**Estimating
Air (Breathing Gas) Consumption
**

by

Larry
"Harris" Taylor, Ph.D.

*This
is an electronic reprint of an article that appeared in SOURCES (Jan/Feb.
1995, p. 51-54.) This material is copyrighted and the author retains all
rights. This material is made available as a service to the diving community
by the author. This article may be distributed for any non-commercial or
Not-For-Profit use.
*

*All
Rights Reserved.
*

**Go
To Site Page: Home
About "Harris"
Articles War
Stories Biblios
Editorials Links
Site Map Fini**

**Jump To: Known Consumption
Boyle Measuring
SAC Pressure
Factors Volume Factors**

Boyle's
law indicates there is less volume of gas available to the diver as the diver
descends in the water column. The actual volume of gas within a scuba cylinder
does not decrease (all of the gas molecules have not been confined to the
bottom of the tank); the tank physically does not shrink under pressure.
However, gas being delivered to the diver is at ambient pressure. This
increased pressure means more gas molecules per unit volume (the gas is more
dense). Since the diver consumes more molecules per breath (constant volume
breathing), the gas in the scuba cylinder will last a shorter amount of time.
Although gas consumption can be affected by numerous factors (such as physical
size, work load, water temperature, use of drugs, anxiety from seeing that 14
ft hammerhead shark, excitement of watching the grace of a large manta ray,
general physical and emotional condition), it can be approximated. The best
approximation comes from personal experience (knowledge of individual gas
consumption rates). It has been stated that the "average" diver (I
personally have never met or known this person!) consumes gas at a surface
consumption rate of one cubic foot (28.3 l) per minute. Since individual gas
consumption rates will change within each diver based on personal comfort,
physical fitness maintenance, and experience, individual surface consumption
rates may vary and MUST BE determined from personal observation.

*The
gas consumption rates in this unit, for purposes of illustration, have
intentionally been made excessive to magnify the decrease in available time at
deeper depths.*

If the average rate of consumption is already known, then this value can be used to determine the duration of any cylinder. This is best demonstrated by numerical example. For our so-called "average diver:"

**EXAMPLE**:
Determine the "Average" duration of an 80 ft^{3} (2266 l)
cylinder at 99 fsw (30.2 msw) for that "average diver" (1 ft^{3}
/min; 28.3 l/min) using an 80 cubic foot (2266 l) cylinder:

a.
estimate the surface duration time:

** Surface
duration =
Volume of cylinder / Consumption
rate**:

Surface duration at one ata

**
****ENGLISH
**

**
**

__80 ft__^{3
}= 80
minutes^{
}

1 ft^{3}/ min

**
METRIC**

__2266 l__ = 80 minutes

28.3 l/min

Convert
the surface duration to an at-depth ESTIMATE:

*First,
determine the ambient pressure at depth*

For our "average diver" at 99 fsw (20.2 msw)

Hydrostatic pressure at depth:

__99 fsw__
= 3 atm

33 fsw/atm

*Next,
determine the absolute pressure at depth (Remembering that gas law problems
require pressure to be expressed in absolute terms)**
*

**ENGLISH:**
Absolute pressure at depth: 3 atm + 1 atm
= 4 ata

**METRIC:**
Absolute pressure at depth:
= 4 bar

To Avoid Confusion As To Whether The "Bar" Is Cylinder Or Water Pressure, We Will Use Ata For Water Pressure And Bar For Cylinder Pressure In The Metric Gas Consumption

Examples.

**Depth duration
= Surface duration **

**Pressure (ata) at
depth**

Depth
duration = __80 minutes at
one ata__

4 ata

Depth
duration =
20 minutes at 4 ata

**Reminder:
Breathing 80 ft ^{3} (2266 l) from an 80 ft^{3} (2266 l) scuba
cylinder would consume the entire contents of the cylinder. This is most
unwise, particularly at depth! Regardless of any calculated numbers, divers
must remember to monitor their gas supply gauges and to begin ascent with
adequate gas for the ascent plus safety stop. Thus, in the example above,
"common sense" would tell the diver that the actual dive time at 80
fsw would be less than the calculated value of 20 minutes.**

