The mathematics of roving searches

[TorpX]

It is commonly believed that cruising around at good speed is essential to searching on patrol. It seems to have become accepted wisdom, that this not only produces better chances for finding a contact, but that the odds are dramatically improved by doing so.

Since this topic comes up periodically, I decided to try to figure out a proper solution to the question of how much continuous cruising helps ones chances of finding a contact.

First off, we need to make some general assumptions about the conditions. I am going to assume that we know the direction of the prevailing shipping traffic, and that the odds of a target transiting through any portion of our search area is the same as for any other area of equal size. That is, that shipping is equally distributed (which it would be, at least as far as we know). I consider it fairly obvious that the best "search pattern" is one that cuts across the greatest number of potential target routes in a given length of time; that is, moving perpendicular to traffic. This means that fancy box or 'x' patterns are less effective, and moving parallel to the direction of traffic is just a waste of fuel.

In the diagram below, we have our sub moving east to west, and enemy traffic moving north to south. We could change the directions any number of ways; the important thing is that our sub is moving perpendicular to shipping traffic. The black lines at either side is the search limits we have marked off for our sub. It will go east to west until it reaches the west limit, then reverse course and go east until it reaches the east limit, and so on. The gray circle is the sub's detection bubble. Any target that comes within that space will be detected. The red arrows represent potential target ships. At first blush, we might be tempted to think that all, or most, of these targets would be detected, but this isn't the case. If we were to stay in place, we would expect to find #6 and #7. Moving to the west, we might hope to find #1 to #7, but it is possible, even likely, that #1, #2 and #3 would get by before we get far enough west, and #7 and the rest would be safe because we will be over to the west as they go by. So the question is how many targets are we likely to detect, compared to the same situation, where we are sitting still?




http://i1130.photobucket.com/albums/m526/TorpX/Roving%20Search/diagram1_zps2j62dnvh.png

We might try to plot out the route and timing of every potential target, dividing the sea lane into 1 nm strips, but life is short and there must be a better way to go about this.

If we adopt a different frame of reference, the problem is soluble. Below, I have diagramed the movement of our sub, using an enemy ship as a frame of reference, instead of a fixed earth frame. The sub appears to move in a zig-zag pattern, though it is really still going east-west. The sub is starting at point A moving to B, reversing course until C, and going east once more to D. At D the sub is again in the middle of it's search zone and the cycle will repeat. I'll explain the reason this is important later. Essentially, we have used vector addition to subtract the target speed, from both sub and targets.




http://i1130.photobucket.com/albums/m526/TorpX/Roving%20Search/diagram2_zpsckhgul37.png

Note that, using this frame of reference, the target ships do not move. Any target that falls within the searched area, will be located, any that are outside will not be. I call the areas computed in this frame, pseudo-areas. I shaded the first segment, AB, manila so we can see that it is a rectangular segment, with a missing semi-circle at one end, and a extra semi-circle at the other. The remaining segments are light green. The concave area at A is there because we only want the newly searched area after the sub passes A. Since this geometrically is equivalent to the semi-circle past B, we can see that the area of this segment is equal to the length of A to B times the width of the segment (2r). Also, it is easy to conclude that the segment CD is the same length as AB and the segment BC is twice AB. So if we multiply the area of segment AB by 4 we should have our total pseudo-area searched by our moving sub.

But wait a minute; there are parts of this area that would be counted twice if we do that. See the wedge shaped area in brown (near C). There is also an equivalent area near B. For accurate results, we mush subtract the areas there, lest we overestimate our search ability. This stems from the fact that when we reverse course, we will be searching an area that we already searched minutes before, so we have to expect some loss of efficiency there. This is why we must be careful to have the sub move a complete cycle; otherwise, we could not properly account for the overlapping sections.

To obtain a ratio for the probability of finding a contact by a moving sub relative to that by a stationary sub, we need to know r, the detection radius of our sub, w, the distance from the center of the search zone to either edge, and b. b is the angle between the horizontal and the line AB. The angle ABC is 2b, as is angle BCD. It depends on the relative speeds of the target and sub.

So, we seek to compute 3 quantities:



the roving 'pseudo-area' (i.e. the area of the 3 segments we diagramed).
the 'wedge-shaped pseudo-area' (to account for the overlapping).
the comparable 'pseudo-area' for a stationary sub.

Note that, for a stationary sub, the graphical representation would be one large segment of the same width, 2r, going from A to D.

For number 1. we have: Roving 'pseudo-area' = 8*r*w / cos b


where

r is the detection radius of the sub
w is the width of the search zone from the center to one edge (i.e. half of the full width)
b is the angle Arctan (Vt / Vu)
Vt is the target speed
Vu is the sub speed


For 2, the 'wedge area', we have:

[I won't go into the details of finding this. Extra credit for those who can figure this out. :) Note that the faster the sub goes back and forth, the greater the overlap there will be. For typical values, it shouldn't be too large.] 'wedge pseudo-area' = 2r^2 * [tan(90-b) - pi*(90-b)/180]


For the static sub computation we can calculate the time interval for the moving sub to complete one cycle, and then substitute that value in the equation for the area, to get our final result.

The time t = 4w / Vu, and the pseudo area = 2r * t * Vt.

This gives us: Stationary 'pseudo-area' = 8*r*w * (Vt/Vu)
For a concrete example, I will use a value of 20 nm for w, 10 nm for r (this is the max. rendering distance for SH4), a Vt of 8 kn. and a Vu of 9 kn.

These values give us 41.63 degrees for b.

The Base 'pseudo-area' is 2140.7.

The 'wedge psuedo area' is 56.2.

The Stationary 'pseudo-area' is 1422.2. Efficiency Ratio = (Roving PA - Wedge PA) / Stationary PA


So, for these numbers we have a ratio of 1.466.


