The work in this paper was done by Dust Puppy

The work in this paper was done by Dust Puppy. It is great work. I have abstracted from the thread on EvE Online, and make no claim whatsoever on the work by doing so. The abstract was put together to help me put together the Excel model, accessible from my website. The Excel work is mine, but is based on Dust Puppy’s work which is abstracted herein.

-- Amunherkhepeshef

http://myeve.eve-online.com/ingameboard.asp?a=topic&threadID=116993

Edited by: Dust Puppy on 18/10/2004 11:22:24
One of the most complicated part of your ship is your capacitor. Most of the pilots in EVE have probably made the mistake of fitting their ship to perfection only to realize in battle that they don't have the juice to run it all.

The capacitor is mostly complicated because we don't really know the recharge rate curve. We know how long it takes for a capacitor to recharge fully and we know how much power it can give when it's fully but we don't really know what happens in between, that is until now.

Many of you have probably thought that the curve is of the familiar exponential form:

C = C0(1-exp(-tau*t))

Well it's close but doesn't quite describe it though. According to the exponential curve we would have optimal recharger at time 0 but according to my experience it is more when the capacitor is at about 30%-40%. I tried a similar curve of the form:

C = C0(1-1/cosh(tau*t))

And that one fitted like a glove. I can understand that you are hesitant to take my word for it but to further prove my point take a look at this picture.

The broken line is when I tried to fit the exponential curve but the solid line is the cosh line. The lines are very similar and that is no coincident as cosh(x) function is defined:

cosh(x) = 1/2(exp(x) + exp(-x))

Now you are probably wondering what the hell tau is. Well it's just a time constant which determines how fast your cap recharges. As you might imagine it is dependant on T the recharge time. To be more exact it is of the form:

tau = k/T

where k = 4.8 according to my measurements.

Taking the tangent of the curve on the figure above would give us the recharge rate. You can see the recharge rate curve with the capacitor curve on this figure.

The figures were made on a hypothetical ship that has 100 cap and 100 charges on 100 seconds. Does that mean that this hypothetical ship can maintain a module that uses over 2 cap per second. Well not exactly. The top that is close to 2.5 cap per second is just an instantanious recharge rate. When dealing with modules and their usage we have to plot a curve over period of time. For example to see how much a cap recharges over given period of time. I plotted a few of those curves which you can see here.

The curves are of the form.

C0(1-1/cosh(tau(t-t0)) - C0(1-1/cosh(tau*t)) = C0(1/cosh(tau*t)-1/cosh(tau(t-t0)))

Where t0 is 1, 2, 4, 8, 12 where 12 is for the top curve and 1 is for the lowest curve. So for example if a module has 12sec in activation time this ship could maintain it as long as it had under 27 cap in activation cost and that would be when the capacitor were 20 seconds from being empty which would be when the cap is around 32%.

The graph I've shown you are kind of useless for practical purposes as we don't know what time it is since the the cap was empty. And since we are always activating modules it's impossible for us to know. A much more useful curve is one that shows capacitor recharge as a function of the state of the capacator. You can see that curve here

As can be seen from that figure the capacitor has the maximum recharge when it is about 30% full.

What does this all mean then and how can you benefit from it. Well you can already benefit from knowing when the capacitor is at maximum recharge and can use that to your advantage. Another useful thing is to compare modules. I used a Moa as a model, why you might ask, well I really really like that ship. It has 1100 cap and recharge time 393sec. I plotted a number of cap-cap recharge curves. You can see the figure here.

I did not apply any skill to my numbers and I used only tech 1 modules. The cap battery is medium cap batter I which gives 240 cap.

I hope this research can be of use to anyone.

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Well if you look at this picture (the lower one) and now that the ship has 100 cap and recharge time of 100 sec which means an average of 1 cap per sec you see that the max recharge rate is a bit less than 2.5 cap per sec. So your theoretical max capacitor recharge is about 2.4*(average recharge rate).

This is a theoretical max recharge rate expect it to appear a little less in reality.

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Edited by: Moominer on 18/02/2005 12:48:26
What is the function for the graph showing the recharge rate as a function of the state of the capacitor?

Edited by: Dust Puppy on 18/10/2004 16:30:59
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Be careful with that maximum cap recharge formula. If you look at the this

figure again. Let's say we are going to see how much cap we can recharge in 12 seconds. Then the top curve applies. We can see that it can recharge about 28cap in 12 seconds. Now let's say we have a module that uses 28 cap every 12. So as long as we activate the module at 30% cap plus 28 (what the hell is the unit on cap anyway). Now the module shoot activate and after 12 seconds we have again reached 28 units above 30% cap so we can keep this module running indefinitly.

The problem how ever that if we don't activate the module at exactly the right time we can't get this recharge and eventually this module will drain the cap. So even if the formula says you can recharge 2.5x(max capacitor)/(recharge time) it is very improbable that you can maintain a module that requires that recharge time.

People have been saying for a while that the max recharge rate is something about 1.63x(max capacitor)/(recharge time) (I think that's it anyway I'm not really good at remembering numbers) which I don't doubt that it is a good number to use in practice.

What you can do though is to take a look at this picture.