How much CO2 is enough?

[DaktariEd]

I have a 10 lb PowerTank...and 33x12.5" BFG M/T tires.
Is there any way to estimate the number of tires I can re-inflate?
I usually run 25 - 28 lbs on the road and air-down to 15 lbs in the dirt.
As I recall, I usually get 2 - 3 full re-inflations of 4 tires out of a 10 lb fill, but I wonder if there is a more accurate way to estimate?

Thanks,
:sombrero:
Ed

 

[slosurfer]

This should help
http://powertank.com/full.chart.html

One other way that I am going to use next time I fill my 20# tank, I'm going to add a little notebook to it so I can mark down each time I use it, how many tires etc.... This should give me a decent idea and I am going to weigh it empty and full this next time.

 

[DaktariEd]

Yeah, I have the empty weight: 18.4 lbs (w/regulator attached).
Today it weighs 25.1 lb. So I have about 7 lbs still in the tank.
That should be fine for this weekends trip, but I'll have to try to track it a bit more closely.
I don't know if ambient temperature affects anything either...any thoughts?

:sombrero:

 

[Lynn]

Let's see if I can get this right... It's been a while since I took Physics...

The Ideal Gas Law is PV=nRT...

Note that n = Avogadro's Number, but since the same gas is used on both sides, it cancels out. (Actually, since the tires are initially filled with air, and the tank has CO2, it doesn't work this way, but I don't want to deal with that*, so I'm going to ignore it in a 'close enough' approach)

... and a derived combined gas law is:


(P1 V1) / T1 = (P2 V2) / T2 where:

P1 is tank pressure
V1 is tank volume
T1 is tank temp
P2 is tire pressure
V2 is tire volume
T2 is tire temp

So, as you can see, tire temp and tank temp are factors. Unless you can let your tires cool to the same temp as the tank. If you can do that then it simplifies to:

P1 V1 = P2 V2

For P1, subtract max tire pressure from starting tank pressure to get available tank pressure (i.e. you can't get 32 psi from a tank that only has 28 psi)

if you solve for P2:

P2 = (P1 V1) / V2

that will give you the total fill pressure available.

If you then divide that available fill pressure by the tire pressure difference per fill (i.e. 32 - 6?), that will tell you how many tires you can 'top off'.

Of course, if you divide that number by four, you will get how many times you can 'top off' all four tires...

Some other factors are involved (such as the fact that tires aren't rigid tanks), but this should get you close enough.

To get the tire volume, calculate the volume of a cylinder equivalent to the wheel/tire combo:

V1 = (tire height / 2) squared * width

Then you have to figure the volume of a cylinder the size of the rim:

V3 = (rim height / 2) squared * width

And subtract the two to get the tire volume (to be used above):

V2 = V1 - V2

Did I get it right?

* I'd rather shoot moles than calculate 'em.

 

[adventureduo]

Yep, check out the chart on the powertank site.

On weekend runs there aren't any worries with our 10lbs tank.. but if we are going on a long haul, we really need to look at how many times we are going to be airing up/down and also account for reserve if we need to use air tools in a emergency situation. Also, if we were going to be gone for a extended period of time, check to see if we can have it fillled anywhere in a passing city.

 

[Bighead]

Let's see if I can get this right... It's been a while since I took Physics...

The Ideal Gas Law is PV=nRT...

Note that n = Avogadro's Number, but since the same gas is used on both sides, it cancels out. (Actually, since the tires are initially filled with air, and the tank has CO2, it doesn't work this way, but I don't want to deal with that*, so I'm going to ignore it in a 'close enough' approach)

... and a derived combined gas law is:


(P1 V1) / T1 = (P2 V2) / T2 where:

P1 is tank pressure
V1 is tank volume
T1 is tank temp
P2 is tire pressure
V2 is tire volume
T2 is tire temp

So, as you can see, tire temp and tank temp are factors. Unless you can let your tires cool to the same temp as the tank. If you can do that then it simplifies to:

P1 V1 = P2 V2

For P1, subtract max tire pressure from starting tank pressure to get available tank pressure (i.e. you can't get 32 psi from a tank that only has 28 psi)

if you solve for P2:

P2 = (P1 V1) / V2

that will give you the total fill pressure available.

If you then divide that available fill pressure by the tire pressure difference per fill (i.e. 32 - 6?), that will tell you how many tires you can 'top off'.

Of course, if you divide that number by four, you will get how many times you can 'top off' all four tires...

Some other factors are involved (such as the fact that tires aren't rigid tanks), but this should get you close enough.

To get the tire volume, calculate the volume of a cylinder equivalent to the wheel/tire combo:

V1 = (tire height / 2) squared * width

Then you have to figure the volume of a cylinder the size of the rim:

V3 = (rim height / 2) squared * width

And subtract the two to get the tire volume (to be used above):

V2 = V1 - V2

Did I get it right?

* I'd rather shoot moles than calculate 'em.

My head hurts now. :smilies27

 

[DaveInDenver]

Expanding on Lynn's post, the calculations are here:

http://www.expeditionportal.com/forum/showpost.php?p=88034&postcount=26

Short answer, 10 lbs of CO2 has about 103 mols (or 88 scf) of gas. A 33x9.50 tire has about 3 cubic feet of volume or about 8 mols at room temp and 35 psi. So if you air down by letting half (just for round numbers, 1.5 mols of the gas) of the air from the tire, you'll get around 103/1.5 fill-ups, so ~68 tire air-ups.

Oh, edit to add this. Notice that I figured there's 88 scf of gas in a 10 lbs Powertank. That means if you run an air tool with the tank, you need to know how much air it takes and for how long it runs to guess what's left. Say an impact wrench uses 20 cfm, you get 4 minutes of tool time.