In other words we can expect to obtain 46.7% more contacts under these circumstances.


How valuable is a 46% 'search bonus' for a moving sub? Well, a lot depends on how much fuel we have to play with. If we have plenty to spare, there would be little reason not to use some for roving. If, on the other hand, our supply is tight, and roving would mean cutting our patrol time in half, it isn't very good at all.



Tomorrow, I will post results for various sub and ship speeds, and add a few thoughts. -TorpX

[Ludwig van Hursh]

*brain melts* :doh:

[Rockin Robbins]

It is also arbitrary. Saying that an area which is searched will not be counted because we don't want it is just arbitrary. It is searched, therefore it contributes the the result. Also, the wedge areas are not researched areas, they are as if they had not been searched at all the second time through because there is a time element here as well. Since you are spending double the amount of time in the wedge and enemy traffic is moving randomly within constraints of traffic patterns there is actually a higher percentage chance of obtaining a target in the wedge than outside the wedge. It is not only your movement that is important, but the movement of traffic into your search area. It is not coherent as you have assumed and they all don't line up side to side in a single line across your search area as you have assumed. They are distributed randomly throughout the area and are moving in randomized directions, yes, constrained by limits but random within those limits.

So while your math is admirable, your premises are questionable. The area searched each day is actually a rectangle based on the width of area searched and the end points of travel PLUS a circle of search radius around the sub. Assuming homogeneous distribution of shipping, your number of targets developed is directly proportional to the length of travel per day times the diameter of your search distance circle, plus the area of that search circle, half of which is added to your search area at the beginning of the day and half to the end of the day. That makes your search area a long hot dog. The longer your travel during the day the more contacts you will develop, nearly proportional to your speed. I say nearly because of what you're going to say next, which is that if your were entirely stationary, shipping would still enter your area because of their velocity and it would be as if you were moving against the velocity of their travel at their speed. That makes contacts found not exactly proportional to distance traveled in a day. It is conceivable if you park at a choke point you could have enough business that it wouldn't matter if you could develop more business because it takes time to deal with each contact. But ignoring random effects and choke points, your number of contacts is nearly proportional to the length of your track during each day.

Now that is contacts per day. You want best results for a cruise. Best fuel economy is 11 knots. WFO is 21 knots, which would double your results. But at WFO your fuel consumption is many times the double search coverage, therefore your patrol contacts actually drop off the proverbial cliff. Therefore, searching on the surface so you can use radar at 11 knots is by far the best way to search.

Yes, we could quantify that more precisely. We could toss the actually variable density of traffic in there to modify our path to more productive areas, and I hope we're already doing that. But the numerical results won't change our behavior at all. Our results and the calculated results will always be different from reality because our assumptions are wrong. We know that but not knowing the actual distribution of shipping, we have to generalize. We are not in total control of our destiny. We are card counters at a blackjack table, numbers on our side but knowing that we can still lose. You can do everything right and still lose. But you can only win if you do the right things......unless......

[ColonelSandersLite]

So here's my take on this, and I would encourage further thought or debate on its merits.

So suppose, for example sake, that you are patrolling a suspected shipping lane that runs north-south.

Consider, that nearly every merchant target moves at a speed of 11 knots or less (usually slower).

Let's further assume that your sensors have a reliable detection range of 13 miles (this is my experience for SJ-1 radar in TMO).

Let's also assume that you want to patrol at a cruising speed of 10 knots.



So, to ensure that no target heading north or south gets past you, the best course of action is to patrol strictly perpendicular to the shipping lane.

If your sensor has a detection radius of 13 miles, it will take a 11 knot target 141 minutes to pass through it completely, meaning that you must be back at your original position within 140 minutes or so.

During your patrol, you must turn 180 degrees twice, taking a total of 7 minutes, leaving a total cruising time of 133 minutes. (may vary by boat, mods, etc. accurate for a balao doing 10 knots in tmo though)

Each leg of the cruise then becomes a 66 minute cruise at 10 knots, for about 11 nautical miles each way.


In this case, it is certain that no target moving at a speed no greater than 11 knots can pass through a 11X26 mile box (286 square nautical miles). Additionally, on the west and east ends of the box, there is a 13 mile radius semicircle of detection. A 11 knot target may not pass through most of either of these areas without detection either. The sole part of the patrol area that a target may pass through undetected would be a segment of the circle defined by a 13 mile cord running north-south at the far end of the circle, an area of 88 miles. This works out to guaranteed detection of any 11 knot targets passing through an area of 641 square nautical miles (with an additional less than 100% chance of detection over 176 square miles as below) vs 531 if you had remained stationary or a 17% increase.

Inside of this small segment, the odds of detection depend on target speed, and are directly proportional to the resulting length of chord. For example, the odds of detecting an 11 knot target passing through a north-south chord of 6.5 miles would be 50%.

I thought it might be helpful to include a diagram of what I'm talking about.

http://i3.photobucket.com/albums/y91/ColonelSandersLite/patrol%20pattern_zps5qj1vhva.jpg (http://s3.photobucket.com/user/ColonelSandersLite/media/patrol%20pattern_zps5qj1vhva.jpg.html)



With other sensors, the amount of time you can spend moving east-west will be reduced proportionally. For example, suppose that your detection radius is half of the SJ-1 range, or 6.5 miles. This would reduce the cruising time of each patrol leg by half.

If you are willing to accept a less than 100% chance of detecting a 11 knot target, lets say guaranteeing detection of 9 knot targets instead, the amount of time spent on each leg of the patrol would then be increased proportionally. That would increase the length of each leg to 13.75 miles, with a 100% chance of detecting targets doing 9 knots.

[Fearless]

All great examples but how does it apply to a simulation that spawns ships at certain points on the map?

