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Why is ther no bat-acitor (hybrid battery/capacitor)?
June 10, 2008 1:02 PM   Subscribe

Why is there no bat-acitor? (hybrid battery/capacity w/best of both) Is there some limitation in physics, chemistry, materials, etc. that prevents it, or has it just not been invented yet?

So as I understand it (generalizing):
1) a Battery can store an electrical charge. It can only be charged by a fixed amount over a period of time, and can only discharge over a period of time. But it can hold its charge for an extended period.
2) a Capacitor can also store an electrical charge. It can be charged to its capacity in either a burst or a trickle; but it discharges all at once. And it can't hold a charge for an extended period.

What I'd like to see, along with my personal jetpack, is a "bat-acitor" which can:
1) be charged either in burst or trickle
2) discharge either in burst or trickle
3) hold that charge, if not indefinitely, then for some reasonable period
4) not be volatile (not gonna go kaboom if you look at it wrong)

I read a lot of Heinlein as a kid, and I remember the Shipstone battery as being a key piece of technology for this in his universe. Physical object (maybe a crystal?) could be charged just as easily by a bolt of lightning as by a solar panel; discharge output had a rheostat allowing it to be a 9v battery lasting for decades - or to let out a lightning bolt all at once.

That's Sci-Fi, understood. But why do I have to wait overnight for a rechargeable battery to "fill up" at a trickle, instead of just letting it "drink from the fire hose" - plugging it in and counting to ten?

Lay some science on me.
posted by bartleby to Science & Nature (24 answers total) 2 users marked this as a favorite
 
blurg- should have proofread; make that 'there' and '\capacitor" (but I stand on principle that jetpack is one word).
posted by bartleby at 1:17 PM on June 10, 2008


A Nicad or NiMH rechargeable battery is pretty close to what you're talking about. It can be charged fast or slow, holds the charge for a couple of weeks or so, and can discharge very quickly if you need lots of power. They do go kaboom every now and then, though.
posted by mmoncur at 1:25 PM on June 10, 2008


A common rechargeable battery is operates via chemistry, not physics. (Or I should say, chemistry as a subset of physics). Chemistry is simply slower. When you charge a chemical battery, you're causing a chemical change. A solution of sulfuric acid becomes mostly watery as it discharges, with the electrodes becoming sulfurous. As you charge it up, the reverse happens. Think about the time it takes to cook food, another chemical change. It can be fast, just not as blindingly fast as a stroke of lightning.

In its simplest version, a capacitor is a pair of plates with an excess of electrons on one and a dearth of electrons on another. A capacitor can discharge nearly as quickly as electrons can flow through a conductor - pretty damn fast. A capacitor with various electronics as a front end can certainly discharge in a burst or a trickle. Right now, not even ultracapacitors have the wonderful energy density of gasoline, much less a lithium-ion battery. Perhaps, in the future ... but not yet.

And my guess is that anything packing a lot of potential energy you can quickly convert to useful energy will always be likely to go kaboom.

That's the quick version, anyway.
posted by adipocere at 1:29 PM on June 10, 2008 [1 favorite]


To correct some misconceptions: Both batteries and capacitors can be charged and discharged at an arbitrary rate below the rated maximums. A battery will have a rated maximum current while a capacitor may or may not really need one in terms of current - small household capacitors can be discharged as fast as the laws of nature allow by shorting the terminals, without damaging them. In general, capacitors tend to have a higher maximum charge/discharge rate than batteries in two senses. First off, for a random capacitor in your home, the energy capacity is very small, so the charge as a percent of maximum capacity increases faster, even if the current used is similar to a household battery, simply because the battery capacity is orders of magnitude more. Secondly, capacitors can be more easily built to provide higher current levels than batteries, in general. Camera flashes work by charging a capacitor over a few seconds which is discharged almost instantaneously - the camera battery cannot provide the required current for the flash by itself. That's sort of an example of the system you describe. The capacitor supplements the ability of the battery to provide a burst of power.

In general, though, there's very little reason to put a power storage capacitor on a battery. You could not gain a sustained higher current with normal capacitors that store orders of magnitude less energy than a battery - you could have the battery charge the capacitor and then quickly discharge the capacitor, but after one capacitor charge's worth of energy you'd have to wait again.

