Please help me do the math...

"kmd1984"Hi,

I did a search on here, but wasn't able to find exactly what I am looking for. I found this, http://airgunnation.dev/topic/simple-conversion-tool/ which very helpful, but it doesn't explain how to get to the end result, and that's what I am after... This is my first post ever, so be nice. : )

I am trying to figure out how to do the math on a few things. 

The tank I am looking at is this one. Carbon Fiber, 88 cu ft at 4500 psi. The gun I am looking at is this one. Benjamin Marauder with 215 cc tank. How does one do the math, if I want to know how many refills I get from that scuba tank?! 

I figured that 88 cubic feet are 2,491,882 cubic centimeter. Since the tank on the gun is 215 cc, does that mean I can refill the tank roughly 11590 times? I seriously doubt that, ha ha. I guess somewhere in this calculation, I have to account for the 3000 psi the 215 cc tank is filled with. Correct?! 

I hope someone can explain this to me...

Thanks,

Kmd

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If you fill to 3K and refill at 2K you will get 55 fills from an 88CF tank that starts at 4500psi.

Here is a calculator
http://www.calc.sikes.us/2/index.php

"kmd1984"If you would have read my post, you would have seen that I posted a link to the same calculator you just did. The calculator help, but I would still like to know how those numbers are being calculated... instead of having some app do it for you.

Thanks,

Kmd

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Sorry I didn't realize you were referencing a link within that older post.

Basically the "CC's" on your tank is the "physical volume" of the cylinder. The CF values in the chart is the actual volume of air that is able to be compressed into that space. (at least that's how I understand it)

If you look at the chart a 48CI tank pumped up to 3K psi will be containing 5.7CF of air. The same tank at 4500PSI will have 8.6CF of air.
So if your tank is 215CC's when you fill it with air to a pressure of 3K psi it was actually be holding 1.6CF of Air. - This means that your 88CF tank (which with 4500psi) is holding 88CF of air) will fill the bottle 55 times (88/1.6=55) The actual physical volume of a 88cf tank is about 7.9Litres.

If you look here this tank is 74CF but also notice in the listing it is 6.8L

http://www.ebay.com/itm/Ninja-4500-psi-Carbon-Fiber-74cu-ft-Air-Tank-and-Fill-Station-for-PCP-Air-guns-/151712265683

"kmd1984"No problem...

You still did not explain the math behind this though... 48 cubic inches and 3000 psi equals somehow 5.7 cubic feet? How?!

Wait, I have an idea!

48 CI is 0.0277778 CF and 3000 psi is 206.8427 bar, thus 0.0277778 x 206.8427 = 5.745! Correct?!

Again,

215 CC is 0.00759265 CF and 3000 psi is 206.8427 bar, so 0.00759265 x 206.8427 = 1.5704 CF!

I believe I get it now!

Thanks,

Kmd

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OK - so this still doesn't tell us how to come about the final #. I think I have that now, see below

Take the amount of air in source tank (Size in CC x BAR) Now if the Air is 4500PSI and you want to fill your tank to 3000psi then your "available air" would be 1500PSI or 103.4214Bar. (SInce once the source tank gets below the pressure you want to fill to it will no longer fill it will be equalized)

A tank rated at 88CF has a physical capacity (or fluid volume) of 7.9L so the "available air would be 7.9 (1000) = 7900CC x103.4214 (1500psi of available pressure) or 817029.06

Now take the size of your tank to be filled (in cc) and multiply by the amount of air needed in BAR. In this case it would be 215 times 68.9476 (1000psi- to take the tank from 2000 to 3000). or 14823.734.

Now divide the available air (817029.060) by the amount needed (14823.734) and you get 55.11 fills.

If you wanted to till to 3000 and refill at 1000 then you would need 137.8951bar (2Kpsi) times 215 which = 29647.4465 which when you divide your source air of (817029.06) by gives you 27.55 fills.
Now if you only want to go from 1000 up to 2000 each time there would be 1361714.31 available (7900cc x 172.3689bar (2500psi)) and it would take 215cc x 68.9476 (1Kpsi) 14823.734 to fill each time so if we divide 1361714.31 by 14823.734 we would get 91.86 fills.


Of course we would then have to figure out the volume of the fill hose and reduce the available air by that # times the # of fills as that will be "wasted" each time you De-pressure the line to remove the tank.

Quite honestly if I had to do all this figuring each time I used my tanks I would just shoot my R9 all the time.

But this was a good brain work out. Thanks for explaining the question better and not just letting it go.

Why not use the Crosman fill calculator?

http://www.crosman.com/discover/airguns/pcp-resources/fill-calculator

Pick your gun (Marauder), pick Scuba tank and enter the actual volume tank size and tank fill pressure, and your gun pressure range.

I will mention, that most SCBA tanks are listed in either minutes or Cubic Feet of compressed air that they'll hold. For example, I have a Draeger 66cft/45min tank, but all the fill calculators ask for the water volume of the tank (ie the actual physical volume of the tank). I haven't been able to find that anywhere. I could probably estimate it by getting the diameter and height of the tank and fudging a bit, but I've not yet found any place that lists the volume of my tank in cubic inches.

