| Author |
Thread Statistics | Show CCP posts - 0 post(s) |
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.
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.10.18 11:19:00 -
[2]
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.
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.10.18 12:57:00 -
[3]
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.
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.10.18 12:57:00 -
[4]
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.
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.10.18 16:23:00 -
[5]
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.
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.10.18 16:23:00 -
[6]
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.
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.10.19 09:25:00 -
[7]
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 
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.10.19 09:25:00 -
[8]
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
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.12.07 23:53:00 -
[9]
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.
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.12.07 23:53:00 -
[10]
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.
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.12.16 20:22:00 -
[11]
Originally by: Uchikage
Dust, to clean up the last graph a bit, which is a super graph, could you just compare cap relay and power diag vs the unmodified? Or at least make two seperate graphs for the midslot and lowslot cap-modifying items? It's kind of hard to see, but your graph makes PDU look like more of a solid mod than I thought before for helping cap.
I can do that but just not right now as I'm stuck in a Java networking assignment and I just spent 2 hours looking for a bug in the wrong file 
You'll just have to use this one. To be more clear then the lowest black one is the unmodified, the green one that has the highest max capacitor recharge rate is the cap power relay and the pdu is the magenta one in the middle that reaches nearly as high as the yellow cap flux coil and a bit lower than the red capacitor recharger.
your right the pdu does pretty well given that it also boosts your grid, shield and shield recharge but it is sadly the only viable low slot cap enhancing module we have. Although the cap flux coil does have a little higher max shield recharge rate it has a lot less cap.
Bah I'm going back to my programming I always meant to do a followup to this thread perhaps during christmas.
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.12.16 20:22:00 -
[12]
Originally by: Uchikage
Dust, to clean up the last graph a bit, which is a super graph, could you just compare cap relay and power diag vs the unmodified? Or at least make two seperate graphs for the midslot and lowslot cap-modifying items? It's kind of hard to see, but your graph makes PDU look like more of a solid mod than I thought before for helping cap.
I can do that but just not right now as I'm stuck in a Java networking assignment and I just spent 2 hours looking for a bug in the wrong file
You'll just have to use this one. To be more clear then the lowest black one is the unmodified, the green one that has the highest max capacitor recharge rate is the cap power relay and the pdu is the magenta one in the middle that reaches nearly as high as the yellow cap flux coil and a bit lower than the red capacitor recharger.
your right the pdu does pretty well given that it also boosts your grid, shield and shield recharge but it is sadly the only viable low slot cap enhancing module we have. Although the cap flux coil does have a little higher max shield recharge rate it has a lot less cap.
Bah I'm going back to my programming I always meant to do a followup to this thread perhaps during christmas.
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.12.26 17:20:00 -
[13]
Originally by: Chris Henry
CCP should have info like this on the site in the first place... If we can fly multi-million ISK ships you would have thought us as the RL pilots should know about things like this!!
My thoughts exactly. There are a number of things about the game we shouldn't be allowed to know behaviour of the capacitor, shield and guns should definitly be information that should be given to us.
Originally by: kebab v2
is it safe to assume that perhaps the same basic formula is used to calculate sheild rechage rates?
I think it's pretty safe to assume that. I do not know for sure but I would be surprised if the shield and the capacitor behaved differently.
Originally by: Ankanos
nice work dust puppy :)
you should look for posts by goldeneye on the eve-i.com forums.. he also
has done some nice work explaining the cap/charge rate issue.. with your knowledge & graphing skills
(add labels please ;p ),you two should get together and make a post that would be the final & definitive guide once and for all, for all of us who have scratched a hole in our heads trying to figure this out..
i think overall, the popular vote was that the capacitor
on eve ships is modeled almost exactly the same as a real life capacitor.
-and that the max recharge rate (iirc) comes into effect around 63%
and slows down when cap is =<30%
Yeah I've read some of Goldeneye's posts and he seems to know what he's talking about and not just about capacitor about lots of other stuff to. The only thing that does not make sense from him is that he assumes that when you increase capacitor the recharge rate stays the same. In order to do that the recharge time would be increased and I have not noticed this behaviour in cap batteries. He does however add some interesting points on how long the cap should last if you can't run all your stuff at once (see his first reply here)
__________
Capacitor research |
Dust Puppy
|
Posted - 2004.12.26 17:20:00 -
[14]
Originally by: Chris Henry
CCP should have info like this on the site in the first place... If we can fly multi-million ISK ships you would have thought us as the RL pilots should know about things like this!!
