by

Larry "Harris" Taylor, Ph.D.

*This is an
electronic reprint of an article that appeared in SOURCES (Sept/Oct. 1994). This
material is copyrighted and all rights retained by the author. This article 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.
*

*All
rights reserved.*

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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?

**ANSWER
(Using barometer in English units):** First calculate the depth of water (x)
that corresponds to one atmosphere at the observed barometric pressure. Remember
that the height of the fluid in a barometer is inversely proportional to the density of
the fluid (1.0 g/cc for water and 13.6 g/cc for mercury) being used to measure
the atmospheric pressure:

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

Thus, every
27.9 feet of fresh water (not 33 fsw or 34 ffw) 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:

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:

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

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:

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

**Answer
(Using metric units for the barometer heights)****:**

Determine the water equivalent of one atmosphere at this
altitude:

This converts
to:

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

At depth of 18.29 mfw, the hydrostatic pressure is:

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:

This corresponds to a sea level pressure
of:

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:

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 seawater 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:

**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:

At this
altitude; corresponding at-altitude ascent rate:

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.**
**

**Problem**

To test your understanding of the above discussion, consider
this scenario:

You have been commissioned by Indiana Jones to help recover a
sacred gold headpiece covered with emeralds. Indy’s map indicates that the
headpiece is located at the bottom of a high mountain lake. Indy will get you to
the lake. Your responsibility is to help plan the dive to the resting place of
the scared treasure.

By lead line, you determine that the actual physical depth of
the lake is 93 feet.

Unfortunately, while you were measuring the depth of the
lake, one of the equipment bearers set fire to the supplies. The altitude
adjusting dive computers, high altitude dive tables and Wienke’s text on
Altitude Diving have been reduced to charred rumble. Interestingly enough, all
that remains is a calibrated mercury barometer and remnants of a US Navy dive
table. Since you do not wish Indy to get bent on his dive, you must use the
barometer, the actual depth of the lake and the heat discolored dive table to
plan Indy’s dive.

The barometer reads the pressure to be 546 mm Hg.
Fortunately, you remember that the specific gravity of mercury is 13.6 and the
specific gravity of water is 1.00.

The charred remain of the table gives the following
time/depth listing

So, as divemaster for Indiana Jones, you need to determine:

a.
What will Indy’s oil filled depth gauge read on the bottom?

b.
What is the equivalent sea level ocean depth?

c.
How long will Indy have to find and recover the artifact
without incurring a decompression obligation?

**Solution:
**

*Although
there are faster ways to solve this problem (e.g. memorizing a specific
formula), I prefer to take the solution in several logical steps so that,
regardless of a particular situation, understanding of what is known,
what is unknown and how I convert
the units of known to the unknown will direct my solution.*

**Water depth for atmospheric pressure at this altitude:**

Depth
of a 1atmosphere column of water will be inversely proportional to specific
gravity:

Converting to feet fresh water

The water pressure at 93 feet of fresh water

This corresponds as an absolute pressure of:

3.81
atm + 1 atm = 4.81 atm total pressure (ata) at altitude

The pressure in mm Hg at this
altitude would be:

This hydrostatic pressure at sea level (where
1 atm is 760 mm Hg) would be:

Converting to a sea level pressure:

Converting sea level atm to salt
water depth:

2.46
atm x 33 fsw / atm = 81.2 fsw

**The ocean equivalent depth would be:**

3.82
atm x
33 fsw / atm = 126.1 fsw

**The US Navy entry would be:**

The 126.1 depth is rounded to the next greater 10 foot entry, so as divemaster, you recommend that Indy’s dive be controlled by the 130 fsw entry allowing him 10 minutes to find and recover the headpiece.

Thus, Indy will have to dive to 93 feet of fresh water
at an altitude near 9000 feet above sea level, his depth gauge will read 81 fsw
and he will treat the dive as if his decompression schedule obligation was
determined by a sea level dive of 130 fsw.

**Comment: **Obviously, this problem is fiction.
Indy would NOT require scuba! He would do the 10 minutes dive on a single
breath. The dive would end with Indy surfacing at sunset in front of a
mid-western archeological museum with the sacred headpiece in the arms of the
beautiful mermaid that assisted his dive. James Bond would do the dive
differently, but that’s another story!

**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.

Layman, L. The Basics of Diving High, Dive Training, August, 2000. 37-42.

Leech, J. McLean, A. & Mee, FB. High Altitude Dives In The Nepali Himalaya, Undersea & Hyperbaric Medicine, 21(4), 1994, 459-466.

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

Lowry, J. Scuba & Altitude, AOPA Pilot, March, 1987, 84-89.

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

Orr, D. An Attitude About Altitude, Alert Diver, March/April, 1999, 22-24.

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.

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

Wienke, B. Up & Down, ADM, Issue 7, 18-22.

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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)

**About The
Author:**

Larry "Harris" Taylor, Ph.D. is a
biochemist and Diving Safety Coordinator 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 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