Capacitor recharge rate

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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.


Overview

Many pilots have observed that the peak capacitor recharge rate seems to occur somewhere between 20% and 35%, as illustrated by this graph:

EVE Cap Recharge Rate.png

One player, 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:

EVE Cap Recharge Rate Formula.png


Analysis

Dust Puppy's original forumula is expressed in ASCII as:

C = Cmax * [ 1 + ( SQRT(C0/Cmax) - 1 ) * EXP((t0-t1)/tau) ] ^ 2

Some mathematical manipulation of this 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, t is time, dC/dt is your current instantaneous capacitor recharge rate, Cmax is the maximum size of your capacitor, and tau is a time constant.

Dust Puppy thinks that tau = "Cap Recharge Time" / 4.8, but I think it's tau = "Cap Recharge Time" / 5.0 . 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, Seamus found that the peak recharge rate, without any effect of boosters or energy draining weapons, is indeed at 25% of capacitor capacity.


Application

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.

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