**Calculations
Analogous to Boyle's Law
**

If time at a
specific depth is already known (the diver has verified individual consumption
by recording pressure, depth, and time values), then there is a
"short-cut" to the two step process outlined above.
This method assumes that ALL factors, except absolute pressure that
govern gas consumption are equivalent at various depths. If breathing is a
constant volume process, then the amount of time available to the diver will
be related to the available volume of the breathing gas. This volume is
inversely proportional to absolute pressure. In other words, a
"form" of Boyle's law can be used to calculate APPROXIMATE gas
consumption rates. Under this assumption:

*(Duration
1) (Pressure 1) = (Duration 2) (Pressure 2)
*

**EXAMPLE:**
A diver's gas supply lasts 60 minutes at 33 (10.1 m) feet. Assuming the same
gas consumption rate, how long will the gas supply last the diver at 99 fsw
(30.2 msw)? (*Again,**Remember, absolute pressure MUST be
used.)
*

Hydrostatic pressures at depth:

__33
fsw__ =
1 atm __99 fsw__
=
3 atm

33
fsw/atm
33 fsw/atm

Absolute
(hydrostatic plus atmospheric) pressures at depth:

1
atm + 1 atm = 2 ata
3 atm + 1 atm = 4 ata

Since:

*
(Duration
1) P1 = (Duration 2) P2*

Substituting
appropriate values for this example:

(60
min) (2 ata) = (Duration 2) (4 ata)

Solving:

Duration
2 = 30 minutes

**REMINDER:
At deeper depths, a wise diver would have less time than the prediction since
a larger safety reserve would be appropriate (ascent would start at a higher
gas supply pressure).**

The
above calculations assumed that the diver either consumed gas at an
"average" rate OR that some estimation of duration had already been
determined. However, gas consumption is individual. Thus, each diver, to
utilize gas consumption values in personal dive planning, must determine
individual rates of gas consumption. Individual gas consumption can be
determined in the following manner:

The
diver descends to a known depth (measured by a marked, weighted line.) At a
recorded depth, the diver remains stationary while recording psig (bar)
consumed over a fixed length of time. (The longer the time interval, the more
representative of the diver the consumption rate in terms of pressure consumed
per minute will be.) This represents a "resting" rate (pressure
consumed/minute) of gas consumption. Since swimming (physical labor or any
stressor) will increase gas consumption, the rate of gas consumption should
also be determined under work load. One method uses a marked line (about 100
ft; 30 m) rigged at constant depth. The diver swims lengths along the line.
The diver monitors number of "kick cycles" (a "cycle" is
each time a diver kicks with both legs; it is routinely measured as each time
one particular leg goes below the plane of the body) and the gas consumed (in
terms of psi or bar per 100 ft (30 m) of line).
The dive buddy measures the time it takes to swim the length of the
line. At the end of each length, the diver records "kicks," and psig
(bar) consumed; the buddy records the time. After swimming several lengths of
the line, the divers switch roles. At the end of this exercise, both divers
will know the average number of kicks, amount of time, and the amount of gas
consumed to travel 100 feet. If the diver wishes to estimate a more realistic
"under work stress" consumption rate, then the diver swims the
length of line while towing a float that has a 10 pound anchor attached.

**EXAMPLE**:
After swimming several lengths of a 100 foot line at a depth of 33 fsw (2 ata),
a diver has consumed an average of 50 psig (3.4 bar) per length. The diver
took 1 minute on average to swim this length. What is the surface consumption
rate?

**ANSWER**:
At depth, this diver consumed 50 psig/min (3.4 bar/min). On the surface, where
absolute pressure is less, the density of the available breathing gas will be
less (Boyle's Law), so the diver has more volume to breathe. So, the diver
will consume less psig (bar) per minute. The amount of increase will be
representative of this change in density described by Boyles's Law.

Thus:

__Surface
Consumption__
=
__Surface Absolute Pressure__

*
At Depth Gas Consumption
At Depth Absolute Pressure
*

Substituting for this particular diver:

**ENGLISH:**

__Surface Gas Consumption__
= __ 1 ata
__

50 psig/min
2 ata

Surface Gas Consumption =
25 psig/min

**METRIC:**

__Surface Gas Consumption__
= __1 ata
__

3.4 bar/min 2 ata

Surface
Gas Consumption = 1.7
bar/min

The
value we have just determined, the Surface Gas Consumption Rate (SAC), can be
utilized in a variety of ways to assist the diver in planning dives.

