Easily convert between volume & pressure

Proper gas planning & management is critical to safe diving since humans cannot breathe underwater without life support equipment.

Unfortunately, many divers don’t understand what gas planning & management is, and simply use the standard “Back on the boat with 500psi” or the rule of “thirds”.

While those types of plans may work in certain circumstances, they can also be very dangerous.

In the first example ("back on the boat..."), the diver is planning his gas so he arrives at the surface with a set pressure in his tank. He’s not planning his gas for what would be needed should an emergency occur underwater, which is our biggest consideration.

In the second example (thirds), he's applying a single rule to all dives. The result may be an unnecessarily overly conservative gas plan, or an inadequate gas plan. Additionally, the ascent takes longer than the descent, thus requiring more gas, which is not accounted for in a straight thirds gas plan.

It’s important to remember that an Out Of Gas (OOG) situation is rarely caused by catastrophic equipment failure. Proper gas planning & management and gear maintenance is all that is required to avoid this type of situation. However, when planning our dive, we plan according to worst case scenarios.

Rock Bottom, or Minimum/Min Gas, is quite simply, planning for the worst case scenario…the instance where a diver in a 2 person buddy team experiences a single catastrophic failure and complete loss of gas at the deepest part of the dive. It’s the minimum amount of gas needed for 2 divers to ascend to the next available gas, completing all required stops, sharing gas from a single gas source/supply.

In your open water class you learned about Boyle's Law. Simply put, Boyle’s Law states that at a given temperature as pressure increases, volume decreases proportionally.

In salt water, every 33’ is 1 atmosphere. At the surface, we are under 1 ata (atmosphere absolute) of pressure. Therefore, at 33’, we’re under 2 ata’s of pressure (the single atmosphere at the surface, and the 33’ of water above us). At 66’, we’re under 3 ata’s of pressure. 99’ is 4 ata’s, and so on.Since every 33’ of saltwater is an atmosphere, to determine the pressure, in ata’s, of any given depth, we simply divide the depth by 33, and add 1 (for the pressure at the surface). In other words;

Ata = Depth / 33 + 1

Likewise, to determine the depth of any given pressure, we simply subtract 1 (for the pressure at the surface) from the pressure, then multiply by 33. Also shown as;

Depth = (ata – 1) x 33

It’s important that every diver know his/her own consumption rate. If you don’t know your consumption rate, and would like to learn more, please Contact Us to schedule a FREE Gas Planning & Management Workshop. Also, check out our Tank Factors and Consumption tu.

At the recreational level, we typically plan for a stressed diver to breathe approximately 1cuft per minute (Respiratory Minute Volume, or RMV), at the surface. Applying Boyle’s Law, from above, if a diver breathes approximately 1cuft per minute at the surface, stressed or working, he’ll breathe 3 cuft per minute at 66’, due to the fact that the 2nd stage regulator must deliver gas to the diver at slightly above the ambient pressure;

1 (RMV) x 3 (ata of 66fsw) = 3

At 99’ the diver will breathe 4 cuft of gas, when stressed or working;

1 (RMV) x 4 (ata of 99fsw) = 4

You can certainly increase your planned stressed RMV upwards, for conservatism, if desired or if you know your working RMV to be higher than 1. However, the goal should be to get your working/stressed RMV consistent with the planned rate of 1cuft/min, by working on the areas that affect consumption rate, such as buoyancy, trim, kicks, s-drill proficiency, situational awareness, and awareness of breathing, among others. These are foundational skills which we focus and build on in all UTD / FKD classes.

Use working RMV (1.0 each if not known, as previously stated)

:01 to donate the regulator, assess the situation and initiate the ascend

Ascend at 30fpm to first stop (50%) (Min Deco ascend)

Ascend at 10fpm from 50% to surface (Min Deco ascent)

One final rule; never use a Rock Bottom of below 500psi. If your calculated Rock Bottom is below 500psi, use 500psi. This is due to the inaccuracy of the spg when reading pressures below 500psi.

When applying the rules and assumptions above, its easiest to visualize the situation in 2 segments; the bottom segment (donation, assessment and initiation of ascent) and the ascent.

