Disclaimer *** No Warranty expressed or implied, scuba diving is inherantly dangerous, don't sue me if you get hurt. Don't blindly trust anything you read on the Internet. *** The following are two writeups on the concept of gas management, from ScubaBoard members. * * * * * * * * * * * * * * * From Lamont at ScubaBoard: Gas Consumption 101 Boyle's Law and Gas Consumption An understanding of Boyle's Law is critical to being able to understand gas management in scuba diving. Boyle's Law can be stated as "if the temperature remains constant, the volume of a given mass of gas is inversely proportional to the absolute pressure." This is critical in scuba diving because the deeper the diver goes, the more pressure they are under. Because of the way a scuba regulator operates the pressure of gas in a scuba diver's lungs will be the same as the pressure of the surrounding water. If the scuba diver is at 33 fsw (10 msw/2 ata) of depth, this means that for a constant mass of air, the volume will be half. Turning this on its head, for a constant volume of air, the mass of air will be doubled. When the scuba diver breathes off of a scuba regulator, the volume of air they draw into their lungs is a constant volume irregardless of where they are in the water column. The mass of that air will be greater the deeper they go, and therefore the scuba diver will consume more air the deeper they go. The formula for how much air they consume is: ( volume consumed ) = ( surface RMV ) * ( atmospheres absolute ) * ( time ) For the US this looks like: ( cu ft ) = ( cu ft / min @ 1 ata ) * [ ( fsw ) / 33 + 1 ] * ( mins ) For the metric world this looks like: ( l ) = ( l / min @ 1 ata ) * [ ( msw ) / 10 + 1 ] * ( mins ) Standard Surface RMV Rates The canonical standard surface RMV rate that we use in these examples is 0.75 cu ft / min for the 'average' diver and 2.00 cu ft / min for two stressed divers sharing air. The actual values may differ greatly from this. New divers may have surface RMVs of slightly over 1.00 cu ft / min while experienced divers usually are closer to 0.60 cu ft / min with some achieving surface RMVs of nearly 0.30 cu ft / min. Rock Bottom Rules The rules for Rock Bottom are that you should immediately begin ascending when you hit the point where if your buddy had an OOA that you could get both of you back to the surface while doing all your stops. Once you have gone beyond the Rock Bottom limit if a failure occurs you could not handle it, and you run an increased risk of DCS or death. When a diver hits their rock bottom pressure they should immediately begin ascending to a shallower depth. If you hit rock bottom and thumb or turn the dive to a DM and they continue diving you should take your buddy and begin your ascent. If you hit rock bottom and thumb and your buddy doesn't respond you should read them the riot act when you get out, and re-consider diving with them. The thumb sign isn't a question, its a statement. To prevent miscommunication underwater these rules should be gone over prior to descending. Halves and Turn Pressures If you are doing a dive where you descend, swim out, swim back and ascend (e.g. dive along a wall) then you are going to want to know your turn pressure. If you would like to return to your starting point, but could make an ascent at any time, your turn pressure is going to be half of the gas you have available after reserving your rock bottom. Multi-phase Diving and Turn Pressures For a dive where the plan is to descend, swim out X minutes, swim around and object (wreck, etc), turn, swim back and ascend the "rule of halves" can be generalized into the principle that you always want to have enough gas to swim back to the upline/shore without violating your rock bottom pressures. If you will never be more than six minutes from your upline then compute your gas consumption at depth for six minutes, add to your rock bottom time and that becomes your 'turn pressure'. If you might experience current, changing conditions or other difficulties you may want to pad this number appropriately. Thirds and Turn