The mathematics of roving searches

[ColonelSandersLite]

Originally Posted by Crannogman

I think you're missing the fact that figures 1 and 2 show the same thing...

It was late and I was exhausted. I shouldn't have been doing any critical thinking then, much less publicly saying the result of said thinking. So disregard the previous. Just a short time beforehand, I had been doing some thinking on an example where you have an idea that a specific target will be transiting an area and know it's general parameters. In that case, we *can* improve the odds of detection by also adding in an element of the targets course to our own. Still, this isn't quite what I was actually replying to. Oops.

Originally Posted by Rockin Robbins

You can do all the right things and still lose. It's fundamental game theory. ...The reason was his strategy: search the maximum number of square miles per day consistent with your mission.

It requires your "beautiful" vector subtraction of an unknown target running an unknown speed at an unknown heading. That, sir, is black magic. Your theory is based on a fallacy: that you can know the course and speed of your enemy before you ever encounter him.... You're a card counter at a blackjack table.

You misunderstand. At no point are we assuming that we know the targets speed, location, or exact heading. We're discussing game theory and probability. Card counting as you put it. This isn't in any way about knowing what the target is doing. It is specifically about understanding how what we are doing interacts with what the target is doing and how it changes the odds. If you look at fig 2 above, we don't need to know the targets actual speed. We understand that if he is moving faster, the angles widen, giving decreased relative coverage. If he is moving slower, the angles narrow, giving increased relative coverage. Again, we don't need to know his speed, we're only working to understand the odds and how to play them.

We can make reasoned generalizations about the traffic direction in an area. We can also generalize speeds by saying that almost all merchants are doing 10 knots or less. This isn't black magic. Not unless you consider understanding the probabilities of your tactical situation such anyways.

[Rockin Robbins]

No, you're right. We have to simultaneously prepare for the sensible and for chaos. Most of the time we have mutually exclusive choices with advantages and disadvantages for each choice. Running a submarine is hell. So many ways to make wrong choices while trying to manipulate the odds in your favor. It's like fishing where science, superstition and guesswork play equal and often indistinguishable roles.

[TorpX]

Originally Posted by Crannogman

I think you're missing the fact that figures 1 and 2 show the same thing - the sub is going due East & West in both, and the ships are traveling North-South. The change is this: in Fig1, the "camera" is hovering above the same spot on the earth. In Fig2, the "camera" is hovering above the same ship. Everything else in unchanged. The sub only appears to have a northward cant because the frame of reference is moving south. To a ship moving south, the same sub would appear to have a southward cant.
It's an exercise in relativity. The reason to use the ship's frame of reference is to visually display the area searched by the sub and the areas to which the sub is blind. Fig3 demonstrates that, as the speed of the sub increases relative to the speed of the ship, the gaps in its search pattern shrink until there is noplace to hide

Yes. This is exactly right.

Originally Posted by Rockin Robbins

You can do all the right things and still lose. It's fundamental game theory. Fluckey was by far the most successful captain of his era of the war. The reason was his strategy: search the maximum number of square miles per day consistent with your mission. Could he search and come up empty? Sure. Was his strategy totally valid? Look at his results. Look at the results of all other boats working in his time frame. What was the difference? Search methods.

Yes, he did very well, but O'Kane also did very well. Flucky's success was also due to his willingness to hunt in shoal waters, that other skippers avoided.

Originally Posted by ColonelSandersLite

You misunderstand. At no point are we assuming that we know the targets speed, location, or exact heading. We're discussing game theory and probability. Card counting as you put it. This isn't in any way about knowing what the target is doing. It is specifically about understanding how what we are doing interacts with what the target is doing and how it changes the odds. If you look at fig 2 above, we don't need to know the targets actual speed. We understand that if he is moving faster, the angles widen, giving decreased relative coverage. If he is moving slower, the angles narrow, giving increased relative coverage. Again, we don't need to know his speed, we're only working to understand the odds and how to play them.

