Capacitor recharge rate

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The capacitor recharge rate is a non-linear function—the rate at any given moment depends on how much energy is stored at that moment. Near zero and near full capacity, the recharge rate is very low, and it peaks around 25 percent.

A player by the name of “Dust Puppy” investigated the recharge rate in-depth and published his findings in this thread. Based on his experiments, he suggests that the formula for calculating recharge rate is:

...where:
C_max = 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 (seconds).
C₁ = The amount of charge in the capacitor (in GJ) at some later time t₁ (seconds).
τ (tau) = “Cap Recharge Time” divided by some constant. Dust Puppy believes this constant to be 4.8 and Seamus Donohue believes it to be 5.0. (The constant is dimensionless, but τ is in seconds.)
“Cap Recharge Time” is the recharge time listed for the capacitor in the Fitting Window, in seconds.

In layman’s terms, if you know the total size of your capacitor and its recharge time (as advertised in 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.

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Some mathematical manipulation of the capacitor recharge rate equation reveals that capacitor recharge is based upon the following differential equation:

...where:
C is your current capacitor level in GJ.
dC/dt is your current capacitor recharge rate in GJ/s. (Formally: The instantaneous rate of change of the capacitor charge C with respect to time.)

Capacitor recharge, therefore, peaks at 25%, and the advertised “Capacitor Recharge Time” is actually the time for the capacitor to go from dead empty to 98.7%, assuming no drains or boosts.

Experimenting with this formula, 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.

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More recent testing by Kivena

Here's a big graph of current capacitor capacity (in percentage) over time since being drained to zero. The blue points are data points from my experiments. The black line is an equation based on Dust Puppy's research (see link at top of this page) which you can see at the top left corner of the image.

• C0 is 100, being as our maximum capacitor capacitor is always 100%.
• x0 is the time taken to recharge the capacitor in seconds, according to the in-game Show Info (x being, obviously, the current time since the capacitor was drained to zero)
• k is a constant (in Seamus' and Dust Puppy's calculations, they used it in a Tau = x0/k format) that Dust Puppy calculated as 4.8, Seamus worked out as 5.0, but I found 4.9 fitted a little better.

It's still not exactly right near zero, but the rest, after around 7-8% capacity, fits it perfectly.

The smaller inset graph (orange) shows a percentage of average recharge rate over current capacitor percentage, thus indicating how quickly the capacitor recharges as your energy restores. I didn't try to equationize (this is now a word) this one, but you can clearly see that the maximum capacitor recharge is 2.5x the average recharge, and that this occurs at 25% of capacitor capacity.

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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