Static Search Vs. Dynamic Search

[TorpX]

There was some discussion in the thread TMO fuel usage at 0 knots, and this lead to the question of which is better, sitting still or cruising around to look for targets. This got me to thinking about it a little more deeply, so I did some math....

To illustrate the idea, lets say you are a new SH 4 Captain, who has just been put in command of a shiney new Gato class fleet boat. You will be shortly sailing from Midway, to a patrol area in the vicinity of the Luzon Strait. Since this is your first war patrol, you are undecided about whether to use a 'static search' or 'dynamic search' method. Fortuantely, your experienced, dedicated, and hard-working XO, has prepared a short report to help you.

Mathematical considerations:

For simplicity sake, we will only consider merchant shipping, and will assume that it is all following a single axis (say north to south and south to north), we will further assume that our cruising in the patrol area is perpendicular to this shipping lane. This provides an optimum chance to obtain a contact if we are using the 'dynamic search'. It is also assumed that ships are randomly distributed in the region we are patroling (i.e. not clustered in any particular line or region).

Once the geometry is done, we have:

Pr = 2 * Rd / sin a
......where a = arctan (Vt / Vu)

Pr is relative probability or finding contact
Rd is detection radius of your boat
Vt is speed of target
Vu is speed of sub

Note that if Vu is 0, a is undefined, but we know from the geometry that a = 90 in this case.

Here is a tabulation to show how the probability of obtaining a contact, in a given time period, is enhanced by the sub cruising at speed (the targets are assumed to all be traveling at 9 kts in this problem):

Vu..................... a ....................Pr
0......................90....................1
5......................60.9.................1.14
10...................42.0.................1.49
15...................31.0.................1.94

The relative probabilities are indexed so the lowest figure is 1, this being the 'static search' value. I call the margin of the higher values the 'search bonus'. So we have a modest 'search bonus' for slow cruise at 5 kts., a slightly higher bonus for 10 kts., and a still larger one for 15 kts. This would seem to settle the issue, but we're not done yet. Let's see how our fuel budget looks for our patrol. For simplicity, we will compare a static search patrol to a dynamic search where we cruise at 10 kts. This allows us to use the quoted endurance figures without having to guess how fuel consumption changes at a higher or lower speed.

STATIC SEARCH
total endurance 11,000 nm @ 10 kts

round trip to patrol area...................7,000 (29 days)
safety/weather allowance................1,000
tactical pursuit/evasion....................1,000
remainder available for search........2,000

31 days using 20/day..........................620
extra* .................................................1 ,380
This allows 31 days on station. I will assume we terminate our patrol at this point. So we could use this to move 20 nm each day a have extra* left over. I'll come back to this later.

DYNAMIC SEARCH
The first four lines are the same, except:

8. 33 days cruising at 10 kts............2,000
So we have only 8 days to search here. When we multiply the relative probabilities of finding a contact by the number of days on station, we get:

static search.............31 * 1.00 = 31
dynamic search....8.33 * 1.49 = 12.4

However, there are also practical considerations:

1. If venturing into shallow water is contemplated, it would be desirable to move in at night, and then leave before daylight, fuel considerations notwithstanding.

2. If the patrol area has prodigous shipping, fuel may not really be a limiting factor. In this case, we have more flexability, as far as fuel is concerned.

3. The 'static search' plan would allow for a limited redeployment, if we should find ourselves in a shipping desert, without cutting short the patrol. (Remember the extra fuel.) The 'dynamic search' plan does not.

4. If we find ourselves in an area where there are no targets, the 'search bonus' does not help us. On the contrary ,cruising around faster will merely exhaust our fuel faster. You can't detect targets that are not there.

Any thoughts?

[gi_dan2987]

I totally see the point you are trying to make. I personally think that if the target is within feasible sailing distance, and you're not nearing the point of no return on your fuel level, then making a solid dash for attack position would be well worth the extra go juice.

I personally find that galavanting around at optimal cruise speed on the surface on a search course is the best way to increase odds at running into something. While surfaced and cruising around, you're covering way more square area in a shorter amount of time than putsing around submerged with the hydrophones. Granted your watch crew may have a detection radius much smaller than your hydrophones, but the larger area you can cover on the surface more than makes up for lack of spotting radius.