Another edit. The volume of a tire is found by finding the volume of a torus with a slightly elliptical cross section. Corrected my estimate of tire volume.

 

[DaveInDenver]

Using a 33" diameter and 12.5" width (exact, which most tires are far from) on a 15" rim. I get a volume of 4 cf for your tire. At 30 psi, that means there's about 9 mol of gas in the tire at 80F. So at 15 psi, 80F, you have about 4.7 mol of gas. You have to refill with 4.3 mol of gas, so a full 10 lbs CO2 tank should give you 20.5 refills max, maybe a safe working number is 16, so 4 sets of 4 tires.

Another edit. Probably wondering how I figured the volume of a tire? The volume of a torus is the cross section of the torus times the length about its center line. So calculate it by knowing the major radius, minor radius and width. So take a 33x12.5 tire on a 15" rim. The major radius 'R' is 33/2 = 16.5", the minor radius 'r' is 15/2 = 7.5" and the width 'W' is 12.5".

First find the intermediate variable of tire body radius, call it 'b', which is b = (R - r) / 2 = 16.5-7.5 / 2 = 4.5" and intermediate width radius 'w', which is w = 12.5 / 2 = 6.25".

Torial volume 'V' is length (say 'L') x cross sectional area (say 'A'):

V = L x A = (2 * pi * (r + b)) x (pi * b * w) = (2 * pi * (7.5 + 4.5)) x (pi * 4.5 * 6.25) = 6660 cubic inches = 3.86 cubic feet

 

[Lynn]

Another edit. The volume of a tire is found by finding the volume of a torus with a slightly elliptical cross section. Corrected my estimate of tire volume.

I thought that the cross section of a radial tire was more square than round, but, you're right, a torus is a better approximation.

 

[DaveInDenver]

I thought that the cross section of a radial tire was more square than round, but, you're right, a torus is a better approximation.

Oh, yeah, I'm far from claiming these estimates are exhaustive or even remotely precise. I'd bet a torus approximation is close enough (not to mention that I'm using rated tire size, forgetting actual internal section).

 

[crawler#976]

I get between 25 and 30 air ups with a 20Lb cylinder on 35/12.5-15's from 8 PSI to 24 PSI - so I'd venture a guess that a 10LB should do eighteen or twenty 33's pretty easy.

I've found that once my tank pressure guage starts to drop from 850 PSI (that's in cool weather - I've seen it register close to 1000 in direct sun on a hot day...) that I can generally complete my airing up on 4, but that's pretty much it.

 

[DaktariEd]

Let's see if I can get this right... It's been a while since I took Physics...

The Ideal Gas Law is PV=nRT...

Note that n = Avogadro's Number, but since the same gas is used on both sides, it cancels out. (Actually, since the tires are initially filled with air, and the tank has CO2, it doesn't work this way, but I don't want to deal with that*, so I'm going to ignore it in a 'close enough' approach)

... and a derived combined gas law is:


(P1 V1) / T1 = (P2 V2) / T2 where:

P1 is tank pressure
V1 is tank volume
T1 is tank temp
P2 is tire pressure
V2 is tire volume
T2 is tire temp

So, as you can see, tire temp and tank temp are factors. Unless you can let your tires cool to the same temp as the tank. If you can do that then it simplifies to:

P1 V1 = P2 V2

For P1, subtract max tire pressure from starting tank pressure to get available tank pressure (i.e. you can't get 32 psi from a tank that only has 28 psi)

if you solve for P2:

P2 = (P1 V1) / V2

that will give you the total fill pressure available.

If you then divide that available fill pressure by the tire pressure difference per fill (i.e. 32 - 6?), that will tell you how many tires you can 'top off'.

Of course, if you divide that number by four, you will get how many times you can 'top off' all four tires...

Some other factors are involved (such as the fact that tires aren't rigid tanks), but this should get you close enough.

To get the tire volume, calculate the volume of a cylinder equivalent to the wheel/tire combo:

V1 = (tire height / 2) squared * width

Then you have to figure the volume of a cylinder the size of the rim:

V3 = (rim height / 2) squared * width

And subtract the two to get the tire volume (to be used above):

V2 = V1 - V2

Did I get it right?

* I'd rather shoot moles than calculate 'em.

:smileeek: :smileeek: :smileeek: :smileeek:


Uhhhhhh....thanks!
My head really hurts too!

 

[vengeful]

My 10lb tank generally lasts me about 4 sets of tires, provided I don't use it for anything else. If I have to use it for air tools, it gets depleted pretty quick. I'm working on a home-engineered electric York setup that'll push about 9cfm at 100psi. I think that'll cover me. Lol.

 

[BogusBlake]

I don't know if ambient temperature affects anything either...any thoughts?

Ambient temperature affects how many air-ups you get. Quite a bit, actually.

CO2 is can't exist as a liquid above 88 degrees F. http://en.wikipedia.org/wiki/Supercritical_fluid

What that means, is when it's cold you stand the chance of putting liquid CO2 into your tires. When it's hot, you're only putting CO2 gas in the tire. When the gas is allowed to expand before you let it out of the tank, you get to use more of it to inflate the tires. When it's liquid in the tire, it will eventually heat up and change phase to become gas, and according to the ideal gas law, the pressure will increase too because the volume is pretty much fixed.

So, if you don't let your regulator freeze, or it's hot out, you'll get more gas out of a given tank size than if you let all the liquid run out.

FYI, I can typically fill 20 37x12.5's from 3 to 25 psi on a 20lb tank.

 

[offroad_nomad]

All these numbers make my head hurt too.

With my homemade 10lbs Co2 system I get about 24 tire refills, mostly mine (285/75/16), from 18 back to 32 psi before exchanging it for a new tank.