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Dust Puppy
Posted - 2004.10.18 11:19:00 - [1]
 

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.

Joshua Calvert
Caldari
Rule One
Posted - 2004.10.18 11:39:00 - [2]
 

Shocked

It's a shame you're not as cute as Carol Vorderman, Dust Puppy, or I'd be sexing you!

Spanker
Bermuda Syndrome Industries
Posted - 2004.10.18 11:52:00 - [3]
 

Edited by: Spanker on 18/10/2004 11:55:58

Nice matlab job =) Or at least I assume your using matlab, that's what I did all day long in brun :p

No but really, your stuff seems to be correct as far as I can tell. If it isn't the cosh then it's some variation that's so similar the difference is negligable. Bravo!

EDIT
I'm printing this Very Happy


Tas Devil
JUDGE DREAD Inc.
Forces of Freedom
Posted - 2004.10.18 11:53:00 - [4]
 

Man some people are scaringly fanatic of EVE ...Shocked

But great info nonetheless....do you have a formula that would be useable with EVE ship stats ? to say give max cap/sec recharge rate at a given %of total cap level ?

Cheers professor

Dust Puppy
Posted - 2004.10.18 12:57:00 - [5]
 

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.

Spanker I did indeed use matlab and you are right even if I am wrong about the formula it makes a little difference as it is close enough.

Joshua I'll get working on getting cuter.

Kayinan Malrean
Viziam
Posted - 2004.10.18 13:11:00 - [6]
 

Excellent job, especially the last picture is extremely good at showing the differences of the different cap and cap recharge mods.

Would be interesting to see the comparisons for the most obvious combinations as well. For instance, for 2xCap Relay vs. Cap Relay + Cap Battery vs. 2xPDU.

Dangard
Posted - 2004.10.18 14:44:00 - [7]
 

Excellent work Dust Puppy just the info iv been hunting for. Thanks a lot for taking the time to work the numbers. Very Happy

Grim Vandal
Burn Proof
Posted - 2004.10.18 14:51:00 - [8]
 

Edited by: Grim Vandal on 18/10/2004 14:57:22
Edited by: Grim Vandal on 18/10/2004 14:54:51
"maximum cap" / "cap recharge" * 2,5 = your max cap recharge each sec

which is about at 30% of your maximum cap...


so if you want to sustain your setup make sure all your mods dont use more cap each sec as you get out of the calculation above...

another little hint which most of you prolly do know is to fit a LARGE cap battery on your cruiser...

Cool

anyway good job dust puppy


Dust Puppy
Posted - 2004.10.18 16:23:00 - [9]
 

Edited by: Dust Puppy on 18/10/2004 16:30:59
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. Now just to be on the safe site you decide to put in a "margin of error". For example let's say you lower the the constant in the max recharge rate formula to 2.0 then you know that between 15% cap and 55% cap your capacitor charges more than that.

Edit: @Kayinan Malrean, I thought about comparing combos of cap modules on certain ships but so far I've only been doing this manually. The combonations of modules are so large that I wouldn't even know how to begin. The best solutions would of course be to create a program where you could select a ship, modules and skills and make it plot the curves for you but I really don't have that much time to do it. Having said that then there is ofcourse nothing to stop anyone else from creating the program after all you all know the formula now.

Morning Maniac
EVE University
Ivy League
Posted - 2004.10.18 18:15:00 - [10]
 

Shocked

And that's why Dust Puppy is our senior professor. Good job Dust!

Ebedar
Gallente
Primary Intelligence
Posted - 2004.10.18 18:30:00 - [11]
 

Originally by: Joshua Calvert
Shocked

It's a shame you're not as cute as Carol Vorderman, Dust Puppy, or I'd be sexing you!

Susie Dent > Carol Vorderman

Oh and nice work Dust Puppy.

Shimatu
Caldari
Infinite Improbability Inc
Dusk and Dawn
Posted - 2004.10.18 18:40:00 - [12]
 

nice work :)
yeh, the problem with using 2.5 (or there abouts) is that if you drop to below 30% cap accidently (very easy to do...) youll then drain total. so your better of using about 2 or so.
btw, the 1.63 is i think the maximum for real life capacitors, though i could be wrong on that. (hmm, that sounds wrong actually. but 1.63 definately has something to do with them.)

Spanker
Bermuda Syndrome Industries
Posted - 2004.10.19 08:19:00 - [13]
 

Edited by: Spanker on 19/10/2004 08:27:07
Originally by: Dust Puppy
what the hell is the unit on cap anyway


I think it's called farad.


Edit: After googling it, I found that 1F = 1C/V. That is, one farad equals one coulomb per volt (or one ampere second (As) per volt). Been a looong time though, must have been in högstadiet :p

Dust Puppy
Posted - 2004.10.19 09:25:00 - [14]
 

Ah yes it is farad although that only tells us the attribute of the capacitor. Whether the capacitor is full or empty it is always X farads. We must be observing the electric potential over the capacitor.

This would be slightly less embarrassing if I hadn't got a B.Sc. in electrical engineering Embarassed

Elrathias
Caldari
Legio Prima Victrix
Posted - 2004.10.19 09:27:00 - [15]
 

kth pwns ^^

"högstadiet"

Spanker
Bermuda Syndrome Industries
Posted - 2004.10.29 15:50:00 - [16]
 

Edited by: Spanker on 29/10/2004 15:52:55
Bump Shocked People need to know how it is!