My thoughts exactly. There are a number of things about the game we shouldn't be allowed to know behaviour of the capacitor, shield and guns should definitly be information that should be given to us.
Originally by: kebab v2
is it safe to assume that perhaps the same basic formula is used to calculate sheild rechage rates?
I think it's pretty safe to assume that. I do not know for sure but I would be surprised if the shield and the capacitor behaved differently.
Originally by: Ankanos
nice work dust puppy :)
you should look for posts by goldeneye on the eve-i.com forums.. he also
has done some nice work explaining the cap/charge rate issue.. with your knowledge & graphing skills
(add labels please ;p ),you two should get together and make a post that would be the final & definitive guide once and for all, for all of us who have scratched a hole in our heads trying to figure this out..
i think overall, the popular vote was that the capacitor
on eve ships is modeled almost exactly the same as a real life capacitor.
-and that the max recharge rate (iirc) comes into effect around 63%
and slows down when cap is =<30%
Yeah I've read some of Goldeneye's posts and he seems to know what he's talking about and not just about capacitor about lots of other stuff to. The only thing that does not make sense from him is that he assumes that when you increase capacitor the recharge rate stays the same. In order to do that the recharge time would be increased and I have not noticed this behaviour in cap batteries. He does however add some interesting points on how long the cap should last if you can't run all your stuff at once (see his first reply here)
__________
Capacitor research |
Dust Puppy
|
Posted - 2005.02.20 23:00:00 -
[15]
Edited by: Dust Puppy on 20/02/2005 23:01:00
Originally by: Moominer
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?
Shown in this graph?
I have been trying to derive this function from the original function of time, but my math is not really up to scratch, so any help is much appreciated.
Well you can start by differentiating the formula for capacitor capacity to get.
dc(t)/dt = tau*tanh(tau*t)/cosh(tau*t)
Then you isolate the t out of the formula for capacitor capacity to get
t = (1/tau)*acosh(1/(1-C/C_0)
Then all that is left is to stick in the t that we have isolated from the capacitor capacity formula and stick it in the formula for capacitor recharge rate and simplify. It's kind of pointless for me to show that though, come to think of it it's probably pointless to show you anything but the final solution Anyway I simplified it as much as I could and this is what I my result.
dc(C) = tau*(1-C/C_0)*sqrt(2*C/C_0 - (C/C_0)^2)
__________
Capacitor research |
Dust Puppy
|
Posted - 2005.02.25 02:05:00 -
[16]
Originally by: FireFoxx80
C = C0(1-1/cosh(tau*t))
Forgive my math, but what does C0 stand for?
I am trying to create an excel spreadsheet so I can get optimal cap/shield recharge.
C0 is the maximum capcitor capacity.
__________
Capacitor research |
Dust Puppy
|
Posted - 2005.05.02 16:34:00 -
[17]
Originally by: Grismar
Edited by: Grismar on 02/05/2005 06:04:28
The one thing that scares me about research into the game this deep is that CCP may decide to change the rules on you at any time, obliterating the usefulness of the research... Had similar things happen with changing starmaps, imp distribution, bounty changes and agent changes to my database.
Don't get me wrong, not saying I disagree with any of the made changes, most improved balance or otherwise improved the game. Just saying that spending this much time and effort in investigating the game always keeps nagging at me as (unlike RL with science) none of the results will be permanently useful...
Yeah you are right about that. I can remember one good example about that there was this guy (forgotten his name ) that did massive testing on large guns. They guy probably spent hours on chaos shooting at a can and posted his results on this forum. Few months later the devs changed the tracking and falloff formula a bit so all his results were outdated. To be honest this research wasn't really that deep. The hardest thing was to guess the formula but once it was there the rest was quite easy since that I had just taken a course in numerical analysis.
Thank you Mindblank, on that note I was thinking about doing some number crunching on the new electronic warfare system 
__________
Capacitor research |
Dust Puppy
|
Posted - 2005.05.08 23:12:00 -
[18]
Originally by: Har Ganeth
Edited by: Har Ganeth on 06/05/2005 16:24:44
Looking at the graphs in this thread, I can't say I agree with the maths at all. From my experiments, the graph is not an exponential, but closer to a third order polynomial. I'll report back when i have some more, but im pretty sure what is said here is only a very rough approximation.
