I spent the last few days fiddling with some spreadsheets to try to figure out the optimal missile area defense/PD layout for a given tonnage. I came to a few tentative conclusions which surprised me a bit and wanted to bounce them off you guys to see if they pass the sniff test. Sorry in advance for the rambling post, I'm mostly just trying to organize my own thoughts hoping somebody will be bored enough to read through it and poke holes in any obvious errors
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I found this super useful thread from way back in VB6 which had a derivation of hit chances for pure final fire vs area defense with a factor 'A' representing all non-range to hit factors (tracking speed, tracking time, etc.) which should be basically the same in both cases. I'm standing on the back of giants here and just assuming their math is right, it looked OK to my eye -
http://aurora2.pentarch.org/index.php?topic=5197.0 Has there been any such discussion for C#? If so, I must have missed it - please point me at the thread
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Anyhow, at the time (2012), they concluded that Final Fire was superior in all cases, even with lasers, and easier to boot as it would work for a single big fat stack of ships. However, looking at this, one major factor has changed since these numbers were crunched - BFCs are smaller now, and FF vs AD BFCs are closer in tonnage.
This leads to a few differences from the VB6 case with the same 1400 T payload, tech, missile speed as they discussed (I assumed fractional guns for ease of calculation):
- higher beam PD efficiency overall in C#
- a slightly better Area Defense (AD) performance for 10mm Lasers vs Final Fire (FF) (7.65A vs 7.16A)
- a slight advantage in some cases to increased BFC range modifiers even for Final Fire, at least with higher ton/shot weapons. A 2x range 200T BFC and yields a FF efficiency of 7.166A vs 6.85A with the 100T 1x.
- For lower weapon counts (<~3/~450Tons) a .6-.9 range BFC may yield superior hits/ton in final fire mode. At ~4+ weapons a 1x range BFC seems ideal for FF and for very large banks of weapons a 2x-3x range BFC may be ideal for FF for the slight to hit-advantage. Also, a 2x-4x range BFC will greatly increase mid-range accuracy for systems like lasers which may also be used against other ships.
Notes: I think missiles are a bit slower in C# due to the engine changes, correct? Maybe I should plug in a new missile speed to be more consistent with this ~4000RP cost low tech example?
I totally eschew power plant tonnage, crew tonnage, and turret tonnage here since I kind of assume it will be 'small' and 'similar' across these cases, this may be a terrible idea but I'm lazy.
In the old thread linked, they made a low tech comparison when 10cm lasers.
Once capacitor 6 is reached, a 15cm laser can give 2x the range at 1.33x the tonnage, and in this example case the range impact will increase the laser AD efficiency vs 10cm lasers to 7.97A, at least for these missiles and all other techs equal. I neglect the 2x power need, which might matter a bit, but efficiency seems pretty similar for the 10cm and 15cm case. I think there is another bump to AD efficiency/ton possible at ~12,25 Cap Recharge where a 10cm, 15cm x.75 laser could have ROF5, but this is probably quite expensive and may not be practical. EDIT: Oops. I trusted the wiki sizes for beams but C# sizes are 3, 4, 5 HS for 10,12,15 not 3,4,4... this changes things a lot :S. Since there is no big nonlinear bump in range/HS in C/#, 10cm stays the most efficient (due to more shots and all shots at closer range, hence better accuracy) for area defense. At larger salvo sizes 12cm and 15cm start to get close, since BFC weight becomes negligible, but they still aren't quite as good. In my 1400T case I now get 7.65A, 6.87A, 6.37A for 10,12,15.
So, does this mean AD is now superior to Final Fire?
Well, not really.... just for lasers, against these particular missiles. The calculation is very sensitive to speed. This strong dependence on relative missile speed means your direction of travel will be very important. In this low tech example, the +/- 4km speed of your ship into or away from the missiles may impact your AD efficiency by +/-20% - so keeping the range open gives 40% higher AD efficiency (~9A) vs closing (~6.5A). When closing in this example, it would be more efficient to blob up and switch to FF mode rather than running a spread formation with advanced AD.
For Gauss or Rails with shorter range, FF is basically always better except with very slow missiles, as you would expect. (Random note - bigger (>=15cm) rails might actually be better in AD than FF as well, but not sure this would ever really come up since they will still be way worse than 10cm on FF)
For a similar low tech example, consider 8.667 10cm rails and a 100T 4x range 1x track BFC to maximize to-hit. Even at 1x tracking (say on a station), I get a PD efficiency of 8.2A due to the smaller 1x tracking BFC needed, meaning more guns in addition to 4x the ROF of the laser FF case leading to slightly more hits overall in final fire mode.