When you finally equip radar, surfaced patrol is undoubtedly the best method, as radar will out range both eyeballs and hydrophone alike. Then of course there's your contact reports to go off of. All in all it's a patrol just to see what's out there, and sometimes there is nothing. Historically many subs went out on patrol for months only to see miles of empty ocean.

I suppose this is why they call it hunting and not killing right? heh
Since we're on this subject of patrols and what not, would you have any suggestions as to plotting accurate speed readings? The stadimeter stopwatch icon seems to give me poor estimates, and the measuring tools have a built-in error margin that increases with distance. There's gotta be a way.....

[magic452]

Originally Posted by gi_dan2987

I suppose this is why they call it hunting and not killing right? heh
Since we're on this subject of patrols and what not, would you have any suggestions as to plotting accurate speed readings? The stadimeter stopwatch icon seems to give me poor estimates, and the measuring tools have a built-in error margin that increases with distance. There's gotta be a way.....

Edit I just read in another post that you don't want to use map contacts so the following is not for you. Maybe will help someone else. Map contacts is a bit too easy and off I really didn't enjoy, so I use contacts on.

Playing with map contacts on just have your sonar man track closest contact and then mark your X at the end of the bearing line.
For a convoy you'll have to pick a target and follow it yourself.
That range is pretty accurate and you can plot course and get speed by the three minute rule. I do 3, 6 and 9 minutes and get a very accurate speed and course. The three minute rule; for radar or sonar contacts wait till the target updates (20 seconds for sonar, 30 seconds for radar).
When it updates place an X on the target or the end of the sonar line.
Start the stopwatch. Wait 3 minutes (3.25 minutes for metric) and mark another X when the target is updated. The distance between the Xs in yards divided by 100 will equal the target speed. 500 yds = 5 knots, 1000 yds = 10 knots. Do this three times and you'll have an very good target course and speed.

Take the ruler and turn on tool helper and you get a compass rose, place the center of the rose on the target course line and read the number closest to the target. That is the target heading in degrees. remember this number. Go to the peri screen and first turn on the PK. Next go to the data input dials and input speed and sent to PK. Third go to the AoB dial and turn the dial to the side of the target you will shoot at, Starboard or Port. Turn the dial a few degrees and send to PK and when you do you'll see the top dial on the left side move and the bow of the target will point to the ring of numbers on the outside of the dial. Those numbers are the target course in degrees (4=40°, 9=90°,etc.) Just turn the AoB dial till the bow of the target ship points to the course you measured on the map. Once the target lines up with that course send to PK. You now have a very good AoB and the PK will keep this for you as long as the target holds course and speed.

You now have two thirds of your firing solution and you haven't even seen the target yet.

A couple of good steadimeter readings to get range/bearing and you're all set. Check the firing solution on the attack map and make any last minute adjustments.

This is called killing.

Magic

[magic452]

I only use a dynamic search even from Pearl and refueling at Midway. I have seldom had any real problem with fuel limiting my patrols. I run out of fish long before fuel becomes a concern. Once I hit very heavy weather all the way back to Midway and just did make it. I usually port in Fremantal or Brisbane and fuel is not any concern at all.

With sonar only I set up a patrol pattern with each leg about 10 nautical miles and do a manual sonar sweep at the end of each leg, I'll wrap the search around the end of each leg to cover my 6. That's one sweep every hour at 10 knots. You cover the most area and find the most targets.

Once you have radar sitting still makes no sense at all.

I don't think I've ever had any patrol last more than 35 or 40 days.

Magic

[TorpX]

Originally Posted by gi_dan2987

I totally see the point you are trying to make. I personally think that if the target is within feasible sailing distance, and you're not nearing the point of no return on your fuel level, then making a solid dash for attack position would be well worth the extra go juice.

I personally find that galavanting around at optimal cruise speed on the surface on a search course is the best way to increase odds at running into something. While surfaced and cruising around, you're covering way more square area in a shorter amount of time than putsing around submerged with the hydrophones. Granted your watch crew may have a detection radius much smaller than your hydrophones, but the larger area you can cover on the surface more than makes up for lack of spotting radius.

