Wrench Wednesday: How much CO2 do I need?

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Editor’s Note: This is the first in a new weekly installment called ‘Wrench Wednesday’ which will feature posts on bike tech, maintenance and repair authored by bike mechanics, or some who play one on tv. Today’s guest wrench is Eric Hansen. – Ed

Eliminating the guesswork from CO2 inflation

If you’re like most people carrying a CO2 inflator, you’ve got a 16g cartridge, and no idea what it’ll inflate your tire to after a roadside tube change. Charts supplied by inflator manufacturers only cover the most common tire sizes, and can be confusing to read. Because none of my bikes are what you would call standard, I bothered to learn how to calculate exactly what each tire needed. In the process, I found a lot of disparate tire sizes that used the same amount of CO2, but many more that were wildly off the mark. This article will explain exactly what’s going on when you use an inflator, and exactly how to size one for your specific situation. Additionally, I have written this procedure into a TI-BASIC program, found here.

The CO2 in your cartridge is what is called a ‘cryogenic liquid’. That is, it’s a gas at normal pressures and temperatures, but has been frozen out of the air, and kept in a liquid state by containing its massive pressure. In pressurized liquid form, the internal pressure ranges from about 600-900 PSI depending on temperature. In the high 90’s (or 30’s, for non-Americans), CO2 can no longer be kept at a liquid by pressure alone, and turns into a superfluid. Don’t leave your cartridges in the sun; they will fail spectacularly. Or do exactly that, but make sure you take video for YouTube. (Really, though, don’t bother. The end foil will rupture and they’ll shoot off in a direction for a half second. It’s not that great.)

How does 600-900 PSI translate to the 60-125 you want in your tire? Under the immense pressures in the cartridge, the CO2 is held in liquid form. But once you release those pressures, the CO2 immediately boils until an equilibrium is reached. Heat is drawn in from outside the cartridge to boil off the liquid. This is why the cartridges get very cold when used, why the cartridge can “recharge” itself after a few seconds pause in its use, and why you need to be very particular about how you use CO2 in conjunction with tubeless sealants. Yes, you can use CO2 with tubeless; any sealant, any brand. Your inflator will either be an all at once type, or one that allows you some measure of control in inflating your tire. Either way, you want to size your cartridge such that the last CO2 boils off into gas just as your tire reaches its operating pressure.

Now we’ve got grams (a weight) of a liquid, which turns into a gas, and is contained to a pressure by a tire of some size, at whatever the outside temperature is. The relation between all those things was discovered in the 1800’s by a lot of people playing at hot air balloons. They all made their individual discoveries, like the relation of pressure and temperature, and eventually all were combined with chemistry into the Ideal Gas Law. The IGL, in its shortest form, is written PV = nRT. Let’s see what all those are!

P – Pressure. Easy enough to figure out.

V – Volume. Similarly, we all know what a volume is. But the volume of what?

n – Number of Moles. What have gas laws got to do with subterranean mammals?

R – What the heck is R? Oh. It’s a Gas Constant, because R makes sense as an abbreviation for that. And boy that’s a lot of values for R!

T – Temperature. Sure. Temperature for what?

We’ll leave the gas constant, R, alone for now, and talk about moles. A mole in chemistry is one Avogadro’s Number of molecules of a particular type. Avogadro’s Number is 6.022×1023, which is a really phenomenally huge figure. It is defined as the number of carbon-12 isotopes contained in 12 grams of the pure substance. In fact, if you have the atomic weight of any atom (or molecule) in grams of any substance, you have one Avogadro’s Number, or one mole of that substance. A mole is a way of counting actual molecules in a human calculable way. We’ll need the atomic weight for CO2. There’s a carbon, which we’ve just decided has an atomic weight of 12, and two oxygens, which have an atomic weight of 15.9994 (far more digits than we need). Combined, we’ll use 44 as our molecular weight, or the weight of one mole of CO2.

