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Altitude Diving: Understanding the Tables

Big Creek LakeWhen most people think of altitude diving they picture diving in the crystal clear waters of glacial-fed alpine lakes. While those types of dives will certainly etch their scenic beauty in your mind forever, they are not the only possibility for altitude diving. PADI defines altitude diving as any dive at an elevation above 1,000 feet. While that is much higher than sea level, it's also much lower than most alpine lakes. In fact, all of Montana, Wyoming, and Idaho—except for the region around Lewiston—has an elevation above 1,000 feet, meaning that essentially all diving in those states is considered an altitude dive!

Although many of the large lakes in the southern Coast Mountains of British Columbia (Harrison Lake, Chehalis Lake, Stave Lake, and Pitt Lake) are at an altitude below 1,000 feet, and Crescent Lake in the Olympic Peninsula of Washington is also below 1,000 feet, most of the larger lakes in the Northwest [NOTE 1] are at elevations greater than 1,000 feet and are therefore considered to be at altitude for dive-planning purposes.

The chapter on altitude diving in the PADI Adventures in Diving manual (as well as the instructor outline for the Altitude Diving Specialty course) contains tables [NOTE 2] that you use to convert your dives at altitude to equivalent dives in the ocean. This Theoretical Ocean Depth (TOD) enables you to use standard dive tables, such as the Recreational Dive Planner (RDP), to correctly plan your altitude dives. These altitude-conversion tables are correct in principle, but they are based on the assumption that you are diving in sea water at altitude, whereas altitude diving is done exclusively in fresh water [NOTE 3].

Fortunately, beginning-level dive courses explain that an additional 1 atmosphere of pressure is exerted for every 33 feet of sea water (fsw) or 34 feet of fresh water (ffw). This makes it straightforward to apply a correction to the altitude diving tables: multiply the Theoretical Depth at Various Altitudes by 33/34, and multiply the Safety/Emergency Decompression Stop Depth by 34/33. The corrected tables are listed below [NOTE 4].

Theoretical Depth at Altitude - Imperial (Updated Version)

Theoretical Depth at Altitude - Metric (Updated Version)

Here's a quick calculator to determine your Theoretical Ocean Depth:

Please select: Imperial Metric

Enter the altitude at the surface (feet or meters above sea level):

Enter the depth to which you are planning your dive (feet or meters):

These updated tables are primarily useful for planning dives at altitude. Bathymetric maps exist for many alpine lakes; these illustrate the depth profiles of the lakes, and often contain other information such as bottom composition. These maps are ideal for dive planning, and all of the depth information given on them is in feet (or meters) of fresh water. Therefore, you would want to use the new altitude dive tables provided here when planning a dive using those maps.

When actually diving, it is important to understand how your depth gauge functions in fresh water at altitude. For example, mechanical depth gauges that use a bourdon tube will read shallower than actual depth, while mechanical depth gauges that use a capillary tube will read deeper than actual depth; some of these can be recalibrated before the dive to correctly read depth in feet (or meters) of sea water. Likewise, some electronic depth gauges are calibrated to read depth only in feet (or meters) of sea water. In these cases, you should use the older altitude tables because the new tables assume that you can accurately measure your depth in fresh water. However, most recent dive computers can be set to read depth in fresh water; some even convert automatically when used above a certain altitude (usually 1,000 – 2,000 feet above sea level). It is for these dive computers—where depth in fresh water is accurately measured—that the new altitude tables should always be used.

Where do these table numbers come from? They are based on two ideas: 1) that we can correctly determine the atmospheric pressure at any given altitude based upon a mathematical model, and 2) that decompression models are based on pressure ratios, rather than on absolute pressures.

The first idea is that we can correctly determine the atmospheric pressure at any given altitude based upon a mathematical model. Such a model exists and it is called the barometric formula. The Wikipedia entry for the barometric formula gives a detailed discussion. Since all diving occurs in the troposphere (the first layer of atmosphere), the barometric formula reduces to the following equation:

For a given altitude A, the atmospheric pressure Pa (in atm) at that altitude is

Pa = (1 atm) * exp(5.255876 * log(1 – (C * A)))

where C = 0. 0000068756 / 1 foot = 0. 000022558 / 1 meter,
depending on whether the altitude is given in feet above sea level or in meters above sea level.

This formula correctly reproduces the values in the standard table of atmospheric pressure as a function of altitude that is provided in the NOAA Diving Manual (1991 Edition, page 10-27).

The second idea to get the numbers in the altitude tables is that decompression models are based on pressure ratios, rather than on absolute pressures. In determining how your body rids itself of excess nitrogen gas, decompression models rely upon the ratios of the pressures you experience at depth to the atmospheric pressure you experience after the dive. The key to not forming nitrogen bubbles in your body (and thereby avoiding decompression sickness) is to keep those pressure ratios within tolerable limits. The purpose of dive tables is to provide guidance about staying within those limits.