Pressures If you are doing a dive where you have an physical or virtual overhead and cannot ascend immediately, you are going to want to dive thirds or sixths. You will also need doubles and other redundant equipment and significantly more training. Rock Bottom vs. 500 psi The rule that you need to be "back on the boat with 500 psi" doesn't help you know when to turn your dive. It also doesn't take into account equipment failures that might cause your buddy to lose all their gas at the worst possible moment. Rock Bottom times give you the information that you need to make a decision about when to turn your dive. Rock Bottom pressures will probably require turning a dive at a surprisingly high pressure. Rock Bottom - Ascents To compute Rock Bottom, we add up the amount of gas we need to: - take a minute at depth to solve the problem (start sharing gas, communicate the plan to turn, collect wits, etc) - ascend to the first stop - do our stops - ascend to surface Individual divers should adjust their rock bottom calcs for how they do their stops. I will be doing my examples assuming the ascent plan is a pause at 80% ata or 50% max depth and stops for 1 min @ 30 fsw, 1 min @ 20 fsw, 1 min @ 10 fsw. The max ascent rate that should be used is 30 fpm. For the purposes of the Rock Bottom calculations I'll be ignoring the pause as not signficant. Rock Bottom - Mathematical Simplification All of the ascent phases can be combined together into a single computation of the air necessary to ascent from depth to the surface. It doesn't matter if the ascent phases have stops in between them, it can be treated seperately as a direct ascent to the surface and the gas consumption at the stops can be computed directly. For the depth of the ascent to plug into the formula you can take the average depth of the ascent which is going to be the max depth / 2. For the stops, I compute them as a single stop at the time-weighted average depth for the total time of the stops. For example: ( 1 min * 10 fsw + 1 min * 20 fsw + 1 min * 30 fsw ) / (3 mins) = 20 fsw So I'll be doing a 3 min stop at 20 fsw. I've plugged thorugh the math and shown that algebraically this is an identical computation to doing three different computations for the three different stops. If your eyes glassed over at the phrase "time-weighted average depth" have no fear and either just use 3 min @ 20 fsw or the canonical 3 min @ 15 fsw that the industry recommends. Rock Bottom - Mathematically Rigorous Example To figure out what the rock bottom volume is for a dive to 60 feet we have three different computations to do and sum up. We need the value for the 'problem time' at the bottom, the ascent phase, and the stops. Those computations are: problem gas = ( 2.00 cu ft / min ) * [ ( 60 fsw ) / 33 + 1 ] * 1 min = 5.63636 cu ft time to ascend = 60 fsw / 30 fpm = 2 mins ascent gas = ( 2.00 cu ft / min ) * [ ( 60 fsw / 2 ) / 33 + 1 ] * 2 mins = 7.63636 cu ft [ note that the depth used is the average depth of the ascent - 60/2 = 30 ] stop gas = ( 2.00 cu ft / min ) * [ ( 20 fsw ) / 33 + 1 ] * 3 mins = 9.63636 cu ft Rock Bottom Volume = 22.9 cu ft Rock Bottom - Mental Example Another way of computing rock bottoms is simply to total up the entire amount of time that you're spending in the water, take the average depth and compute the gas consumption. This is very easy and not precise, but the whole model of rock bottom times is not going to precisely model an actual emergency anyway. For the example above, you are spending 1 minute at depth, 2 mins going up in the water column and 3 mins at your stops for a total of 6 mins. Your average depth (just take max depth / 2 ) is going to be 30 feet or about 2 atmospheres. This gives: 2 cu ft / min * 2 ata * 6 mins = 24 cu ft For a dive to 100 fsw you're going to spend 3 mins ascending for a total of 7 mins at 2.5 ata: 2 cu ft / min * 2.5 ata * 7 mins = 35 cu ft For a dive to 130 fsw you're going to spend 4 mins ascending for a total of 8 mins at 3 ata: 2 cu ft / min * 3 ata * 8 mins = 48 cu ft Rock Bottom - Volume to Pressure Conversion To be mathematically