Static Search Vs. Dynamic Search - Page 2

TorpX · 01-21-12, 04:50 PM

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?

01-21-12, 04:50 PM	#1
TorpX Silent Hunter Join Date: Sep 2010 Posts: 3,975 Downloads: 153 Uploads: 11	Static Search Vs. Dynamic Search 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?