Easy Scuba Maths In Metric
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    Lightbulb Easy Scuba Maths In Metric

    [Or how an American Diver figured out the logical use of a Bar SPG]:

    How much easier & intuitive is it to work with "1 bar/min" Metric vs "14.5 psi/min equivalent" in US Imperial Units???


    My Surface Consumption Rate (SCR) after drift diving so many years on holiday in Palau's 28deg C tropical water temp is a personal best 11 litres/min per ATA.

    Using this SCR value with a 11 litres/bar tank (i.e. an AL80 Cylinder):
    Divide 11 litres/min per ATA by 11 litres/bar equals 1 bar/min per ATA .

    So again --How much easier, intuitive & advantageous is it to work with "1 bar/min" and the metric system in general for Scuba? Well, the arithmetic can all be figured easily & quickly in your head and on-the-fly:

    All my dives were on Nitrox32, averaging 20 meters depth always going with the drift current; 20 meters is 3 ATA (divide 20 by 10 and add 1 gives a depth in atmospheres absolute of 3 ATA).

    Therefore at 20 meters, my 1bar/min per ATA gas pressure consumption rate will increase threefold --that is 1bar/min per ATA multiplied by 3 ATA equals a depth consumption rate of 3 bar/min at 20 meters. Hence checking my elapsed bottom time every 10 minutes, I expect to consume 30 bar (3 bar/min multiplied by 10min equals 30 bar), and accordingly I already know my SPG will read 30 bar less in that 10 minute time frame. (If however the actual SPG reading indicates 30% or more consumption than expected, then there is a leak problem or I am physically exerting/breathing harder than normal and probably would consider aborting the dive).

    So by the first 10 minutes delta time at 20 meters, I expect to be down 30 bar from a full AL80 tank at 200bar, or 170bar remaining actual SPG reading (3bar/min multiplied by 10min is 30bar consumed; and 30bar consumed from 200bar total full tank is the SPG showing 170bar remaining pressure). At the end of another 10 more minutes delta time drifting along at 20 meters, I've consumed 30bar from 170bar, or 140 bar remaining in tank. And finally after another 10 minute period at the elapsed dive time mark of 30 minutes total, I've consumed 30bar delta from 140bar, or 110bar remaining and nearing half tank.

    At 40 minutes elapsed time, I'm ascending off the deep wall into the shallow coral plateau around 9 meters (down 30bar from 110bar, or 80 bar remaining in tank). And finally at the 45 to 50 minute mark, I'm at 6m and my 3-5min safety stop with 60 to 70 bar left. I surface and I know even before looking at my SPG that I have around 50 bar remaining in my tank.


    This is how you should actively use your SCR with your particular tank, knowing how much breathing gas you have left not only on pre-planning, but also during the actual dive at depth, real-time-on-the-fly --all with easier to use metric units . . .additionally, you have a SPG that reads in units of pressure: why not convert your SCR to a Depth Consumption Rate (DCR) in pressure units to make use of it???

    In summary & recap: divide your volume SCR (or SAC/RMV rate) by your particular tank's cylinder rating factor to get a figure in pressure units per minute since your SPG reads in pressure units -not volume units. Multiply this SCR in pressure units by your planned depth in ATA, and you'll know what your Depth Consumption Rate (DCR) per minute in pressure units at that depth will be. And the Metric System for Scuba diving makes the arithmetic much easier especially if your pressure Surface Consumption Rate (SCR) turns out to be roundable up to convenient integer like 1 or 2bar/min per ATA.

    ----
    Some example pressure SCR values for a variety of common cylinders, given a arbitrary nominal constant volume SCR of 22 litres/min per ATA (a reasonable & achievable breathing RMV for most novice divers):

    11L/bar tank (AL80): 2bar/min per ATA;
    12L/bar tank (Steel HP100): 1.8bar/min per ATA;
    13L/bar tank (AL100): 1.7bar/min per ATA;
    15L/bar tank (Steel HP119): 1.5bar/min per ATA;
    16L/bar tank (Steel HP130): 1.4bar/min per ATA;
    11L Twins (Double AL80's): 1bar/min per ATA;
    12L Twins (Double HP100's): 0.9bar/min per ATA;
    16L Twins (Double HP130's): 0.7bar/min per ATA.
    Last edited by kevrumbo; 15-10-15 at 11:49 PM.