If indeed it were a third order polynomial, the cap recharge at any point would be given by dy/dx, which would be a quadratic (dy/dx again to find the stationary point and therefore the max recharge point...)
Actually the 5th order polynomial fits rather well. I fitted a fifth order polynomial to my measurements which you can see here. The problem I see with the capacitor recharge being a polynomial is that it's not a stable function. In the end it will always head towards infinity and it just seem slobby to have a function you need to stop.
The formula that is used in the game is really irrelevant as we just need a function that fits the "real" recharge curve well enough. The formula that I suggested fits well enough in my opinion.
I updated the figure showing the different modules which you can see here.
__________
Capacitor research |
Dust Puppy
|
Posted - 2005.05.08 23:13:00 -
[19]
Originally by: Pwn4ge P4nts
buhues,you math geeks take all the fun and "wtf-factor" out of it with your graphs and your formulas!! 
Go awaaaaay.
All us hardcore alts despise math and anything remotely associated with it!!11one 
That's ok we hardcore math geeks are not overly fond of alts either
__________
Capacitor research |
Dust Puppy
|
Posted - 2005.05.09 16:22:00 -
[20]
Edited by: Dust Puppy on 09/05/2005 16:22:19
Originally by: Matthew
Edited by: Matthew on 09/05/2005 14:05:04
Very nice work Dust Puppy 
Thank you
Originally by: Matthew
Am looking into making a tanking simulator, and thus factoring in shield and cap recharges would be kinda useful.
My current plan is to simulate with a resolution of 1 second, using the equation you got of:
dc(C) = tau*(1-C/C_0)*sqrt(2*C/C_0 - (C/C_0)^2)
Obviously taking the cap/sec instantaneous recharge and applying that value for that 1 second.
What do you think of this plan? Would it be better to use C as the value at the start of the second, or at the end of the second (i.e. before or after all the drains get taken out)?
First thought to me is that it makes more sense to do the drain and then check the recharge rate. You should probably do both though and compare the results. If you are getting some big difference in results then give it some thought. If you are still undecided after that it's probably just best to increase the resolution (decrease maybe, well make it more accurate )
Look forward to see that tanking simulator 
__________
Capacitor research |
Dust Puppy
|
Posted - 2005.05.09 17:44:00 -
[21]
Originally by: Har Ganeth
I suspect I may have just found (or got close to) the taylor approximation of the real function, rather than is actually being a 5 order polynomial. And as you say, it would be kind messy for the game to use a polynomial.
You've obviously put a lot of work into this (i've only spent about 30 minutes, and that included taking cap readings every 5 seconds etc...) and i look forward to seeing your tank simulator. :D
I'm not totally sure that I have the exact formula and I won't get offended if someone brings a better fit than the formula that I offered because I know I'm pretty close even if I'm not spot on
In fact if someone has an idea about a curve that could be a better match then by all means post it here and I'll check it fits better.
Also it's Matthew that's doing the tanking simulator 
__________
Capacitor research |
Dust Puppy
|
Posted - 2005.07.14 09:49:00 -
[22]
Edited by: Dust Puppy on 14/07/2005 09:50:20
Originally by: Nytemaster
This is all fine and dandy, but I have no clue what all these variables are nor how I could put them in a simple f(x) function for graphing. I would like to know this exact formula so I can play around with the numbers a bit.
Capacitor capacity vs. time
C = C_0(1-1/cosh(tau*t))
Recharge rate vs. time
dc(t)/dt = tau*tanh(tau*t)/cosh(tau*t)
Recharge rate vs. Capacitor capacity
dc(C) = tau*(1-C/C_0)*sqrt(2*C/C_0 - (C/C_0)^2)
C_0 is the maximum capacity of the capacitor
tau is 4.8/T => T = average recharge rate
|
Dust Puppy
|
Posted - 2006.06.26 09:15:00 -
[23]
Riebart, I have a B.Sc. in Electronic Engineering which involves a fair bit of calculus. Also the peak happens at around 18% time, that is if you would leave the capacitor empty you would notice the peak when about 18% of the recharge time has passed but by then the capacitor will be around 30% full.
Whether I'm right or wrong about the formula is really irrelevant. Actually the chances of me "guessing" the right formula is pretty slim, it must be thousunds of formula that actually fit that curve. The important part is really that this is close enough that it makes no difference, at least not in practice. Well in practice then I guess all you need to know is the maximum possible recharge rate and when it occurs, which people already kind of knew by observation.
Original Mr Floppyknickers sig |
| |
|