Quote:
Originally Posted by TorpX
Pardon for the double post. 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.
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You're confusing yourself by uncalculable random effects. If you are standing still they can miss you in any direction. If you are moving the same is true. You can't count the ones you miss. That's the defect in your method of calculation.
It is much better to think of searching in the same way Eugene Fluckey of the Barb did. He spent a lot of time explaining the situation, so I'm going to condense it.
The fact is, we don't know the disposition of the enemy on the ocean. If you are static in the middle of the horde, you're going to be successful. If you're static in a vacuum, you're coming back with a goose egg.
So you say, if you get a goose egg in 24 house, move! That's fine. Murphy's Law says you just moved from the next hot spot.
The only thing we can say for sure is that in any moment in time, the enemy is distributed in an unknown array over the surface of the ocean.
According to Fluckey, and I agree, the odds of finding a target approach unity when the distance between your sub and a target is within sensor range. So your job is to get within sensor range of as many targets as possible in a 24 hour period.
The corollary of that statement is that the number of targets you encounter is directly proportional to the number of square miles of ocean surface you search each day.
Let's do the math! You're static with a visual search radius of about 5 miles and a sonar search range of 20 miles on a good day. So you're searching a circle 20 miles in radius. The area you've searched is 3.14*20^2 square miles or 1,256 square miles.
Let's move out! We'll assume a 20 mile range for our radar and we're moving on the surface for 24 hours at our best fuel economy speed of 9 knots. Now your searched area approximates a rectangle 40 miles wide and 216 miles long. That's 8,640 square miles.
Since the enemy is moving and the effect of that movement is random we can safely ignore any effects on our results. Our movement will bring as many targets in range as it will leave beyond range. Therefore the comparison in the number of targets we develop can be expressed as the ratio between the two numbers of square miles searched.
So you are 8640/1256 times more likely to develop a target when moving. That is 6.88 times more likely. Another valid way to interpret the data is that a patrol during which you are actively searching at 9 knots, you will develop 6.88 times more targets in the same number of days as you would be searching statically.
But that is not the entire story. There are monstrous advantages to searching on the surface as opposed to searching submerged. Of most importance is the value of fully charged batteries. They can save your life, you know!