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