[Crannogman]

I was not aware that ships spawn randomly - I thought their spawning and routing was encoded in the campaign files

[ColonelSandersLite]

Crannogman has it right. The ships aren't just a random distribution. They spawn at and despawn at ports. Not actually at the docks, but fairly close.

The big exception is the set piece battles, like midway. They spawn a *long* way from the battle, but not actually in ports. The do go to ports when their part is done though. I'm just guessing here, but I suspect that getting the timing of the ship movements for the battles down perfectly was just too much work when spawning them all the way back at port.

If you want to see for yourself, open up the .mis files with the editor. They are in "\sh4\Data\Campaigns\Campaign". The yellow diamonds are spawn points.

As an aside, I have never gone out of my way to watch any of those set piece battles. I really should one of these days. The only time I've actually seen one by pure chance was in SH3+GWX. I was harbor raiding during the invasion of norway and all of a sudden, some german surface vessels showed up and starting shooting everything. At first I thought they where enemy destroyers bearing down on me and shooting at my periscope the way destroyers do in these games...

[Rockin Robbins]

So here's my take on this, and I would encourage further thought or debate on its merits.

So suppose, for example sake, that you are patrolling a suspected shipping lane that runs north-south.

Consider, that nearly every merchant target moves at a speed of 11 knots or less (usually slower).

Let's further assume that your sensors have a reliable detection range of 13 miles (this is my experience for SJ-1 radar in TMO).

Let's also assume that you want to patrol at a cruising speed of 10 knots.



So, to ensure that no target heading north or south gets past you, the best course of action is to patrol strictly perpendicular to the shipping lane.

If your sensor has a detection radius of 13 miles, it will take a 11 knot target 141 minutes to pass through it completely, meaning that you must be back at your original position within 140 minutes or so.

During your patrol, you must turn 180 degrees twice, taking a total of 7 minutes, leaving a total cruising time of 133 minutes. (may vary by boat, mods, etc. accurate for a balao doing 10 knots in tmo though)

Each leg of the cruise then becomes a 66 minute cruise at 10 knots, for about 11 nautical miles each way.


In this case, it is certain that no target moving at a speed no greater than 11 knots can pass through a 11X26 mile box (286 square nautical miles). Additionally, on the west and east ends of the box, there is a 13 mile radius semicircle of detection. A 11 knot target may not pass through most of either of these areas without detection either. The sole part of the patrol area that a target may pass through undetected would be a segment of the circle defined by a 13 mile cord running north-south at the far end of the circle, an area of 88 miles. This works out to guaranteed detection of any 11 knot targets passing through an area of 641 square nautical miles (with an additional less than 100% chance of detection over 176 square miles as below) vs 531 if you had remained stationary or a 17% increase.

Inside of this small segment, the odds of detection depend on target speed, and are directly proportional to the resulting length of chord. For example, the odds of detecting an 11 knot target passing through a north-south chord of 6.5 miles would be 50%.

I thought it might be helpful to include a diagram of what I'm talking about.

http://i3.photobucket.com/albums/y91/ColonelSandersLite/patrol%20pattern_zps5qj1vhva.jpg (http://s3.photobucket.com/user/ColonelSandersLite/media/patrol%20pattern_zps5qj1vhva.jpg.html)



With other sensors, the amount of time you can spend moving east-west will be reduced proportionally. For example, suppose that your detection radius is half of the SJ-1 range, or 6.5 miles. This would reduce the cruising time of each patrol leg by half.

If you are willing to accept a less than 100% chance of detecting a 11 knot target, lets say guaranteeing detection of 9 knot targets instead, the amount of time spent on each leg of the patrol would then be increased proportionally. That would increase the length of each leg to 13.75 miles, with a 100% chance of detecting targets doing 9 knots.
Excellent! That's a great analysis for detection of shipping through a choke point. And a choke point is the goal of our searching if one is attainable. Looks like a closed door to me too. Good job.

[ColonelSandersLite]

Oh, I may have a critical error in the post #4 above. I'll have to think on it some more later though. Gonna head to the range. I may get a chance to think it through tonight, but it might be tomorrow before I get to it.

Edit: I see RR posted something while I was typing that. He agrees with me, so I know it's got to be wrong :O:.

[Rockin Robbins]

I was not aware that ships spawn randomly - I thought their spawning and routing was encoded in the campaign files
I didn't say they spawn randomly. I said that they were distributed more or less randomly along their routes. That they didn't proceed in line abreast as your example showed. They're like raindrops. And we're trying to walk through a rainfall getting as wet as possible. Those raindrops didn't spawn at random locations--well they did within constraints. But by the time they get to us their distribution looks random. Shipping is like that.

Now if you're coming up with a specific way to game RSRDC then, since I haven't looked at the campaign files, you might have a way. But I choose not to game the system and not to analyze the campaign files to get dates of departure, exact route and timing. The real sub skippers didn't have that information and I consider that if we use historical information to game the game we've broken the simulation irretrevably ourselves.

[Rockin Robbins]

Oh, I may have a critical error in the post #4 above. I'll have to think on it some more later though. Gonna head to the range. I may get a chance to think it through tonight, but it might be tomorrow before I get to it.

Edit: I see RR posted something while I was typing that. He agrees with me, so I know it's got to be wrong :O:.
I can see that it's only good for a choke point 37nm wide. That's still a useful tool though at that. If a ship enters your box and you're at the other end it's an hour before you're to the near end to him. He's still in the 100% detection box so you've got him unless you see something I missed.

[TorpX]

Ok, I haven't read all the comments and criticisms yet. I want to finish the problem and add a little math first. I'll try to get back to the comments, as time permits.



I've computed some figures for typical (and maybe not so typical ship/sub speeds.