exact we can take our rock bottom pressures in cu ft and convert them to psi using as exact of values as we have for tank capacities. For the standard AL80 those values are 77.4 cu ft @ 3000 psi. Therefore the computation is: 24 cu ft * (3000 psi / 77.4 cu ft) = 930 psi 35 cu ft * (3000 psi / 77.4 cu ft) = 1356 psi 48 cu ft * (3000 psi / 77.4 cu ft) = 1860 psi Rock Bottom - Tank Factors We can introduce a concept known as a "tank factor" which is the number of cu ft in the tank per 100 psi. In other words, every time your SPG drops by 100 psi this is the amount of cu ft that you consume. For an AL80 this works out to: ( 77.4 cu ft / 3000 psi ) * 100 = 2.5 cu ft For a PST E8-130 tank this works out to: ( 130 cu ft / 3500 psi ) * 100 = 3.7 cu ft We can use these values mentally to convert from volume to psi. For example to convert from 24 cu ft to psi in an AL80: 24 cu ft / 2.5 is appx 10 => 1000 psi. For doubles, it should hopefully be obvious that the Tank Factors are multiplied by two (double E8-130s would be 7.4). Rock Bottom - Lowest Pressure Rule No rock bottom pressure should be lower than 500 psi to take into account the possibility that an SPG doesn't read zero accurately. Even for a 30 fsw dive on dual LP-120s the rock bottom pressure should be 500 psi. Rock Bottom - Table Values I would suggest using tables like the following for an AL80: 30 fsw - 700 psi 60 fsw - 1000 psi 100 fsw - 1300 psi 130 fsw - 1800 psi This works just like dive tables in that if you are at 75 fsw you'd use the 100 fsw value. The important point here is that the table is very easy to memorize and use on a working basis. It doesn't require calculations and doesn't require extensive wet-notes. You can easily shift where you are in the table on-the-fly to adapt to changes in your dive plan. Rock Bottom - Planning Note It is common to hear people state "rock bottom for this dive is 1300 psi" which is not an entirely rigorous statement. If you've turned the dive and are back at 30 fsw your rock bottom is now 700 psi (assuming an AL80) and if you are above that value you can swim around or do skills for awhile. You don't have a rock bottom for a dive, you have a rock bottom for a depth, and you have a planned max depth for a dive, and a rock bottom at that depth. Rock Bottom - Turn Pressures Example If we're doing a wall dive at 100 fsw on a single AL80 our rock bottom will be 1300 psi. If the plan is to descend, travel the wall, return on the same path and ascend, then the turn pressure will be: usable gas = 3000 psi - 1300 psi = 1700 psi gas used on swim out = 1700 psi / 2 = 800 psi turn pressure = 3000 psi - 800 psi = 2200 psi In other words, we expect to use 1700 psi on this dive by the time we get back to the up-line in order to still have our rock bottom pressure at the up-line. We will therefore turn the dive after we have used half of that. If we had been doing a drift dive, we could have continued at 100 fsw until we hit our 1300 psi rock bottom and then ascended. In either case the actual total bottom time of the dive will be the same -- but in the case of the wall dive it will be composed of two phases going out and back. SAC rates - E-Bay your Air Integrated computer. In addition to calculating your Rock Bottom times you can also plan and calculate your SAC rates on-the-fly. Using tank factors we can convert the 0.75 cu ft / min value into a psi / min value. For the example of an AL80 with a tank factor of 2.5: ( 0.75 cu ft / min ) / 2.5 = .30 --> 30 psi / min For the example of an E8-130 with a tank factor of 3.5: ( 0.75 cu ft / min ) / 3.7 = .21 --> 20 psi / min This is the amount of air that you expect to consume on the surface. At depth you just multiply this value by the atmospheres that you are at, e.g. for an AL80: 30 psi / min * 2 ata = 60 psi / min @ 33 fsw 30 psi / min * 3 ata = 90 psi / min @ 66 fsw 30 psi / min * 4 ata = 120 psi / min @ 100 fsw 30 psi / min * 5 ata = 150 psi / min @ 133 fsw You can then multiply this number by 5 or 10 to give you the amount of gas that you expect to be using per a manageable time