If
the diver monitors gas consumption (in terms of psig or bar consumed), the
duration of the dive, and holds a constant monitored depth, then an average
rate of gas consumption at depth (in terms of psig/ata-min or bar/ata-min;
analogous to miles per gallon or km per liter in a car) can be calculated.
This rate of consumption (psig/min or bar/min) can then be converted to a
surface psig/min (bar/min) value based on the assumptions of Boyle's Law. This
value is called the SAC (Surface Gas Consumption) Rate.

**EXAMPLE:**
A diver consumes 200 psig/min (13.7 bar/min) at 99 fsw (10.2 msw, 4 ata); what
is this diver's SAC?

**ANSWER:**
SAC rate is expressed in terms of psig per minute (bar/min) at some
measurement of pressure. Conversion to surface (or any other depth)
consumption is then merely a function of determining absolute pressure at
depth desired:

*First,
determine the absolute gas consumption (in terms of pressure):*

**ENGLISH**
__200 psig__
= 50 psig /
ata-min

4 ata-min

**METRIC:**
__13.7 bar__
= 3.4
bar/ ata-min

4 ata-min

Then, since the surface pressure is 1 ata, the ENGLISH SAC value is:

50
psig/ata-min x
1 ata/min =
50 psig/min

The metric SAC equivalent in this example is 3.4 bar/min.

An individual
diver's absolute gas consumption can then be used to estimate the gas
consumption at any other depth.

**EXAMPLE**:
Calculate gas consumption at 132 fsw (10.5 msw) using the above diver's
absolute gas consumption rate:

**ANSWER:**
*Convert the absolute consumption rate to an at-depth consumption rate:*

First,
as above, convert depth to an absolute pressure; 132 fsw (10. 5 msw)
= 5 ata

*Then,
convert the absolute consumption rate to an at-depth rate *

**ENGLISH:**
__50 psig__
x 5 ata
= 250 psig/min

ata-min

**METRIC:
**__3.4
bar__
x 5 ata
= 17 bar/min

ata-min

**REMEMBER: The deeper
the depth, the more rapid the gas in a scuba cylinder is consumed!**

The
absolute gas (in terms of pressure) consumption rate can be used to estimate
duration of the dive.

**ENGLISH
EXAMPLE**:
A diver has an absolute pressure gas consumption of 50 psig/ata-min. The diver
wishes to begin ascent at 1000 psig. Assuming the diver reaches the desired
depth with 2800 psig, determine the duration of the dive at both 33 and 99 fsw.

**ANSWER:**
*Determine the amount of gas available for the planned conditions of the
dive*

2800
psig - 1000 psig = 1800 psig for the dive.

*Next,
convert the cylinder pressure reading to duration using absolute SAC:
*

For
33 fsw (2 ata):

1800
psig x
__1 ata-min__ x __
1 __ =
18 minutes

50 psig
2 ata

For 99 fsw (4 ata):

1800
psig x
__1 ata-min__ x
__1 __
=
9 minutes

50 psig 2 ata

**METRIC
EXAMPLE:**
A diver has an absolute SAC rate of 3.4 bar/ata-min. Assume the diver begins
dive with a gauge reading of 200 bar and wishes to begin ascent at 70 bar. How
long will the diver be able to dive at 10 msw (2 ata) and 20 msw (3 ata)?

**ANSWER**:
*Determine the amount of gas available for the planned conditions of the
dive*

200
bar - 70 bar = 130 bar for the dive.

*Next,
convert the cylinder pressure reading to duration using absolute SAC:*

For
10 msw:

130 bar
x __1 ata-min__
x __ 1
__ = 19 minutes

3.4 bar
2 ata

For
20 msw

130 bar
x __1 ata-min__
x __
____1 __
= 13 minutes

3.4 bar
3 ata

Again, The deeper the dive, the shorter
the duration of gas supply!

There
is a circular slide rule device (SAC calculator) based on the above procedure
in English units available from several different recreational training
agencies for doing these calculations. The diver monitors depth, pressure
used, and time. These values are selected on a circular scale to give a SAC
rate. This SAC rate (in terms of psig/fsw-min) can be used to estimate gas
consumption at various depths.

