Bottom Gas Volume Calculations

Hello! Welcome back.

In our last lesson, we established the critical safety foundation of technical diving gas planning: the Rock Bottom reserve. We learned how to calculate the absolute minimum gas required for a safe emergency ascent, which partitions our total gas supply into a non-negotiable reserve and the "usable" gas for the dive.

Today, we'll focus on that usable gas. We will build directly on the Rock Bottom principle to answer the practical questions at the heart of dive planning: "How much gas do I need for my planned bottom time?" and "How much bottom time can I get with the gas I have?"

This lesson is dedicated to the learning outcome: Calculate bottom gas volume requirements for a planned technical dive profile. By the end, you'll be able to confidently determine if your equipment and gas supply are sufficient for your intended dive.

1. The Foundation: Gas Consumption at Depth

Before we can calculate the gas needed for the bottom phase of a dive, we must have a solid grasp of how much gas we breathe. This is quantified by your Surface Air Consumption (SAC) rate, also called Respiratory Minute Volume (RMV) at the surface.

• SAC Rate: The volume of gas (in litres) you breathe in one minute at the surface (1 atmosphere absolute, or 1 ata).

Your SAC rate is a personal value that you should calculate from your own dive logs. It varies with exertion, stress, and thermal comfort. For planning, you should have a good idea of your typical, relaxed SAC rate.

Once you know your SAC rate, you can calculate your gas consumption at any depth. This is your Respiratory Minute Volume (RMV) at depth. Because gas is denser under pressure, you consume a greater volume from your cylinder for every breath you take at depth.

The relationship is simple and linear:

${\text{RMV}}_{\text{depth}}(\text{L/min})=\text{SAC Rate (L/min)}\times \text{Ambient Pressure (ata)}$

2. Calculating Bottom Gas Volume

With the concept of RMV at depth established, calculating the gas required for the bottom phase of your dive is straightforward. You simply multiply your gas consumption rate at your planned bottom depth by your planned bottom time.

The formula is:

$\text{Bottom Gas Volume (L)}={\text{RMV}}_{\text{depth}}\times \text{Bottom Time (min)}$

Or, expanding the formula:

$\text{Bottom Gas Volume (L)}=\text{SAC Rate (L/min)}\times \text{Pressure at Depth (ata)}\times \text{Bottom Time (min)}$

This calculation gives you the total free gas volume (the volume the gas would occupy at the surface) required for the time you plan to spend at your maximum depth.

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Worked Example: Calculating Bottom Gas for a Planned Dive

Let's put this into practice.

• Dive Plan: 20 minutes at 45 meters.
• Diver's SAC Rate: 18 L/min (a reasonable average for a relaxed technical diver).
• Pressure at Depth: $(45\text{ m}/10)+1=5.5\text{ ata}$.

Now, we calculate the required bottom gas volume:

$\text{Bottom Gas Volume}=18\text{ L/min}\times 5.5\text{ ata}\times 20\text{ min}=1980\text{ Litres}$

This means you will consume 1980 litres of gas during the 20-minute bottom phase of this dive.

3. Putting It All Together: Is the Dive Plan Feasible?

The 1980 litres we just calculated is only part of the story. To know if our dive is possible, we must compare our total planned gas consumption against the usable gas we have available, as determined by our Rock Bottom calculation from the last lesson.

Let's continue the example:

• Cylinders: Double 12L (24L total volume), filled to 200 bar.
• Total Gas: $24\text{ L}\times 200\text{ bar}=4800\text{ Litres}$.
• Rock Bottom Reserve (from previous lesson's method): Let's assume for a 45m dive, we calculated a Rock Bottom pressure of 110 bar.
• Rock Bottom Volume: $24\text{ L}\times 110\text{ bar}=2640\text{ Litres}$.
• Usable Gas Volume: $4800\text{ L}-2640\text{ L}=2160\text{ Litres}$.

We have 2160 litres of usable gas. We've already allocated 1980 litres for the bottom time. Is the remaining gas enough for the descent and ascent?

• Descent Gas: Assume a 2-minute descent. Average depth is 22.5m (3.25 ata).
  $\text{Descent Gas}=18\text{ L/min}\times 3.25\text{ ata}\times 2\text{ min}=117\text{ Litres}$
• Ascent Gas (to first deco stop): Assume ascent to a 21m stop at 9m/min. Time = (45-21)/9 = 2.7 min, let's say 3 mins. Average depth is 33m (4.3 ata).
  $\text{Ascent Gas}=18\text{ L/min}\times 4.3\text{ ata}\times 3\text{ min}=232\text{ Litres}$

Now, let's sum up our planned gas usage from our back gas:

$\text{Total Planned Gas}=\text{Descent}+\text{Bottom}+\text{Ascent}$
$\text{Total Planned Gas}=117\text{ L}+1980\text{ L}+232\text{ L}=2329\text{ Litres}$

Conclusion: Our planned gas consumption (2329 L) is greater than our available usable gas (2160 L). Therefore, this dive plan is not feasible with D12s filled to 200 bar. We would either need larger cylinders, higher pressure fills, or we must reduce our planned bottom time.

4. Working Backwards: Calculating Maximum Bottom Time

This leads to the second common planning question: "How much bottom time can I get?"

Let's use the same dive parameters but work backwards to find our maximum allowable bottom time.

1. Find Gas Available for the Bottom Phase:

   • Start with our Usable Gas Volume: 2160 Litres.
   • Subtract the gas needed for descent (117 L) and ascent (232 L).
     $\text{Gas for Bottom}=2160-117-232=1811\text{ Litres}$

2. Calculate Gas Consumption Rate at Depth (RMV_depth):
   ${\text{RMV}}_{\text{depth}}=18\text{ L/min}\times 5.5\text{ ata}=99\text{ L/min}$

3. Calculate Maximum Bottom Time:
   $\text{Max Bottom Time}=\frac{\text{Gas Available for Bottom}}{{\text{RMV}}_{\text{depth}}}=\frac{1811\text{ L}}{99\text{ L/min}}=18.3\text{ minutes}$

So, with these cylinders and this reserve, the maximum bottom time we could safely plan for is 18 minutes.

This process of calculating available dive time based on usable gas is a crucial skill.

Conclusion

You now have the tools to perform the core calculations for bottom gas planning. By combining the Rock Bottom principle with SAC/RMV calculations, you can move from abstract safety margins to concrete, data-driven dive planning.

Key Takeaways:

• Your gas consumption at depth (RMV) is your surface consumption (SAC) multiplied by the ambient pressure in ata.
• The gas volume needed for the bottom phase is your RMV at depth multiplied by your planned bottom time.
• A dive plan is only feasible if the total gas required for descent, bottom time, and ascent is less than or equal to your usable gas (Total Gas - Rock Bottom Reserve).
• You can work backwards from your usable gas to calculate the maximum, non-negotiable bottom time your gas supply allows for a given depth.

Preview of the Next Lesson:

We have now planned for our reserve and our bottom gas. The final piece of the puzzle is accounting for the gas needed for decompression. In our next lesson, we will learn to calculate decompression gas volume requirements based on a planned decompression schedule, allowing us to build a complete gas plan for an entire technical dive.