DoomLabs: The Science of CO2
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The Science of CO2
When designing cannons it is instrumental to know a bit about CO2 - particularly
to design for maximum efficiency (most shots per tank). It's otherwise interesting
to understand why your marker freezes up under sustained fire with CO2 and
also why your burst discs sometimes blow when your tank gets hot or is over
The pressure and thermal characteristics are both particularly important
when using CO2 for PVC based cannons. We don't want to over pressurize our
PVC and we also don't want to freeze down the PVC while filling the chamber.
The over pressurization, which you may have noticed as "sometimes my gun
shoots hot" is of particular concern with PVC. Your marker "shoots hot"
when some liquid gets past the regulator and then turns to gas. This is
also of particular concern when a CO2 tank and it's regulator are installed
horizontally on a cannon - more opportunities for liquid flow.
So let's take a peak at The Science of CO2 and then relate that to markers,
tanks, cannons, and cannon design.
CO2 is not an ideal gas.
CO2, as we will see is absolutely not an ideal gas, and there is significant
hysterisis in it's state chart. This state chart:
is from WarPig
and is cached here. The WarPig
article has a good discussion of CO2 and it's attributes relative to Paintball.
I highly suggest you read the WarPig
article. For safety's sake please pay particular attention to the critical
temperature and pressure of CO2. The critical temperature and pressures are
critical for safe designs and we'll address them in these discussions on this
page an on this site. While I'm at it, a good site for conversions is http://www.Convert-Me.com.
Although CO2 is not an ideal gas, for most of these discussions, we can
get pretty close if we (1) follow the Ideal Gas Law equations, (2) use known
values for CO2, and (3) check to make sure we're starting and ending where
we want in the phase chart. Staying in a safe zone essentially means ensuring
we will always have gas (primarily as that means we don't have liquid available
to make even more gas available - we've only got temperature vs pressure scaling)..
The Ideal Gas Law & CO2
The ideal gas law can be stated as P*V = (m/MW)*R*T
P = pressure in atmospheres, where 1 atm = 14.7 PSI at sea
Now, to simplify for STP (standard temperature & pressure)
V = volume of gas in liters, where 1L = 61.02 in3
m = mass in grams of CO2
MW = molecular weight of CO2; MW = 12+32=44
R = 0.082 liter*atm/K
T = temperature in kelvins [which is 298 K at 25 C or 77 F]
(1atm)*(1L) = (mg/44)*(0.082)*(298tk)
So, to simplify for "paintball normal conditions" for CO2, we assume 77F,
CO2, pressure in PSI, and volume in cubic inches and yield:
1.8 grams CO2 == 1 Liter volume at 1 atmpsphere pressure (sea level) at
298 kelvin temperature (77F)
1.8 grams CO2 = 61.02in3
In general, and for our purposes, this equation holds as long as the
pressure is below the vapor pressure for any temperature we're interested
in. And this is the primary check we're interested in for our computational
tests and design rules checks as if we're under the vapor pressure we know
we're dealing with gas.
Some practical examples
for cannon design:
For some quick examples consider a 12 gr CO2 cyclinder. How much
liquid and how much gas is inside? It's actually a tough question as for a
fixed temperature we'll maintain pressure as the volume increases up until
the liquid is gone. So it's suicidal to say "the 12 gram is at 1200 PSI so
if I make a chamber 3 times as big I'll have gas at 400 PSI and that's safely
at the upper limit of my Whistle Valve". And that would be incorrect and perhaps
hazardously so. All we know is that there is supposed to be 12 grams of CO2
For cannons, we typically want to know:
of CO2 at a given pressure for a given amount
This is commonly asked "how big of a chamber do I need for
150 PSI PVC fed with a 12 gram cartridge. So that will be our example.
We know that 1.8 grams of CO2 == 61.02in3 so (12/1.8)(61.02)=406.7Vin3 at
We know that 1atm == 14.7 PSI so (406.7) * 14.7 / 150 = 39.86in3
So 12 grams of CO2 will fill 39.86in3 at 150 PSI at 77F.
This is safe because we are well below the critical temperature and pressures.
Having safety checked we can now find how much of what sized pipe will give
us that volume.
of CO2 at a given volume for a given amount
This is commonly asked as "if I dump a 12 gram into this
chamber ,what is the pressure?" We have to watch this as if the pressure
shows liquid state in the phase chart for that temperature then we do not
have gaseous CO2 (which may or may not be a problem).
Let's assume a 1.5" PVC chamber 12" long. So it's volume V = ( pi *(1.592/2)**2
) * 12 == 23.87 in3
We know that 1.8 grams of CO2 == 61.02 in3 at 1atm so
(12/1.8)*(61.02/23.87)*(14.7) = 250 PSI.
This is safe from a CO2 perspective because we are well below the critical
temperature and pressures. This is borderline (to me dangerous) from a PVC
If we wanted to lower the pressure to 150 PSI (my target maximum) with the
same diameter pipe we'd have
250 / 150 * 12 == 20"
If we wanted to lower the pressure to 150 PSI with the same length pipe.
Again, we scale the volume.
250/150 * (23.87/12) = 3.32in2 where 3.32in2 = pi (r**2) so r = 1.028 so
d = 2.056 inches
We see that 2.056 inches is very close to the 2.049 inch ID of 2" PVC so
we are done. If the computation had yielded a diameter that was not close
to a standard pipe sise then we would need to go either up or down a size
and accept either a different chamber length, a different working pressure,
or both (always double checking for safety).
CO2 Resources & References
DoomLabs PVC & Copper Pipe Specifications
google search for CO2, pressure, and atmosphere
http://newton.dep.anl.gov/askasci/chem00/chem00306.htm for some CO2
and for units conversions
WarPig for Paintball
Gases page. This has CO2 Phase
chart and CO2
Dynamics page as well as other gas related information.
of Steel & PVC sch 40, sch 80 & class 160