interval: 33 fsw = 600 psi / 10 mins 66 fsw = 900 psi / 10 mins 100 fsw = 1200 psi / 10 mins 130 fsw = 1500 psi / 10 mins This can be very useful since if you're at 66 fsw with 1900 psi you know that you've got another 10 mins left before hitting rock bottom. You now don't need to be checking your SPG, but only need to check your BT/computer for your dive time. You can also monitor your SAC rate underwater by taking SPG readings at 5 or 10 minute intervals. SAC rate calculations can be useful for planning a dive since they can tell us how long we expect to be able to dive before hitting rock bottom. They can also be useful while actually executing a dive since we can adjust our expectations for dive time based on how rapidly we are actually using our air. Canonical RMV vs. actual RMV rates Obviously, if you're a person that normally has an RMV rate lower than 0.75 cu ft / min you should adjust your SAC calculations accordingly. You should not adjust the Rock Bottom RMV of 2.0 cu ft / min even if you tend to use less gas. The assumption is that you may be buddied up with a hoover like me on any particular dive who can easily exceed 1.0 cu ft / min when I'm excited. DIR / GUE This is a compendium of my own thoughts that I've learned from various sources. I'm not claiming or trying to offer exactly what GUE teaches. Although I do owe GUE, fifthd and the DIR guys on scubaboard a debt of gratitude for most of this information. * * * * * * * * * * * * * * * From Roakey at ScubaBoard: First off, "500psi back on the boat" or "back on the ladder" is just plain wrong - this isn't planning, it's a guessing game. It's giving someone directions to your house like: "Turn one mile BEFORE the big red barn." If they guess the correct turn without any real information, they're OK. Otherwise they get back on the boat with 300psi or 700psi - they "lose" the guessing game. Or they really lose and try and get back on the boat with -300psi. In addition, this guessing game will add more stress to an already stressful OOA situation. It probably takes the new OW student about one or two "real" dives to realize that they're playing a guessing game. After all, they don't know at the bottom when to turn the dive in order to get back on the boat with 500psi and they probably missed the mark by a mile on those first couple of dives! Now put them in an OOA situation and suddenly one or both divers will realize "HS! Do we have enough air to make it to the surface?" The hoovering begins, a bad situation gets worse and it's either just plain scary or we read about a diving death the next morning. Replacing that unknown with a simple demonstration of gas planning and some REAL gas management rules will allow the OOA diver and donor to relax and know that they not only have enough gas to make it to the surface, but they can do so with a normal ascent rate and safety stops. They relax, consume less air, manage their buoyancy better and come back on board with a story, rather than shaking in fear wondering if they're going to get bent from a Poseidon-missile-like ascent. What I'm going to describe is basically GUE's "Rock Bottom" calculation, with some simplifications in order to make the numbers easy so what's going on can be understood; once understood someone can go off and calculate exactly what they use for ascent rates, safety stops, etc. Think of the initial cut here "Rock Bottom for OW divers." Here's the goal of correct gas planning: Get two stressed divers to the surface safely from depth with normal ascent rates and safety stops. So here are the assumptions, to simplify things: 80cf@3000psi cylinder Stressed diver has a SAC of 1cf/min @ 1ATA The divers spend 1 minute at depth to sort things out. Ascent rate of 33ft/min (1ATA/min) - chosen just to simplify things. 1 safety stop for 2 minutes at 16.5 feet (1.5ATA - again, to simplify) The dive ends with a direct ascent to the boat (no swimming back underwater) So let's calculate how much air is required for the goal, stated above, at depths of 33, 66, 99 and 132 feet (2, 3, 4 and 5ATA): For 33feet (2 ATA): How much gas is consumed at 33feet for a minute to sort things out? 2ATA * 1 min * 1cf/min = 2cf. Note: I'm going to drop the 1 cf/min calculation from here on out, since multiplying by 1 does nothing... How much gas is consumed in the ascent from 33 feet to the surface? 