Let's consider a familiar example to illustrate the importance of pressure ratios in preventing bubble formation: a can of soda. You could take a can of soda into a recompression chamber and increase the pressure in the chamber to the point where when you opened the can the soda would be flat because the surrounding air pressure would be great enough to prevent the bubbles from forming. Likewise, when you open a can of soda during an airplane flight, it is likely to fizz more than if you had opened it on the ground because the airplane cabin is at a reduced pressure. How much the soda fizzes does not depend on just the internal pressure of the unopened can, nor on the external air pressure, but it instead depends on the pressure ratio between the pressure in the unopened can and the pressure of the surrounding air when you open it. That’s also why an opened can of soda eventually goes flat—the internal gas pressure of the carbon dioxide in the soda slowly equalizes with the external gas pressure in the atmosphere, at which point no more bubbles form in the soda.

Dive tables such as the RDP are based upon the maximum depth divers reach during their dives. To be conservative, the tables assume that divers drop immediately to their maximum depth and stay at that depth for the duration of their dive. Essentially, it is the ratio of the pressure at this maximum depth with the pressure of the atmosphere at the surface that the dive tables’ decompression model uses. By keeping that pressure ratio within tolerable limits, it is assumed that the divers can safely off-gas at the surface after being at that maximum depth. This pressure ratio can be expressed as

R = Pd / Ps,

where Pd is the pressure at maximum depth, and Ps is the pressure at the surface.

Dive tables are based on the assumption that people are diving in the oceans, where the surface pressure is 1 atm and the pressure at maximum depth is the surface pressure (1 atm) plus an additional 1 atm for every 33 feet of depth in sea water. So, for ocean diving,

Ps = 1 atm, and

Pd = 1 atm + Do * (1 atm / 33 fsw),

with Do being the maximum depth of the ocean dive measured in feet of sea water (fsw).

Therefore, for an ocean dive,

R = Pd / Ps = 1 + (Do * (1 atm / 33 fsw) / 1 atm).

At altitude, though, the surface pressure is the pressure at altitude and is given by the formula for Pa that was discussed previously. In addition, the diving is in fresh water, so the pressure at maximum depth is the surface pressure (which will be less than 1 atm) plus an additional 1 atm for every 34 feet of depth in fresh water. Therefore, for altitude diving,

Ps = Pa,

where Pa is the pressure at altitude that was discussed as the first idea, and

Pd = Pa + Da * (1 atm / 34 ffw),

with Da being the maximum depth of the altitude dive measured in feet of fresh water (ffw).

For altitude diving, then,

R = Pd / Ps = 1 + (Da * (1 atm / 34 ffw) / Pa).

The pressure ratio R is what must be kept within tolerable limits, according to the decompression models. The R from ocean diving is the same as the R from altitude diving, as far as the decompression models are concerned. However, dive tables are not tabulated in terms of R; rather they are based upon the maximum depth of a dive in the ocean (Do). So, given a maximum depth of a dive at altitude (Da), we can calculate its value of R, equate that to the R of an ocean dive, and then find the equivalent depth of a dive in the ocean (Do). This Do is the Theoretical Ocean Depth (TOD), and with it we can use the dive tables that are based upon diving in the ocean, such as the RDP. Equating the values of R, we find that

TOD = Do = Da * (1 atm / Pa) * (33 fsw / 34 ffw).

The PADI table of Theoretical Depth at Various Altitudes simply omits the conversion factor of feet fresh water to feet sea water, which is why the numbers in it should be multiplied by (33/34) to be completely correct.

Likewise, we know that a safety stop should be performed at a depth of 15 fsw when diving in the ocean. To determine the equivalent depth at which to do a safety stop at altitude, rearrange the equation to solve for Da, while putting Do = 15 fsw. This gives

Safety Stop Depth at Altitude = (15 fsw) * (Pa / 1 atm) * (34 ffw / 33 fsw).

Again, the PADI table of Safety/Emergency Decompression Stop Depth simply omits the conversion factor of feet sea water to feet fresh water, which is why the numbers in it should be multiplied by (34/33) to be completely correct.
Without the fresh water & sea water conversions, the above formulas for the TOD and Safety Stop Depth at Altitude produce the following tables, which generally match the PADI altitude tables (the 13 numbers in red in the Imperial Theoretical Depth at Various Altitudes table are 1 foot greater than the corresponding numbers on the PADI table). Note, though, that if we assume a safety stop is made at a depth of 4.6 meters of sea water (which is equivalent to 15 fsw), the metric PADI table for Safety/Emergency Decompression Stop Depth is entirely incorrect. Even if we assume a safety stop depth of 4.8 msw (equivalent to 16 fsw), only the safety stop depths at altitudes of 300 meters and 600 meters above sea level match the numbers in the PADI table; after that, the values quickly diverge. Therefore, even if we ignore the missing conversion of sea water to fresh water, PADI’s metric table for Safety/Emergency Decompression Stop Depth for altitude diving is incorrect and should not be used.