"ztirffritz"Why not use the Crosman fill calculator?

http://www.crosman.com/discover/airguns/pcp-resources/fill-calculator

Pick your gun (Marauder), pick Scuba tank and enter the actual volume tank size and tank fill pressure, and your gun pressure range.

I will mention, that most SCBA tanks are listed in either minutes or Cubic Feet of compressed air that they'll hold. For example, I have a Draeger 66cft/45min tank, but all the fill calculators ask for the water volume of the tank (ie the actual physical volume of the tank). I haven't been able to find that anywhere. I could probably estimate it by getting the diameter and height of the tank and fudging a bit, but I've not yet found any place that lists the volume of my tank in cubic inches.

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I'm guessing, even after the detailed explanation you haven't read his post. He wanted the "Math" behind the calculator.

Anyway your Draeger 45min tank (it's actually 46 min according to Draeger) would be 6.8L water volume (or fluid capacity as I had mentioned above). You can get that information from page 5 of the below linked PDF.

http://www.draeger.com/sites/assets/PublishingImages/Products/cre_cylinders/global-blueprint/compressed-air-breathing-cylinders-pi-9046796-en-gb.pdf

Sorry, it sounded to me like the original post was looking for the number of fills of a Marauder one could expect from an 88ft^3 4500psi tank, the request for the math was simply because the number of fills was eluding the poster in the first place. 

edit: OK, I see now. In a reply later the original poster asked for the math behind the calculators...got it. Sorry about that. I can't give you an answer, but I'm sure Boyle's Law factors into it somehow. 

I'll let you know if I get a response.

https://www.facebook.com/AskThePhysicist

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I have a pressure vessel that is 88ft^3 at 4500psi. I'm pressurizing smaller 215in^3pressure vessels from 2000psi up to...Posted by Frank Hieber on Monday, February 22, 2016

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"ztirffritz"Sorry, it sounded to me like the original post was looking for the number of fills of a Marauder one could expect from an 88ft^3 4500psi tank, the request for the math was simply because the number of fills was eluding the poster in the first place. 

edit: OK, I see now. In a reply later the original poster asked for the math behind the calculators...got it. Sorry about that. I can't give you an answer, but I'm sure Boyle's Law factors into it somehow.

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Wondering, did you even read thru the replies? We have the answer.......
http://airgunnation.dev/topic/please-help-me-do-the-math/#post-71450

but let's see what the physicist has to say......

I'd think it would be more complicated than what you posted. Since the pressure is in the source is changing the fill rate won't be linear. There's probably a formula that would get close enough though.

"ztirffritz"I'd think it would be more complicated than what you posted. Since the pressure is in the source is changing the fill rate won't be linear. There's probably a formula that would get close enough though.

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I hope the expert does reply back to you. I worked it out using my "UN-complicated" method and based on using the 88CF tank starting at 4500psi and using it to fill a 215c bottle from 2000 to 3000psi each time. Below is the pressure remaining after each fill is taken from the main tank. Now this based on there being ZERO waste from bleeding the hose.
4500.00
4472.78
4445.57
4418.35
4391.14
4363.92
4336.71
4309.49
4282.28
4255.06
4227.85(after 10th)
4200.63
4173.42
4146.20
4118.99
4091.77
4064.56
4037.34
4010.13
3982.91
3955.70(after 20th)
3928.48
3901.27
3874.05
3846.84
3819.62
3792.41
3765.19
3737.97
3710.76
3683.54(after 30th)
3656.33
3629.11
3601.90
3574.68
3547.47
3520.25
3493.04
3465.82
3438.61
3411.39(after 40th)
3384.18
3356.96
3329.75
3302.53
3275.32
3248.10
3220.89
3193.67
3166.46
3139.24(after 50th)
3112.03
3084.81
3057.59
3030.38
3003.16 (after 55th)
2975.95 
As you can see after the 55th fill you will not have enough pressure to do a 56th fill and the pressure in both tanks would then equalize at 2975.95 My figure in the prior reply was 55.11 fills. As you should be able to see it is NOT any more complicated then what I posted.

Good enough for me then. Empirical data trumps theoretical.

I'll be the first to say all this is way over my math abilities, but the question I have is my tank says 45 minutes as well. What the heck are they talking about in minutes? Thanks Brian...

"briansmith"I'll be the first to say all this is way over my math abilities, but the question I have is my tank says 45 minutes as well. What the heck are they talking about in minutes? Thanks Brian...

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Brian - that is the rating on the tank based on the time the air should last when used with a "breathing regulator". These tanks are SCBA which stands for Self Contained Breathing Apparatus. They are designed as 30min, 45 min and 60min being "standard". They do make others, but these are the most popular.

If you have a 45min tank then when filled to 4500psi you will have "approximately" 66CF of air.

Ah, so I see said the blind man as he picked up his hammer and saw. ;o) I have the scott scba tank. Marked at 45 minutes. Your a wealth of info today. TNX once again. Brian <><