1551

The 3 knot speed is typical of economical searched cruising, 6 kn. is good for a S-boat, 9 is economical for a fleetboat, and faster speeds to see how more intensive searches might fare.


You might ask, could we go faster and eliminate the gaps between segments? The answer is yes; if our sub goes fast enough, we could theoretically, detect every ship making a transit through this search zone (for our assumed conditions).

To show how fast we would have to go, it helps to reconfigure the diagram. Below, we see the segments of our search are much closer together (like a coilbound spring); so much so that there are no spaces uncovered between the segments. I didn't shade the overlaps, but you can easily see that there would be a large 'wedge area' or amount of overlap here.




http://i1130.photobucket.com/albums/m526/TorpX/Roving%20Search/diagram3_zps0egfajbw.png

To achieve this level of coverage, our sub must go across the zone to the west and back again, so the detection circles at A and C are tangent. Mathematically, this means the sub must move the length of 4w in 't' hours, while the target ship moves 2r in 't' hours:

Vu = 4w / t

Vt = 2r / t

From here, all we need to do is solve the second equation for t and substitute the result in the first equation. Doing this, we obtain: Vu = Vt * (4w / 2r)

Putting in the numbers we used for our earlier example, we find that we would need to have a speed of 4 times the target's speed, or 32 knots!

These results helps explain why sub operations in WWII didn't sink enemy ships at a blinding pace, and individual subs might spend days, or even weeks, between ship sightings.

It also shows why aircraft were such useful sub hunters. They had an enormous speed advantage over any submarine.

[Crannogman]

I didn't say they spawn randomly. I said that they were distributed more or less randomly along their routes. That they didn't proceed in line abreast as your example showed. They're like raindrops. And we're trying to walk through a rainfall getting as wet as possible. Those raindrops didn't spawn at random locations--well they did within constraints. But by the time they get to us their distribution looks random. Shipping is like that.

Now if you're coming up with a specific way to game RSRDC then, since I haven't looked at the campaign files, you might have a way. But I choose not to game the system and not to analyze the campaign files to get dates of departure, exact route and timing. The real sub skippers didn't have that information and I consider that if we use historical information to game the game we've broken the simulation irretrevably ourselves.

I was responding to a different comment about random spawning. RSRDC cannot be gamed because the shipping routes have variable waypoints (some as much as 20nm radius), and thus their heading is fairly unpredictable.

It seems that a formula will be forthcoming to calculate a minimum average speed "x" to patrol a chokepoint of width "y," variable of course on the range of your sensors. Another formula could tell you your miss percentage based upon how far below "x" you go (if, as TorpX posited, "x" is impossible or overly inefficient).

Since RSRDC includes the variable waypoints, your detection chance is probably improved since ships will generally not be sailing in a direct line from origin to destination - thus it will take them longer to transit your patrolled box

[TorpX]

It is also arbitrary. Saying that an area which is searched will not be counted because we don't want it is just arbitrary. It is searched, therefore it contributes the the result.
You have to make some assumptions to solve the problem. Otherwise all you can do is speculate and theorize. I freely admit that traffic will not always be traveling alone a single axis, but frequently much of it will be. If you want to calculate a comprehensive figure for X% going N-S, and Y% going E-W, you can break the problem down in cases and do that. I am assuming a best case situation (for the sub), where they do know the axis of traffic. It is certainly possible to have the traffic on a different axis, not perpendicular, but I wanted to show what the best possible results would be.

Every area was counted, I just didn't count any area twice.

Also, the wedge areas are not researched areas, they are as if they had not been searched at all the second time through because there is a time element here as well. Since you are spending double the amount of time in the wedge and enemy traffic is moving randomly within constraints of traffic patterns there is actually a higher percentage chance of obtaining a target in the wedge than outside the wedge. The wedge areas overlap and you must account for this or the results are not correct. You are ignoring the fact that in diagram 2, I have subtracted the vector velocity of the target from both target and sub (I.e. different frame of reference). In diagram 2 the target does not move. To say that simply moving fast without regard to this fact, would be like expecting if you went very fast in a small circle, you would still get lots of contacts. By the same token, moving fast parallel to shipping will not avail you anything.





It is not only your movement that is important, but the movement of traffic into your search area. The expressions I have posted use the target's speed and it is expressly mentioned in the text. In fact, that is the whole basis of the computation. If you look over the results in the table, you will see, that increased sub speed does help with the chances, just not as much as some might expect. Also, a 3 kn. sub vs. a 6 kn. ship will give the same results as a 6 kn. sub and a 12 kn. ship. Iow, it is the ratio of sub speed to target speed that is important.
Assuming homogeneous distribution of shipping, your number of targets developed is directly proportional to the length of travel per day times the diameter of your search distance circle, plus the area of that search circle, half of which is added to your search area at the beginning of the day and half to the end of the day. That makes your search area a long hot dog. The longer your travel during the day the more contacts you will develop, nearly proportional to your speed.
I don't know where you get that idea. It just isn't true. I've never seen any such thing in a sub ops document, and furthermore, O'Kane downplayed the idea of searching this way. [For those who still doubt, read CLEAR THE BRIDGE.] Of course, he didn't lay out the geometry, but from what he said, it is plain he understood the concept very well.

The reason the search bands are not "hot dogs" is that if a target was in the first circle, it would have already been detected before we started. We want those targets that would have been detected from time '0' to time 'x', x being the time for the sub to make one complete cycle. The same applies to our stationary 'control' sub.


***
If the game was "Stealth Blockage Runner", instead of Silent Hunter, and we were playing a merchant skipper, diagram 2 is what it would look like using the 'God's eye view' option over a period of time, with our ship locked in the center of our map. If there were spaces between the sub's search bands (as there are in the diagram 2), we might be able to get through. It would depend on exactly where we attempted our transit. If there were no spaces, our cause would be hopeless. If we could increase speed, the diagram would change, with the space between the segments opening up and our chances improving.