Theoretical Depth at Altitude - Imperial (Old Version)

Theoretical Depth at Altitude - Metric (Old Version)

I hope this discussion has taken some of the voodoo out of altitude diving and has helped explain where the numbers in the various altitude tables come from. By better understanding the theory behind altitude diving you can make better-informed decisions and be a safer diver.

Inspire the world,

Todd Stedl
PADI Instructor # 184495
8th Element Diving
www.8thElementDiving.com

Additional references

The following references were recommended by Gene Hobbs of the Rubicon Foundation:

The following two DSAT articles published in their 1979 Decompression in Depth Symposia (RRR ID: 4230):

"And yet another approach to the problems of Altitude Diving and Flying After Diving." by Bruce Bassett

"The theoretical structure and testing of high altitude diving tables." by Richard Bell, Anthony Thompson, and Reid Borowari

There are also some other good papers available:

"The theory of high-altitude corrections to the U.S. Navy standard decompression tables. The cross corrections." Bell and Borowari. Undersea Biomed Res. 1976 Mar;3(1):1-23. RRR ID: 2748

"Diving at diminished atmospheric pressure: air decompression tables for different altitudes." Boni, Schibli, Nussberger, and Buhlmann. Undersea Biomed Res. 1976 Sep;3(3):189-204. RRR ID: 2750

"Automatic compensation by capillary gauge for altitude decompression." MacKay. Undersea Biomed Res. 1976 Dec;3(4):399-402. RRR ID: 2440

"Converting standard air decompression tables for no-stop diving from altitude or habitat." Hennessy. Undersea Biomed Res. 1977 Mar;4(1):39-53. RRR ID: 2784

"Decompression Procedures for Flying After Diving, and Diving at Altitudes above Sea Level." Bassett. USAF Technical Reports. 1982. RRR ID: 4531

"Diving at altitude: a review of decompression strategies." Egi and Brubakk. Undersea Hyperb Med. 1995 Sep;22(3):281-300. RRR ID: 2194

Notes

NOTE 1: I consider the Northwest to be the region of the US and Canada that is roughly from 51°N (the northern tip of Vancouver Island) south to 42°N (the southern borders of Oregon and Idaho), from the Pacific coast east to the eastern foothills of the continental divide. This region encompasses southern British Columbia, Washington, Oregon, Idaho, western Montana, and the northwest section of Wyoming. This region is generally characterized by mountainous terrain, cold water, and large tidal exchanges along the coasts, but it is not as extreme as the conditions found in Alaska and northern British Columbia.

NOTE 2: PADI’s tables for altitude diving mention a 1970 copyright from Skin Diver Magazine, and that the tables are reprinted with permission. For convenience, I will refer to the tables as PADI’s, even though Skin Diver Magazine may have been the original publisher.

NOTE 3: Any saltwater lakes at altitude would likely have different salt concentrations than sea water. Consider, for example, the Great Salt Lake, which has such a high salinity that most sea life cannot survive in it. The salt concentration in the water directly affects the density of the water, and the density of the water directly affects the pressure experienced at depth. So, for example, if you dove in water that had the salinity of the Great Salt Lake, you would experience an additional one atmosphere of pressure at a depth that was shallower than the 33 feet where you would experience that pressure in sea water. The consequence of all this is that you cannot directly convert to a Theoretical Ocean Depth if you are diving in salt water at altitude because the salinity of the saltwater lake will not be the same as the salinity of sea water. However, see also NOTE 5.

NOTE 4: Rather than rely on the depths of fresh water versus sea water, it is best to obtain the conversion factor by going directly to the source of its cause: the different densities of fresh water and sea water. The density of fresh water is 1.000 kg per liter, and the density of sea water is 1.027 kg per liter. This gives a sea water to fresh water conversion of 1.027 / 1.000 = 1.027, and a fresh water to sea water conversion of 1.000 / 1.027 = 0.9737. The text will continue to use fsw and ffw for the conversions to simplify the understanding of the discussion, but the tables are based on the more-exact densities discussed in this note.

NOTE 5: Based upon the information in NOTE 4, we can estimate a TOD for the Great Salt Lake, which is at an altitude of 4,200 feet above sea level. First, the Great Salt Lake is effectively divided in two by a railroad that significantly inhibits mixing between the north and south portions. The salinity of the north portion is about 28%, while the salinity of the south portion is about 14%. (For comparison, the salinity of the ocean is 3.5%.) Working with a water temperature of 20°C (68°F), this gives densities of 1.23 kg per liter for the north portion, and 1.11 kg per liter for the south portion. These densities lead to Great Salt Lake-to-sea water conversion factors of 1.23 / 1.027 = 1.20 and 1.11 / 1.027 = 1.08 for the north and south portions, respectively. By using these conversions instead of the (33 fsw / 34 ffw) conversion in the TOD formula, we find the TOD for diving to a depth d in the Great Salt Lake to be, approximately,

TOD = 1.40 * d, for diving in the north portion of the Great Salt Lake, and

TOD = 1.26 * d, for diving in the south portion of the Great Salt Lake.


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