Fully charged shields do not recharge in battle. The recharge increases linearly inversely with remaining shield amount up to 25% of non-combat recharge at 0 shields. Note that shields have a recovery time and thus will stop recharging upon reaching 0, but start recharging again once the recovery time is over.
http://oldsite.star-made.org/conten...ttle-new-shield-recharge-mechanic-theoretical
The amount of DPS (assuming completely constant damage) needed to take out a shield of a given amount is simply one quarter of the recharge rate as damage (it should be obvious why). However, this DPS is
extremely low compared to the shield capacity and it will take a lot of time. One of the examples I used was 10K shield capacity. The minimum DPS to take it out is 184.63, a bit under 2% of the shield capacity per second. Note that the shield value is still above 0 at 250 seconds (a bit over 4 minutes). At more reasonable DPS values, shields go down extremely fast (pretty much linearly, 1K DPS will take out 10K shields in around 11 seconds).
The interesting thing to note is that weapons scale better than shields even when just using one group of AMCs; combined with the near-linear behavior when DPS approaches even a tenth of shield capacity, it is fairly obvious why weapons systems now require ridiculous amounts of power and are still going to be changed for further balancing.
Recharge rate 1000: you can take a maximum of 250 constant continuous DPS when sitting still.
In practice, the enemy will need a lot more to take you down due to small gaps in damage from the discontinous nature of AMCs as well as large gaps from dodging giving your shields extra time to recover in-between damage.
It's very hard to account for gaps in damage due to the damage over time function becoming discontinuous and thus ds/dt not really existing. I'm not sure how to solve the system of differential equations with damage gaps.
My guess would be that at least 500 DPS is needed for a competent pilot.
Also, my original post is a bit unclear on fss, f0, sss, and s0. ss and 0 are meant to be subscripts meaning "steady-state" (the limit of something as t goes to infinity) and "initial state" (the limit of something as t goes to 0).