But why do I have to wait overnight for a rechargeable battery to "fill up" at a trickle, instead of just letting it "drink from the fire hose" - plugging it in and counting to ten?


You could design a system where you charged a capacitor at "fire hose" as part of a battery-capacitor system, and then the capacitor transfers the energy to the battery at a trickle. However, you would have to go to great expense to find a capacitor able to hold enough energy to significantly fill the battery.

So from the camera example, things like this are done, but only when needed.
posted by TheOnlyCoolTim at 1:32 PM on June 10, 2008 [1 favorite]


Perhaps what you are thinking of are supercapacitors, which are electric double-layer capacitors that have some of the characteristics that you describe. Their use is relatively new in electronics. They combine the very high current density, low resistance and unlimited life cycles of traditional electrolytic capacitors with higher energy density of batteries. They are more expensive and store less energy than a battery but find some use in smoothing of energy storage and release in combination with batteries. Small supercaps are used like a battery in small electronic devices that need a few minutes or hours of backup during a power interruption. While most electrolytic capacitors have capacities measured in micro-farads, supercaps are available in the multi-farad range -- a million times greater. However they tend to have very low voltage ratings -- three volts or lower that require some tricks to use them for higher voltages.
posted by JackFlash at 1:50 PM on June 10, 2008


Seconding Supercaps.

That's what you're looking for.
posted by SlyBevel at 2:07 PM on June 10, 2008


Camera flashes work by charging a capacitor over a few seconds which is discharged almost instantaneously - the camera battery cannot provide the required current for the flash by itself. That's sort of an example of the system you describe. The capacitor supplements the ability of the battery to provide a burst of power.

Interesting. I used to have a really old-skool flash unit (separate from the camera, metal pie-dish type segmented reflector) that belonged to my grandfather that was powered by both a battery *and* a removable capacitor, so what the OP is asking about has existed in some form at one point.
posted by LionIndex at 2:19 PM on June 10, 2008 [1 favorite]


But why do I have to wait overnight for a rechargeable battery to "fill up" at a trickle, instead of just letting it "drink from the fire hose" - plugging it in and counting to ten?

The Energizer 15 minute charger is awesome if you don't want to wait a long time for your batteries to charge. It has fans, but they're quiet. Dashed handy.
posted by mumkin at 2:34 PM on June 10, 2008


I've built a few things powered by capacitors instead of batteries. I really like capacitors. I'm not so keen on batteries.

Supercaps, as noted, meet all four of your points. They have a lower energy density than (modern) battery chemisty though, so to carry the same amount of power, you will need a larger volume. They are however very lightweight, so might not involve much more mass.

There is a significant difference between caps and batteries that you missed though: Battery discharge is at the voltage of the chemical reaction, meaning a NiMH battery outputs approx. 1.2V until it is flat. This is very useful if you want to power a device - you know what voltage to expect from the power supply. (Alkalines vary a bit more: 1-1.6V, but this is still stable compared to caps)

A capacitor does not have a default voltage - or even a ballpark output voltage - the voltage it outputs is directly the result of how charged it is. A 10V cap that is fully charged will not supply 10V until it is flat, the moment you start using it the voltage will start falling, and the faster you take energy out of it, the faster and further the voltage falls - like drinking water out of a glass - the more you drink, the lower the water level (voltage). Conversely, the more water you add, the higher the level rises again.

For this reason, powering devices from capacitors requires jumping through a few extra design hoops. You need either a DC-DC converter to make a variable voltage into a stable one. Or use far more capacitance than you need and never dip into most of it (ie always have them charged between 90% and 100%), or else restrict your circuitry to things that will work acceptably even if powered by a wide and changing range of supply voltage.
On the flip side however, the recharging circuitry is greatly simplified, so your design complexity evens out.

But another advantage of caps is that batteries can be charged hundreds of times, while caps can be charged millions of times, so batteries end up in landfill by the droves.
posted by -harlequin- at 3:16 PM on June 10, 2008 [1 favorite]


Incidentally, capacitors keep their charge fairly well over an extended period, and rechargeable batteries lose more charge over time than it sounds like you realise. I'd suggest that keeping charged is not a point that can really be ceded to batteries, except for some non-rechargeable chemistries. So the shipstone battery is a capacitor - there doesn't seem to be anything to be gained by combining caps and batteries, all you would get is a fixed output voltage, at cost of a great redundant increase in battery size, since you have two storage units, one charging the other, which seems like an inelegant wasteful solution to a largely cosmetic problem.