33 feet deep/33 feet per minute = 1 minute. What's the average ATA? 2ATA (@ 33 feet) + 1ATA (@ surface) / 2 = 1.5ATA How many CF will one diver consume? 1.5 ATA * 1 minute = 1.5 cf of gas How much is consumed at the safety stop? 1.5ATA * 2 min = 3cf So ONE diver would consume 2cf + 1.5cf + 3cf = 6.5 cf of gas in this situation and two would consume 13cf. What PSI is that? 14cf/80cf*3000psi = 487psi. So to allow two divers to surface from 33 feet at a normal rate with a safety stop requires 487psi of gas, so the dive is called at 487 psi. Personally, I'd round this up to 500 psi. For 66feet (3ATA): Sort things out: 3ATA * 1min = 3cf Ascent: ((3+1)/2 average depth in ATA) * 2min = 4cf Safety stop: 2 min * 1.5ATA = 3cf (this is always the same, so we can just assume 3cf from here on out) One diver's ascent consumption: 3+4+3 = 10CF, two would be 20cf. Turn pressure: 20/80*3000=750psi For 99feet (4 ATA): Sort things out: 4ATA * 1min = 4cf Ascent: ((4+1) / 2) * 3min = 7.5cf Safety stop: 3cf (4+7.5+3)*2 divers = 29cf, 29/80*3000=1088 psi turn pressure or 1100 psi. For 132 feet (5 ATA): Sort things out: 5cf Ascent: ((5+1)/2) * 4min = 12cf Safety stop: 3cf (5+12+3) * 2 divers = 40cf, 40/80*3000=1500 psi turn pressure. In conclusion: Now that you have some really hard numbers, pad if you like with a hundred or two PSI... The important part is you have some REAL gas planning numbers to offer your students, something they can use DURING the dive rather than something to see how well they guessed once they're back on the boat. Personally, I'd demonstrate the calculations for the 66foot dive. Expect 90% of your student's eyes to glaze over, but for most in the back of their minds they'll know they will have enough air to safely ascend with an OOA diver, which won't be lost on them if it ever happens... After they unglaze, offer the following numbers for their gas planning (and it's real planning now, what pressure to turn the dive DURING the dive!) Less than 30feet, call the dive at 500psi MINIMUM 31-60feet, 750psi MINIMUM 61-100feet, 1100psi MINIMUM 101-130feet, 1500 MINIMUM And stress that this allows a safe, unhurried ascent with the required safety stop. Also emphasize that the limit is not based on a square profile; if you do a dive that starts off going to 130, your turn is 1500psi, if at say, 2000psi you ascend to 100feet, now your turn is 1100psi. If you further ascend to 60feet, do you can now wait until 750psi. This can also be used to limit your dive. if you're at 60feet and you're at 1000psi, and you see a neat thing 20feet below you, you CAN'T descend because that'll put you at less than your limit (1100psi at depths between 60-100 feet). End of basics. Now for extra credit: Personally, I wouldn't do only one safety stop at 16.5 feet on a 120 foot dive, so what are the REAL numbers for, say, a 120 foot dive? If I was doing a 120 foot dive, my profile would be from 120 feet, ascend at 30ft/min to 60feet, 1 min deep stop at 60, 30 ft/min to 30, 1 min "deep stop" at 30, then my normal safety stops of 1 min at 20, 2 min at 10. So, how much air to sort things out for a minute at 120 feet? (120/33feet per ATA + 1) = 4.6cf Ascent: 120/30 = 4 min CF used during ascent: ((4.6+1)/2) * 4 min = 11cf CF used during 1 minute 60 foot deep stop: 60/33+1 = 2.8cf CF used during 1 minute 30 foot deep stop: 30/33+1 = 1.9cf CF used during 1 minute 20 foot safety stop: 20/33+1 = 1.6cf CF used during 2 minute 10 foot safety stop: (10/33+1) * 2min = 2.6cf Total CF required for ascent: 4.6+11+2.8+1.9+1.6+2.6 = 24.5cf For two divers: 24.5*2 = ~50cf, 50/80*3000=1875 psi turn pressure for the dive. So you only have 1125psi to consume at 120 feet, at which point you turn the dive. That's about 13 minutes of bottom time at a SAC of 0.5. Hope this helps some folks with real gas management...