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    Sorry for being a dick jb2cool's Avatar
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    Welcome to the metric system. Now if you could just pass the word around a bit then this might catch on in America.

  4. The Following User Says Thank You to jb2cool For This Useful Post:

    kevrumbo (17-10-15)

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    Easy Partial Pressure Blending With a Bar Gauge

    [Gas Blending in Metric makes greater sense in learning and is a lot more intuitive as well. . .]

    Starting from an empty tank or set of tanks (5.5L or AL40 deco cylinder; and 11L or AL80 twinset backgas Cylinders), and filling to a full total pressure of 200 Bar:

    Nitrox 50 (add 37% O2):
    For every 100 bar of Eanx50 deco mix, you need 37 bar of pure O2 and top off the remainder with [hyper-filtered clean] Air;

    Nitrox 32 (add 14% O2):
    For every 100 bar of Eanx32 mix, you need 14 bar of pure O2 and top off the remainder with Air;

    20/20 Trimix (add 4% O2 & 20% Helium):
    For every 100 bar of 20/20 Trimix, you need 4 bar of pure O2, 20 bar of He and top off remainder with Air;

    25/25 Triox (add 12% O2 & 25% Helium):
    For every 100 bar of 25/25 Triox, you need 12 bar of pure O2, 25 bar of He and top off remainder with Air;

    30/30 Triox (add 19% O2 & 30% Helium):
    For every 100 bar of 30/30 Triox, you need 19 bar of pure O2, 30 bar of He and top off remainder with Air;

    21/35 Trimix (add 9% O2 & 35% Helium):
    For every 100 bar of 21/35 Trimix, you need 9 bar of pure O2, 35 bar of He and top off remainder with Air;

    18/45 Trimix (add 8% O2 & 45% Helium):
    For every 100 bar of 18/45 Trimix, you need 8 bar of pure O2, 45 bar of He and top off remainder with Air;

    15/55 Trimix (add 7% O2 & 55% Helium):
    For every 100 bar of 15/55 Trimix, you need 7 bar of pure O2, 55 bar of He and top off remainder with Air;

    12/60 Trimix (add 5% O2 & 60% Helium):
    For every 100 bar of 12/60 Trimix, you need 5 bar of pure O2, 60 bar of He and top off remainder with Air;

    10/70 Trimix (add 4.5% O2 & 70% Helium):
    For every 100 bar of 10/70 Trimix, you need 4.5 bar of pure O2, 70 bar of He and top off remainder with Air.

    So, using a 11L (AL80) cylinder, or set of twin 11L doubles (double AL80's) for a total of 22L, a full tank or set of tanks is 200 bar:
    -->Therefore, all you need is 2 times the amount in bar for O2 for a Nitrox Blend (and 2 times the amount in Helium for a Trimix Blend), taken and applied from the above recipes for a particular mixture blend.

    Example)
    21/35 Trimix requires blending 9% Oxygen and and 35% Helium; Therefore a full 11L (Al80) cylinder(s) at 200 bar total pressure needs 18 bar of O2 (2 times 9 bar equals 18 bar), and 70 bar of Helium (2 times 35 bar equals 70 bar); and top off remainder to 200 bar with [hyper-filtered clean] Air.

    Now how did we get the "cookbook recipes" for blending the particular mixtures above? And why for instance with Nitrox 50, can't we use 50 bar of Oxygen and 50 bar of Nitrogen for every 100 bar of Eanx50 to blend a seemingly real intuitive "half & half" mixture?

    The answer is YES! You can blend 50 bar of O2 and 50 bar of N2 -->If you are mixing pure O2 AND PURE N2 TOGETHER!!! But for practical means, why do you need pure N2 when you can just use Air with its natural constituent contribution of 21% Oxygen & 79% Nitrogen?