ColonelSandersLite,

It looks like you anticipated my question in part 2.

It is certainly worthwhile to consider larger search zones and different parameters. I thought 40 nm was a good 'typical' idea of a sea-lane. If there were a narrow choke point that would make things easier, or one might try a larger zone. At some size, I think it gets ridiculous, though. Saying we want to search a 120 nm zone is like saying we haven't the slightest idea where the enemy is. :)

[ColonelSandersLite]

Yeah, I did make a major mistake above. The boundary that I had previously called the guaranteed detection line is actually the 50% line. The line I have previously called the 50% line is actually the 25% line. Notice that this would be defined by a logarithmic function. The 100% line would be where the north/south @11knts contact moves just under 26nm except for the fact that radar coverage at both ends of the patrol zone extend past this. Apparently, I need to put more thought into this problem.

[merc4ulfate]

@ Rockin Robbins

"They're like raindrops. And we're trying to walk through a rainfall getting as wet as possible"

:Kaleun_Salute: That is absolutely beautiful :Kaleun_Salute:

Let us now go and seek the rain of war in hopes that we do not drown in it's sorrow.

[ColonelSandersLite]

Poetics aside, wouldn't one just stand in the rain to get as wet as possible?

[TorpX]

Ever ride a bike in the rain, you get wet fast.



I approached the problem from the standpoint of 'search efficiency' (meaning the ratio of contact of a moving sub compared to a stationary one), as this seemed easier than figuring on complete coverage in a certain zone, or specific probabilities.


I thought about putting together a simple program that would track randomly generated ships through an area, and tally the number that were 'detected', but this seems like more trouble. If one wanted to know how well particular search patterns worked, with traffic on multiple axes, it might be necessary to do that kind of thing.

[ColonelSandersLite]

Ever just stand in the rain? You get wet pretty fast. Just saying. I've never really seen a study on it, but I suspect that how wet you get is more of a function of time rather than speed.

I thought about putting together a simple program that would track randomly generated ships through an area, and tally the number that were 'detected', but this seems like more trouble. If one wanted to know how well particular search patterns worked, with traffic on multiple axes, it might be necessary to do that kind of thing.

I've been thinking about doing just that as well. I'm reasonably certain that the math is solvable but the problem is pretty complex and I'm not a mathematician. I do know enough math and have put just enough thought into it to understand just how complex calculating the probabilities is though. I strongly suspect that it would be easier and faster for me to come up with a computer simulation that would provide a reasonable approximation.

[ColonelSandersLite]

Actually, Check this out, it might actually answer the question but I suspect a big flaw
https://www.youtube.com/watch?v=3MqYE2UuN24&feature=youtu.be

If we assume that like the rain in this math problem:

We must assume that you have no prior knowledge besides the reasoned deduction that you are patrolling a likely transit area and it's general direction (we'll use north-south for example sake).

Therefore, the only direction worth moving is perpendicular to the transit area (east-west in this example).

Without prior knowledge to the contrary, we must also assume that traffic flow is statistical uniform. I.E. The odds of a contact being 20 miles due north of you at the moment are the same as the odds the contact being there 4 hours later.

At any given time, a target could be anywhere in the patrol zone that is outside of your current sensor range.

If all of the above is ture you need to be moving e-w but loiter time needs to be maximised. I.E. Gas milage is unimportant, but rather consumption rate is.



The suspected flaw:
"Without prior knowledge to the contrary, we must also assume that traffic flow is statistical uniform."
When you move through an area, we know that no traffic moving at x speed can be in certain locations. For example, a 10 knot target could not have moved all the way through an area you searched with SJ-1 radar half an hour ago if you are cruising at 10 knots. This means that you do have some prior knowledge of where targets are not at any given time. Let's call these areas cavities.

In the question of rain on a person, rain falls at a relative velocity that the cavity is insignificant. I suspect that the relative velocities of ships means that the cavities are potentially quite significant when trying to form a statistical understanding.

[aanker]

I could have sworn it was in, 'Clear The Bridge', however I have read so many books - it could have been a different Skipper.

Whomever it was wrote that upon reaching his assigned area, he tried 'All Stop' and performed high-scope & radar searches at that location all day. The next day he would move 20 nm, and conduct the high-scope search at the new location all day, sail 20 nm the next day, and repeat the procedure until he found a contact.

Sadly, unlike SH1, SH4 doesn't model the larger horizon gained by using 'high-scope' searches, although in real life many patrolled using the high-scope farther horizon advantage.

What SH4 does correctly is model the almost daily position reports the Japanese (and Germans) were required to report. These reports would be intercepted and decoded becoming the ULTRA reports our Commanders received, and that We receive in-game as the red boxes with directional tails on our chart/map screen, along with the position report messages. This is why it doesn't bother me that those position reports are on the Nav map, although of course there are too many in Stock... (as was the case in SH1)

Unlike the Axis, US boats did as little communicating as possible - mostly none - because they were the 'silent service'. The few US wolfpack missions required some communication between the boats, and a small handful of boats reported that they were under attack, however most did not even report that. After a period of time they would be declared overdue and lost at sea.

This topic, "The mathematics of roving searches" is very interesting and is interesting to compare with the above static search method that conserves some fuel.

I've been a fan since the excellent tutorial on how to make a torpedo attack without the use of a TDC (S-boats didn't have a TDC) written by someone whose initials are, 'Frank Kulick'.

Happy Hunting!