Another ding on rechargeable batteries is that some of our best ones, (Li-ion, perhaps li-po too, not sure), have a shelf-life due to oxidation increasing their internal resistance, rendering them useless - whether you're using them or not, they will fail after a few years. Caps and otherwise inferior battery chemistries like NiMH are better in that respect.

Another ding on rechargeable batteries is that significant energy is lost during the charging process. Caps are far more efficient - pretty much all of your input energy is stored as charge. (You might lose this edge if you need to add a DC-DC regulator step to your circuits, but if you don't need that, you'll save energy)
posted by -harlequin- at 3:32 PM on June 10, 2008


> But why do I have to wait overnight for a rechargeable battery to "fill up" at a trickle, instead of just letting it "drink from the fire hose" - plugging it in and counting to ten?

As mentioned above, there are faster battery chargers out there. The limiting factor seems to be heat -- the chargers have fans blowing over the batteries as they charge, but even so the batteries get hot -- almost too hot to touch.
posted by neckro23 at 3:45 PM on June 10, 2008


The main problem with capacitors is that their energy density just isn't anywhere near what a battery's is. Read the math here.

Another potential problem with capacitors is that their discharge rate is frighteningly fast. You think those smoky melty Dell batteries were bad? Not even close.

Each has its place, but they aren't the same.

(The flash unit wasn't powered by the cap- the circuitry in a camera takes power from the battery and pushes it slowly, over time into the capacitor (that fweeeeeeee noise cameras used to make) so that when you hit the button, you can get a flash. Because a battery doesn't have the ability to give enough power fast enough to make a flash bulb go.

Incidentally, as another example of the good/bad aspects of using capacitors- have you even been in a car with the stereo turned up way loud, and where the lights would brighten and dim to the beat of the music? To solve that, people put in giant capacitors between the cars power and the radio amp. 1-2-3 farad caps, the size of soda bottles. They discharge fast enough to "prop up" the power for those quick moments. But they can't contain nearly enough power to do much more than that.
posted by gjc at 4:41 PM on June 10, 2008


gjc: the math in the link is either way off, or not referring to what modern caps offer. (it suggests a 1V 1 Farad cap would be anywhere from the size of a tuna can to a soda bottle, but these days, for a few dozen dollars you can get, off the shelf, nearly 1000F in the volume of a can of tuna, and at 3V (which is a lot more than 3x the energy of 1 F at 1V)) It's still larger than an AA battery, but not these supposed orders of magnitude (that once was the case). Let's hear it for aerogel!

For example, supposedly this capacitor-powered car runs for 20 minutes (and only takes 30 seconds to charge). Really, it's closer to a golfcart than a car, but even in a golf cart (especially in a golf cart!) the batteries take up a fair bit of space. If this thing is capacitors sufficient for 20 minutes, they're not taking up much space! (I also suspect that trying to charge that thing in 30 seconds requires a fatter pipe than the average house has :-)
posted by -harlequin- at 5:24 PM on June 10, 2008


OP back again. OK, so it sounds like I'm looking for some kind of super-DUPER-capacitor.
Even present supercapacitors as described seem to be incapable of powering devices more than temporarily. Accepted.
But is that because of some absolute limit, or just the present design & materials?
(Like, is this impossible, or is this one more item on the list of things that we have to wait for carbon nanotubes available by the kilo or something to solve?)
I'm just trying to gauge if we are presently at the primitive "vacuum tube" stage in capacitor technology, and if I just wait around a decade or two, we'll reach the "multi-core 45-nanomenter chip" stage, where charging the "ultracapacitors" on my electric car (ornithopter? chevaline?) takes less time and lasts longer than filling a tank with gasoline today?
posted by bartleby at 5:39 PM on June 10, 2008


bartleby:"But is that because of some absolute limit, or just the present design & materials?"

