Gas Consumption Calculations

Have you ever wondered how to compare your breathing efficiency? You cannot directly compare any two dives you have done, or two divers on the same dive profile using different cylinders. The dives are likely to be at different depths so the volume of each breath is different (Boyles law), and different cylinders have different capacities and rated pressures.

As a common reference point we convert our measurements to the surface, and imagine all the air has been decompressed from the cylinder into a large volume. That is why we call it Surface Air Consumption rate (SAC_{rate}).

To find our physiological rate we need to account for varying depth, and measure independently of cylinder size. We use the Respiratory Minute Volume (RMV_{rate}), that is the amount of gas that we breathe per minute at the surface. Taking 10 breaths at \mathrm{66\ [ft]} (\mathrm{3 [ata]}) would be the same as taking 30 identical breaths at the surface (\mathrm{1 [ata]} at sea level). Another problem is that we measure pressure, but this needs to be converted to an actual volume of air.

SACrateSurface Air Consumption rate [psi/min]The equivalent rate that the cylinder is consumed at the surface without depth pressure.
RMVrateRespiratory Minute Volume rate [ft3/min]The equivalent volume of gas in cubic feet, consumed at the surface.
PratePressure rate [psi//min]The rate of gas consumption at depth, as measured by a pressure gauge.
DfactorDepth factor [ata]How much consumption is increased by due to depth pressure.
TfactorTank factor [ft3/psi]A tank-specific number to convert tank pressure [psi] to gas volume in cubic feet [ft3].
VcylinderTank volume [ft3]The volume of gas in the cylinder

The equations we need are:

(1)   \begin{equation*}  % use "\text" in an equation* environment and "\mathrm" outside SAC_{rate} = \dfrac{ P_{rate} }{ D_{factor} } \hspace\textup{[psi/min]} \end{equation*}

(SAC_{rate} is specific to each cylinder, probably between \mathrm{20\mbox{--}50\ [psi/min]} )

(2)   \begin{equation*}  RMV_{rate} = SAC_{rate} * T_{factor} \hspace\textup{[ft^3/min]} \end{equation*}

RMV_{rate}  is our actual physiological consumption rate, approximately \mathrm{0.5\mbox{--}1.0\ [ft^3/min]} )

We start with a pressure rate (P_{rate}), say consuming \mathrm{2000\ [psi]} at an average depth of \mathrm{50\ [ft]} for \mathrm{30\ [min]}. Using an average accounts for the varying depth of most dives, we don’t usually dive true square profiles. We can use max depth in lieu of the average depth, but the calculated SAC_{rate} or RMV_{rate} will be higher. Fancy computers can provide average depth, but the Subgear XP10 rental computer does not.

    \[ \begin{split} P_{rate} &= \dfrac{ \left(  P_{start}\hspace\mathrm{[psi]} - P_{end}\hspace\mathrm{[psi]} \right) }{ T_{dive}\hspace\mathrm{[min]} } \\ &= \mathrm{2000\ [psi]} / \mathrm{30\ [min]} \\ &= \mathrm{2000\ [psi]} /  \mathrm{30\ [min]} \\ &= \mathrm{66.66\ [psi/min]} \end{split} \]

Our depth factor (D_{factor}) accounts for depth, (using average if available) by scaling our measurement by the total pressure at depth plus the air pressure, in atmospheres-absolute \mathrm{[ata]}. The depth factor indicates how much additional ambient pressure there is from depth. \mathrm{33\ [ft]} of sea water is equivalent to \mathrm{1\ [atm]} of gauge pressure. Assuming that our computer tells us the average depth was \mathrm{50\ [ft]},

    \[ \begin{split} D_{factor} &= \left(\dfrac{depth_{average}}{\mathrm{33\ [ft/atm]}}\right) + \mathrm{1\ [atm]} \\ D_{factor} &= \left(\dfrac{\mathrm{50\ [ft]}}{\mathrm{33\ [ft/atm]}}\right) + \mathrm{1\ [atm]} \\ &= \mathrm{2.515\ [ata]} \end{split} \]

We can now calculate the equivalent consumption rate of the cylinder at the surface in \mathrm{[psi/min]}:

    \[ \begin{split} SAC_{rate} &= \dfrac{ P_{rate} }{ D_{factor} }\\ &=  \mathrm{66.66\ [psi/min]} / \mathrm{2.515\ [ata]} \\ &= \mathrm{26.5\ [psi/min]} \end{split} \]

SAC_{rate} is only valid for comparing identical tanks, so we want to remove the influence of the cylinder and work out the volume of gas consumed. We want to know volume, so we use a tank factor (T_{factor}) to convert from pressure to volume. We know the rated pressure of the cylinder when it is full, at Pro Scuba Dive Center the Worthington High Pressure steel cylinders are pressurized to \mathrm{3442\ [psi]} when full with \mathrm{80\ [ft^3]}.

    \[ \begin{split} T_{factor} &= \dfrac{ Volume_{cylinder}  \mathrm{[ft^3]} }{ Pressure_{cylinder} \mathrm{[psi]}  } \\ &= \mathrm{80\ [ft^3]} / \mathrm{3442\ [psi]} \\ &= \mathrm{0.02324\ [ft^3/psi]} \end{split} \]