So then a 20g cartridge has a half a mole of CO2 inside. Interesting, but not useful. We want to find how many moles of gas we need to get to some desired pressure. Algebraically manipulating the IGL, we can write it as  n= PVRT That form lets us input values for P, V, R, and T, and gives us a number of moles required to reach those conditions. The values we select for P, V, and T, have to be consistent with the value we use for R, so let’s talk about that. The gas constant can be defined in a lot of ways, many of which I am not familiar with. It is a Useful Thing. For the purposes of this calculation, we just need to select one that jives with the rest of our figures. Being an American, that poses some problems. For starters, temperature MUST be in either Kelvin or Rankine, because the percent difference between 94°F and 32°F is HUGE, while the percent difference between 492°R and 554°R is tiny. It messes up the model, and causes it to be wildly inaccurate. If you’re wondering “what the hell is a Rankine?” it is like Kelvin for the Fahrenheit scale. It starts at absolute zero, and uses the same temperature divisions as Fahrenheit. We’ll not use it here, but you could if you absolutely wanted to use Fahrenheit directly in your calculation. Straight away, we’re going to have to convert degrees Fahrenheit to Centigrade, then to Kelvin. It doesn’t get any easier for the rest. Volume: virtually all the gas constants were calculated with metric measurements of some type, which is handy because tires are measured in millimeters. At most we’ll have some power of 10 to deal with. For pressure, we could choose a value for atmospheres, bars, kiloPascals, or PSI. I’ll use one for ‘atmospheres’ because it makes things difficult for everyone. If you want to directly use your native pressure measurement, look up an appropriate R value on the page linked to earlier. We’ll use 0.0820573614 Liter Atmosphere/Kelvin moles

Now that’s decided, all we need is to get our P, V, and T, into acceptable forms, and calculate. Using my 3-speed, I pressurize to 80 pounds, at 74°F.

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Volume is a bit trickier. I have a 38-622 tire, and for the volume of a torus, we need a major and minor radius. The minor radius is half the sectional width, or 38/2 = 19mm. The major radius runs through the center of the tube, so it is (622+38)/2 or 330mm. Liters are also cubic decimeters, and we’re using cubic millimeters, so we need to convert.

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Now we have all the things in place to see how much CO2 is required for my application!

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So we can see a 20g cartridge will inflate my tire, but not to its normal operating pressure. It will be rideable, but feel like pedaling through a bit of mud. We can see I don’t want to use a 25g cartridge, since at 85 PSI max, the tire might blow off. Also, at a summer temperature, a 20g cartridge will be nearly perfect.

The really surprising results come in with mountain and fat bike tires. A 116mm sectional width tire can be inflated with the same 25g cartridge of CO2 in the winter, unlike the ignorant Pearl Izumi April Fool’s article would have you believe. Seemingly minor changes in one parameter can lead to massive changes in CO2 requirements. If you’ve got a bike with oddly sized tires, or run odd pressures in them, give this procedure a shot.

CO2 is notorious for ruining tubeless set-ups, but it doesn’t need to. The latex doesn’t react with the gas directly, but it can be shocked into coagulation by the extreme cold imparted by rapid inflation from a cartridge. If you turn the valve stem to the bottom, let any sealant inside it drain out, then turn the stem to the top, THEN inflate, you won’t have any issues with instant coagulation.

Final note – if you’re one to let all the CO2 out of your tube before refilling it with air, don’t bother. If you really want to calculate out the difference, you’ll need the table here (http://eesc.columbia.edu/courses/ees/slides/climate/table_1.html) and the van Der Waals equations. I have a feeling the differences are going to be vanishingly small, and haven’t bothered with them myself.

About Eric Hansen

Eric started commuting by bike in 2011, and has turned into an avid cyclist. After a decade of fixing all types of things for the Army, he is currently studying electrical engineering at tOSU, and wrenching for rent money cheap bike parts at BikeSource. He can be reached via the Plus and the Tweets.

Comments

  1. Bill Lougheed says:

    Thank you for this article. It has been extremely helpful! My family operates a mobile bicycle repair, assembly and accessories business in the Tampa area. We offer the Air Kiss products and the education received in this article will be extremely useful in helping our customers make choices about Co2 based inflator products. The one thing I would suggest to your readers before running the calculations is to go look at some schematics online of a torus to better understand what that is and how to gather the information for the tubular volume formula. I’d never heard of it before. I now understand it.

    Interestingly, it wasn’t our business that drew me to the article; rather, it was my hobby. I’m a motorcyclist and have recently noted claims by motorcycle repair kit retailers that 1 or 2 16g Co2 cartridges will inflate average sized motorcycle tires. Those claims aren’t at all reasonably consistent with my bicycling/business experiences. I took four AirKiss 16g cartridges out of inventory and tested them on my tubeless 180/55×17 rear motorcycle tire that specs at 42 psi. Those four 16g cartridges (64g of Co2) produced 22psi leading me to extrapolate that that up to an amount of 122 grams (or 8 16g cartridges) to fully inflate the tire. When I later applied all the actual metrics to your approach and formulas, the result was 132 grams. That’s pretty close! Thank you again.