[Rockin Robbins]

I base my theories on those of Admiral Eugene Fluckey, who with the USS Barb found targets when nobody else did. He didn't know the shipping lanes because he couldn't open his game box and dig one up or do a Google search. In Thunder Below he goes into great detail explaining exactly what I've laid out. All things being equal, your number of contacts developed is proportional to the number of square miles of ocean surface you search in a day.

Of course that has to be modified by the length of the cruise, the amount of fuel you have and having enough torpedoes to cruise the distance without running out.

Fluckey, starting his career when boats routinely returned to base without finding a single target, set the world on fire simply by staying on the surface, covering the most ground per day and using the longest range sensors he had (unlike SH4, radars broke painfully often). He pioneered using the scope on the surface, extended to its highest position to extend the horizon enough that he could double his visual search area.

So in real life they had to use raindrop theory at best to search for targets. Because of hindsight, we might come up with better methods but they would be bogus, based on assumptions real sub skippers couldn't make.

[ColonelSandersLite]

He didn't know the shipping lanes because he couldn't open his game box and dig one up or do a Google search.
No, they had compiled inteligence reports from sighting reports and radio intercepts. This aspect is mostly overlooked and missing in the game.

So in real life they had to use raindrop theory at best to search for targets. Because of hindsight, we might come up with better methods but they would be bogus, based on assumptions real sub skippers couldn't make.
If raindrop theory is to be used, then that would advocate just moving at 1 knot to maximise loiter time. See my previous post.



I've started putting together a simple computer model to help out and give us some actual hard data to think on. I should have it done in a day or two.

[Rockin Robbins]

No, they had compiled inteligence reports from sighting reports and radio intercepts. This aspect is mostly overlooked and missing in the game.


If raindrop theory is to be used, then that would advocate just moving at 1 knot to maximise loiter time. See my previous post.



I've started putting together a simple computer model to help out and give us some actual hard data to think on. I should have it done in a day or two.
Actually at any given time the air of a certain volume is occupied by a certain number of raindrops. In a flow that dense you encounter the same number of raindrops no matter what speed you run until you start to go faster than the time it takes the drop to fall your height. Then your horizontal velocity brings you into more raindrops than you would encounter standing still or going slower than that speed.

Let's quote Admiral Eugene Fluckey, quoting himself on page 65 of Thunder Below, in a conversation with Admiral Lockwood, who Fluckey would replace later.

"Luck is where you find it--but to find it you have to look for it. During her seventh patrol Barb was submerged every day waiting for the enemy to pass her way. It's no good. The area os search is practically nil.

"There's a big ocean out there. I search it on the surface with our high periscope up and a wide, sweeping zig plan, using as high speed as our fuel supply will allow. Now I realize that we may be sighted, depth charged, and bombed more often, but we'll find a helluva lot more targets. On our last patrol we spent only one full day submerged to check their biggest harbor.Pretty clear that ULTRA position reports were rare. Pretty clear that Lockwood didn't micromanage his skippers. Pretty clear that he didn't mention shipping lanes. Yes, he spent every moment reading war patrol reports for the purpose of figuring out where to hunt and what mistakes to avoid. Pretty clear that Fluckey's method is what I've copied and it works. Wide, sweeping zig plan, speed highest for patrol time: 11 knots for fleet boat, longest range sensors available.

This was the most successful sub captain in WWII for innovation, turning a slow part of the war into a bonanza. Heck, he sank a train.

[ColonelSandersLite]

Actually at any given time the air of a certain volume is occupied by a certain number of raindrops.

Now *this* is the critical factor that makes things pretty complicated. At what point exactly is it? I suspect that it depends very much on a number of factors, which is why I'm just writing a computer simulation. These factors would include:

Sensor range (maybe patrolling works better with SJ-1 while lookouts work better stationary?)
Target speed (maybe patrolling gives better odds of finding ships under a certain speed while having little or no effect on targets above a certain speed.
Patrol speed (maybe patrolling at 10 knots doesn't significantly change your odds from patrolling at 3 knots?)

The easiest way to get useful info that I see is just to write a computer program to try them all like 500,000,000 times.


Oh, and I wasn't talking about radio stuff specifically. More along the lines of something as simple as taking a map and putting a pin in it for every contact report. You know where all the ports are, and often logical deductions can be made just by connecting the dots. Other efforts will provide more data to work with, but the basic concept remains the same really. In other words, if you never look anything up in your sh carreer, you get the amount on intel you personally generate (and probably don't store it all that well), whereas a sub skipper in ww2 was additionally getting intel from other sources. That being said, I don't tend to look up things very often as the information revealed can be way too precise.

[TorpX]

Actually, Check this out, it might actually answer the question but I suspect a big flaw
https://www.youtube.com/watch?v=3MqYE2UuN24&feature=youtu.be



That's a pretty good analogy there.


The suspected flaw:
"Without prior knowledge to the contrary, we must also assume that traffic flow is statistical uniform."
When you move through an area, we know that no traffic moving at x speed can be in certain locations. For example, a 10 knot target could not have moved all the way through an area you searched with SJ-1 radar half an hour ago if you are cruising at 10 knots. This means that you do have some prior knowledge of where targets are not at any given time. Let's call these areas cavities.



I consider this the beauty of my solution. I've used vector addition to subtract the target ships' speed. (This sort of thing was done with a 'maneuvering board' for various problems.) Working the problem this way, the ships in diagram 2 (if there are any) do not move. We need not make any assumptions of how many, or where the ships are located. All that need to be done is compare the respective areas cut out, of the moving sub and the stationary one.


Here is another way to look at it. If the sub is going W and a ship is just far enough to the E to escape detection, it only needs to get through before the sub reverses course and can reach that area again. If the width of the search zone is very narrow, the sub will reach that area faster, and it will be hard or even impossible for the ship to get through here, but that also means there is more space on either side that is not being searched. Take this to it's logical conclusion and you are back to being stationary; no ship within your detection radius will get through, but every ship on either side will.