Additionally, there are only 3 pieces of information needed to calculate Rock Bottom;

How deep (depth)

How long (time)

Breathing rate (combined RMV for TWO divers, since they'll be breathing off a single gas source)

Depth and time are both variable. The deeper the dive, the more gas that is needed/used in the bottom segment, due to the increased depth. Likewise, the deeper the dive, the longer the ascent time.

When calculating Rock Bottom, we use the average depth of the ascent, including the :01 on the bottom. The ascent time includes the :01 on the bottom. Last, remember that both divers are sharing gas off a single gas source, and both are stressed, so we use an RMV of 1 for each diver, for a total of 2.

Here's an example;

The average depth of the ascent is 50fsw (:04 at or below 50fsw & :04 at or above 50fsw. The minute on the bottom is included when calculating average depth). The total ascent time, including the minute on the bottom to sort out, clean up and prepare for the ascent, is :08. The breathing rate for each diver is 1 cuft per minute, times 2 divers.

So, in the example above, a buddy team experiencing an OOG emergency at 100’ will need 40cuft of gas to ascend safely, completing all stops, sharing gas from a single source.

However, since we work with pressure and not volume while underwater, we must convert the volume (40cuft) to pressure, or psi.

To do that, we’ll simply run a quick calculation using tank factors.

Interested in learning more about Tank Factors?

Check out our Tank Factors tutorial

Tank factors are simply the volume of cubic feet per 100 psi, for a given tank. Using tank factors is a very easy way of converting between volume (cuft) and pressure (psi).

To calculate a tank’s tank factor, you simply divide the tank’s rated pressure by the tank’s rated volume, then multiply by 100;

Tank Factor = (rated volume / rated pressure) x 100

For an al80 (al80’s actually contain 77cuft, not 80), the tank factor would be:

(77 / 3000) x 100 = 2.66

This means on an al80, there are 2.66 cuft per 100psi.

To make life simple, we’ll just call it a tank factor of 2.5.

It’s important to remember that you must use the rated pressure and volume.

Now that we know the tank factor of an aluminum 80, we can convert the volume (40cuft) to psi in the above example, using a simple formula. The diagram below is actually a formula in itself. If you want to know the volume, you’d simply multiply pressure by the tank factor. If you want to know the pressure (psi), you’d simply divide the volume by the tank factor.

For more information on Tank Factors, see our Tank Factors tutorial.

So, using the formula above, to determine how many psi 40cuft of gas in an al80 is, we simply divide the volume (40) by the tank factor (2.5);

40 / 2.5 = 16 or 1600

Though the answer is 16, remember, we're dealing in 100's of psi. So 1600.

Applying this to the above example of a Rock Bottom Ascent, we’d get this:

1600psi is needed for the 2 divers to ascend from 100’, sharing air on a single al80, completing all required stops. Since this is based on assumptions, if you’d like to add a buffer of 200 or 300psi, making the Rock Bottom 1800 or 1900, that is acceptable. However, you should never lower the Rock Bottom number.

There are other gas plans as well, as Rock Bottom by itself doesn’t work in every scenario (overheads, such as caves or wrecks, where additional gas is needed to get to the ascent point). But for most everyday recreational dives, Rock Bottom gives you the knowledge that you need to safely execute a dive with proper gas reserves.

It’s important to understand that Rock Bottom is for a specific depth, and not a specific dive. In other words, 100’ has a different Rock Bottom than 90’. For instance, if you hit your Rock Bottom at 100’, and ascend up to 80’, you must ensure that you don’t exceed your Rock Bottom for 80’.

It’s a good idea to make note of your Rock Bottom in 10’ increments, from 60’ to the maximum depth you dive to. An easy way of doing this is to keep them in your wetnotes.

If you know the volume, you need only use the tank factor to adjust it for the tank you are using.If you’re interested in learning more about Gas Planning & Management, please Contact Us to schedule a free Gas Planning & Management Workshop

Interested in learning more about consumption? Check out our Consumption tutorial.

Nothing is more critical to a diver than having gas to breathe.

Having a gas plan, and managing your gas, is critical to safe diving. And, with a few minutes playing with numbers, calculating your Rock Bottom (Min Gas) becomes a quick and easy exercise.