I don't know much about that side of things, but judging by how much their energy density has been noticeably increasing year after year, while the price drops, the limiting factor is pretty clearly at the "present design & materials" end of things. How long that can hold out until limits of physics comes into play, I don't know, but as the energy density of even batteries is rubbish compared to that of liquid fossil fuels, and that charge is a function of sub-atomic particles, suggesting that nano materials would be the natural thing to use, I would suspect that things can continue to be improved for quite a while yet.
posted by -harlequin- at 5:49 PM on June 10, 2008


As I understand the limitations of the Maxwell supercaps, which I have used in a design recently, the charge is contained in microscopic pores in the material. It seems that the enormous increases in capacitance of late have come about as a result of this. (In the past, it was stored on conductive films separated by paper, mica, and a whole bunch of other exotic and common materials.) The new stuff looks like shipping foam.

The thing that limits the voltage is a characteristic of the material called dialectric strength. It is about 3 volts in the Maxwell caps. They rate the caps at 2.7 volts. Their basic capacitance is a C-battery sized cap of 340 Farads capacitance.

If you connect caps in series, their voltage rating adds, but their capacitance decreases. The math is basically the reciprocal of the sum of the reciprocals of the capacitor size. ( 1/[(1/c1)+(1/c2)+...(1/cn)].

So to maintain the same capacitance as you increase the voltage, you have to parallel strings of caps wired in series. That's why the volumetric efficiency of large caps/higher voltages decreases.

Also, as you increase series caps, you have to balance the charges and that is done with either active or passive parts. Each has advantages.

Over time, the increase in capacitance is likely to continue, and if something exotic is discovered perhaps a new material will arise with higher dielectric strength that will allow the magic combination of high capacity and high voltage. We're not at the primitive stage you suspect right now, as the current crop of stuff is pretty exotic, but we do have new applications that have never been considered before and lots more people working on efficient ways of storing energy. Things usually improve under such scenarios.

Incidentally, the self-discharge rate of a Maxwell super cap is about 1% a day. Not bad, really.

And also, the charge rate limitation of lead acid cells is related to two major factors. One is the production of heat which will distort the mechanical form of the plates forming the electrodes and the other is electrolyte mobility. The chemistry that causes the charging occurs close to the plates' surfaces and the electrolyte is not homogeneous as a result. It has to move away from the plates via convection in lead acid (liquid and gel cells) and that takes time. The same effect is responsible for a very high discharge rate for a fully charged battery initially, which quickly declines during discharge to a flat rate. (The charge and discharge rates of batteries are one of the many specs engineers use to select and design circuits around specific battery species. ) (Lots of engineers are not familiar with batteries. Much about them is misunderstood.)

Caps, OTOH, push as much current out as the wiring will handle. The equivalent series resistance of a Maxwell supercap is milliOhms. It is very easy to melt wires with them. Neat parts to play with. (When they fail from overcharge, they stink like hell.)
posted by FauxScot at 6:53 PM on June 10, 2008


Here is some info on the EEStor super cap that is supposed to have 10x the energy density of a LiIon battery . It's actually their patent.

Note that is it not commercially available yet, but one of my old employers, Lockheed Martin, likes it and that says a lot.
posted by FauxScot at 7:25 PM on June 10, 2008


If you start talking about absolute limits, let's start with the most ridiculous and work our way down from there:

1) Little bitty black holes. Mass of the Earth in the size of a marble. A mountainsworth might be visible with a microscope. Bonus: the smaller they are, the faster they evaporate (theoretically) via Hawking radiation! That's a lot of juice in a tiny package. Limitation to energy storage: Few. Downside: containment sucks. Sure, you could keep it charged and spinning, try to cage it that way, but once you get the mass low enough that it's portable, it'll be very close to a runaway stage at which point is explodes in a spray of exotic particles. Where's that Earth-shattering ka-boom? Right in your jetpack, baby!

2) Direct mass-energy conversion. We'll, we're not so hot at that yet, nuclear weapons and power plants aside - that pesky conservation of baryon number keeps getting in the way! Still rather bulky, might pan out one day. Maybe we'll get a Mr. Fusion. I hear it's only fifty years away (too bad the years they're talking about are as measured from Pluto). Limitations to storage: E=mc^2. Past chunks of tungsten for fuel, you're looking at trying to keep some kind of degerate matter stable, maybe scooped off the crust of a neutron star. Good luck with that. Downsides: dirty kabooms that make your bones glow in the dark.

