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.

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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 Consumption Rate Is Known

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 ft3 (2266 l) cylinder at 99 fsw (30.2 msw) for that "average diver" (1 ft3 /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 ft3              =  80 minutes

1 ft3/ 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 ft3 (2266 l) from an 80 ft3 (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:

Measuring Consumption Rate

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.

SAC CALCULATIONS

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.

Cylinder Pressure Factors

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 ft3                     V2

Solving:

V2 =  40.2 ft3  (1138 l)

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

2489.7 psia    =        1514.7 psia

71.55 ft3                     V2

Solving:

V2 =  43.5 ft3  (1232 l)

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

2029.7 psia    =        1514.7 psia

14.06 ft3                   V2

Solving:

V2 =  10.5 ft3  (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.

Cylinder Volume Factors

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 ft3    =   1.33 ft3 /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 ft3      x   3 ata  x  45 min  = 179.6 ft3

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 ft3   x 1 ata-min   x    1            = 22.6 minutes

1.33 ft3        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 ft3 / 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  ft3    x   3000 psig   =    49.4  psig/ata-min

ata-min          80.7 ft3

For the "72" cylinder:

1.33 ft3     x   2475 psig   =    46.1  psig/ata-min

ata-min          71.44 ft3

For the "50" cylinder:

1.33 ft3    x   2475 psig   =    63.13  psig/ata-min

ata-min         52.14 ft3

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.

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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)

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.

Copyright 2001-2004 by Larry "Harris" Taylor