We can make reasoned generalizations about the traffic direction in an area. We can also generalize speeds by saying that almost all merchants are doing 10 knots or less. This isn't black magic. Not unless you consider understanding the probabilities of your tactical situation such anyways.

This is also correct.







The point to the OP is not for me to convert everyone from patrolling in their favorite way, to patrolling in my favorite way, but rather to provide some kind of objective guideline for players (especially newer ones), who may not want to do the geometry.



A while ago, I was watching one of the 'Let's Play...' videos about SH4 (not anyone here). The author sailed from base to patrol area, and another area, burning through a lot of fuel at high TC. He seemed genuinely surprised and frustrated that he didn't find anything before having to find a place to refuel. As far as he knew, he was doing what he was supposed to, going to an enemy controlled sea, looking around, then going to another, and another... Most experienced SH players develop an intuitive understanding of good patrol practice, even if they can't follow all the math. They would not have made such a mistake. New, or casual, players may be in the dark about this.

Originally Posted by ColonelSandersLite

The actual math on this sort of thing was probably worked out a *long* time ago due to how pertinent this thinking is to every navy on the planet. The thing is that I have no idea where to find the information.

You know, you're right. They had to know this. Perhaps they didn't put it in all the usual manuals because they considered it elementary.





Oh, and the link should work now. I changed to a different table to make clear I was using Vu for sub speed, Vt for target speed, etc.

[ColonelSandersLite]

Originally Posted by TorpX

You know, you're right. They had to know this. Perhaps they didn't put it in all the usual manuals because they considered it elementary.

Well, a couple of things occur to me.

First, it's not really a particularly romantic subject. Sure, everyone likes looking at battle tactics, but the mundane details of how to steer the ship aren't particularly sought after information in general.

Second, it's not particularly useful information outside of a martial context. In the civil world, rendezvouses at sea aren't really commonly done and when they are both parties are probably willing to openly communicate with each other. The closest common concern that I can think of in the civil world would be potential search and rescue operations and buoys and such. The theory there is pretty different though, since in that case you're trying to find something that's either stationary or drifting.

[CaptBones]

The most enjoyable part, so far, was...

"Gotta agree here. The actual math on this sort of thing was probably worked out a *long* time ago due to how pertinent this thinking is to every navy on the planet. The thing is that I have no idea where to find the information. I can most likely find the answer for myself more easily than I can research it."

Quite right…WRT the real world, the math in this thread isn’t entirely complete, but it is very much on target, since the solutions in real life are based on vector analysis. None of the naval commanders in the USN during WWII (including O'Kane and Fluckey) had to make things up entirely on their own; there was a large knowledge base available from the pre-war "Battle Problems", in which the submarine force was used almost exclusively for scouting, searching and patrolling large open ocean areas. Following the war, specific methods for search, patrol and detection, became part of the tactical doctrine for USN and NATO navies that is (or at least was) in ATP-1 (Allied Tactical Publication) and other ATP series books, as well as NTP (Naval Tactical Publication) series books. Of course, they are all classified; at least CONFIDENTIAL and most at SECRET level. Another problem is that almost all of the doctrine used since WWII is based on using aircraft to conduct large open ocean area searches. Oh, well...

The fundamentals are all part of the science of Operational Research/Operations Analysis, going back at least as far as the late 19th/early 20th Century. OR/OA became a recognized science during and after WWII and is an essential element of Military Science today. If you want a more thorough discussion of the real world math and real world sensors, much of the fundamental theories and math is openly available. You might consider getting and studying “Naval Operations Analysis” and “Principles of Naval Weapons Systems”, both from U.S. Naval Institute Press. I rummaged through an old Cruise Box ("Sea Chest" to some) of mine and found a copy of OEG Report 56, "Search and Screening" and some big 3-ring binders with hand-outs and class notes from Sub School, Destroyer School and War College. So, from the “real world” I offer the following…