Calculations
based on cylinder pressure changes will vary when different scuba cylinder
sizes are used. For example, a 1500 psig (102 bar) change in a 14 cubic foot
(416 l) pony bottle is NOT the same volume of gas as a 1500 psig (102 bar)
change in an 80 cubic foot (2266 l) aluminum cylinder. Therefore, divers must
insure that their absolute gas consumption factor (based on psig or bar
consumed) is used ONLY with the cylinder size for which the SAC value was
determined. Those using SAC devices will find conversion factors for various
cylinders on their particular device. (Later, in this section we will
demonstrate how these conversion factors are determined.) This difference is
best illustrated by numerical example.

**EXAMPLE:**
Determine the volume of gas represented by a 1500 psig (102 bar) change in the
following scuba cylinders: an aluminum "80" (2266 l), a steel
"71.2" (2016 l) and an aluminum "14" (416 l).

**ANSWER**:
*The volume of gas available from a fixed volume cylinder will be directly
proportional to the absolute pressure. Converting
gauge pressure to absolute*:

1500
psig = 1514.7 psia (102 bar)

3000 psig = 3014.7 psia (205 bar)

2475 psig = 2489.7 psia (169 bar)

2015 psig = 2029.7 psia (138 bar)

For
the aluminum 80 (80 cubic feet of gas at 3014.7 psia):

Setting up the direct proportion:

__3014.7 psia__ =
__1514.7 psia__

80 ft^{3}
V2

Solving:

V2 =
40.2 ft^{3}
(1138 l)

For
the steel "72" (71.55 cubic feet of gas at 2489.7 psia):

__2489.7 psia__
= __1514.7
psia__

71.55 ft^{3}
V2

Solving:

V2 = 43.5 ft^{3}
(1232 l)

For
the aluminum pony bottle (14.06 cubic feet at 2029.7 psia):

__2029.7 psia__ = __1514.7
psia__

14.06 ft^{3}
V2

Solving:

V2 =
10.5 ft^{3}
(297 l)

So,
a diver using 1500 psig (102 bar) would respectively consume 40.2 cubic feet
(1138 l) with an aluminum "80," 43.5 cubic feet (1232 l) with a
steel "72" or 10.5 cubic feet (297 l) with an aluminum
"14" pony. This is why the same pressure-based (psig or bar)
consumption factors cannot be used for scuba cylinders of different volumes.

The
SAC method, in essence, uses psig or bar as a measurement of volume consumed.
The numerical value of the absolute gas consumption factor (in terms of psig
consumed/min or bar/min) will vary with the size of the cylinder used.
However, if the volume of tank for which this psig/min (bar/min) determination
is known, then this absolute gas consumption value may be converted to an
absolute volume consumption factor. The advantage of this is that volume
consumed is independent of the size of the breathing gas supply. Thus, the
same factor can be used in dive planning for a variety of different sources of
breathing gas.

**ENGLISH
EXAMPLE**:
Above, when using an aluminum "80," a diver had an absolute gas
consumption of 50 psig/ata-min. Convert this to a volume measurement knowing
that an "80" contains 79.87 cubic feet of gas at a pressure of 3000
psig.

**ANSWER:
***Convert
pressure factor to volume factor by appropriate multiplication. Examination of
the units of the pressure factor indicates the arrangement of the cylinder
volume and pressure to obtain the appropriate volume factor:
*

__ 50 psig__ x
__79.87 ft__^{3}
= 1.33 ft^{3 }/ata-min

ata-min 3000 psig

**METRIC
EXAMPLE**:
A diver's scuba cylinder has a rating of 2400 l at 200 bar. Using the metric
absolute SAC value from the above example (3.4 bar/ata- min), determine the
absolute volume value.

**ANSWER:**
*Convert pressure factor to volume factor using cylinder values:*

__3.4 bar__ x
__2400 l__
= 40.8 l /ata-min

ata-min
200 bar

This
Volume measurement can then be used to determine either the duration of a dive
(knowing the volume of gas available) or the volume of gas needed to conduct a
particular dive.**
**

**ENGLISH
EXAMPLE**:
How much gas is required to allow a diver with the above absolute volume
consumption factor (1.33 cubic feet/ata-min) to dive to an ocean depth of 66
feet (3 ata) for 45 minutes?

**ANSWER**:
*Use the volume factor and multiply values to obtain a volume:
*

__1.33
ft ^{3}__

ata-min

**COMMENT**:
Obviously, this diver is NOT able to make this dive with a typical single
scuba cylinder

**METRIC
EXAMPLE**:
How much gas is required for a diver with the above absolute volume
consumption factor (40.8 l/ata-min) to dive to an ocean depth of 30 meters (4
ata) for 15 minutes?

