KC,
I was looking over your example and I have a few comments. I'll post some comments about the sub tactics at the end of the post, but I wanted to start with the sonar range calculations. Before I get too far into this, I want to recommend that you go to the Admiralty Trilogy CIC at the Clash of Arms website and download the H4 Sonar Calculator Excel file (http://www.clashofarms.com/the-cic.html and look under Harpoon for the calculator).
It seems like you are using the hull mounted sonars for both vessels, so I won't worry about towed arrays right now.
For the calculations I'm assuming you are using a Sea State of 1 - 4 (so the modifier is x1). Also, you have the sub approaching at Intermediate I depth, which is considered below the layer, so all the detection attempts are cross-layer.
For the T56 ASW DD, the DUBV 23/43 is a MF sonar with a base range of: Active 3.4 nm and Passive 1.3. Looking at the modifiers for sonar I see the following modifiers (Note: I only included those that are not x1):
Active: Target has Anechoic coating (x.5), Target Cross-layer (x.5). The base 50% range calculation is 3.4x.5x.5 = 0.85 rounded to 0.9. So the detection ranges turn out to be: 75% = 0.4, 50% = 1.0, 25% = 1.4. If the sub is above the layer this changes to a base 50% range = 1.7 with detection ranges of 75% = 0.7, 50% = 1.9, 25% = 2.6.
Passive: If the ship decides to use passive sonar, the modifiers are Target is VQuiet (x.5), Target Speed 20kts (x6), Own Speed 12kts (x.5), Target cross-layer (x.5). The base 50% range calculation is 1.3x.5x6x.5x.5 = 0.975 rounded to 1.0. So the detection ranges turn out to be: 75% = 0.4, 50% = 1.1, 25% = 1.5, which is slightly better than the active ranges.
For the LA class SSN, the BQQ-5C/D is a LF-MF sonar with a base range of: Active 4.7nm and Passive 3.8nm. I'll only look at the passive modifiers for this example.
Passive: Target is Noisy (x2) [Note: if the DD uses active sonar it is considered a Loud noise rating, which is x4. I will show the calculations for both an active and passive DD], Target Speed 12kts (x2) [Note: the DD is considered to be cavitating, so the final passive detection range is doubled], Own Speed 20kts (x.25), Target cross-layer (x.5). The base 50% range calculation vs. a passive DD is 3.8x2x2x.25x.5 = 1.9, doubled for cavitation to 3.8. So the detection ranges turn out to be: 75% = 1.5, 50% = 4.2, 25% = 5.7.
If the DD is using active sonar, use the Loud noise modifier (x4); but you wouldn't apply the cavitation modifier, since the reason the DD is Loud is its active sonar.
With those basic calculations from your example out of the way, I want to talk about a couple other things. First off let's look at towed arrays.
If the sub is really chasing the DD, then it will be in the destroyer's baffles, making detection from the ship's hull array impossible. However, the French DUBV 23/43 is combined hull and towed (VDS) array, so deploying the VDS will still provide detection capability and it could be deployed below the layer to avoid the cross-layer modifier (Note: if the VDS is deployed below the layer, the base range for active is 1.7 and for passive is 2.0).
For the sub; if you allow it to deploy the TB-16D towed array and make course changes to allow the towed array to be in detection arc, you get a longer detection range for the sub. TB-16D base range is 5.1 nm and the modifiers are Target is Noisy (x2), Target Speed 12kts (x2) [Note: the DD is considered to be cavitating, so the final passive detection range is doubled], Own Speed for high speed array 20kts (x.5), Target cross-layer (x.5). The base 50% range calculation vs. a passive DD is 5.1x2x2x.5x.5 = 5.1, doubled for cavitation to 10.2. So the detection ranges turn out to be: 75% = 4.1, 50% = 11.2, 25% = 15.3. It should also be noted that the TB-16D would not get the Loud target modifier if the DD is using active sonar since it has a VLF-LF frequency range.
Next up, let's look at some tactics for the sub. Rather than driving directly toward the target (I'm assuming that sub already has an idea of where the target DD is) at high speed (20 kts), I would use a sort of sprint and drift type of tactic, where high speed is used while diving below the layer (speed could even go up to 24 kts without changing the passive detection modifiers) and a slow speed (8 kts for best detection, but up to 14 kts still gives a good detection range) above the layer used to find the target and for course corrections to intercept.
A quick look at the detection ranges for the slower speeds shows:
At 8 kts:
BQQ-5C/D base 50% range = 30.4, detection ranges: 75% = 12.2, 50% = 33.4, 25% = 45.6
TB-16D base 50% range = 20.4, detection ranges: 75% = 8.2, 50% = 22.4, 25% = 30.6
At 14 kts:
BQQ-5C/D base 50% range = 15.2, detection ranges: 75% = 6.1, 50% = 16.7, 25% = 22.8
TB-16D base 50% range = 20.4, detection ranges: 75% = 8.2, 50% = 22.4, 25% = 30.6
One thing about the report; submarine/ASW is a slow long term thing, so I think the longer reports are fine. If you want to shorten, just move from the starting point to the first detection point without writing out all the attempts.
I hope that helps out and I really recommend getting the Excel file.
Dave