Difference between revisions of "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 [http://www.eveonline.com/ingameboard.asp?a=topic&threadID=116993 this thread]. Based on his experiments, he suggests that the formula for calculating recharge rate is: | |
| − | + | [[File:EVE_Cap_Recharge_Rate_Formula.png|center]]<!-- TeX: {\color{White}C_1=C_\mathrm{max}\left(1+e^{t_0-t_1\over\tau}\left(\sqrt{C_0\over C_\mathrm{max}}-1\right)\right)^2} --> | |
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| − | [[File:EVE_Cap_Recharge_Rate_Formula.png|center]] | ||
...where:<br /> | ...where:<br /> | ||
| − | + | ''C''<sub>max</sub> = The size of the capacitor in gigajoules (GJ). This value is given in the Fitting Window.<br /> | |
| − | + | ''C''<sub>0</sub> = The amount of charge in the capacitor (in GJ) at some initial time ''t''<sub>0</sub> (seconds).<br /> | |
| − | + | ''C''<sub>1</sub> = The amount of charge in the capacitor (in GJ) at some later time ''t''<sub>1</sub> (seconds).<br /> | |
| − | tau = | + | 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.)<br /> |
| − | + | “Cap Recharge Time” is the recharge time listed for the capacitor in the Fitting Window, in seconds. | |
| − | In | + | 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: | Some mathematical manipulation of the capacitor recharge rate equation reveals that capacitor recharge is based upon the following differential equation: | ||
| − | dC | + | [[File:EVE Cap Recharge Rate Diff Formula.png|center]]<!-- TeX: {\color{White}{dC\over dt}={2C_\mathrm{max}\over\tau}\left(\sqrt{C\over C_{\mathrm{max}}}-{C\over C_\mathrm{max}}\right)} --> |
...where:<br /> | ...where:<br /> | ||
| − | C is your current capacitor level | + | ''C'' is your current capacitor level in GJ.<br /> |
| − | dC/dt is your current | + | ''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% | + | 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 | + | Experimenting with this formula,<ref>https://spreadsheets.google.com/ccc?key=0AnYZ5Ix967m9dGR1YTY2emRGaXgyR3k4QlBnYng3SlE&hl=en</ref> 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 | + | The full derivation may be found at http://forum.eveuniversity.org/viewtopic.php?f=222&t=30652. |
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For more on maximizing your capacitor performance, see this UNI class syllabus: [[Capacitor Management 101]] | For more on maximizing your capacitor performance, see this UNI class syllabus: [[Capacitor Management 101]] | ||
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| + | ==References== | ||
| + | <references /> | ||
[[Category:Guides]] | [[Category:Guides]] | ||
Revision as of 07:01, 25 July 2013
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:
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 (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.
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,[1] 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