Perhaps this wasn't clear from my OP, but I consider there is a BIG difference between using fuel to pursue a known contact, and using fuel to cruise around aimlessly. I think most, if not all, skippers would have used almost any amount of fuel to attack a definate target. Also, I should clearify what I mean by a 'static search'. In my example, I allowed for 20 nm movement each night. ( O'Kane mentions this as a safeguard, in case they had been spotted by an aircraft and the enemy was routing ships around their position. Maybe I'm the only one who reads O'Kane. )



Anyway, to return to my example, searching at 5 knots only increases your chances by 14%. Searching at 10 kts. gives a 49% greater chance per day. This sounds good but.... this is at the cost of reducing your time on station by a substantial margin; hence your gains are illusory.

One thing I didn't include in the OP, because I hadn't thought of it at the time. The figures if calculated are based on a searching boat moving at a right angle to the shipping lane. If the searching boat is to stay inside the lane, it must periodically reverse course and backtrack. This would have the effect of reducing somewhat the 'search bonus'. (The boat would be searching water just recently travelled through.) How much, would depend on how often it would turn around.

While surfaced and cruising around, you're covering way more square area in a shorter amount of time than putsing around submerged with the hydrophones

It is not the square area, but the radius that is important. If you can see 5 nm and you detect X % of ships transiting the area, a 10 nm visibility will allow you to detect 2X %,(not 4X %). This may seem counter-intuitive, but if you diagram it, you will see it is true.



If you want a rule-of-thumb, I would say limit your fuel use in such a way that you would be able to complete your patrol schedule. That is, for a fleetboat, be able to remain at sea for at least 60 days. I'll admit, it is more "fun" to be cruising around "doing something" than sitting still, but this is not the same as saying it is a more successful tactic.

I was thinking it would be interesting to try to pin down the math more, so different search patterns could be analyzed according to the assumptions used, but as you are the only one to post a reply, I'm guessing there is limited interest in this topic. Anyway, thanks for the response.

[Armistead]

The formula probably has more bearing historically than it does in game. Course he may have readjusted fuel for 2.5, I'm still playing 2.2 where fuel really isn't an issue.

Even before that fuel has never been an issue, stay in shipping lanes and the traffic will come.

[magic452]

Just a few thoughts.

If I remember right you wouldn't get a mission to Luzon from Pearl via Midway. You would go to Japanese home waters that are closer so you have more fuel for patrolling. This would hold for both methods but with the static patrol the extra fuel would do you much good because you are already staying out 60 days.

I can only think of a single time I've spent anything near 1000 nm in pursuit and evasion. I chased a fast TF in heavy weather at flank speed for something like 200 nm. Even at that I RTB for torpedoes not fuel, I had one left. I was out of Brisbane so fuel wasn't a real factor.

Safety/weather allowance of 1000 nm. seems rather excessive.

So in my experience I have a lot more fuel than you are allocating for patrolling. I can't think of a single time I patrolled for only 8 days, it just hasn't happened.

31 ships in 31 days of paroling. Nice if you can sink 31 ships with only 24 torpedoes. In my experience two fish for every target and some times three.
dynamic search = 12.4, two torpedoes per ship = 24+ torpedoes.
A static search will net you 12 ships at best in 12 days or more patrolling and you RTB for lack of fish and fuel is no factor. I've gone many a day without seeing anything at 10 knots and that is covering 220 nm. more than a static search would and that's at 0.49% higher rate.

The idea is to sink enemy shipping not stay on patrol as long as possible.

The only time a static search would be of any real value is if you are assigned to patrol the entrance of a major port, a choke point or a mission to the Sea of Japan and even at that I think a dynamic search would be more productive. These areas are patrolled by aricraft and you can get down much faster at 10 knots than you can at zero. What O'Kane did or didn't do has little relevance to playing this game. Things just don't work like they did in real life.

Where do you get that PR figure? 1.0 verses 1.49 at 10 knots.

I don't patrol perpendicular to a shipping lane but rather zig zag along it's length.