    Using Air this time, let's blend 100 bar of deco mix Nitrox 50:
    We know empirically that for every 100 bar of Eanx50, 50 bar must be O2 and 50 bar must be N2;
    Quantitatively then, how much Air do we need to add in order to give us a N2 amount of 50 bar?

    Algebraically and by Dalton's Law, you divide 50 bar N2 by 79% (the %age of Nitrogen in Air), and this yields approximately 63 bar of Air needed. And of this 63 bar of Air, 21% of it (the %age of Oxygen in Air) contributes to the amount needed for O2: approx 13 bar of Oxygen.

    Therefore, instead of initially mixing in 50 bar of O2, and since we're using Air instead of pure N2, you only need 50 bar minus the 13 bar Oxygen contribution from Air, which equals 37 bar. Hence the cookbook recipe for every 100 bar of Nitrox 50, add 37 bar of pure O2, and fill the remainder with Air to 100 bar.

    Now to fill an empty 5.5L/bar deco tank (same as an AL40) with Nitrox 50, we need 200 bar of the above recipe (i.e. "For every 100 bar of Eanx50, add 37 bar of pure O2, and then fill the remainder with Air"). Therefore just multiply 37 bar by 2 which equals 74 bar of O2 needed, and then fill the remainder with Air to the total fill pressure of 200 bar.

    Similarly it all applies to the Trimix recipes as well, with the additional accounting for the percentage and amount in bar of the Helium constituent in the final total mixture . . .

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    Modified Thirds,Turn-Around Pressure and Lost Buddy Search Gas Availability Calculations are easier with a bar SPG too. . .

    Suppose you originally planned a wreck penetration starting with 200 bar at the entrance, with an openwater absolute "Rock Bottom" emergency contingency reserve pressure of 50 bar. 200 minus 50 bar equals 150 bar usable for the penetration --Modified Thirds of this value is 50 bar (one-third of 150 equals 50), so you would turn-around for egress when you consume 50 bar of gas with an actual SPG reading of 150 bar. If you needed to do a gas-sharing emergency egress with your buddy at this point, you would both need 100 bar to get out of the wreck, with 50 bar openwater Rock Bottom remaining to get both of you to the surface (or switching to your Oxygen deco cylinders at 6m).

    Let's say you used up 30 bar already getting to the entrance of the wreck for a total of 170 bar pressure available --can you quickly recalculate Modified-Thirds?

    No problem with bar pressure metrics: 170 bar minus 50 bar Rock Bottom yields 120 bar usable for the penentration; One-Third of 120 bar is 40 bar which is your new Modified Thirds turn pressure value. Therefore you would turn the dive when you consume 40 bar for an actual turn pressure SPG reading of 130 bar (170 bar minus 40 bar equals the actual turn pressure SPG reading of 130 bar).

    What if you lose your buddy at this instant, at the farthest distance inside the overhead that your Modified Thirds value allows? How do you calculate the amount of gas to do a Lost Buddy Search?

    Easy! At your turn around pressure reading of 130 bar on the SPG, simply add your Rock Bottom value to your Modified Thirds value (50 bar Rock Bottom plus 40 bar Modified Thirds equals 90 bar); Put a line-arrow pointing the way out on your mainline that you just placed, and take reference note of where you are inside the overhead at that exact point as well. Now with your primary reel, go and search for your buddy with the understanding that you must be back at the line-arrow marker by the time your SPG reads this actual value (90 bar). So you would have from 130 bar down to 90 bar reading on your SPG, or 40 bar delta of gas to search for your buddy --if you were to do a straight line search down a long corridor inside the wreck for example, tactically you should use 20 bar out and 20 bar back to your line-arrow marker for a delta of 40 bar, and an actual end of search SPG reading of 90 bar-- you must start your egress whether you found your buddy or not when you use up this 40 bar delta of gas, at the line arrow marker, with the actual 90 bar final reading on your SPG.

    At any point before your Modified Thirds turn pressure, for a lost buddy search, the final egress pressure is figured just by adding your Rock Bottom value to the amount of gas you've consumed on the penetration up to that point --for example you start with 170 bar on your SPG and you lose your buddy with 140 bar SPG reading for a delta consumption of 30 bar. 50 bar Rock Bottom plus delta consumption of 30 bar equals 80 bar. Drop a line arrow, and now you've got from 140 bar down to 80 bar (a tactical delta search pressure of 60 bar) to look for your buddy, and be back to your line arrow to egress smartly when your SPG reads 80 bar.