The problems you are looking to solve are mostly dealt with by “Area Searches” and “Barrier Patrols”. The latter is more commonly used because the subject(s) of most searches is/are operating in one of three specific cases: 1. the target’s intention is to traverse a fairly straight “channel”, which may be a wide portion of the ocean (such as a known or suspected shipping lane), or; 2. the target is proceeding from a known point on the ocean (typically an island or harbor), or; 3. the target is proceeding toward a known point on the ocean (a mission objective area or an island or harbor). In case 1, the target vector velocities at all points are parallel and equal, a translational vector field, as shown in the OP. In case 2, the target vector velocities are all equal but are all directed away from that specific point, a centrifugal radial vector field. In case 3, the target vector velocities are all equal but are all directed inward toward that specific point, a centripetal radial vector field. In each case the problem is solved using either crossover patrols (when aircraft are searching for ships) or linear patrols (when ships are searching for ships). Let’s call the speed of the target “u” and the speed of the search vehicle “v”.

There are many variables that we don't have in the game, such as multiple sensors with different detection probabilities for different types (sizes) of targets under various weather (signal propagation) conditions. So, ignoring all of the variables that are not present in both the game and in real life, the simplest crossover patrol solution, gives us the geographic path, or course of the patrolling vehicle, across the width of the area being searched, to be done at an angle “a” from a line perpendicular to the axis of the search area, such that sin a = u/v. In real life, the width of the search area is based on the "sweep width" (sensor range) and desired probability of detection, applying the Inverse Cube Law of Detection and the normal probability tables (found in OEG Report 56), not "black magic" but requiring either a computer or good calculus skills...too much for any other than the hard-core fans here...yes?

You’ll note that solving for the angle "a" is essentially pointless as u and v get closer to the same value. The crossover patrol for ships searching for ships then becomes a linear patrol instead. The solution is to convert the angle from sin a = u/v into tan a = u/v, which commonly produces a recommended course line 45deg off the axis of the search area. The usual assumption is that surface ships will proceed at approximately the same speed; if Intelligence tells you otherwise, act on it.

BTW, it works both ways, giving us either an Advancing Barrier Patrol or a Retiring Barrier Patrol...and it can be stationary as well, useful for "choke points". You'll also note that none of the real world solutions offers a 100% probability of detection; the goal is to do just as others have stated here...cover the maximum search area possible in the amount of time available, with the highest detection probability possible.

BTW, you might be surprised to know that the search patterns in stock SH4 (and SH3) are almost right out of ATP-1 and the OA (Operations Analysis) books; they include the “Ladder Search” the "Crossover Barrier Patrol" and the "Expanding Square Search" (which the developers got completely backwards!!!). Unfortunately, none of them can be rotated; they are all fixed with a search axis along straight N-S/E-W lines and course lines of fixed length...oh well, again.

[ColonelSandersLite]

So my computer simulation is almost done. Ships and subs are moving and subs are detecting ships. And data is being stored. All that needs to be done now is making it spit out usable statistical data. I'll get to that in the next couple of days.

If you have any particular patrol patterns you would like to see tested, I would be happy to run them.

just format them like this for me:
All waypoints should be a pair of coordinates, listed in nautical miles. The origin is the southwest corner of a hypothetical north-south running shipping lane with dimensions of 55 miles east/west X 500 miles north/south. The sub will loop through the waypoints if it finishes its path. The program will run the patrol at all speeds from 1 to 20 knots.

For example, the below is a 28 X 28 mile square roughly centered in the north/south axis.

41.5, 213.5
13.5, 213.5
13.5, 241.5
41.5, 241.5

[TorpX]

Originally Posted by CaptBones

None of the naval commanders in the USN during WWII (including O'Kane and Fluckey) had to make things up entirely on their own; there was a large knowledge base available from the pre-war "Battle Problems", in which the submarine force was used almost exclusively for scouting, searching and patrolling large open ocean areas. ... Of course, they are all classified; at least CONFIDENTIAL and most at SECRET level.