This is neglecting the tonnage savings of not using turrets, and that a ship speed somewhat over the minimum BFC speed would allow for a 1.1x-1.25x track BFC for the rails and thus a to-hit chance >25% of the turret to hit chance, which with 4 shots might push rails up to ~10-11A vs lasers ~7-9A. It also neglects that for a high accuracy ‘A’ you might want to add another BFC to avoid overkill, which would push efficiency back down ~ 8%.
It appears that high ROF (4+) turreted Gauss in FF mode is King of PD. Considering a higher tech case with UV 15mm lasers & 400T BFC vs ROF4 Turreted Gauss with 100T FC vs a 48kkm/s missile, I get a similar ~6-9A for laser AD (closing range vs opening) to the low tech case vs ~13.115-15.5A for Gauss PD. This Gauss range is based on 1-3 100T BFCs - for a high value of A (near 1), smaller expected volley sizes with multiple volleys/intervals will require more BFCs and push down Gauss efficiency/ton, but probably not enough to get back down to laser AD efficiency.
Again I didn't even consider power plant tonnage, so really Gauss PD efficiency would be somewhat higher vs lasers than shown. And again the laser AD efficiency is really sensitive to speed - against a lower tech 24km/s missile AD efficiency will go up 2x and approach the gauss efficiency.
Anyhow, to summarize my findings :
- Using lasers in Final Fire mode is not very efficient compared to other weapon options. Standard (full size) 10cm Lasers are worse for Final Fire not just than Gauss, but also appear worse than unturreted 10cm rails, assuming you are just trying to protect one task group.
- Lasers in FF mode are so inefficient compared to Gauss at higher tech ROF (and maybe rails at higher track bonus) that two task groups would likely be better off covering themselves with gauss/rails rather than mutually interlocking lasers set to FF. You might need 3-4 mutually supporting task groups at large spacing to justify using lasers in FF mode vs other weapons options.
- Laser as a screen in Area Defense mode may be better than lasers in FF mode, but it seems very situational depending on your opponents missile velocity and your velocity.
- Lasers in AD mode have similar (at low tech) or lower (at high tech) efficiency to other weapon options in FF mode. Thus, the main draw of smaller lasers should be for their potential utility against other targets rather than pure PD utility.
- Since lasers utility should be considered instead of pure PD efficiency, 15cm @ 6 cap on an escort in advance of the fleet may be the way to go - they appear to give a ~83% efficiency in AD mode (&60% in FF) compared to 10cm lasers while giving more utility for pew-pewing other ships. For pure PD efficiency, 10cm would still be best if you are doing a pure laser playthrough and need more PD oomf without cheating and going to gauss.
- Lasers set to AD in the main body (and so only able to engage inbound missiles and not missiles that pass them moving towards other targets) will be super duper inefficient vs FF mode unless the missile is hecka slow. You probably should not do this (I was doing this, lol).
Brainstorming some doctrine ideas for a laser focused playthrough based on this finding:
- It may be safest to start in FF mode in one big ball to guarantee some hits if the enemy missile speed is unknown. If speed is found to be low, PD escorts could be broken off to screen while you back away to open up the engagement envelope- if not, they could stay put in FF mode and you can close with the enemy, since relative motion is irrelevant to FF efficiency (except perhaps to spread out the incoming volleys over more intervals in a very dense threat environment).
- I should probably roll in at least some Gauss PD to address fast missile threats if I encounter them. It might be worth rolling in some 10mm rails for FF defense as a patch until I reach Gauss ROF3-4.
- A formation with inbound missiles -> Laser Escorts (AD) -> Gauss Escorts (FF) -> Main Body all in line astern moving away from the missiles, such that the Gauss FF fire can cover both the Laser AD escorts and the main body might be viable. The longer FF range would not hurt the gauss much, but the smaller engagement envelope would impact the AD lasers significantly - perhaps 22%,40% for 10cm, 15cm beams respectively.
- If 10-15cm lasers are 'optimal' for area defense - 20cm are suboptimal but still ~50-70% as effective at Cap10 due to their slightly longer range. Maybe at high tech just forget about differentiating 'PD' and 'Anti-Ship' lasers, throw skads of high cap 20-30cm beams in quad turrets with fast fire controls, and just shoot whatever happens to be in range at a given interval? Even a 2x Track BFC and Turret would potentially give a 20-30% hit chance vs missiles (with tracking bonus) while allowing you to demolish smaller craft and sandpaper down armor. The raw DPS would not be bad since the ROF is high. You would do a lot less armor pen and shock damage compared to very large lasers, but a darn sight more than a dedicated PD 10mm laser.