    At any point after your Modified Thirds turn pressure, all you need to do to figure out a final egress pressure for a lost buddy search is to subtract your Modified Thirds value from your actual pressure reading, and place a line-arrow pointing out at this point on your mainline. For example, if you're egressing and you lose your buddy with 120 bar actual reading on your SPG: Subtract the Modified Thirds value of 40 bar from 120 bar -which equals 80 bar- and it is this actual reading that you must have on your SPG when you get back to your line arrow to successfully exit the wreck with all your Rock Bottom still available to reach the surface. Another way of looking at this, at your nominal turn-around point & afterward on egress, the amount of gas tactically available for a lost buddy search is always just your Modified Thirds value --in this case 40 bar.

    Remember that on a lost buddy search, you will deliberately encroach and use up the Modified Thirds Reserve Value needed for an emergency gas-sharing egress contingency (and possibly use up Rock Bottom as well) --in other words, if you do find your lost buddy and worst of all worst case scenarios he happens to be out-of-gas in a total silt-out . . .well deus ex machina. I hope you're in a 3-person Team, somehow make it out and run into other divers on the outside who can donate gas & assist. . .

    [Note: the above gas plan is taken from wreck penetration dives on the HMCSYukon (San Diego); USS New York (Subic Bay Philippines); HMAS Perth/USS Houston (Sunda Strait Indonesia); and various wrecks in Truk Lagoon. Depth 30m using twin 11L/bar tanks (double AL80's) and Oxygen 5.5L deco bottles.]
    Last edited by kevrumbo; 06-12-15 at 09:18 PM.

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    DiveNav said: ↑
    Sorry for asking .... could you explain it again?
    I still haven't figure out on how to use it during a multi-level (with a lot of levels ....) dive :oops:
    Given you are an advanced diver with a 1 bar/min per ATA pressure Surface Consumption Rate for a particular tank, then all you need for multi-levels are the depths in ATA, the time you spent at each multi-level depth, and then you can figure out your consumption for each particular depth, confirming it with an SPG or AI reading. ("AI" is an optional dive computer "Air Integration" electronic digital pressure data logger display function with either direct high pressure hose connection, or a wireless transducer/transmitter to a regulator's first stage HP port).

    So you're at 30 meters depth; that's 4 ATA (30 divided-by 10 plus 1 equals 4 ATA); you stay 5 minutes. 1 bar/min per ATA multiplied by 4 ATA multiplied by 5 minutes equals 20 bar consumed. Confirm with SPG or AI, your delta remaining pressure reads 20 bar less --so if you start with a full tank of 200 bar, the SPG or AI should indicate "180 bar". (200 minus 20 is 180 bar).

    You then ascend to 21 meters depth; that's 3.1 ATA (21 divided-by 10 plus 1 equals 3.1 ATA); you stay 10 minutes. 1 bar/min per ATA multiplied by 3.1 ATA multiplied by 10 minutes equals 31 bar consumed. Confirm with SPG or AI, your delta remaining pressure reads 31 bar less --SPG or AI should indicate "149 bar". (180 minus 31 is 149 bar).

    You then ascend to 15 meters depth; that's 2.5 ATA (15 divided-by 10 plus 1 equals 2.5 ATA); you stay 30 minutes. 1 bar/min per ATA multiplied by 2.5 ATA multiplied by 30 minutes equals 75 bar consumed. Confirm with SPG or AI, your delta remaining pressure reads 75 bar less --SPG or AI should indicate "74 bar". (149 minus 75 is 74 bar).

    Finally ascend to 6 meters depth; that's 1.6 ATA ( 6 divided-by 10 plus 1 equals 1.6 ATA); you stay 10 minutes. 1 bar/min per ATA multiplied by 1.6 ATA multiplied by 10 minutes equals 16 bar consumed. Confirm with SPG or AI, your delta remaining pressure reads 16 bar less --SPG or AI should indicate "58 bar". (74 minus 16 is 58 bar).