Well, that explains why we don't see the these at hnsa.org.

I'm surprised that so much of these subjects would be classified. It seems like we sell off technology that is much more of a concern.

I can imagine O'Kane or others giving some more detailed explanations of these things, only to be told by their publisher to cut it down to a couple paragraphs - nobody will want to read about that.

BTW, you might be surprised to know that the search patterns in stock SH4 (and SH3) are almost right out of ATP-1 and the OA (Operations Analysis) books; they include the “Ladder Search” the "Crossover Barrier Patrol" and the "Expanding Square Search" (which the developers got completely backwards!!!). Unfortunately, none of them can be rotated; they are all fixed with a search axis along straight N-S/E-W lines and course lines of fixed length...oh well, again.

Not surprised; I mean about the getting it backwards part.



Very interesting post, very worthwhile.

[CaptBones]

Hello TorpX...

You're right..."overclassification" was a real concern during the 60's, 70's and 80's. At one point someone had the bright idea that we would be better off declassifying everything but a very very few documents. The theory behind that was that classifying information just told the "enemy" what to look for and what was good information worth getting and keeping; we were just making his job easier for him. One could imagine what it would take for some "enemy" or potential enemy to have to collect EVERYTHING and then wade through it to figure out what was good and worth keeping. Of course that was then and this is now...the computing power available today would make that "sorting" job much easier.

Yeah, the volume of dry, boring text and mind-numbing graphs, charts, tables, etc. is enough to make just about anyone put those books down and walk away. The 3-ring binders I have are each 3-4 inch "D" ring binders and are overflowing with that stuff (all stamped SECRET, but there is a letter taped to the inside of each front cover that identifies all of them as being past their respective "automatic downgrade/declassification" dates). Not to mention more than 350 pages in OEG Rpt 56; it's published title was "Search and Screening", certainly something you'd grab off the bookshelf if you saw it there!!!

Glad you enjoyed reading it. BTW, if you (or anyone else) knows how to rewrite the "Expanding Square" search to make it work correctly, please let me know...I would use it in both SH4 TMO and OM.

P.S. I asked Gene Fluckey once about his "daring-do" in risking his boat in shallow, poorly charted and/or ASW infested waters...he laughed and said nobody else was "stupid enough" to try it. Then again, you gotta' admire someone who said he'd pass up the chance to sink an enemy ship in exchange for rescuing some of our downed fliers.

[ColonelSandersLite]

So here's some preliminary results and a few notes:

sub 1 finished patrol
   0kts, Simple Stationary Baseline
   Radar, SJ-1 detections 15087/30000, 50.29%
   Radar, SJ detections 10269/30000, 34.23%
   Hydrophone, JP detections 9504/30000, 31.68%
   Visual, Day detections 6105/30000, 20.35%
   Hydrophone, WCA detections 5802/30000, 19.34%
   Visual, Night detections 3957/30000, 13.19%

sub 2 finished patrol
   10kts, Back and forth accross the whole lane
   Radar, SJ-1 detections 19939/30000, 66.46%
   Radar, SJ detections 14324/30000, 47.75%
   Hydrophone, JP detections 13301/30000, 44.34%
   Visual, Day detections 8757/30000, 29.19%
   Hydrophone, WCA detections 8347/30000, 27.82%
   Visual, Night detections 5688/30000, 18.96%

sub 3 finished patrol
   10kts, Back and forth accross the whole lane minus 13.5 miles on each side.
   Radar, SJ-1 detections 21707/30000, 72.36%
   Radar, SJ detections 15563/30000, 51.88%
   Hydrophone, JP detections 14502/30000, 48.34%
   Visual, Day detections 9719/30000, 32.40%
   Hydrophone, WCA detections 9271/30000, 30.90%
   Visual, Night detections 6399/30000, 21.33%

