Author Topic: Interesting missile defense math  (Read 903 times)

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Offline byron

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Interesting missile defense math
« on: April 22, 2016, 04:49:36 PM »
I was thinking about the problem of early-game AMMs, and the best relation between AMM launchers and fire control.  I worked out a spreadsheet, and discovered something interesting.  There are points where the system 'chokes', and adding more launchers doesn't actually help.  For instance, if you have a reload rate of 15 seconds and an incoming salvo size of 8 (1v1 or 2v1 engagement), then there is no advantage to having more than 12 launchers until you get to 16.  The extra tubes are wasted, because you end up shooting only some of your ready tubes at salvos you've already partially engaged, and the rest end up 'trapped' behind those.  Generally, going to 2v1 doesn't improve things much over 1v1.  3v1 does usually improve the tube utilization. 
What appears to happen is that, as full firing would 'overengage', the tube utilization seems to spread out, and drops into a repeating pattern.  For instance, in the salvo size 8 ROF 15 example, with tube numbers between 12 and 15, you fall into a pattern where 16 shots are fired every 20 seconds (4 increments), no matter how many tubes you have (1v1 patterns, some are slightly different for 2v1):
12: 4 4 4 4
13: 5 3 5 3
14: 8 4 2 2
15: 8 6 1 1
Here are the numbers of tubes ready at the beginning of each increment:
12: 4   4 4 4
13: 5   5 5 5
14: 10 4 2 8
15: 13 6 1 8
Note that these are steady-state patterns, and take between 4 and 10 increments to develop, so they're of limited relevance if you only expect to have a short time to engage.  For instance, in all 1v1 cases, you get off all tubes twice in 30 seconds, but it only takes 25 seconds in 2v1 cases. 
I've attached my spreadsheet.  It may be a bit confusing.  Specifically, the 'Parity' column is there to handle engaging salvos that have already been partially targeted.  User input goes into the yellow boxes only (unless you're trying to modify the formulas).  The boxed column(s) can be copied if you want to compare more than two different launcher counts at the same time.  Enjoy.
This is Excel-in-Space, not Wing Commander - Rastaman
 
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Offline byron

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Re: Interesting missile defense math
« Reply #1 on: April 25, 2016, 02:10:50 PM »
I added some new features to the spreadsheet, looking at cases where two fire controls were engaging at the same time and a little bit at what happens when the FC has to fire second shots at missiles that survived the first wave of fire.  The former exhibits similar behavior to the single-FC system, although it's usually slightly more efficient than a single FC with the same number of tubes.  The patterns are much more complicated, so I won't attempt to describe any here.
The follow-up shot system was basically intended to look at what inserting arbitrary 'breaks' into the 'primary' system would do.  As a general rule, it doesn't do much.  You get a small swing in total shots (usually in the range of + or - 2 shots), and it quickly settles back into a pattern (although not always the same pattern).
I'm not attaching the spreadsheet because some of the modifications I had to make are not really suitable for general use, and I need to clean it up a bit before I post it.
This is Excel-in-Space, not Wing Commander - Rastaman
 

Offline byron

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Re: Interesting missile defense math
« Reply #2 on: April 25, 2016, 11:16:37 PM »
Right.  New spreadsheet is attached.  I hid the sheet I used for doing second shots because it was too complicated to explain, but the dual-launcher system was working well.
This is Excel-in-Space, not Wing Commander - Rastaman
 

 

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