I could have sworn it was in, 'Clear The Bridge', however I have read so many books - it could have been a different Skipper.



Yes, thank-you. It's on page 54. I'm glad I'm not the only one who remembers that. I think O'Kane did a good job of explaining it.


Sadly, unlike SH1, SH4 doesn't model the larger horizon gained by using 'high-scope' searches, although in real life many patrolled using the high-scope farther horizon advantage.

Yeah, Ubisoft sure could have done better.





I base my theories on those of Admiral Eugene Fluckey, who with the USS Barb found targets when nobody else did. He didn't know the shipping lanes because he couldn't open his game box and dig one up or do a Google search. In Thunder Below he goes into great detail explaining exactly what I've laid out. All things being equal, your number of contacts developed is proportional to the number of square miles of ocean surface you search in a day.




Not to criticize Fluckey, but iirc, he did run short of fuel on one patrol, and had to go home empty handed; the point being that roaming doesn't guarantee results, and may leave you low on fuel.


Because of hindsight, we might come up with better methods but they would be bogus, based on assumptions real sub skippers couldn't make.

Not sure what you mean here. None of the math I've used requires quantum mechanics, string theory, or black magic.


I wouldn't even say that I've come up with a new method. It's more along the lines of a guideline as to what one can expect from roaming, so one can decide if it is worthwhile. In any case, O'Kane did do stationary patrolling on at least one war patrol, so it is not a gamey-hindsight deal.

[Crannogman]

IIRC, there is no gain in efficiency below 10-11kts. So you won't gain any distance by going slower than that, but you will remain on station for more time. I guess the moral may be that efficiently patrolling a barrier longer than ~35nm will allow an increasingly large fraction of shipping to escape detection. However, a barrier shorter than 35nm allows you to spot anything transitting while moving slower and staying on station longer.

[ColonelSandersLite]

I consider this the beauty of my solution. I've used vector addition to subtract the target ships' speed. (This sort of thing was done with a 'maneuvering board' for various problems.) Working the problem this way, the ships in diagram 2 (if there are any) do not move. We need not make any assumptions of how many, or where the ships are located. All that need to be done is compare the respective areas cut out, of the moving sub and the stationary one.
Yes, except I see big flaw in the reasoning here. Suppose we are patrolling roughly E-W in a hypothetical N-S shipping lane. We add a northward cant to our patrol as in your examples. This absolutely does decrease the speed vector of any ship moving north, thus giving better odds of detection. Shipping lanes go both ways though and it also has an inverse effect on any ship heading south, decreasing odds of detection. Supposing that you're trying to find a target you have some prior knowledge of (a radio reported convoy for instance), reducing the speed vector would surely help to actually locate them. Otherwise, I suspect that it doesn't actually help due to the inverse nature this has on finding targets going the other way. Though it might due to reasons I can't quite fully articulate at the moment.

Oh, been meaning to tell you that your link to table.txt above is broken.


Not sure what you mean here. None of the math I've used requires quantum mechanics, string theory, or black magic.

I wouldn't even say that I've come up with a new method. It's more along the lines of a guideline as to what one can expect from roaming, so one can decide if it is worthwhile. In any case, O'Kane did do stationary patrolling on at least one war patrol, so it is not a gamey-hindsight deal.

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.

[Crannogman]

Yes, except I see big flaw in the reasoning here. Suppose we are patrolling roughly E-W in a hypothetical N-S shipping lane. We add a northward cant to our patrol as in your examples. This absolutely does decrease the speed vector of any ship moving north, thus giving better odds of detection. Shipping lanes go both ways though and it also has an inverse effect on any ship heading south, decreasing odds of detection. Supposing that you're trying to find a target you have some prior knowledge of (a radio reported convoy for instance), reducing the speed vector would surely help to actually locate them. Otherwise, I suspect that it doesn't actually help due to the inverse nature this has on finding targets going the other way. Though it might due to reasons I can't quite fully articulate at the moment.


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

[Rockin Robbins]

Not to criticize Fluckey, but iirc, he did run short of fuel on one patrol, and had to go home empty handed; the point being that roaming doesn't guarantee results, and may leave you low on fuel.
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.


Not sure what you mean here. None of the math I've used requires quantum mechanics, string theory, or black magic.
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. The only valid strategies must assume that you don't know that information.

Again, searching is a numbers game. You're a card counter at a blackjack table. Are the odds in your favor? Sure. Are you going to win every time? Don't make me laugh. But does an example of failure invalidate card counting in blackjack? Not on your life. Play long enough and you win. Trotting out an example of Fluckey not finding anything is like that. He played long enough and cleaned out the house.

Also, if you're running RSRDC, it's fatally broken. The enemy shipping is coming no matter what. You can sit there sinking ships in a single choke point for the entire war and they just keep coming. In the quest for historical accuracy Lurker put the war in a stratjacket. He turned a living breathing war into a wind-up clock. In reality, when a target was sunk the Japanese rerouted shipping to avoid the submarine. This made covering ground as I've laid out an absolute necessity if you wanted to sink more than one or two targets.

As flawed as it is, the unmodified game traffic does a much better job of portraying the situation from the sub skipper's point of view. Actually some of the middle TMO versions were even better because they had more variety in their encounters.

[ColonelSandersLite]

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.


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]

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.





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.






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.






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]

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]

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. :03:



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)

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]

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]

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 http://www.subsim.com/radioroom/smartdark/viewpost.gif (http://www.subsim.com/radioroom/showthread.php?p=2338182#post2338182)
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 :arrgh!:).

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?:hmmm:


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]

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]

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.