Shamis Orzoz
Sniggerdly
Pandemic Legion
Posted - 2004.10.29 17:33:00 - [17]
 

Shocked

Nicely done.

Imhotep Khem
Minmatar
Doom Guard
Wildly Inappropriate.
Posted - 2004.11.02 18:29:00 - [18]
 

Originally by: Dust Puppy
Ah yes it is farad although that only tells us the attribute of the capacitor. Whether the capacitor is full or empty it is always X farads. We must be observing the electric potential over the capacitor.

This would be slightly less embarrassing if I hadn't got a B.Sc. in electrical engineering Embarassed


The farad is one capacitor metric of behavior. What we are concerned about is of course, energy. You can measure the caps stored energy in the unit of your choice, Joule, Watt-hours, calories, etc. Probably the typical unit of measure is the joule.

Time to dust off those old text books (or cheat by using google) I got a BSEE as well.

blahh
Posted - 2004.11.08 16:48:00 - [19]
 

Edited by: blahh on 08/11/2004 16:56:41
thanks for this.. extremely useful info Wink

Seems that if an apoc (or any ship really) depends on the regen at ~30% cap it could have its tanking capability severely disrupted with just one heavy nos.. could be taken down from running 2large 1 medium to barely sustaining 1 large repairer (unless they turn off a rep before its too late). People running ganking setups could probably make good use of this info Twisted Evil

Piscis
Gallente
0utbreak
Outbreak.
Posted - 2004.11.30 11:23:00 - [20]
 

Argh! Label the damn graphs! how are we supposed to know what all the units are!! :(

Nyphur
Pillowsoft
Posted - 2004.11.30 12:19:00 - [21]
 

Edited by: Nyphur on 30/11/2004 12:30:23
Dude... You are the new king.. of everything.
As soon as I get home, I'm sending you 1million of my 3million ISK I have left.

You are a goddamn mathimagician! :D

EDIT: I'm totally printing this right now. I can't risk not being able to find the thread when I get home :P.

Noriath
Posted - 2004.11.30 12:53:00 - [22]
 

Hmm... I kinda new that the cap recharged best around 30-40%, but I don't think the curve is perfectly acurate, because to me it seems that the last 10% of it take just about as long to recharge then the rest of the thing sometimes.

Still, good post, the graphs of how different modules change it around are very interesting. Can you make one that shows MWD also?

Azure Skyclad
Amarr
Jericho Fraction
The Star Fraction
Posted - 2004.11.30 14:23:00 - [23]
 

If i lick the terminals...will it tingle?


Dust Puppy
Posted - 2004.12.07 23:53:00 - [24]
 

Edited by: Dust Puppy on 08/12/2004 01:00:21
First sorry for bumping this old thread but I felt like answering some questions and explain myself a little better.

Originally by: Piscis
Argh! Label the damn graphs! how are we supposed to know what all the units are!! :(


Yeah sorry about that I do tend to be a bit careless about labeling the graph and axis which is weird because I get really annoyed when other people don't do it.

Originally by: Noriath
Hmm... I kinda new that the cap recharged best around 30-40%, but I don't think the curve is perfectly acurate, because to me it seems that the last 10% of it take just about as long to recharge then the rest of the thing sometimes.

Still, good post, the graphs of how different modules change it around are very interesting. Can you make one that shows MWD also?


There is bound to be some error mostly because I used a timer and then took measurements every 10 seconds and then there is the fact that I have roughly 10 fps on my crappy computer. The numbers are actually more accurate then I would have expected.

Your perception on that the last 10% take about half the time recharging just further proves my case. If you look a the cap versus time graph you can see that it takes little less than 60 seconds to charge that battery to 90% and it isn't full until after just over 100 seconds.

I did do a graph with an mwd in it before I took the measurements needless to say the penalty for fitting an mwd is very high.

Skelator
Stronghold corp
CORPVS DELICTI
Posted - 2004.12.08 00:49:00 - [25]
 

Dust Puppy is Really Ken Jennings the Jeapordy champ Razz


babo
Gallente
Eye of God
X-PACT
Posted - 2004.12.08 17:58:00 - [26]
 

It was funny when I realized I have cap rechargers fitted that are worth more than the ship they are fitted to. All in the name of getting insanely low recharge times so I run a medium shield booster all day long a never come close to running out of cap :)

Jhodas
Minmatar
FATAL REVELATIONS
FATAL Alliance
Posted - 2004.12.09 15:39:00 - [27]
 

Where the h3ll are th ISDs?

THIS NEEDS A STICKY DAMMIT!!!!!!1111ONEONEELEVEN

Reptar
Posted - 2004.12.13 23:48:00 - [28]
 

This was the sexesit bit of research I had ever seen in eve.

qrac
Caldari
Caldari Provisions
Posted - 2004.12.14 00:59:00 - [29]
 

Originally by: Reptar
This was the sexesit bit of research I had ever seen in eve.

i wonder who your alt is...

Kelhund
Posted - 2004.12.14 21:00:00 - [30]
 

SITCKY THIS!!!! NOW!!!! hehe GREAT research, helped me understand my Raven's cap just a bit more :)


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