sub 4 finished patrol
   10kts, Back and forth 13.5 miles.
   Radar, SJ-1 detections 20659/30000, 68.86%
   Radar, SJ detections 14885/30000, 49.62%
   Hydrophone, JP detections 13859/30000, 46.20%
   Visual, Day detections 9322/30000, 31.07%
   Hydrophone, WCA detections 8880/30000, 29.60%
   Visual, Night detections 6220/30000, 20.73%

sub 5 finished patrol
   10kts, 13.5X13.5 mile box.
   Radar, SJ-1 detections 18074/30000, 60.25%
   Radar, SJ detections 12638/30000, 42.13%
   Hydrophone, JP detections 11600/30000, 38.67%
   Visual, Day detections 7528/30000, 25.09%
   Hydrophone, WCA detections 7124/30000, 23.75%
   Visual, Night detections 4737/30000, 15.79%

sub 6 finished patrol
   10kts, 13.5X13.5 mile upright hourglass.
   Radar, SJ-1 detections 18399/30000, 61.33%
   Radar, SJ detections 13084/30000, 43.61%
   Hydrophone, JP detections 12234/30000, 40.78%
   Visual, Day detections 8403/30000, 28.01%
   Hydrophone, WCA detections 8023/30000, 26.74%
   Visual, Night detections 5799/30000, 19.33%

sub 7 finished patrol
   10kts, 13.5X13.5 mile sideways hourglass.
   Radar, SJ-1 detections 18015/30000, 60.05%
   Radar, SJ detections 12295/30000, 40.98%
   Hydrophone, JP detections 11511/30000, 38.37%
   Visual, Day detections 7954/30000, 26.51%
   Hydrophone, WCA detections 7605/30000, 25.35%
   Visual, Night detections 5683/30000, 18.94%

sub 8 finished patrol
   10kts, wide box.
   Radar, SJ-1 detections 18654/30000, 62.18%
   Radar, SJ detections 13388/30000, 44.63%
   Hydrophone, JP detections 12504/30000, 41.68%
   Visual, Day detections 7978/30000, 26.59%
   Hydrophone, WCA detections 7202/30000, 24.01%
   Visual, Night detections 5037/30000, 16.79%

sub 9 finished patrol
   10kts, wide upright hourglass.
   Radar, SJ-1 detections 19759/30000, 65.86%
   Radar, SJ detections 14425/30000, 48.08%
   Hydrophone, JP detections 13558/30000, 45.19%
   Visual, Day detections 9774/30000, 32.58%
   Hydrophone, WCA detections 9407/30000, 31.36%
   Visual, Night detections 7244/30000, 24.15%

sub 10 finished patrol
   10kts, wide sideways hourglass.
   Radar, SJ-1 detections 20349/30000, 67.83%
   Radar, SJ detections 15110/30000, 50.37%
   Hydrophone, JP detections 13892/30000, 46.31%
   Visual, Day detections 8255/30000, 27.52%
   Hydrophone, WCA detections 7686/30000, 25.62%
   Visual, Night detections 4649/30000, 15.50%

While I haven't fully crunched the numbers yet, some preliminary notes:

I ran the simulation a few times and compared results. Maximum deviation seems to be 1% with about 0.5% being more typical. I will increase the number of tests by a couple of orders of magnitude when I'm fully happy with all of it to reduce error. That will take a while to run though.

There was a general trend for detection odds to go up with sub speed (multiple subspeeds not shown here) in a nonlinear fashion. For example, going from speed 0 to speed 1 might yield a 0.75% increase, but going from 15 to 16 might yield a 3% increase. There is certainly a point where decreased loiter time, causing a reduction in total targets to detect, will cut into total number of detection. I haven't done any math on this yet, but soon.

With shipping going both ways, adding a north/south component to the patrol has decreased odds of detection in all cases with one unusual exception. The upright hourglass pattern has better odds of detecting targets with some of the games more close range sensors. I ran it 3 times to be sure it wasn't some kind of statistical anomaly.