#3 With a dynamic search you will leave that shipping desert just by the fact you are moving and patrolling the biggest possible area.
With a static search you leave that desert 20nm. a day or the the whole fuel thing falls apart. There are lots of shipping deserts out there and you go where you are sent. If you're playing by the book you do your patrol and call in for another mission, can get sent to many shipping deserts this way.

Anyway for my torpedoes I'll patrol at 10 knots and take my chances.

Magic

[Stealhead]

I fully agree with Magic your duty is destroy enemy shipping therefore one should use the tools at hand to maximum effect by staying in one spot your are adding the Japanese because now they just need to have the poor luck to come to you by being mobile they now must deal with the bad luck of being within 200 miles of you.I think like a tiger each tiger has a large bit of land that is his and he roams it constantly.

Considering that all of the most successful US Navy submarine captains all firmly believed in actively patrolling or "dynamically" searching it seems to me that it is the best method.Why sit in one spot and wait when you are very likely missing something 30 miles away that is not headed in your direction.I have never had fuel consumption issues myself with various versions of the game even if having to leave a dry area.I would say in most cases performing an active search in the typical "patrol this area for X hours" and covering a 100-120 miles radius I very rarely wind up not finding a ship or ships often I will find a convoy attack it and move on and wind up finding and hitting another convoy 40 or 50 miles and few hours searching later.Seems to me by sitting in one spot you are greatly lowering the odds of finding a ship unless you knew for certain that something was going to pass your position which in most SH4 missions you do not.I find a known lane and go hunting.If you ever read "Thunder Below" by Gene Fluckey you will be firmly convinced how much more effective it is to actively search but all the successful skipper where like minded they would have felt that being static and conserving fuel would be counter productive to searching the greatest area and therefore increasing your of finding ships which of course is the primary mission to seek out and destroy enemy shipping.

[TorpX]

Originally Posted by magic452

Just a few thoughts.

If I remember right you wouldn't get a mission to Luzon from Pearl via Midway. You would go to Japanese home waters that are closer so you have more fuel for patrolling. This would hold for both methods but with the static patrol the extra fuel would do you much good because you are already staying out 60 days.

The reason for conserving fuel is so you have it when you need it. If you get an ultra message or decide to move 300 nm to a different area, it is nice to have the fuel to do it.

I can only think of a single time I've spent anything near 1000 nm in pursuit and evasion. I chased a fast TF in heavy weather at flank speed for something like 200 nm. Even at that I RTB for torpedoes not fuel, I had one left. I was out of Brisbane so fuel wasn't a real factor.

The 1,000 nm is not to be taken at face value. 1,000 endurance at 10 kts is likely to be more like 250 at 20 kts. I tried to stick to the 10 kt endurance figures, since those are the figures quoted. If anyone knows the actual fuel consuption at 15 or 20 kts, please help me out.

Safety/weather allowance of 1000 nm. seems rather excessive.

See above.

So in my experience I have a lot more fuel than you are allocating for patrolling. I can't think of a single time I patrolled for only 8 days, it just hasn't happened.

First, I used a fairly distant patrol area for the example. Second, mod and game issues change what the in-game fuel consuption will be. I just used the quoted 11,000 nm @ 10 kts. figure.

31 ships in 31 days of paroling. Nice if you can sink 31 ships with only 24 torpedoes. In my experience two fish for every target and some times three.

Don't get hung up on the exact figures. These are relative numbers of contacts. In a low traffic area, the "31" contacts could be 3 or 4. The point is that if one method gives 30 relative contacts and the other gives 15, this says you can expect twice as many. The actual number would depend on the volume of shipping and your luck.

dynamic search = 12.4, two torpedoes per ship = 24+ torpedoes.
A static search will net you 12 ships at best in 12 days or more patrolling and you RTB for lack of fish and fuel is no factor. I've gone many a day without seeing anything at 10 knots and that is covering 220 nm. more than a static search would and that's at 0.49% higher rate.

As I said above, these are the relative probabilities of a contact, not the actual number of ships. This is impossible to calculate with very specific data for a particular area.

The idea is to sink enemy shipping not stay on patrol as long as possible.

