Spherical Chicken

Inadequate gas management has been involved in many diving fatalities in Puget Sound over the years and is one of the most consistent factors that is repeatedly involved in accidents. By practicing adequate gas management (which does not need to be difficult), divers can avoid placing themselves in situations where they are low on gas, out of gas, or entire buddy teams of divers are low on gas. This information is not presented in the typical agency open water, advanced open water, rescue or even deep diving courses — which seems nearly negligent. If all that you’ve been taught is “be back on the boat with 500 psi” without any information on how to execute a dive which guarantees that, you should read on. Check the URLs at the bottom of this article for other information as well.

The old version of this post is still available here if you prefer it, it will not be getting any updates or bugfixes.

Note: this article was written after an incident in 2006 where a group of divers, including me, attempted a rescue of a diver off Alki in Seattle that wound up being a fatality and is at least 51% personal therapy and written for myself, so there are obvious flaws in his article as an educational presentation to others. If you want more ‘educational’ resources and less of a core dump out of my brain, then you should check the links all the way at the bottom.

Disclaimer

No warranty expressed or implied, scuba diving is inherently dangerous, don’t sue me if you get hurt. Don’t blindly trust anything you read on the Internet.

Metric Disclaimer

Sorry, this was enough work to put together for imperial units. I always intended to make this document “bilingual”, but for now at least, metric divers are on their own…

DIR Disclaimer

This is a document influenced heavily by DIR, but aimed solidly at recreational divers and the widest possible audience. Many things in this document do not adhere strictly or at all to DIR protocols.

Background

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:

( consumption rate ) = ( RMV ) * ( atmospheres absolute ) * ( time )

For the US this looks like:

( cu ft ) = ( cu ft / min @ 1 ata ) * [ ( fsw ) / 33 + 1 ] * ( mins )

RMV and Consumption Rate

Respiratory Minute Volume (RMV) is the volume of gas at ambient pressure and temperature being breathed by the diver per minute. This value is expressed in cu ft / min and the value does not vary with the depth and is a measure of how fast the diver is breathing. This is commonly (and incorrectly) referred to as the “SAC rate”.

Surface Air Consumption Rate (SAC) is the pressure of gas in the tank at ambient pressure and temperature being consumed. It is equivalent to the RMV but is expressed in psi / min, and is dependent upon the size of the tank.

Consumption rate at depth (Cd) is a measure of the amount of gas which is actually being used at depth. This is measured in cu ft / min similarly to RMV, but measures how fast the tank is actually being drained. It is the volume of gas being breathed adjusted for a pressure of 1 atmosphere.

These definitions agree with both the US Navy and NOAA definitions.

Standard RMV Rates

The canonical standard 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 RMVs of slightly over 1.00 cu ft / min while experienced divers usually are closer to 0.60 cu ft / min with some achieving RMVs of nearly 0.30 cu ft / min.

When I started out diving the first time I checked my RMV I measured it as 1.10 cu ft / min averaged over the course of the entire dive (this was in Puget Sound in spring-time pea soup sometime around dive #10). After I gained considerable diving experience I got my RMV down to 0.60 cu ft / min on a good day and 0.75 cu ft/min when stressed where it stayed for a quite awhile. Eventually I managed to hit 0.45 cu ft / min which feels like a good minimum value for me since if I start to breathe more relaxed than that I tend to build up CO2. Divers should assess their own RMV on a regular basis to build up a good understanding of how fast they use up gas and how it changes over their diving career.

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

Recreational divers will often do a dive where at 2/3rd of their supply remaining they turn the dive, and with 1/3rds of their supply remaining they begin their ascent. This is actually not diving thirds the way that a technical diver would dive thirds. What they are doing is diving halves and reserving 1/3rd of their gas for rock bottom. The actual rockbottom calculations below are much better to determine what is actually needed for the dive rather than just using a value of 1/3rd of available for the rockbottom value.

Diving recreationally on thirds would mean computing rockbottom and reserving that gas. Then taking the rest of the available gas supply and turning when thirds was hit. This might be appropriate on a deeper wreck in the open ocean where there were significant currents and returning to the upline was considered essential to the safety of the dive. In this case the dive would be turned considerably before the tank was drained to 2/3rds.

The rationale behind thirds is that the trip back will take as much time as the trip out, and if your buddy has an OOA at the worst possible moment the trip back may take twice the gas ( 1/3 + 2 * 1/3 = 1.0) and you still need to reserve enough gas for both divers to ascend the upline.

If it is possible that there may be a gas emergency at the turn point and there may be stiff current on the way back, then thirds may not be conservative enough. At this point in complexity the dive is also starting to become a technical dive and probably needs technical equipment (doubles, long hose) and technical 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.

Rules of Thumb

Warning

These rules of thumb are not the whole story. They are simplified as much as possible to make them more widely accessible. As with all massively oversimplified rules they may not apply well in every circumstance and are necessarily aimed at the worst case of beginning divers and harsher conditions. They are hopefully simple enough for all divers to be able to employ with minimal math and should be able to be recalled even through the haze of narcosis.