With the exception of a stationary submarine, Slower target speeds increase the odds of detection while faster target speeds decrease the odds of detection.

Movment perpendicular to the targets course seems to increase the odds of detection up to a point. Past this point, such movement seems to decrease odds of detection. I need to do more data sifting to be sure, but I suspect that each sensor and sub speed combination has an optimum distance that this occurs. Without diagraming it, it would seem to have something to do with the rate at which a target can traverse an area you have just searched. (I.E. knowing where targets cannot be, as mentioned above)

Originally Posted by CaptBones

There are many variables that we don't have in the game, such as multiple sensors with different detection probabilities for different types (sizes) of targets under various weather (signal propagation) conditions.

A lot of that actually is in the game but it tends to be subtle enough that its effects aren't noticed. The most obvious examples are hydrophones and how rough the sea is and watch crew and light level. Target aspect has an effect, and I have noticed that some targets can be detected further away than others.

Good posts though.

[TorpX]

Originally Posted by CaptBones

Glad you enjoyed reading it. BTW, if you (or anyone else) knows how to rewrite the "Expanding Square" search to make it work correctly, please let me know...I would use it in both SH4 TMO and OM.

Doubt it can be fixed.

My appraisal of SH4: There are about a thousand things I'd like to fix. Of these, there might be a hundred things that are fixable. Of that number, there might be ten things that I could fix. It seems like that for every one thing that is fixed, or improved, you find several more that are 'broken'.

ColonelSandersLite,

Do you have shipping going in both directions? From N and S or just just from one direction?

What speed are you using for targets?

And what are you using for various detection radii?

I notice some of the individual categories like hydrophone or night visual don't seem to follow the radar numbers. Not sure what to make of that.

[ColonelSandersLite]

1: Yes, traffic is bidirectional.
2: In that test, it was between 8 and 10 knots inclusive. The final test will be from 5 to 25 knots inclusive and will report details based on target speed.
3: I measured the detection radiuses directly in TMO. All measurements where made with the default crew skill in a single mission, clear visibility, wind speed 5 knots. Of the targets I tried (I didn't try all of them) heito maru was the hardest to detect on radar by a small margin (a few tenths of a mile or so) so it is the target I used. All numbers where measured from AOB 0. Values:

        subSensors[0] = new SubSensor("Radar, SJ-1",      13.5);
        subSensors[1] = new SubSensor("Radar, SJ",         9.3);
        subSensors[2] = new SubSensor("Hydrophone, JP",    8.6);
        subSensors[3] = new SubSensor("Visual, Day",       5.6);
        subSensors[4] = new SubSensor("Hydrophone, WCA",   5.3);
        subSensors[5] = new SubSensor("Visual, Night",     3.575);
        subSensors[6] = new SubSensor("Periscope, Day",    3.3);
        subSensors[7] = new SubSensor("Periscope, Night",  2.05);

I'll put the source up in a couple of days, after I have had time to fine tune and clean it, should you want to look through it.

[ColonelSandersLite]

Originally Posted by CaptBones

Glad you enjoyed reading it. BTW, if you (or anyone else) knows how to rewrite the "Expanding Square" search to make it work correctly, please let me know...I would use it in both SH4 TMO and OM.

I meant to ask earlier but forgot: What was actually wrong with it? It's been so long since I've used the plot patrol button in any version of the game with any mod that I just have no recollection of how it is. Is it actually a shrinking square?

[CaptBones]

Quote:
Originally Posted by CaptBones
There are many variables that we don't have in the game, such as multiple sensors with different detection probabilities for different types (sizes) of targets under various weather (signal propagation) conditions.

Quote: A lot of that actually is in the game but it tends to be subtle enough that its effects aren't noticed. The most obvious examples are hydrophones and how rough the sea is and watch crew and light level. Target aspect has an effect, and I have noticed that some targets can be detected further away than others.