3) The second excited metastable state of the Hafnium-178 isotope (hf-178m2). Very, very new technology. So new it doesn't really exist so much as it is theoretical. Long story short, you know how you can excite electrons, which then dump their energy in the form of photons, and you can do anything from make stuff glow to make lasers? Well, this would be nuclear. Think gamma ray lasers. Think a possibly useful "nuclear battery" with which you might actually be able to send a probe to another planet in a reasonable amount of time. Maybe a gram of it would replace a plane's jet fuel. Limitations: Pretty specific, these guys have only one energy storage level. "One gram of pure Hf-178-m2 contains approximately 1330 megajoules of energy, the equivalent of exploding about 317 kilograms (700 pounds) of TNT. " Downsides: Not a lot of hafnium-178 around to charge up. Still prone, on the drawing board, to dumping all of its energy in a messy spray once you flick the "on" switch.

4) Good ole-chemistry. While the strong nuclear force rules the school at the short scales, the electromagnetic force is only a few orders of magnitude less powerful, and it operates on longer distances. Think TNT, gasoline, thermite, hydrogen. On the lower-end of the scale, think standard electrochemical batteries. Limitations: Once you pack too much energy into some kind of chemical bond, what you've done is "liberate" various atoms from various other atoms, resulting in not what you wanted at all. Also slow to make. Downsides: Kabooms in the form of burning and small smoky explosions.

5) Capacitors, supercapacitors, ultracapacitors. Well, they exist, that's the good news. And yes, caps can go bang and release that magic smoke that made it all work. There's that kaboom again. Limitations: various physical constants, and the fact that you can make the charge surfaces in question only so fractal (ie, more surface area) before you start trying to split atoms (see #3). It would be an interesting exercise to work out the precise limitations and whether or not the energy density will exceed #4.

6) Further on down the line you have things like compressed air storage, flywheels, springs, dams, and other stuff. Energy density: crap.

My guess is that there are definite limits to #4 and #5, which we will approach almost asymptotically. A well-controlled #3 would be my science-fiction supertechnology of choice.
posted by adipocere at 7:28 PM on June 10, 2008 [1 favorite]


Incidentally, the self-discharge rate of a Maxwell super cap is about 1% a day. Not bad, really.

In fact, I think that's comparable to standard rechargeables.

Battery discharge is at the voltage of the chemical reaction, meaning a NiMH battery outputs approx. 1.2V until it is flat.


This is definitely an approximation. A fully charged 1.2V nominal NiMH cell will have a significantly higher voltage (maybe 1.3 or 1.4?) when you begin to discharge it. This voltage will drop steeply to the neighborhood of 1.2, at which point it will start dropping at a slow approximately linear rate. At some point it will begin dropping steeply again, and somewhere around here you figure the voltage is too low and declare the battery discharged, though, in fact, you could still extract some heat energy from it by short circuiting the terminals, etc. But that higher initial voltage and slow drop near nominal voltage mean you probably still need to give yourself some breathing room and voltage regulation depending on how narrow your devices' voltage ratings are.

All this and the variation between batteries makes measuring remaining capacity difficult, which is why the batter meters on your cell phone and laptop never seem that accurate. Furthermore, when your cell phone declares that the battery is dead and it won't start up, it's actually doing that with a margin of error such that you see a nice understandable error message rather than the very unpredictable behavior that would be exhibited otherwise if the battery was allowed to completely run out, and which would make your cell phone seem like a shoddy piece of junk.
posted by TheOnlyCoolTim at 7:32 PM on June 10, 2008


One of the reasons why recharging of batteries takes a long time is because of cooling, or rather the lack thereof.

As a LiIon or NIMH battery gets close to full charge, a larger and larger percentage of the applied power gets converted into heat instead of into chemical changes. With LiIon batteries, when they get to this point the back resistance starts to rise, but with NiMH batteries it remains the same.

So with NiMH batteries, if you keep pumping current through them when in this end stage, the battery will melt or explode. That wouldn't be a problem if there was water cooling, but of course no one does that. LiIon batteries aren't quite as dangerous in this regard but it's still a problem.

To get the last 10-20% of charge in, it's necessary to do what's known as "topping off". That means the charger pumps current for one second, and does nothing for three seconds. The purpose of that is to give the battery time to cool after each pulse.

With all rechargeable batteries, a fair proportion of the current in all stages of recharging, from bottom to top, is converted into heat. (See "Law of Thermodynamics, Second".) If you try to recharge the battery too fast, you get melting or explosion.