Understanding how much gas you consume over a given period of time, and how depth, conditions and your own health (mental and physical) can affect your gas consumption allows you to better manage your gas plan, as well as make informed and educated decisions on which equipment (such as cylinders) are most appropriate for a given dive.

It’s important to understand that several factors can affect your consumption.

ENVIRONMENT / CONDITIONS

Conditions, such as strong current, will affect how hard you have to work during your dive. If you’re kicking into the current, you’ll be working harder, and thus breathing heavier, than if you were simply drifting with the current. This is no different than varying conditions here on land. Your breathing rate right now, as you read this, is different than if you were outside walking up to the store, and significantly different than if you were running or cycling.

HEALTH

Just as on the surface, your health directly affects your consumption rate. Someone in very good physical shape who is kicking against a stiff current will not exert as much energy as someone in poor physical health.

DEPTH

Your depth on a dive has a very significant and direct effect on your consumption. In order for a diver easily breathe underwater, their regulator needs to deliver gas properly. The 1st stage regulates the high pressure from the cylinder down to intermediate pressure (usually ~145psi), the pressure the gas is delivered to the 2nd stage. The 2nd stage then reduces the pressure down to just above ambient pressure. If it were less than ambient pressure, the diver would have to work very hard to suck air.

If the 2nd stage delivers delivers gas at just above ambient pressure, at 100fsw (4 ata’s), the regulator is delivering gas at just over 4ata’s. In other words, it’s provided gas at over 4 times the pressure than that at the surface (1ata). So, you can expect to go through your gas at 100fsw 4 times faster than the same amount of gas at the surface (1ata), all other factors being equal.

“All other factors” are rarely equal, however. Another consideration of depth is the role narcosis plays. At 100fsw, the diver is narc’d, to varying degrees. Narcosis has a significant impact on consumption, and once stress or task loading enters the equation, consumption will increase very rapidly.

STRESS

Stress psychologically triggers humans to breathe faster. It’s no different underwater. A stressed diver is going to breathe heavier (any many instances dramatically heavier), than a non-stressed diver.

All individual factors above can significantly impact a diver’s consumption rate. Often times, there isn’t one single factor in play, however. And building an awareness underwater, to recognize when, and why, your consumption is higher than normal or expected, is very important to managing the gas plan. Understanding why allows the diver to make adjustments (decrease depth to decrease narcosis, change direction to prevent swimming directly into current, etc).

There are two ways to work with consumption….pressure and volume. Typically, when discussing consumption on land, or when planning a dive, volume is used, as it’s easier to work with (explained in the next paragraph). However, when underwater, we use pressure, as that is the information our SPG’s provide us.

Working with volume is often easier than working with pressure because our volume is consistent, where the pressure will vary, depending on the cylinder. In short, if your average consumption volume is .75cuft per minute, it’s .75cuft/minute, regardless of the gas source. However, that .75cuft/minute will be a different pressure when breathed from an al80, than when breathed from a hp130.

Because of this, the most common and easiest method is to work with volume when developing a gas plan, then use Tank Factors to convert to pressure specific to the tanks being used.

SAC, or Surface Air Consumption (also called SCR or Surface Consumption Rate), is simply the amount of gas you breathe, in pressure (psi), in one minute, at the surface (1 ata).

Consumption by volume is called Respiratory Minute Volume, or RMV, and is simply the volume (in cubic feet) breathed in one minute at the surface (1 ata).

Before moving further, it’s important to note that “SAC” is the slang term often applied when discussing consumption rates. However, the RMV number (volume) is what is typically being discussed….ie “My typical SAC rate is .7”, meaning the diver is saying he breathes .7cuft/minute at the surface (his RMV).

When calculating consumption rates, we typically start with SAC, since we’ll be logging the information while underwater. We then convert it to RMV once on the surface. As you gain more comfort through practice and repetition, you’ll be able to easily work with SAC and RMV in your head.

To calculate your SAC rate, you need 3 pieces of information:

Depth (in ATA)

Time

Gas consumed (in psi)

For a refresher, when converting depth in feet to ATA:

Pressure (ATA) = depth / 33 + 1

For example, 50fsw, converted to ATA is:

50 / 33 + 1 = 2.515 ATA

Rounding to single decimal, or 2.5, is acceptable, and makes it easier to work with. At 50fsw, your regulator is delivering gas to you at slighter more than 2.5 times what it would at the surface.