Hhhmmm..."apples and oranges" there...I've tinkered with most of those parameters and variables myself in trying to get my crew's behavior and the AI's behavior to more closely match the real world (such as I experienced and remember it). But those aren't the variables I was talking about. What is missing is actual data and data-based algorithms to apply probabilities of detection of different sensors and sensor systems (being employed simultaneously when possible) under various environmental conditions and states of operator proficiency (not to mention countermeasures and counter-countermeasures) to produce the tables graphs and charts that would normally (in pre-computer days) be used to lay out our patrol areas and search patterns. The simplified and simplistic techniques used by the game do not even approach the most basic level of usefulness as compared to real-world detection modeling.

Of course, this is a PC game. It has been made much closer to a real simulation by the amazing work of the modders in this community. But true simulators that apply the aforementioned techniques are multi-million dollar networked computer facilities that occupy thousands of square feet of floor space in multi-story buildings on military and naval bases that I can't even get into anymore without a special escort (sometimes my younger son gets to be that escort; I think he might end up out-ranking me one of these days ).

Quote: Good posts though. Thank you...and BTW, your simulation is producing some very good and very very interesting results. You sure you don't work for ONR in Anacostia?

I meant to ask earlier but forgot: What was actually wrong with it? It's been so long since I've used the plot patrol button in any version of the game with any mod that I just have no recollection of how it is. Is it actually a shrinking square?

Yes, exactly. The devs got it exactly backwards; they have you starting on the outside and working your way in. The Expanding Square (which, in real life, can be modified to an Expanding Rectangle if there is information on a more probable target course) is used to search for a target from a known "datum", when the target's course and speed are not known, but one or both are known to be within known limits (i.e., a submarine fired a "steam" torpedo from an observed location and we know it can't go any faster than 8 kts submerged). The starting point is at Datum and the search legs are based on the target's "farthest on circle" depending on the time difference between last target observation/sighting and time of arriving at datum.

[ColonelSandersLite]

Originally Posted by CaptBones

You sure you don't work for ONR in Anacostia?

Hah, no. I'm just some guy that likes to code for fun once in a while. Not even a major project, just 750 lines or so of code.

[Barkerov]

Originally Posted by ColonelSandersLite

        subSensors[0] = new SubSensor("Radar, SJ-1",      13.5);
        subSensors[1] = new SubSensor("Radar, SJ",         9.3);
        subSensors[2] = new SubSensor("Hydrophone, JP",    8.6);
        subSensors[3] = new SubSensor("Visual, Day",       5.6);
        subSensors[4] = new SubSensor("Hydrophone, WCA",   5.3);
        subSensors[5] = new SubSensor("Visual, Night",     3.575);
        subSensors[6] = new SubSensor("Periscope, Day",    3.3);
        subSensors[7] = new SubSensor("Periscope, Night",  2.05);

I'll put the source up in a couple of days, after I have had time to fine tune and clean it, should you want to look through it.

Are these the detection radii of the various sensors in nautical miles?
Also where are you up to with these simulations?

I am fairly new to the game but I have a search strategy which involves going to where I am ordered, then choosing a small area within that location where a shipping lane or bottle neck might be. Then I arrange a search pattern perpendicular to what I think the traffic path will be. Becasue I am using a radarless S class I travel back and forth along that path diving periodically, ordering all stop, manning the hydrophones myself and continuing on if nothing is found.

The question I was asking myself is how often would I have to dive when traveling at a reasonably economical speed to detect a 12 knot target passing through my least covered area? I chose a 12 knot target since it seemed intuitive that I would find a slower target more easily. Up till now I have been assuming its 20nm but since I am not 100% sure what the hydrophone range is in RFB this has been impossible to improve. If anyone could clear this up I would really appreciate it.

Also I would be more than happy to lend this project a hand in return for that info. I have done numerous simulations in my role as a statistician and, as you might imagine, I also have an excellent grasp of probability.