local disturbances along its length by measuring the distortion from the baseline uninterupted path of the beam - presto!

The tachyon beam may be perturbed by some influence that extends beyond the hull of the ship- an influence that may or may not be caused by the claoking field.

For example, warp drive fields might very well distort or interfere with tachyons, so that a ship traveling at warp in the vicinity of a tachyon beam will distort that beam, regardless of whether you cloak it or not.

That's just off the top of my head.

WATCH-MAN wrote: And what do you think, are the "gravitic sensors" doing?

Something that detects gravity fields, small enough of those emanating from something the size of a ship. A cloaked ship still has mass.

So you actually want to arrange the buoys so that the spheres of detection they support will form a packing something like this. Unfortunately I'm having trouble researching "what is the smallest number of circles you can use to do this." As a question it seems to be less popular than the question "what is the most non-overlapping circles you can fit in a rectangle," which in our case would be useless because we want NO gaps and therefore must accept overlap.

Actually gaps might not be a problem. If the buoys have a spherical detection radius and you arrange them in a 3-dimensional pattern so that there is minimal overlap, it is true there would be a great deal of empty space in the center. But there are two reasons why this isn't an issue. First, you'd need to pass through the detection radius of at least one buoy to GET to the empty space to begin with. Then when leaving the empty space you'd have to risk detection a second time. If you manage to sneak in but can't sneak out, you're bottled up until a Federation ship comes to investigate.

Secondly, if it becomes imperative that the gaps be as small as possible, you can still plant a smaller buoy in the center of the empty space and reduce the "safe" space to a sliver that would greatly reduce how much the cloaked ship can maneuver without being seen.

Khaat wrote:

WATCH-MAN wrote:How could the tachyon receiver on a buoy notice that a ship merely flies in the vicinity of a beam projected at it if the beam is not interrupted by the ship?

If the beam acts as an "antenna" sensitive to the local disturbances along its length by measuring the distortion from the baseline uninterupted path of the beam - presto!

Simon_Jester wrote:The tachyon beam may be perturbed by some influence that extends beyond the hull of the ship- an influence that may or may not be caused by the claoking field.

For example, warp drive fields might very well distort or interfere with tachyons, so that a ship traveling at warp in the vicinity of a tachyon beam will distort that beam, regardless of whether you cloak it or not.

That's just off the top of my head.

Okay - something like gravity or space bending warp fields emanating from the cloaked ship changes the path of the tachyon beam. That seems to me possible / plausible. And if the tachyon beam can be influenced that way, one only has to consider all known sources of influence (celestial bodies, matter, radiation e.t.c.) and look what path-changes can't be explained by those. And if there are changes in the tachyon beam that can't be explained, one knows that there has to be some unknown cause - probably a cloaked ship.

Prometheus Unbound wrote:

WATCH-MAN wrote: And what do you think, are the "gravitic sensors" doing?

Something that detects gravity fields, small enough of those emanating from something the size of a ship. A cloaked ship still has mass.

Of course does even a cloaked ship has mass. But as this mass is - compared to the mass of celestial bodies - nearly infinite small and gravitation propagates only with light-speed whereas ships are flying with speed faster than light, you have to have again a really dense grid of such "gravitic sensors". If the distance between the sensor and the cloaked ship is to big, the sensor may not be able any more to differentiate between the gravity emanating from all the celestial bodies and a cloaked ship. And if the distance between a sensor and a ship it to big, the sensor would receive any changes in the gravitation field caused by the ship only after the ship has crossed the border. If the distance between the ship and the sensor is e.g. one day-light, the sensor would detect any changes in the gravitation field only after one day - while the ship is flying with warp to wherever it wants to go.

How do you imagine such "gravitic sensors" to work?

How sensitive do they have to be to be able to detect the difference in the gravitation field caused by a ship that is flying between all those celestial bodies?

And how many of those "gravitic sensors" would be necessary to cover a several light year long and broad border?

They use subspace sensors to get the info straight away magic subspace

Borgholio wrote:

So you actually want to arrange the buoys so that the spheres of detection they support will form a packing something like this. Unfortunately I'm having trouble researching "what is the smallest number of circles you can use to do this." As a question it seems to be less popular than the question "what is the most non-overlapping circles you can fit in a rectangle," which in our case would be useless because we want NO gaps and therefore must accept overlap.

Actually gaps might not be a problem. If the buoys have a spherical detection radius and you arrange them in a 3-dimensional pattern so that there is minimal overlap, it is true there would be a great deal of empty space in the center. But there are two reasons why this isn't an issue. First, you'd need to pass through the detection radius of at least one buoy to GET to the empty space to begin with. Then when leaving the empty space you'd have to risk detection a second time. If you manage to sneak in but can't sneak out, you're bottled up until a Federation ship comes to investigate.

You're misunderstanding. I'm talking about creating one layer of detection, of trying to ensure that every ship passes a detector at least once. Thus, the layer is in effect two-dimensional, although it occupies 3D space.

If you have twice the required number of detectors you'd create two such layers, one behind the other; this serves several valuable functions.

Secondly, if it becomes imperative that the gaps be as small as possible, you can still plant a smaller buoy in the center of the empty space and reduce the "safe" space to a sliver that would greatly reduce how much the cloaked ship can maneuver without being seen.

Smaller buoys may not be much cheaper than full-sized ones, especially if maintenance costs are factored in when you're busy tending all these little automatic platforms floating in space.

WATCH-MAN wrote:How do you imagine such "gravitic sensors" to work?