Tank Size

The rule of thumb is that you should not dive to a greater depth in fsw than your tank capacity in cu ft. This works reasonably well for most beginning and intermediate recreational divers and caps the depth that an Al80 should be dove to to 77 fsw (Al80 == 77.4 cu ft). A steel 100 tank should not be dove past 100 fsw and a steel 130 should not be dove past 130 fsw (which is the limits of recreational diving as well).

In some circumstances, experienced divers in good viz and warm waters may do dives to 100 fsw routinely on Al80s so this rule may clearly be stretched.

It is probably not a good idea to be doing dives to 130 fsw on Al80s under any circumstances, though, and inexperienced divers (100 dives or less) doing coldwater dives to 100 fsw on Al80s are what this rule is squarely aimed at preventing. Also, the diver with 100 dives who think they’re okay with an Al80 at 100 fsw in warm water and good viz is probably at the edge of being overconfident.

Simplified Rock Bottom Values

For HP120/HP130/LP104/LP95s (big tanks) use a rockbottom value equal to 10 times the depth in fsw that you are at. So, for an X8-130 high pressure Worthington tank at 110 fsw, you must leave the bottom with at least 1100 psi.

For Al80s/HP100s/LP80s/LP72s (small tanks) use a rockbottom value of 10 times the depth in fsw plus 300 psi. So, for an Al80 at 60 fsw, you must leave the bottom with at least 900 psi left in the tank.

For both of these rules, never use a rockbottom value of less than 500 psi.

Be aware that this simplified extrapolation breaks down as you go deeper. For an E8-130 at 130 fsw the appropriate rock bottom value is closer to 1600 psi. If you are diving deeper than 100-110 fsw you should be able to follow the full rockbottom and SAC rate calculations below.

Rock Bottom

Rock Bottom – Ascent Protocol

To compute Rock Bottom, we add up the amount of gas we need to:

• take a minute at depth to solve the problem
• 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 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.

The rock bottom ascent is your bailout plan if anything goes badly wrong. If you plan on always doing 1 min stops from 50% of max depth (i.e. 1 min stops from 50 fsw on a 100 fsw dive), or you start stops 50 fsw off your max depth and start at 70 fsw on a 120 fsw max depth dive then rockbottom should be adjusted accordingly. This becomes more important when diving with 30/30 helium mix and is on the edge of what is recreational and what is technical and requires additional training and equipment.

For those familiar with GUE rockbottom protocols this may look different from what they are used to. There is no 80% pause, but I believe this is consistent with what GUE is currently teaching which is to simply stop at 50% of max depth (at 80% of depth/ATAs on recreational dives divers are still rapidly ongassing). I am mentioning but not using the 50% max depth rule because with recreational diving on nitrox/air mixes in an emergency situation I feel ascending to 30 fsw is more appropriate and is what I would do. Add in the deeper stops and pad the rockbottom time appropriately if you disagree.

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 separately 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 through the math and shown that algebraically this is an identical computation to doing three different computations for the three different stops.

NOTE: If your eyes just glassed over all I’m saying is that 1 min stops at 30/20/10 fsw is mathematically identical to a single 3 min stop at 20 fsw. I’ll be using the latter in all future computations, but doing the former on the ascent.

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 fsw / 2 = 30 fsw

stop gas = ( 2.00 cu ft / min ) * [ ( 20 fsw ) / 33 + 1 ] * 3 mins = 9.63636 cu ft

Rock Bottom Volume = problem gas + ascent gas + stop gas = 22.9 cu ft

Rock Bottom – Mental Simplification

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

While not entirely precise, values computed this way work fine in practice.

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:

66 fsw: 24 cu ft * (3000 psi / 77.4 cu ft) = 930 psi
100 fsw: 35 cu ft * (3000 psi / 77.4 cu ft) = 1356 psi
130 fsw: 48 cu ft * (3000 psi / 77.4 cu ft) = 1860 psi[*]

[*] using an Al80 to 130 fsw is not a good idea under any circumstance.

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 Worthington X8-130 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. I have retired an SPG which consistently read 300 psi over actual tank pressure when measured against a variety of other calibrated pressure gauges at different shops. At 0 tank pressure it still read 300 psi. Vacation divers who rent all their gear should probably take note.

Rock Bottom – Mental Table Values

I would suggest using tables like the following:

Depth	Rock Bottom	Al80 pressure	LP80/HP100 pressure	LP95/HP120 pressure	LP104/HP130 pressure
30 fsw	12 cu ft	700 psi	500 psi	500 psi	500 psi
60 fsw	24 cu ft	1000 psi	800 psi	700 psi	700 psi
100 fsw	35 cu ft	1300 psi	1200 psi	1000 psi	1000 psi
130 fsw	48 cu ft	1800 psi	1600 psi	1400 psi	1300 psi

This works just like dive tables in that if you are at 80 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 60 fsw on a single AL80 that has cooled to 2800 psi our rock bottom will be 1000 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 = 2800 psi - 1000 psi = 1800 psi
gas used on swim out = 1800 psi / 2 = 900 psi
turn pressure = 2800 psi - 900 psi = 1900 psi

In other words, we expect to use 1800 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 60 fsw until we hit our 1000 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.