Now that we’ve converted depth to pressure, we can calculate our SAC rate from a dive.

SAC = Gas Consumed (psi) / Time (minutes) / Depth (ATA)

For example, on a dive averaging 50fsw, for 20 minutes, a diver consumed 1500psi:

1500 / 20 / 2.5 = 30

The SAC rate for that diver, on that dive, was 30 psi per minute.

A couple of points, before moving on…

First, it’s important to use average depth, as that provides an accurate number for your depth for the entire dive. Using max depth will provide a unrealistically high SAC number, and using a shallower depth will yield an unrealistically low SAC number.

“On that dive” is important. As mentioned above, many factors affect your SAC rate. It’s important to determine your SAC rate over several dives, in varying conditions, to gain a better understanding of your average SAC rate.

Also, that SAC rate is specific to the tank used on that dive. If another diver on that team breathed the exact same amount of gas (in psi), but using a different size tank, he would have a different SAC.

Now that we’ve calculated our SAC rate, we can now convert it to RMV, which is a more useful number, as it is not specific to any tank.

To convert SAC to RMV, we need to account for the tank that was used. To do that, we calculate the tank’s “baseline”, which is similar to its tank factor, without multiplying by 100.

Baseline = cylinder’s rated volume (cuft) / cylinder’s working pressure (psi)

It’s critical to use the cylinder’s rated volume. That is, how many cubic feet the cylinder holds when it is filled to its working pressure. Additionally, it’s equally important to use the cylinder’s working pressure. That is, what pressure the cylinder is rated to be filled to, not what it was actually filled to for the dive.

For this example, let’s use an aluminum 80:

77.4 / 3000 = .026

The baseline for an al80 is .026. That number represents how many cubic feet of gas are in 1psi in that cylinder. If you want to determine its tank factor, you simply multiply that number by 100, which is 2.6. If you were using an hp100, you’d simply divide 100 by 3500, getting .029.

If you know the cylinder’s tank factor, you can simply divide that by 100.

Note that an al80 actually has a rated volume of only 77.4cuft, and not 80cuft.

Now that we know our SAC rate from that dive (30 psi/min), and the baseline of the tank used (.026), we can convert to RMV:

RMV = SAC x Baseline

Or

30 x .026 = .78cuft

In this case, the diver breathed the equivalent of .78cuft per minute, at the surface.

Now that we know both the SAC and RMV, we can make some calculations to help get a better idea of our consumption while at depth. For instance, if the diver breathes ~.78cuft / minute at the surface, what would he breathe at 100fsw (4 ata)? You’d simply multiply the RMV by the depth, in ATA:

DCR (Depth Consumption Rate) = RMV x Depth (ata)

.78 x 4 = 3.12 cuft / minute

If the diver is using an al80 again, we can use his SAC number (30psi/minute), multiplied by depth in ata:

30 x 4 = 120psi/minute

We can also determine if the tank we want to use has enough gas for us to safely execute a dive. For instance, the diver with a SAC rate of 30psi on an al80, RMV of .78, wants to do a dive for 20 minutes at 100fsw. How much gas can he expect to use. For SAC:

30 x 4 x 20 = 2400psi

For RMV:

.78 x 4 x 20 = 62.4cuft

While 62cuft is certainly less than 77.4cuft, it would appear an al80 is adequate for this dive. However, we still have Min Gas / Rock Bottom to consider, in which case the diver does NOT have enough gas to spend 20 minutes at depth, and still have enough for Rock Bottom requirements

Consumption rates are a range, and will vary not only dive to dive, but will vary throughout a single dive as well.

For consistency and simplicity, we use the following consumption rates:

Resting (deco, ascent) - .5

Bottom (some finning/kicking, light work) - .75

Working & stressed – 1.00

Some considerations with these average consumption rates…

First, if you know your consumption rates are higher than the average, use your true consumption rates in your gas plan calculations.

Second, if you know your consumption rates are higher than the average, work to get them down to the average. There are many factors that can impact your consumption rate, including kicks, buoyancy control, trim, cardiovascular health and experience, to name a few.