How sensitive do they have to be to be able to detect the difference in the gravitation field caused by a ship that is flying between all those celestial bodies?

And how many of those "gravitic sensors" would be necessary to cover a several light year long and broad border?

Star Trek has a variety of sensors that, however they work, clearly propagate at FTL speeds (because they can, for instance, give you a clear picture on the viewscreem of an object that is moving FTL, not only relative to normal space but relative to you). Some of them appear to be sensors devoted to detecting normal things like light and particles.

I see no reason they wouldn't also be able to detect gravitational distortions in real time over a wide area; it's no more scientifically problematic than any number of other systems aboard the ship. Which makes the question 'how do you think they work' kind of silly, since it's not like we know how the transporters work.

Also- remember, the warp drive is implicitly a distortion of space time (which is what gravity is). By definition, it is an effect that propagates faster than life. There is no reason to assume that other distortions of time and space cannot be entangled with or interacted with from a distance via faster than light mechanisms, at least in the context of Star Trek physics.

I wonder if the detection network is "there's no way of getting thru this without getting detected" or "It's too much effort/risk to get thru this compared to the gains I would get from it for it to be worth it"(like modern day burgular alarms)?

We know that pre-nemesis cloaks weren't perfect just very, very hard to detect and we know from the TNG episode with Troi as an Romulan ("Face of the Enemy" I think) that the cloak on Warbirds "leak" when at warp and that causes limits as to how high warp factor the Warbirds can go and still maintain the cloak effectively.

So it's possible that while it's possible for the Romulans to go around the detection grid in theory. It's too much effort or too risky to attempt that in practice, after all there's only so many Warbirds that can "get lost" and end up in Federation space before UFP either beefs up the security to make even harder to get past or starts to consider it an act of war and that's assuming they're in Federation space when they get detected and not for example in Klingon space.

if you didn't get it that "get lost" part refer to the cases where Russian fighters "got lost" in finnish air space, but do so frequently that it's clear they were sent into finnish air space on purpose and by mistake.

If I were the Romulans, what I'd do is to send very obvious and uncloaked science ships near the border, and have them conduct "legitimate" sensor scans/probes. I'd keep that up until the Federation basically gets used to it, that way, I could just send a cloaked ship along with one of these science vessels, if I ever wanted to get a ship through.

I wonder hod difficult it would be to alter the course of an asteroid with similar mass to a starship, and how feasible it would be to basically disguise a starship as an asteroid, (given how sensors can sometimes be blocked by various naturally occurring minerals).

An asteroid wouldn't be moving at faster than light speeds, so it wouldn't cross the border in a tactically useful amount of time.

The Romulans sending science ships is all very well except that the treaty rules feature a neutral zone; there is a broad space that neither side is supposed to put ships in without an unusual justification for doing so. Routine science ship missions would have to stay on the Romulan side of the neutral zone, and could not effectively cover for cloaked ships crossing the Federation side of the zone.

Do they ever portray 3rd party merchants/traders that deal with both the Federation and the Romulans, (or on both sides of the Neutral Zone, at least)?

If there are such merchants, they probably operate under very close supervision by both sides, crossing the Neutral Zone only at specific points, just as there are very few places where you can cross the DMZ into North Korea.

Also because some of those merchants are probably Ferengi and who wouldn't keep a close eye on Ferengi?

Another thing to consider is that, if fast warp is more easily detected than slow warp, then forcing someone to crawl though the sensor grid at a snails pace can be a mission kill even if they are never detected. More time to be detected by other means, more time for things to go wrong, more time for the target of interest to just wander away.

We should remember that the UFP/RSE Neutral zone has existed since the 2160s meaning it's been monitored for over 200 years at most distant part of the canon Prime-timeline (at ST Nemesis) so there's been more then enough time for UFP and RSE to fine tune their sensors to not give exessive amounts of "false positives".

After all we shouldn't assume "they're stupid and didn't think of this" as default when we see an simple counter to something, but rather we should first assume that there is a counter to that tactic we've not seen unless there's a reason to assume otherwise.

Don't forget there were all those outposts along the Neutral Zone designed to detect Romulan incursions. Well until the Borg scooped them up anyways (was it ever mentioned whether or not those outposts were rebuilt?) IMO it's plausible that a planet-grade sensor system would be able to detect ships far greater range than a set of buoys, which is why we don't see hundreds of thousands of buoys along the border. Plus, there are usually ships on patrol too. IIRC the tachyon grid was an ad-hoc thing that the E-D cooked up since there wasn't any detection equipment along the Klingon-Romulan border that the Feds had access to.

Also, the Cardassians were inferior to the Feds tech wise and didn't have cloaking tech so a sensor buoy network would have been sufficient to detect any ships going into the DMZ. All they'd have to do is detect a warp signature, and most sensors can easily do that from light years away.

The Cardies not having cloaks doesn't change the problem that any border large enough they can't just go around it is going to require either a ridiculous number of sensor installations or pretty damned impressive sensor range (which admittedly seems to be all over the place).
While I think S-J was being conservative WRT sensor range, I think he was also being so WRT the expanse of the border (both, I very much assume, on purpose).
A square 1000 ly border would only be 32 ly a side. Even at VOY's 'we can keep this up forever despite investigating every anomaly of the week and going out of our way to piss off the natives' 1,000c, that's about a one week detour to get around,
Given the required number of sensor installations in S_J's scenario is already absurd, imagine what it would look like for a border you really 'can't just go around in a realistic timeframe.