This is an electronic reprint of an article that appeared in SOURCES
(Sept/Oct. 1994). It is part of the diving physics chapter of NAUi's
Advanced text, Mastering Advanced Diving. This material is copyrighted
and all rights are retained by the author. This material is made available
as a service to the diving community by the author and may be distributed
for any non-commercial or Not-For-Profit use.

Depth gauges DO NOT MEASURE water depth! They measure pressure.
Inside the device, a mechanical mechanism, coupled with a printed scale
on the face of the instrument converts a measured pressure into an
equivalent scale reading for water depth. The gauge will be accurate
only if it is used in the environment for which it has been calibrated.
When the device is taken to a different environment, such as high
altitude, the reading of water depth on the gauge may be substantially
different from the actual measured water depth. This is most often a
problem when depth gauges calibrated at sea level are taken to altitude,
as illustrated by the following numerical example.

*EXAMPLE:* You are diving at a high altitude mountain lake. The barometer
reads 24.61 inches (625 mm) Hg. Thus, at this altitude, 24.61 inches
(625 mm) Hg (not 29.92 inches (760 mm) Hg) is the atmospheric pressure!
Consider also that high mountain lakes usually are filled with fresh
water (density about 62.4 lbs/cubic foot; 1.00 g/cc), not salt water
(density of 64 pounds/cubic foot; 1.03 g/cc). What will the depth gauge
read at an actual depth of 60 ffw (18.29 m) in this lake?

*ENGLISH ANSWER:* First calculate the depth of water (x) that corresponds
to one atmosphere at the observed barometric pressure. Remember that
atmospheric equivalent height is inversely proportional to the density
of the fluid being used to measure pressure:

24.61 in Hg 1.0 g/cc
----------- = --------------
x in H20 13.6 g/cc
x = 334.7 inches water

*NOTE:* This means that one atmosphere of pressure at this altitude
corresponds to a water column depth of about 334 inches of water. In
feet:

334.7 in x 1 ft = 27.9 feet
------
12 in

Thus, every 27.9 feet of fresh water (not 33 fsw) at this altitude
corresponds to one atmosphere of pressure at this altitude.

At this altitude, a depth measured by a lead line (not gauge) of 60 feet
will be:

60 ffw = 2.15 atm
------------
27.9 ffw/atm

In terms of "at-altitude" atmospheres, the absolute pressure would be:

2.2 atm + 1 atm = 3.2 ata

This corresponds to a pressure of:

24.61 in Hg x 3.2 ata = 78.75 in Hg
-----------
ata

*NOTE:* The depth gauge "senses" a pressure corresponding to 78.75 in Hg.
The mechanism inside the device converts this pressure to:

78.75 in Hg = 2.63 sea level ata
--------------------------
29.92 in Hg/sea level ata

This would then correspond to a hydrostatic sea level pressure of:

2.6 ata - 1 atm = 1.6 atm

Which would be read on the sea level calibrated scale as:

1.6 atm x 33 fsw = 52.8 = 53 fsw
------
atm

So, for a measured depth was 60 feet, at this altitude, the sea
level calibrated gauge reads 53 feet.

*METRIC SOLUTION:*br>
Determine the water equivalent of one atmosphere at this altitude:

625 mm Hg 1.00 g/cc
----------- = --------------
x mm H20 13.6 g/cc
x = 8500 mm H20

This converts to:

8500 mm x 1 m = 8.5 m
-------
1000 mm

Thus, at this altitude, 8.5 m corresponds to 1 ata pressure.

At depth of 18.29 mfw, the hydrostatic pressure is:

18.29 m = 2.15 atm
----------
8.5 m/atm

This is an absolute "at altitude" pressure of:

2.2 atm + 1 atm = 3.2 ata

This means the gauge at this altitude is responding to a pressure of:

3.2 atm x 624 mm Hg = 1996.8 mm Hg
---------
atm

This corresponds to a sea level pressure of:

1996.8 mm Hg = 2.63 sea level ata
--------------------------
760 mm Hg/sea level ata

This would then correspond to a hydrostatic sea level pressure of:

2.6 ata - 1 atm = 1.6 atm

Which would be read on the sea level calibrated scale as:

1.6 atm x 10.1 m = 16.2 m
------
atm

So, the measured depth was 18.29 meters; the sea level depth gauge at
this altitude would read 16.2 m.

If the sea level calibrated gauge were to be used for extended
diving, then a series of corrections (generally at 10 foot (3 m)
increments) could be calculated to be added to in-water depth readings
for use at this altitude. True depth could then be determined by adding
this "correction factor" to the observed sea-level calibrated depth
gauge reading. Tables of these correction factors are available. (See,
for example: ALTITUDE PROCEDURES FOR THE DIVER, by C.L. Smith.)

*BOTTOM LINE:* Depth gauges measure pressure, not depth! The water
depth indicated on the gauge dial reflects the actual depth ONLY if used
in the environment for which the gauge was calibrated.

* OCEAN EQUIVALENT DEPTH (FOR DECOMPRESSION OBLIGATION)*

Decompression obligation (Dive Table) calculations are based on
pressure ratios, not actual measured in-water depths. Thus, when a diver
changes altitude, the diver must be careful about the decompression
tables and procedures used. Unless the dive table/computer specifically
states that it has procedures for varying altitudes, divers should
assume that the table/computer is only valid at sea level.

*Comment:* The following is a physics discussion on the method used to
obtain Ocean Equivalent Depth for use with sea level based tables. Such
conversions are not as desirable as using tables or computers
specifically designed for use at altitude.

