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 (
.
To find our physiological rate we need to account for varying depth, and measure independently of cylinder size. We use the Respiratory Minute Volume (
), that is the amount of gas that we breathe per minute at the surface. Taking 10 breaths at
(
) would be the same as taking 30 identical breaths at the surface (
at sea level). Another problem is that we measure pressure, but this needs to be converted to an actual volume of air.
Symbol | Variable | Description |
SACrate | Surface Air Consumption rate [psi/min] | The equivalent rate that the cylinder is consumed at the surface without depth pressure. |
RMVrate | Respiratory Minute Volume rate [ft3/min] | The equivalent volume of gas in cubic feet, consumed at the surface. |
Prate | Pressure rate [psi//min] | The rate of gas consumption at depth, as measured by a pressure gauge. |
Dfactor | Depth factor [ata] | How much consumption is increased by due to depth pressure. |
Tfactor | Tank factor [ft3/psi] | A tank-specific number to convert tank pressure [psi] to gas volume in cubic feet [ft3]. |
Vcylinder | Tank volume [ft3] | The volume of gas in the cylinder |
The equations we need are:
(1) ![Rendered by QuickLaTeX.com \begin{equation*} % use "\text" in an equation* environment and "\mathrm" outside SAC_{rate} = \dfrac{ P_{rate} }{ D_{factor} } \hspace\textup{[psi/min]} \end{equation*}](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-624590481cfbd99abbcc9e8dba996a15_l3.png)
(
is specific to each cylinder, probably between
)
(2) ![Rendered by QuickLaTeX.com \begin{equation*} RMV_{rate} = SAC_{rate} * T_{factor} \hspace\textup{[ft^3/min]} \end{equation*}](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-00927943d8c86297a98b805643eb33a8_l3.png)
is our actual physiological consumption rate, approximately
)
We start with a pressure rate (
), say consuming
at an average depth of
for
. 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
or
will be higher. Fancy computers can provide average depth, but the Subgear XP10 rental computer does not.
![Rendered by QuickLaTeX.com \[ \begin{split} P_{rate} &= \dfrac{ \left( P_{start}\hspace\mathrm{[psi]} - P_{end}\hspace\mathrm{[psi]} \right) }{ T_{dive}\hspace\mathrm{[min]} } \\ &= \mathrm{2000\ [psi]} / \mathrm{30\ [min]} \\ &= \mathrm{2000\ [psi]} / \mathrm{30\ [min]} \\ &= \mathrm{66.66\ [psi/min]} \end{split} \]](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-248ef5a0dd53fe4a74c918bfe4d66d0f_l3.png)
Our depth 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
. The depth factor indicates how much additional ambient pressure there is from depth.
of sea water is equivalent to
of gauge pressure. Assuming that our computer tells us the average depth was
,
![Rendered by QuickLaTeX.com \[ \begin{split} D_{factor} &= \left(\dfrac{depth_{average}}{\mathrm{33\ [ft/atm]}}\right) + \mathrm{1\ [atm]} \\ D_{factor} &= \left(\dfrac{\mathrm{50\ [ft]}}{\mathrm{33\ [ft/atm]}}\right) + \mathrm{1\ [atm]} \\ &= \mathrm{2.515\ [ata]} \end{split} \]](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-afdf665ff34f5de24d320cadd6cb6fcb_l3.png)
We can now calculate the equivalent consumption rate of the cylinder at the surface in
:
![Rendered by QuickLaTeX.com \[ \begin{split} SAC_{rate} &= \dfrac{ P_{rate} }{ D_{factor} }\\ &= \mathrm{66.66\ [psi/min]} / \mathrm{2.515\ [ata]} \\ &= \mathrm{26.5\ [psi/min]} \end{split} \]](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-c9d79797759bf5fd67bea6a1dddbc2a1_l3.png)
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 (
) 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
when full with
.