When lithium batteries were first introduced, there was at least one case I heard of where the battery exploded and shrapnel killed someone. In those early Lithium batteries, if you tried to recharge too fast another bad thing that happened was a buildup of gaseous hydrogen inside the case. Too much of that and the pressure ruptures the case -- which is what happened.
posted by Class Goat at 8:15 PM on June 10, 2008


The essential difference between batteries and capacitors is that batteries store energy in chemical bonds, while capacitors store energy in electric fields.

Capacitors can discharge quickly because miniscule changes in the geometry of a distribution of charges can dramatically change the electric field. A one foot signal cable will delay the edge of a pulse by a few nanoseconds, pretty close to the fundamental limit, but the actual speed with which electrons drift down the metal of that cable is only a few inches per second. Beefy capacitors store more charge per volt because the electric field passes through some "dielectric" material that polarizes the other way. Capacitors fail when the dielectric breaks down and conducts a current --- you have seen this in air when the doorknob shocks your finger, or during thunderstorms. In any material, there will be some electric field strength that pulls electrons off of their molecules. For that matter, there is an electric field strength where the energy density is large enough to make electron-positron pairs. I don't have any feeling for what electric fields in common capacitors are, so I don't know how close manufacturers are to that fundamental limit, or what hurdles of electrochemistry lie along the way.

The rate of discharge from a capacitor is limited by its inductance: changing an electric field makes a magnetic field, which acts to slow the change in the electric field, as if the electric field had some "inertia." You can design systems where inductance and capacitance are equally important (these are "oscillators" or "radios") or systems where the inductance can be safely ignored (e.g. a camera flash), but inductance plays a part in limiting how fast you can get energy out of a system.

The simplest possible battery has three different materials: two with one sort of charge carrier connected by one with a different sort. In textbook examples, you use two different kinds of metallic (free-electron) conductors and some electrolyte solution with ions as charge carriers. In wet-cell batteries like these, the limit on the current you can draw is the rate at which electrons can enter and leave the solution at the interface between the electrodes and the electrolyte. This can only happen at the interface, and is much slower than electrons traveling through the bulk metal of a capacitor. The chemical reaction takes energy, which is why a shorted battery gets hot. If you're clever you can choose a reversible reaction, but driving it electrically is inefficient: recharging a battery heats it up, too. And eventually, your electrodes get coated in detritus from your reaction, or your electrolyte gets depleted of its catalyst, or some such. You might be able to clean the electrodes and replace the electrolyte, but that's essentially getting a new battery.

As hinted above, you can certainly design an electrical device that meets your Shipstone criteria (fast or slow charge and discharge, long-lived, stable) at the expense of efficiency, cost, size, and/or lifetime.

On preview, it seems worth mentioning that batteries and capacitors are great for energy storage, but irrelevant from a standpoint of energy production. This is also true of hydrogen, hafnium, antimatter, and anything else that doesn't come out of the ground by itself.
posted by fantabulous timewaster at 8:35 PM on June 10, 2008 [2 favorites]


So to maintain the same capacitance as you increase the voltage, you have to parallel strings of caps wired in series. That's why the volumetric efficiency of large caps/higher voltages decreases

I believe this is inaccurate (or I'm misreading you). The volumetric efficiency does not decrease, because more energy is stored per additional volt - one Coulomb of charge at 2V does a lot more work than one Coulomb of charge at 1V.
It takes one 1F 1V cap to store a farad at 1 volt. It takes four of these caps to store a farad at 2V. It takes nine to store a farad at 3V. But you are astoring nine times as much energy even though it's only three times the voltage. You're not getting three time less efficiency - a Farad is not like an ampere in this way (or there would be no need for Farads).
posted by -harlequin- at 2:03 AM on June 11, 2008


I agree, harlequin. Poor choice of wording on my part. Thanks.
posted by FauxScot at 8:10 AM on June 11, 2008


Strange the Batacitor has existed since July of 2006. Yet you said it does not!
My Rechargeable Batttery can be drained down to 0.0 volts and 0.0 amps with
no damage or harm. Yeilding a gain of 3.5 time the power. All the benefits of a
capacitor with none of the flaws.

See http://www.youtube.com/watch?v=PFcylXFGTgk for more details.

Yes, there are no Limits to Physics for if there were, I could not have found the key to
solve this problem.

Thank the Inventor.

epicbill
posted by epicbill at 12:28 PM on July 11, 2008


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