    Do a slow ascent to the surface --on the surface inflate your BCD/Wing/Drysuit and you know even before looking at your SPG that you have 50 bar remaining in your tank.

    With repetition, experience & persistent rote practice-- you will know what your SPG nominally reads at depth after an arbitrary time interval like five or ten minutes. Or, in the case of an AI, your total running gas remaining estimate over a five or ten minute interval should be similar to the algorithm's displayed value. The point is do not take for granted the calculations of AI --the features & functions of AI (like Air Time Remaining or real time SAC rate displays) are ancillary to what you already know how to do in your head. . .

    (If the expected SPG or AI reading is 30% or more than you figured, then that indicates you are physically working & breathing harder than normal, or have a leak somewhere in your reg/gear set-up, and should consider aborting the dive).
    Last edited by kevrumbo; 25-01-16 at 05:06 AM.

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    Rule of Thirds with Unequal SAC Rates & Dissimilar Tanks: How it Works. . .

    Hypothetical example of extreme differing SAC Rates and Dissimilar Cylinders showing that proper application of Third's Turn Volume still works:

    Given: 9 meter depth overhead cave dive.

    Diver A:
    4 l/min Sac Rate with double AL40's (11 l/bar) at 200bar.

    Diver B:
    28 l/min Sac Rate with double hp190's (36 l/bar) at 300bar.

    Diver A has smallest total volume of backgas at 2200 liters so we take Third's of this which is 733 liters (the Team Turn Volume);

    Diver B uses this 733 l to figure his consumed delta pressure at 20bar. His SPG turn pressure is 300bar minus this 20bar, and he calls for the dive turnaround at 9 meters (1.9ata) depth after ~14min cave penetration elapsed time.

    In that 14min,
    Diver A uses: 4 l/min x 1.9ata x 14min = 106 liters;
    and Diver B uses: 28 l/min x 1.9ata x 14min = 745 liters.

    So for the penetration, Diver A uses 106 l and Diver B uses 745 l.

    If Diver A or Diver B loses all his gas at the turnaround, the donating diver needs a combined sum of 106 l and 745 l to exit the overhead (851 liters).

    Check if Volume Reserves at Turnaround are enough:
    Diver A uses 106 l out of his 2200 l supply, and has remaining 2094 liters;
    Diver B uses 745 l out of his 10800 l supply, and has remaining 10055 liters.

    So the answer is yes - that both teammates have enough Reserve Gas to cover, even Diver A in this extreme inequality of Sac rates and dissimilar tanks.
    -------------

    --->What happens if Diver A mistakenly thinks he controls the turnaround with Third's?

    He consumes the same team volume 733 l and calls for the turnaround at ~96min with a SPG reading of 133bar at 9 meters (1.9ata) depth.

    In that 96min,
    Diver A uses: 4 l/min x 1.9ata x 96min = 730 liters;
    and Diver B uses: 28 l/min x 1.9ata x 96min = 5107 liters.

    So for the penetration, Diver A uses 730 l and Diver B uses 5107 l.

    If Diver A or Diver B loses all his gas at the turnaround, the donating diver needs a combined sum of 730 l and 5107 l to exit the overhead (5837 liters).

    Check if Volume Reserves at Turnaround are enough:
    Diver A uses 730 l out of his 2200 l supply, and has remaining 1470 liters;
    Diver B uses 5107 l out of his 10800 l supply, and has remaining 5693 liters.

    So in this case the answer is No -they will go Out-of-Gas inside the cave, because Diver A mistakenly thought he determined the Third's Turnaround at 96min.

    The point is:

    SAC Rates are in fact directly proportional to the gas volume consumed of each diver, and will determine who reaches team turn volume first. So to claim "Regardless of SAC", or that "SAC Rates don't matter, are irrelevant, or not needed" in calculating Third's Turn Volume is misleading and incorrect -You must also know which diver nominally controls the Turnaround at a particular elapsed time, and that diver has to be the one with Highest SAC Rate.

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