![Rendered by QuickLaTeX.com \[ \begin{split} T_{factor} &= \dfrac{ Volume_{cylinder} \mathrm{[ft^3]} }{ Pressure_{cylinder} \mathrm{[psi]} } \\ &= \mathrm{80\ [ft^3]} / \mathrm{3442\ [psi]} \\ &= \mathrm{0.02324\ [ft^3/psi]} \end{split} \]](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-7a824d4762b499cf181e29822d0599b6_l3.png)
We can now convert the rate we are consuming cylinder pressure
to the rate we are consuming gas volume
using the Tank Factor
:
![Rendered by QuickLaTeX.com \[ \begin{split} RMV_{rate} &= SAC_{rate} * T_{factor} \\ &= \mathrm{26.5\ [psi/min]} * \mathrm{0.02324\ [ft^3/psi]} \\ &= \mathrm{0.62\ [ft^3/min]} \end{split} \]](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-73855b0a4d860ae703850d2feb2d80f1_l3.png)
You can use
to calculate how long you expect any sized cylinder to last at any planned depth. For example, a low pressure
aluminium
cylinder at a planned depth of
with a
of
:
![Rendered by QuickLaTeX.com \[ \begin{split} Duration &= \dfrac{ V_{cylinder} / RMV_{rate} }{ D_{factor} } \\ &= \dfrac{ \mathrm{63\ [ft^3]} / \mathrm{0.5\ [ft^3/min]} }{ \left( \dfrac{\mathrm{50\ [ft]} }{ \mathrm{33\ [ft/ata]} } \right) +\mathrm{1\ [ata]} \right) } \\ &= \mathrm{50.1\ [min]} \end{split} \]](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-af8094240491e06329cf3f354afc83fe_l3.png)
(The cylinder is fully consumed with no reserve gas.)
We will practice calculating
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 …
is often confused with Respiratory Minute Volume (
), they are not the same thing.
is more useful for gas planning because it applies to any sized tank
Some things to be aware of are:
- You can only use
to compare two dives of similar workload. If you use
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
to
and
to
s.
For the sake of comparison
is an example of a low
and
is a high
.
- 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
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
and
are equivalent surface pressure values, at
you will consume gas 4 times faster!
Examples
Calculate the
and
for a training dive, avg depth
for
. The diver is using a Worthington HP steel cylinder
at
. The diver begins with a full cylinder and ends with
.
![Rendered by QuickLaTeX.com \[ \begin{split} P_{rate} &= \dfrac{ \left( P_{start}\hspace\mathrm{[psi]} - P_{end}\hspace\mathrm{[psi]} \right) }{ T_{dive}\hspace\mathrm{[min]} } \\ P_{rate} &= \dfrac{ \left( \mathrm{3442\ [psi]} - \mathrm{1800\ [psi]} \right) }{\mathrm{20\ [min]} } \\ &= \mathrm{1642\ [psi]} / \mathrm{30\ [min]} \\ &= \mathrm{54.73\ [psi/min]} \end{split} \]](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-2c03bfa6c965a1cb754f802bffacb120_l3.png)
![Rendered by QuickLaTeX.com \[ \begin{split} D_{factor} &= \left(\dfrac{depth_{average}}{\mathrm{33\ [ft/atm]}}\right) + \mathrm{1\ [atm]} \\ D_{factor} &= \left(\dfrac{\mathrm{20\ [ft]}}{\mathrm{33\ [ft/atm]}}\right) + \mathrm{1\ [atm]} \\ &= \mathrm{1.606\ [ata]} \end{split} \]](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-3f9f7947b901c7c648fa8faad8c0d243_l3.png)
![Rendered by QuickLaTeX.com \[ \begin{split} T_{factor} &= \dfrac{ Volume_{cylinder} \mathrm{[ft^3]} }{ Pressure_{cylinder} \mathrm{[psi]} } \\ &= \mathrm{80\ [ft^3]} / \mathrm{3442\ [psi]} \\ &= \mathrm{0.02324\ [ft^3/psi]} \end{split} \]](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-7a824d4762b499cf181e29822d0599b6_l3.png)
![Rendered by QuickLaTeX.com \[ \begin{split} \boldsymbol{SAC_{rate}} &= \dfrac{ P_{rate} }{ D_{factor} }\\ &= \mathrm{54.73\ [psi/min]} / \mathrm{1.606\ [ata]} \\ &= \boldsymbol{\mathrm{34.07\ [psi/min]}} \end{split} \]](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-dc4d6199c52a52d50ad86c36caab7fad_l3.png)
![Rendered by QuickLaTeX.com \[ \begin{split} \boldsymbol{RMV_{rate}} &= SAC_{rate} * T_{factor} \\ &= \mathrm{34.07\ [psi/min]} * \mathrm{0.02324\ [ft^3/psi]} \\ &= \boldsymbol{\mathrm{0.791\ [ft^3/min]}} \end{split} \]](http://www.dankelly.net:443/wordpress/wp-content/ql-cache/quicklatex.com-5ad3333b5344b12c7896977d9068d3ad_l3.png)
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