Decompression procedures are based on some maximum theoretical
pressure ratio that can be tolerated within the tissue compartments
without injury to the diver. This amount of pressure may vary with the
depth of the diver and the particular mathematical simulation being
used. The important consideration is that the PRESSURE DIFFERENCE (i.e.,
ratio between the current pressure and the pressure at some more shallow
depth reached on ascent), not the actual water depth, controls the
decompression obligation. This is best illustrated with a numerical
example:

*EXAMPLE:* At the altitude above, one atmosphere of pressure corresponds
to 27.9 feet (8.5 m) of fresh water. Thus, the pressure at this altitude
would increase by 1 at-attitude-atm every 27.9 feet (8.5 m) of
descent/ascent (as opposed to every 33 feet (10.1 m) of sea water) at
sea level. This means every 27.9 feet (8.5 m) at this altitude would
correspond to a pressure (in terms of atmospheres) equivalent of 33 feet
(10.1 m) of sea water at sea level. So, to maintain approximately the
same pressure ratios as the U.S. Navy tables (or equivalent sea level
derived tables) for determining decompression obligations, one needs to
determine the actual number of "atmospheres pressure" at altitude and
convert this to a sea level salt water depth. For the high altitude dive
at 60 feet (18.29 m) (2.16 "altitude" atmospheres) example above:

ENGLISH: 2.16 atm x 33 fsw = 71.3 fsw
------
atm
METRIC: 2.16 atm x 10.1 msw = 21.8 msw
--------
atm

*NOTE:* In the above high altitude example. our actual in-water depth was
60 feet (18.3 m). The depth gauge indicated a depth of 53 fsw (16.2
msw). The equivalent sea level depth to maintain the same pressure
differential as the U.S. Navy Table between bottom depth and safe ascent
depth was 71.3 fsw (21.7 msw). Thus, using gauge pressure measured depth
at altitude to enter the sea level computed decompression tables would
allow the diver far more bottom time (increase risk to DCS) at depth
since the diver would be entering the table at too shallow a depth.

*EQUIVALENT ASCENT RATES*

Finally, ascent rates are part of the decompression calculations. US
Navy sea level tables ASSUME a rate of 60 fsw per minute. The BSAC
tables recommend an ascent rate of 15 m/min. This ascent rate is part of
the calculations used to derive the decompression schedules. Since, at
altitude, the actual amount of water column that "defines" one at-
altitude-atmosphere is less than 33 feet (10.1 m) of sea water, an
ascent in a high altitude mountain lake must be slower than an ascent
from the corresponding depth at sea level to maintain the same rate of
pressure change with time. Again, this is best illustrated with numbers.
For the example above:

At sea level; recommended ascent rate is:

ENGLISH: 60 fsw x 1 atm = 1.82 atm
------ ------- ----
min 33 fsw min
METRIC: 15 m x 1 atm = 1.49 atm
---- ------ ---
min 10.1 m min

At this altitude; corresponding at-altitude ascent rate:

ENGLISH: 1.82 atm x 27.9 ffw = 50.8 ffw
-------- -------- ----
min atm min
METRIC: 1.49 atm x 8.5 m = 12.7 m
--- --- ----
min atm min

Thus, while diving to a measured depth of 60 feet (18.29 m) in this high
altitude mountain lake, your pressure gauge would read 53 fsw (16.2 msw)
and your No-Stop decompression obligation would be determined by the 80
foot (24 m) sea level schedule using a recommended ascent rate of either
50.8 ffw/min or 12.7 mfw/min.

*BOTTOM LINE:* Sea level based dive procedures (tables or calculators) are
inadequate for determining decompression obligations at high altitude
dive sites. Divers at high altitudes (above 1000 feet; 300 meters)
should consider high altitude conversion tables (The Cross Tables) based
on the above technique, dive tables with variable altitude entries
(Swiss, DCIEM, or BSAC air tables) or altitude compensating dive
computers. Also, there is a high altitude ocean depth calculator
available from NAUI for determining ocean equivalent depths to use sea
level tables at altitude. In general, these methods are considered
theoretical, without extensive experimental validation. There is more
discussion in the altitude diving section of this textbook. However,
those who wish to dive at altitude should obtain specialty training in
high altitude diving procedures.

*Additional Reading:*

Bassett, B. "Diving And Altitude: Can They Be Mixed," Sport Diver, Sep/Oct. 1980, 120-124.

Egi, S. & Brubakk, A. "Diving At Altitude: A Review Of Decompression Strategies," Undersea & Hyperbaric Medicine, 22(3), 1995, 282-300.

Lenihan, D. & Morgan, K. HIGH ALTITUDE DIVING, US Dept. Interior, Santa Fe, NM. 1975, 23 pages.

Millar, I. "Post Diving Altitude Exposure," SPUMS, 26(2), June, 1996, 135-140.

Rossier, R. "Altitude Diving," Dive Training, August, 1995, 38-44.

Schwankert, S. "Going Up To Get Down," Discover Diving, February, 1996, .24-28.

Smith, C. ALTITUDE PROCEDURES FOR THE OCEAN DIVER, NAUI, Colton, CA. 1975, 46 pages.

Taylor, G. "Diving At Altitude," Immersed, Summer, 1997, 54-55.

Taylor, L. "Altitude Arithmetic," Sources, October, 1994, 42-44.

Wienke, B. HIGH ALTITUDE DIVING, NAUI, Montclair, CA> 1992, 40 pages.

*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.