[Berserker]

I go to my patrol area and wait for a ship to come by,sink it and wait for the next one...I average about 30,000 tons per patrol...Anybody want a drawer full of navy crosses???:haha:

[ColonelSandersLite]

Yes, nautical miles.
Honestly, I got distracted by a shiny new thing, and need to come back to this. That shiny new thing led directly to the advanced convoy attack tutorial if I recall correctly.


The question about how often to dive for maximum search is a fairly complicated one and in your case, depends largely on two large unknown variables. Those variables being detection ranges for visual and hydrophones in RFB. Without knowing those, I can't even begin to speculate, except to say that I don't think that WCA should have a detection range of anywhere near 20 miles. I could be wrong on that, but I don't think I am.


The best thing you can do is just find the range for yourself. Here's how I did it:
I used a boat equiped with radar and WCA.
Map contacts on.
Detected target on radar, then turned radar off.
Waited for target to show up on hydrophones.
Turned radar on and marked position on map.
Measured distance on the map.

The same procedure was used for JP, just a different boat configuration.

I would be quite interested in knowing what numbers you get out of RFB.



I should run a test on it, but I suspect that in tmo at least, the answer is really simple. Basically, my suspicion is that you want to use the best sensor you have as much as possible. With radar, this is always going to mean surfaced. With JP and no radar for some reason (damaged radar for example), this would mean staying submerged as much as possible. With WCA, this would boil down to the current visibility level on the surface. I.E., surfaced during the day as long as weather is clear and submerged at night or in otherwise poor visibility.

If minimizing the enemies opportunities to detect you is the priority, you are trading away sensor effectiveness for stealth. Particularly by submerging during the day when sonar isn't your best sensor. In this case, you are reducing your effective search area quite substantially during the day, due to the lower search speed and lower detection radius. This stance would necessitate surfacing at night to recharge, and doing this would significantly reduce your detection radius if you are relying of visual detection.

[merc4ulfate]

I just hunt in the shipping lanes. It is easy to find ships with TMO and RSRD.

[Barkerov]

I should run a test on it, but I suspect that in tmo at least, the answer is really simple. Basically, my suspicion is that you want to use the best sensor you have as much as possible.

Your suspicion would be correct becasue we are talking about circles and its easy to prove that the biggest one is best whether moving or stationary. S = 2rd/A where S = the sweep fraction, r is the detection range, d = the maximum distance of the search, A = the size of the search area.

I found this formula but I don't know how useful it is:
With a random search the probability of any given target being detected is then D = 1 - exp(-pS) where p = the probability of detection of a ship within the detection range r.

I think the answer with radar is simpler than it is with hydrophones. With the radar you can go with continuous sweep and so the only question that remains is how far back and forth do you travel. With the hydrophones you have to choose how far to go back and forth and also when to dive to use them.

[TorpX]

About the hydrophone detection; the early war equipment was probably only good to 7,000 or 8,000 yds. In RFB, the detection range is much greater, if you listen yourself. This however is a game bug, you can usually get a big advantage just by using the hydrophones yourself, while the crew performance is modded to be realistic. Don't know how much/when performance improved.

If you are trying to play realistically, your best bet is probably to submerge and go at most economical speed, 3 kn. during the day, and either sit still, or move at 6.5 kn. during the night (if you have enough fuel for that). On my last patrol, I followed the above procedure, only moving about 20 or 30 nm overnight to save fuel. This allowed for a fairly long patrol, while permitting me to cover a good chunk of my zone, bit by bit.

[Barkerov]

About the hydrophone detection; the early war equipment was probably only good to 7,000 or 8,000 yds. In RFB, the detection range is much greater, if you listen yourself. This however is a game bug, you can usually get a big advantage just by using the hydrophones yourself, while the crew performance is modded to be realistic. Don't know how much/when performance improved.

If you are trying to play realistically, your best bet is probably to submerge and go at most economical speed, 3 kn. during the day, and either sit still, or move at 6.5 kn. during the night (if you have enough fuel for that). On my last patrol, I followed the above procedure, only moving about 20 or 30 nm overnight to save fuel. This allowed for a fairly long patrol, while permitting me to cover a good chunk of my zone, bit by bit.


I just had a look at the uboat.net article on hydrophones.

"To avoid own noises, a submarine could use underwater sound detector if her speed was up to 6 knots. If a submarine speed was 4 knots, the submarine's underwater sound detector average distance of detecting another object was: - for a destroyer- 5 to 10 nautical miles,
- for a cargo ship- 3.5 to 7.5 nautical miles,
- for a convoy- up to 50 nautical miles."

Obviously this is for U-boats though and it also doesn't say when. I would like to play as realistically as possible, but I have no idea how far hydrophones can detect ships in game or in real life, just that for the latter it varied a lot with weather conditions.

[TorpX]

In my recollection, the 7,000 yd. figure was for detecting a single ship 50%, detection, at war's start, so convoys, and maybe larger/noisier ships would be more easily detected. USN sound gear seemed to behind German equipment, at least at the start.

I can't remember where I saw this, but it was a surprise to me, as I had assumed the range was longer.

[merc4ulfate]

Sonar ranges when listen was greater than you think and less than you think depending on sea state and weather.

http://www.hnsa.org/wp-content/uploads/2014/07/11730rb.mp3

http://www.hnsa.org/wp-content/uploads/2014/07/11720ra.mp3 (reference to a 20,000 yard target being heard)

http://www.hnsa.org/wp-content/uploads/2014/07/11722rb.mp3 (12,000 yards)

I love these recordings

[aanker]

I love these recordings
Thanks for these merc4ulfate, I do too and didn't know these even existed in digital form. 'Roving Searches' assistance from the hnsa, how nice these were saved.

I even learned winter survival techniques (for winter camping) years ago and many other things from old WW II USAAF & USN films.

Happy Hunting!