Here is a slightly different example to further illustrate the concept:

Suppose you are astride a N-S sealane and want to "search" it. I will assume, as before, freighters traveling 9 kts. and a 10 nm detection radius. (This is good for SH 4, since nothing is rendered beyond 10 nm anyway.) If you sit still you will detect 100% of ships in a 20 nm "slice" (10 nm East and 10 West). If you want to move E-W across the sealane (in effect yo-yoing back and forth), how far can you go East or West, without letting ships "slip through"? If you are cruising at 10 kts., you can go 11.1 nm on either side, and still make sure nothing gets by in the center. Why do I say 11.1 nm? Because in the time it takes you to go 11.1 nm East and 11.1 nm West (back where you started), an enemy ship could move through the 20 nm deep band you are searching. Going any farther would allow some ships to slip past. Following this plan, you will detect 100% of ships within this 22.2 nm zone, and some of the ships within a 10 nm 'fringe' zone on either side. If you wanted to cruise at 15 kts., the figures would be 33.3 nm with a 10 nm 'fringe'.

The math I used does not require a particularly wide or narrow sea lane. You can use different figures with these calculations and get substantially the same results. Fuel not being as much an issue is due to shortcomings in the game. In RL rough weather would slow you down much more. Even as it is when I am playing an S-class, fuel is indeed an issue. If I cruised continously in an S-class, it would be a short and unhappy patrol.

I'll grant you targets zigging will give you more of a chance to detect them, but this doesn't fundamentally alter the math.

I would say you are giving away contacts by wasting fuel and terminating the patrol prematurely.

I'm not disputing the usefulness of radar (or sonar or anything else). Anything that doubles your detection range will double your chances, likewise anything that halves your detection range will halve your chances. This is true whether you are moving or not. Radar really has nothing to do with it. If you want to compare a radar equipted boat to one without radar, the radar boat will obviously win.

In any case, if you have a 20 nm radar, you can cover most of the area of a choke point even if your not moving.

OK, lets say you arrive at your patrol area on monday. No matter how quickly or intensely you search search your box. You will have to do it again tuesday, and wednesday and thursday....... However quickly you search, you cannot pull the targets to your location. If the area has an average of 2 ships transiting each week, it will take weeks to obtain a good number of contacts. And it is unlikely you would find them all. Realistically, most areas would not give you a contact every day, but by continuously cruising you would be burning a lot of extra fuel each and every day.

Look, I can see your just a bit skeptical. ;) I am not trying to convince you to do it my way, but the math is the math.

The bottom line is a moving search is not as big a help as you like to think. When you are moving to the east, targets can slip by to the west, when you move to the west, targets might slip by to the east. If you go farther to the east to "cover more ground", a target could go past in the center or the west. You cannot be in two places at once, nor can you hasten or delay their arrival.

Not true.

Fluckey did a lot of unorthodox things. As I recall part of his efforts involved probing/ raiding coastal anchorages where enemy ships were hiding out during the night. Is this what you are refering to? Looking for anchored ships or raiding coastal locations is not quite the same as searching for ships moving thru an area.

How does this invalidate anything I said?

This is only true if you are searching for things that are not moving. While you are searching one end of your area, targets can move through the other and you'll never know it. Moving from one part of an area is not the same as being in both places at once.

Again, the square area is not what is important. If you were trying to find sea shells on a strip of beach, this would work ok. You could search an area, cross it off your list and move on to the next section. However, if the "sea shells" have the ability to move out from the water to the beach, and back into the water again, you will not be able to find nearly as many. They would be moving about in sections that you had "cleared". Your search efforts are only effective if there is a target nearby at the moment you are there. If the target moves thru either before or after you go by, you won't find it. Based on your analysis, it doesn't matter how fast enemy targets move, or if they move at all! An enemy cruiser moving at 30 kts could be found as easily as a drifting barge. You should see this is obviously not the case.

This is patently absurd if you think about it for two seconds.

If the first statement were true, it suggests there would be no difference.

OK, if this was really true, then you would get 2*6.88 times the number of targets in two days and 7*6.88 the number in a week. Do you really think just by moving at 9 kts this will get you 48 targets for every one I get in a single week? At this rate you could sink nearly 200 times as many targets in a month. Nice try, but your math does not hold up. Assuming that the number of contacts found will be proportional to the sq. area is a gross oversimplification.

I never suggested submerged searching was better than surfaced searching. In fact the opposite is implied. Anything which increases your detection range (visual or otherwise), will improve your number of contacts by the same proportion. People seem to be reading things into this that I didn't write and don't intend. I never said it was better to drop anchor and remain motionless as if in a coma, or hide on the bottom of the ocean. Please, if you want to criticise what I've written, at least read it a little more carefully.