We can now convert the rate we are consuming cylinder pressure \mathrm{[psi/min]} to the rate we are consuming gas volume \mathrm{[ft^3/min]} using the Tank Factor T_{factor}:

    \[ \begin{split} RMV_{rate} &= SAC_{rate} * T_{factor} \\ &= \mathrm{26.5\ [psi/min]} * \mathrm{0.02324\ [ft^3/psi]} \\ &= \mathrm{0.62\ [ft^3/min]} \end{split} \]

You can use RMV_{rate} to calculate how long you expect any sized cylinder to last at any planned depth. For example, a low pressure \mathrm{3000\ [psi]} aluminium \mathrm{63\ [ft^3]} cylinder at a planned depth of \mathrm{50\ [ft]} with a RMV_{rate} of \mathrm{0.5\ [ft^3/min]}:

    \[ \begin{split} Duration &= \dfrac{ V_{cylinder} / RMV_{rate} }{ D_{factor} }  \\ &= \dfrac{ \mathrm{63\ [ft^3]} / \mathrm{0.5\ [ft^3/min]} }{ \left( \dfrac{\mathrm{50\ [ft]} }{ \mathrm{33\ [ft/ata]} } \right) +\mathrm{1\ [ata]} \right) }  \\ &= \mathrm{50.1\ [min]} \end{split} \]

(The cylinder is fully consumed with no reserve gas.)

We will practice calculating RMV_{rate} after every scuba dive when we log our dives. You can use the above equation, or an online calculator, or an app (iPhone or Android), or a slide wheel, or an abacus …

SAC_{rate}  is often confused with Respiratory Minute Volume (RMV_{rate}), they are not the same thing. RMV_{rate} is more useful for gas planning because it applies to any sized tank

Some things to be aware of are:

  • You can only use RMV_{rate} to compare two dives of similar workload. If you use RMV_{rate} to plan how long you expect a cylinder to last you at a given depth, you need to be conservative to account for possibly swimming harder, more currents, being cold (consumes more oxygen), anxiety of an unfamiliar dive driving faster breathing, etc.
  • You cannot use the above equation for metric tanks, they are measured differently and the tank volume does not mean the same thing. It is not sufficient to convert \mathrm{[psi]} to \mathrm{[bar]} and \mathrm{[ft^3]} to \mathrm{[liter]}s.
    For the sake of comparison \mathrm{0.5\ [ft^3/min]} is an example of a low RMV_{rate} and \mathrm{1.0\ [ft3/min]} is a high RMV_{rate}.
  • Smaller people often require less air (oxygen) to sustain their smaller bodies under the same conditions.
  • Performing drills and exercises in a class is not a good indicator of true RMV_{rate} because a lot of gas is vented by regularly inflating and deflating the BC, not to mention free-flows 🙂 You will get a more accurate measurement from the fun dives on the final day of class.
  • Remember that SAC_{rate} and RMV_{rate} are equivalent surface pressure values, at \mathrm{99\ [ft]} you will consume gas 4 times faster!


Calculate the \boldsymbol{SAC_{rate}} and \boldsymbol{RMV_{rate}} for a training dive, avg depth \mathrm{20\ [ft]} for \mathrm{30\ [min]}. The diver is using a Worthington HP steel cylinder \mathrm{80\ [ft^3]} at \mathrm{3442\ [psi]}. The diver begins with a full cylinder and ends with \mathrm{1800\ [psi]}.

    \[ \begin{split} P_{rate} &= \dfrac{ \left(  P_{start}\hspace\mathrm{[psi]} - P_{end}\hspace\mathrm{[psi]} \right) }{ T_{dive}\hspace\mathrm{[min]} } \\ P_{rate} &= \dfrac{ \left( \mathrm{3442\ [psi]} - \mathrm{1800\ [psi]} \right) }{\mathrm{20\ [min]} } \\ &= \mathrm{1642\ [psi]} / \mathrm{30\ [min]} \\ &= \mathrm{54.73\ [psi/min]} \end{split} \]

    \[ \begin{split} D_{factor} &= \left(\dfrac{depth_{average}}{\mathrm{33\ [ft/atm]}}\right) + \mathrm{1\ [atm]} \\ D_{factor} &= \left(\dfrac{\mathrm{20\ [ft]}}{\mathrm{33\ [ft/atm]}}\right) + \mathrm{1\ [atm]} \\ &= \mathrm{1.606\ [ata]} \end{split} \]

    \[ \begin{split} T_{factor} &= \dfrac{ Volume_{cylinder}  \mathrm{[ft^3]} }{ Pressure_{cylinder} \mathrm{[psi]}  } \\ &= \mathrm{80\ [ft^3]} / \mathrm{3442\ [psi]} \\ &= \mathrm{0.02324\ [ft^3/psi]} \end{split} \]

    \[ \begin{split} \boldsymbol{SAC_{rate}} &= \dfrac{ P_{rate} }{ D_{factor} }\\ &=  \mathrm{54.73\ [psi/min]} / \mathrm{1.606\ [ata]} \\ &= \boldsymbol{\mathrm{34.07\ [psi/min]}} \end{split} \]

    \[ \begin{split} \boldsymbol{RMV_{rate}} &= SAC_{rate} * T_{factor} \\ &= \mathrm{34.07\ [psi/min]} * \mathrm{0.02324\ [ft^3/psi]} \\ &= \boldsymbol{\mathrm{0.791\ [ft^3/min]}} \end{split} \]