Precise Tables

These tables all use the computationally precise method of determining rockbottom.

Precise tables for different tanks and Source Code.

Depth	Rock Bottom	HP80	Al72	Al80	LP72	HP100	LP80	Al100	HP119	LP95	HP130	LP104
10 fsw	13.01 cu ft	569 psi	542 psi	504 psi	500 psi	500 psi	500 psi	500 psi	500 psi	500 psi	500 psi	500 psi
20 fsw	14.59 cu ft	638 psi	607 psi	565 psi	534 psi	510 psi	500 psi	500 psi	500 psi	500 psi	500 psi	500 psi
30 fsw	16.36 cu ft	715 psi	681 psi	634 psi	600 psi	572 psi	540 psi	500 psi	500 psi	500 psi	500 psi	500 psi
40 fsw	18.34 cu ft	802 psi	764 psi	710 psi	672 psi	642 psi	605 psi	550 psi	539 psi	509 psi	500 psi	500 psi
50 fsw	20.53 cu ft	897 psi	855 psi	795 psi	752 psi	718 psi	677 psi	615 psi	603 psi	570 psi	552 psi	521 psi
60 fsw	22.91 cu ft	1002 psi	954 psi	887 psi	840 psi	801 psi	756 psi	687 psi	673 psi	636 psi	616 psi	581 psi
70 fsw	25.49 cu ft	1115 psi	1062 psi	988 psi	934 psi	892 psi	841 psi	764 psi	749 psi	708 psi	686 psi	647 psi
80 fsw	28.28 cu ft	1237 psi	1178 psi	1096 psi	1037 psi	989 psi	933 psi	848 psi	831 psi	785 psi	761 psi	717 psi
90 fsw	31.27 cu ft	1368 psi	1303 psi	1212 psi	1146 psi	1094 psi	1032 psi	938 psi	919 psi	869 psi	841 psi	793 psi
100 fsw	34.46 cu ft	1507 psi	1436 psi	1335 psi	1263 psi	1206 psi	1137 psi	1033 psi	1013 psi	957 psi	927 psi	874 psi
110 fsw	37.86 cu ft	1656 psi	1577 psi	1467 psi	1388 psi	1325 psi	1249 psi	1135 psi	1113 psi	1052 psi	1019 psi	961 psi
120 fsw	41.45 cu ft	1813 psi	1727 psi	1606 psi	1519 psi	1450 psi	1368 psi	1243 psi	1219 psi	1152 psi	1116 psi	1052 psi
130 fsw	45.25 cu ft	1979 psi	1885 psi	1753 psi	1659 psi	1583 psi	1493 psi	1357 psi	1330 psi	1257 psi	1218 psi	1148 psi

Precise Tables for Pony Bottles

Since pony bottles only have one second stage regulator these values assume a RMV of 1.0 cu ft / min for a single diver. Source Code.

Depth	Rock Bottom	Al6	Al9	Al13	Al19	Al30	Al40
10 fsw	6.51 cu ft	N/A	2379 psi	1478 psi	980 psi	650 psi	500 psi
20 fsw	7.29 cu ft	N/A	2668 psi	1657 psi	1099 psi	729 psi	546 psi
30 fsw	8.18 cu ft	N/A	2993 psi	1859 psi	1233 psi	818 psi	613 psi
40 fsw	9.17 cu ft	N/A	N/A	2084 psi	1382 psi	917 psi	687 psi
50 fsw	10.26 cu ft	N/A	N/A	2332 psi	1547 psi	1026 psi	769 psi
60 fsw	11.45 cu ft	N/A	N/A	2603 psi	1726 psi	1145 psi	859 psi
70 fsw	12.75 cu ft	N/A	N/A	2897 psi	1921 psi	1274 psi	956 psi
80 fsw	14.14 cu ft	N/A	N/A	N/A	2131 psi	1414 psi	1060 psi
90 fsw	15.64 cu ft	N/A	N/A	N/A	2357 psi	1563 psi	1172 psi
100 fsw	17.23 cu ft	N/A	N/A	N/A	2597 psi	1723 psi	1292 psi
110 fsw	18.93 cu ft	N/A	N/A	N/A	2853 psi	1892 psi	1419 psi
120 fsw	20.73 cu ft	N/A	N/A	N/A	N/A	2072 psi	1554 psi
130 fsw	22.63 cu ft	N/A	N/A	N/A	N/A	2262 psi	1696 psi

Gas Planning

On-The-Fly SAC rates

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, to get your air consumption rate at depth, 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 on any particular dive who can easily exceed 1.0 cu ft / min and that everyone will be breathing heavier in an emergency. You plan the non-emergency part of the dive with your own non-emergency RMV rate. You plan the emergency part of the dive with the standard emergency RMV rate of 2.0 cu ft / min.

Other Resources

• Bob Bailey’s site
• Peter Rothschild’s site