Putting it Together

You’ve probably noticed this isn’t an exact science. Our underwater adventures are very dynamic, with lots of variables that change often…environmental conditions, physical health, mental health, dive profile, task level, the unexpected big life encounter, etc. Those variables are the reason that calculating your consumption rate often is important. By doing so, you get an accurate portrait of your consumption in a variety of conditions and situations, allowing you to make educated decisions when formulating your gas plan, as well as managing the plan.

Want to learn more? Contact us to schedule a Gas Planning Workshop, and check out our Rock Bottom and Tank Factors tutorials

Tank factors are a handy quick and easy method of converting between volume (cuft) and pressure (psi). It's especially handy when teammates are using dissimilar tanks.

Simply put, tank factors are the volume of gas per 100 psi, for a given tank.

To calculate a tank’s tank factor, you simply divide the tank’s rated pressure by the tank’s rated volume, then multiply by 100;

Tank Factor = (rated volume / rated pressure) x 100

For an al80 (al80’s actually contain 77cuft, not 80), the tank factor would be:

(77 / 3000) x 100 = 2.66

This means on an al80, there are 2.66 cuft per 100psi.

To make life simple, we’ll just call it a tank factor of 2.5.

It’s important to remember that you must use the rated pressure and volume.

Using the aluminum 80's tank factor allows us to start converting between pressure and volume. This diagram is actually a formula in itself, known to many as the "circle T".

If you want to know the volume, you’d simply multiply pressure by the tank factor. If you want to know the pressure (psi), you’d simply divide the volume by the tank factor. Simply cover the item you wish to solve for.

For example, using the example on our Rock Bottom tutorial, the 2 divers need 40cuft of gas. However, we typically work with volume on land, but pressure underwater, since that is what our spg's read. So, we need to convert that 40cuft to psi.

By covering up the psi section of the above equation, you can see we must divide the volume (40cuft) by the tank factor (2.5);

40 / 2.5 = 16

Keep in mind that tank factors represent the volume of gas, in cubic feet, per 100 psi. So, we must multiply the 16 by 100;

16 x 100 = 1600

So the Rock Bottom pressure for the Rock Bottom example, in an al80, is 1600psi.

To convert a pressure to volume, you'd cover the "volume" section in the formula above. So, to convert that 1600psi back into volume (if it were not already known), you'd multiply the tank factor and the pressure;

2.5 x 16 = 40 (cuft)

Remember, we multiply by 16, and not 1600, because the tank factor is solved for 100's of psi.

Tank factors are often used for double tanks as well. Perhaps moreso than single tanks.

When calculating the tank factor for your doubles, you use the same formula as above. Keep in mind that the rated volume of gas has doubled, due to the second cylinder. However, the rated pressure remains the same.

So, for a set of double AL80's;

154 (77 cuft each cylinder x 2 cylinders) / 3000 (rated pressure) x 100 = 5.13, round to 5

Using the Rock Bottom example from above, our Rock Bottom pressure in a set of AL80's is;

40 (cuft) / 5 (TF) = 88 x 100 = 800psi

Tank factors for some commonly used tanks

To keep our dives consistent, flexible and as simple as possible, we use standardized mixes. Each mix allows us a range of depths to explore and provides a similar decompression. This eliminates the need to remember a bunch of numbers and the use of decompression tables, since the ascent profiles are consistent within the mixes. In other words, a dive to 150' using 21/35 will have a similar ascent profile as a dive to 200' on 18/45. The primary difference is we'd simply add a 2nd decompression gas (O2) on the 200' dive.

- Bottom mixes have an MOD PPO2 of 1.4 ata
- Bottom mixes have an average PPO2 of 1.2 ata for our working depth
- Bottom mixes have a buffer from our working depth and the MOD of 1.4
- Bottom mixes are created by adding HE, then topping with 32% (easy for banking 32% and doing trimix fills) or by quick formulas for "air tops"
- Deco mixes have an MOD PPO2 of 1.6 ata
- Deco mixes have an average PPO2 of 1.2 ata (averaged over the range the deco mixed is used), except for O2 at 20'
- Deco mixes are used over an average of 5 10' stops, except for when using O2 for decompression
- The higher the HE content, the better, however the HE content must always be enough to provide an END of 100' or less, based on the conservative formula; END = (1 - HE)*ATA's. This formula assumes O2 to be narcotic