A short patrol runs the risk of having few (or no) contacts. It's possible to run around like a speedboat and find a good number of contacts if there is a high volume of traffic to find. It's just as possible to burn up your fuel and be forced to RTB emptyhanded. There were war patrols where boats came back after 60 days with all their torpedos. Since you have no good way of knowing how many or when you will get contacts, it makes sense to plan for a long patrol from the start.

The only time a static search would be of any real value is if you are assigned to patrol the entrance of a major port, a choke point or a mission to the Sea of Japan and even at that I think a dynamic search would be more productive. These areas are patrolled by aricraft and you can get down much faster at 10 knots than you can at zero. What O'Kane did or didn't do has little relevance to playing this game. Things just don't work like they did in real life.

You may not like O'Kane. I started this thread for those who are interested in the RL techniques/math of patroling. I agree SH 4 is not too much like the actual war. IMO, it is rather too easy to come up with targets in the game. It depends a lot on your style of play.

Where do you get that PR figure? 1.0 verses 1.49 at 10 knots.

I gave the formula used in the OP. I have no easy way to post a diagram ATM.

I don't patrol perpendicular to a shipping lane but rather zig zag along it's length.

Going back and forth perpendicular to the shipping lane is the optimum method. This is easily visualized if you imagine going parallel to the shipping lane. You would not make contact with any ships that were not going make contact anyway. You would only hasten the contact from one direction or delay them from the opposite direction. Zigging has some advantage if you just "passing through" an area, but I don't see much advantage if you have reached the area you want to patrol.

#3 With a dynamic search you will leave that shipping desert just by the fact you are moving and patrolling the biggest possible area.
With a static search you leave that desert 20nm. a day or the the whole fuel thing falls apart. There are lots of shipping deserts out there and you go where you are sent. If you're playing by the book you do your patrol and call in for another mission, can get sent to many shipping deserts this way.

Again, you are not understanding the concepts here. I don't want to get into the whole mission/patrol area thing. I know some people ignore mission orders altogether, some are diligent in following them. I doubt many will spend a whole patrol in an unproductive area. If you use a static search technique, you can search an area for a week or two, and if you have not found anything you have plenty of fuel for a redeployment ( within reason). If you are using a dynamic search, and you spend a week or two and come up empty, you may not have enough fuel to do much about it.

Anyway for my torpedoes I'll patrol at 10 knots and take my chances.

Magic

Anyone is free to play as they please. I should like to reiterate this concept is not really mine originally. O'Kane mentions this in his book. I don't remember the exact words but the jist of it is that racing around did not provide much advantage in searching for contacts. He said this could be shown mathematically. I just did the math.

Many times new people have made posts asking why they can't find targets, or why they don't have enough fuel. Often, the response is to go here or there, because there is a lot of traffic over there in that time period, or a battle will happen on such and such date. RL captains did not have this advantage. They had to rely on sound technique and perserverence. I have attempted to show how they were able to do this.

[TorpX]

Originally Posted by Armistead

The formula probably has more bearing historically than it does in game. Course he may have readjusted fuel for 2.5, I'm still playing 2.2 where fuel really isn't an issue.

Even before that fuel has never been an issue, stay in shipping lanes and the traffic will come.

I did intend this more for historical interest than as being essential for SH. People seem to either have a hard time understanding the math or just don't want to change their prefered game style. Oh well.

[Armistead]

Originally Posted by TorpX

I did intend this more for historical interest than as being essential for SH. People seem to either have a hard time understanding the math or just don't want to change their prefered game style. Oh well.

Yea, I get it, problem is odds math seldom worked in history or in real game, but interesting concept.

I sort of static and dynamic, depends where I'm hunting. If I'm in Formosa I know groups going north or south cant get past me, so I can sit there. The same with the shipping lane off the west coast of Borneo, you can sit 30 nms of Brunei and catch the large RSRD or TMO for that matter convoys coming either way. Simply, if you know the right places, you can sit and the traffic will come to you. That's the problem with predetermined traffic, easy to deal with once you know it.

Seldom did subs static search historically, they were basically always moving, moreso when they started acting like surface raiders. I think in Wahoo, the first patrol with an old Captain Wahoo spent over 500 dived, when Morton took over, it was 60 hours the first patrol......that's balls. He made subs moving surface raiders.