**ANSWER**:
*Use the volume factor and multiply the conditions given in the problem to
obtain a volume:*

__40.8
l __ x
4 ata x
15 min = 2448 l

ata-min

**Comment:
Examination of the gas consumption of this diver should indicate that this
dive on a single 2400 l cylinder would be most unwise!**

**ENGLISH
EXAMPLE**:
How long will a diver with an absolute volume consumption factor of 1.33 cubic
feet/ata-min take to consume 60 cubic feet of gas at an ocean depth of 33 feet
(2 ata)?

**ANSWER**:
*Use the volume factor; use the conditions desired to arrive at a duration:*

60 ft^{3}
x __1 ata-min__ x
__ 1
__ =
22.6 minutes

1.33 ft^{3}
2 ata

**METRIC
EXAMPLE**:
How long will it take a diver with the absolute volume consumption factor of
40.8 l/ata-min to consume 1200 l at an ocean depth of 30 meters (4 ata)?

**ANSWER**:
*Use the volume factor and conditions desired to obtain a duration:*

1200 l
x __1 ata-min__
x __
____1 __
=
7.35 minutes

40.8
l
4 ata

Remember,
the absolute volume consumption factor is independent of scuba cylinder
volume. It can also be used to calculate an absolute pressure consumption (in
terms of psig or bar/min) for any sized cylinder. Again, this is best
illustrated by numerical example.

**ENGLISH
EXAMPLE**:
A diver has an absolute volume consumption of 1.33 ft^{3} / ata-min.
Determine this diver's absolute pressure consumption factor for an aluminum
"80" (80.70 cubic feet at 3000 psig), a steel "72" (71.55
cubic feet at 2475 psig) and a steel "50" (52.14 cubic feet at 2475
psig)

**ANSWER:**
*Start with absolute volume consumption rate; convert to units of pressure
consumed based on individual tank characteristics*.

For
the "80" cylinder:

__1.33 ft ^{3}__
x

ata-min
80.7 ft^{3}

For the "72" cylinder:

__
1.33 ft ^{3}__
x

ata-min
71.44 ft^{3}

For the "50" cylinder:

__1.33 ft ^{3}__
x

ata-min
52.14 ft^{3}

When estimating consumption based on pressure, it is imperative that the pressure factor calculated is based on the size of the cylinder used. The smaller the cylinder, the higher the psig consumption per minute.

**METRIC
EXAMPLE**:
A diver has an absolute volume consumption of 40.8 l/ata- min. Determine the
absolute pressure consumption for this diver when using a cylinder rated at
3105 l (207 bar) and a cylinder rated at 1000 l (200 bar).

**ANSWER**:
*Start with the absolute volume consumption and use individual cylinder
characteristics to determine an absolute pressure consumption for that sized
cylinder.*

For
the "3105 l" cylinder:

__40.8
l__ x
__207 bar__ =
2.72 bar/ata-min

ata-min
3105 l

For
the "1000 l" cylinder:

__ 40.8
l__ x
__200 bar__ =
8.16 bar.ata-min

ata-min
1000 l

**BOTTOM
LINE:**
Divers must learn to think in terms of volume (cubic feet or liters) of gas
consumed at an absolute pressure!. Calculations are used primarily for
planning dives. Divers should remember to include additional time (volume) for
ascent and safety stops. Finally, regardless of what the calculations have
determined, there is **NO SUBSTITUTE** for monitoring actual gas
consumption at depth using the submersible pressure gauge.

**Jump
To: Known Consumption
Boyle Measuring
SAC Pressure
Factors Volume Factors**

**Go
To Site Page: Home
About "Harris"
Articles War
Stories Biblios
Editorials Links
Site Map Fini**

**Credit:**

Portions of this article were used in my chapter on Dive Physics appearing in:

Bove
and Davis' Diving Medicine (4 ^{th} Edition), published by Saunders
(Elsevier)

**About
The Author:
**

Larry
"Harris" Taylor, Ph.D. is a biochemist and scuba instructor at the
University of Michigan. He has authored more than 100 scuba related articles.
His personal dive library (See Alert Diver, Mar/Apr, 1997, p. 54) is
considered by many as one of the best recreational sources of information in
North America.

All rights reserved.

Use of these articles for personal or organizational profit is specifically denied.

These articles may be used for not-for-profit diving education