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Untangling cubic feet, litres, PSI, bar for scuba tanks and RMV / SAC calculations

Discussion in 'Basic Scuba Discussions' started by Lemmeron, Jun 4, 2010.

  1. Lemmeron

    Lemmeron Solo Diver

    # of Dives: 100 - 199
    Location: Australia, NSW
    I have looked around the forums, done a number of searches, and also looked at various wikis ect to find an easy way to switch between the US standard of cubit feet and PSI and Australian Litres and Bar.

    Hopefully this guide will be helpful to others seeking to understand the differences and show how to work out the amount of air available to a diver in a tank regardless of where it is from.
    Conversion units and SAC / RMV formulas will also be given for completion and easy access.

    Tank Size
    In the US it is common to have a scuba tank referred to as an "80 or 100 cubic foot cylinder"
    In Australia/UK it is common to have a "10 or 12 Litre cylinder"

    The US normally refers to cylinder capacity as free-air equivalent at its working pressure, rather than the internal volume of the cylinder, which is the measure commonly used in metric countries.

    To convert between these measures the following formula can be used.

    AV = CV * CP / AP

    AV = Air volume (at 1 ata)
    CV = Internal Cylinder Volume (obtained by filling with water)
    CP = Pressure of the air the cylinder is filled to (at room temperature)
    AP = Ambient Pressure

    So a typical US "100 cubic foot tank" to an Aussie would be a 12 Litre tank that has been filled to a pressure of 236 bar (3420 psi) and thus contains 100 cubic foot of air. However the normal working pressure of steel cylinders in Australia is usually 232 bar, but will vary to be 200, 220 or 232 bar (yoke, +10%, din and of course the actual dive shop filling the tank) so the cylinder actually contains between 84 - 98 cubic ft of air.

    It is important to note that the actual capacity of tanks vary - just look at faber tank specs - it is a nightmare ! - these values give a rough standard comparison between the 2 methods of naming tanks.

    So using standard Australian Sizes:
    10L tank = 80 cu ft tank (when filled to 226.5 bar / 3285 psi)
    12L tank = 100 cu ft tank (when filled to 236 bar / 3420 psi)
    15L tank = 125 cu ft tank (when filled to 236 bar / 3420 psi)
    18L tank = 150 cu ft tank (when filled to 236 bar / 3420 psi)
    please note these calculations are using Australian conversions where 1 ata = 1 bar = 14.5 psi and 1 cu ft = 28.32 Litres

    So Using standard US capacity:
    80 cu ft tank (ie contains 80 cu ft of air when filled to a standard 3000 psi) will hold 677 cubic inches (11.1 L) water (OMG agrees with Faber specs woohoo)
    100 cu ft HP tank (ie contains 100 cu ft of air when filled to 3441 psi) will hold 738 cubic inches (12.1 L) water
    so as you can see in this example although we jumped 20 cu ft of air (because we jammed the air in at higher pressure) , we actually only gained 1L of actual tank capacity in this case - which would be only about a 87 cu ft tank at 3000 psi.

    Hopefully this highlights just how much variance there is between tanks - so just because it is an 80 or a 100 cu ft tank ... doesn't really mean it is :headscratch:

    Ok so how do we use this to calculate anything meaningful....

    In Australia you need to know the actual capacity of the tank (CV) you are buying in Litres
    In the US you need to know either the actual capacity of the tank in cubic inches (good luck) OR the designated air volume AND at what pressure the tank needs to be filled to achieve it, ie a 677 cubic inch tank OR a 80 cu ft at 3000 psi.

    once you have these values, then you can work out how much air you actually have available in your tank to plan your dives with OR what tank you need to achieve a set plan.

    Tank Available Air
    AV = CV x CP
    AV = Usable air volume (Litres)
    CV = Cylinder Volume (Liquid required to fill tank in Litres)
    CP = Pressure reading on your SPG after tank has cooled to room temperature (Bar)
    so a 12L tank filled to 200 bar will give us 2400 Litres of air

    if you know the liquid volume of the cylinder in cu inches:
    AV = CV/1728 x CP/14.7
    AV = Usable air volume (cu ft)
    CV = Cylinder Volume (Liquid required to fill tank in cu inches - we divide by 1728 to convert to cu ft)
    CP = Pressure reading on your SPG after tank has cooled to room temperature (PSI - we divide by 14.7 to get value at 1 ata)
    so a 677 cubic inch tank filled to 3000 psi will give us 80 cu ft of air

    if you know the designated volume (ie 80cu ft) and working pressure (at 3000 psi), as long as you fill the tank to exactly the working pressure, you can just use the designated volume - if you fill the tank to a different pressure you have to play with some algebra to find your CV and then use it in the above formula
    AV = CV/1728 x CP/14.7
    thus AV / CP x 14.7 x 1728 = CV

    so for an 80 cu ft tank with a working pressure of 3000 psi and an unknown liquid volume :
    80 / 3000 x 14.7 x 1728 = 677 cubic inch tank
    so now we use this CV with the new fill pressure of the tank to find our new AV

    Ok so now we know how much actual air is in our tank to breathe.

    NEED SLEEP...:sleeping2:

    Still to come .. SAC RMV

    Max Breathing Time / Bottom Time

    Conversion Rates
    ata psi bar kpa
    cu ft cu inch litres

    Last edited: Jun 4, 2010
  2. Lemmeron

    Lemmeron Solo Diver

    # of Dives: 100 - 199
    Location: Australia, NSW
    just incase i need a 2nd spot :)
  3. vondo

    vondo Manta Ray

    # of Dives: 200 - 499
    Location: Aurora, IL
    Thanks. One correction, though. An Al80 in the U.S. is typically 80 c.f. at 3100, not 3000 p.s.i. Very confusing, yes.
  4. fire_diver

    fire_diver Solo Diver

    # of Dives: I just don't log dives
    Location: NW Oklahoma, USA
    OK, you posted the math behind tank volume. What does this have to do with calculating RMV or SAC? All of this is simple math as long as you know a few specific numbers.

    And yes, an AL80 is actually 77.4 CF IIRC.
  5. fnfalman

    fnfalman Orca

    # of Dives: 200 - 499
    Location: Southern California, USA
    He said RMV and SAC calculations come next.
  6. Rhone Man

    Rhone Man Divemaster

    # of Dives: 1,000 - 2,499
    Location: British Virgin Islands
    Great post, but I wonder if it should be moved from 'Basic' to 'Advanced'?
  7. Randy43068

    Randy43068 Orca

    # of Dives: 100 - 199
    It's basic stuff, don't'cha think?
  8. Herk_Man

    Herk_Man Solo Diver

    # of Dives: I'm a Fish!
    Location: Landlocked
    Head hurts. I'm going diving. I think I'll get "a tank" fill it to 3000 psi, dive until it reads 800, surface, have a snack, repeat.

    That's basic.

    His post belongs in advanced.
  9. TSandM

    TSandM Missed and loved by many. Rest in Peace

    I think knowing how cylinders in the US compare with cylinders elsewhere is quite basic. If you're accustomed to diving a 100 cf cylinder in the US and you rent a tank in Australia, it might be quite useful to know whether the tank you rented is bigger or smaller than the one to which you are accustomed. Nothing advanced about that.
  10. fnfalman

    fnfalman Orca

    # of Dives: 200 - 499
    Location: Southern California, USA
    Knowing how to calculate for SAC/RMV and plan for bottom time based on air consumption should be basic knowledge as well. It should be mandatory teaching in OW class as far as I'm concerned.

    Basic OW teaches you not to exceed NDL, but it doesn't teach you how to calculate to see if you have enough air to do a dive.

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