Capacitor recharge rate
Many EVE pilots have tried to determine the precise formula for the capacitor recharge rate - that is, the speed at which your ship's capacitor draws energy from the reactor. The cap recharge rate is not a linear function, however - the rate is dependent upon the amount of energy stored in your capacitor at any given point in time. If the capacitor is near full capacity, the recharge rate is very low; likewise, if the capacitor is near empty, the recharge rate is also very low.
Many pilots have observed that the peak capacitor recharge rate seems to occur somewhere between 20% and 35%.
A player by the name of "Dust Puppy" investigated the cap recharge rate in-depth and published his findings in this thread: http://www.eveonline.com/ingameboard.asp?a=topic&threadID=116993
Based on his experiments, he suggests that the formula for calculating recharge rate is actually:
...where:
Cmax = The size of the capacitor, in Gigajoules (GJ). This value is given in the Fitting Window.
C0 = The amount of charge in the capacitor (in GJ) at some initial time, t0 (in seconds)
C1 = The amount of charge in the capacitor (in GJ) at some later time, t1 (in seconds)
tau = "Cap Recharge Time" / constant , where Dust Puppy believes this constant to be 4.8 and Seamus Donohue believes it to be 5.0. ("constant" is dimensionless, "tau" is in seconds.)
"Cap Recharge Time" is whatever recharge time is given for the capacitor in the Fitting Window, in seconds.
In layman's terms, if you know the total size of your capacitor and it's recharge time (as advertised by the Fitting Window), and if you also know how much charge the capacitor currently holds at any given point in time, then you can calculate how much charge the capacitor will hold at any later point in time. This assumes that the capacitor will be left alone to recharge by itself and is neither being drained nor boosted.
Some mathematical manipulation of the capacitor recharge rate equation reveals that capacitor recharge is based upon the following differential equation:
dC/dt = (SQRT(C/Cmax) - C/Cmax) * 2 * Cmax / tau
...where:
C is your current capacitor level (in GJ) at time t (in seconds).
dC/dt is your current instantaneous capacitor recharge rate, in GJ/s. (Formally: The first derivative of capacitor with respect to time.)
Capacitor recharge, therefore, peaks at 25% capacitor, and the advertised "Capacitor Recharge Time" is really the time for the capacitor to go from dead empty to approximately 98%, assuming no drains or boosts.
Experimenting with this formula (https://spreadsheets.google.com/ccc?key=0AnYZ5Ix967m9dGR1YTY2emRGaXgyR3k4QlBnYng3SlE&hl=en), it has been found that the peak recharge rate, without any effect of boosters or energy draining weapons, is indeed at 25% of capacitor capacity.
The full derivation may be found at: http://forum.eveuniversity.org/viewtopic.php?f=222&t=30652
Bottom line for EVE capsuleers: remember that the recharge rate declines dramatically once it falls below 25% of capacity. Therefore, if in a fight, leave yourself a margin of safety and consider escaping if it appears that you will soon fall below this amount.
For more on maximizing your capacitor performance, see this UNI class syllabus: Capacitor Management 101
