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  Diving At Altitude
(A simplified method to obtain the correct pressure)
by John Ware, PhD


[CAUTION: Diving at altitude requires special training which is available from
any of the major SCUBA training agencies.  The purpose of this note is
to supplement, not replace, such training for divers who are interested in
more technical detail than is commonly availble.  There is relatively little
data on the risks of diving at altitude compared to diving at sea level.  No
tables, or table corrections, can guarantee that DCI incidents will not occur.
The author of this note takes no responsibility for use of the information
and/or data contained in this note, whether used correctly or not.]

In his short paper on depth gages at altitude, Dr. Taylor makes the very important observation that depth gages are actually pressure gages (with a very few exceptions, such as the upward looking sonars used on submarines). However, his explanation and derivation of the gage correction at altitude, while perfectly correct, is much longer and more complex than is required. For those SCUBA depth gages which do not measure absolute pressure and do not
automatically compensate for changes in ambient pressure such as occur at altitude, which is the case that Dr. Taylor considers, only a very simple computation and correction is needed.

When the ambient pressure is reduced due to a change in altitude, these gages will read zero feet when submerged to a depth such that the total pressure (water pressure plus overlying air pressure) equals one atmosphere. (One atmosphere being defined as the pressure at sea level and standard temperature).  As the gage is taken deeper, the gage reading will increase by 1 foot for each additional increment in pressure equal to 1 foot of seawater. (Note: Most analog depth gages read pressure in units of Feet of Salt Water, abbreviated FSW).  Thus, it is only necessary to add a correction to the gage reading equal to the depth at which the gage sees a pressure equal to one standard atmosphere. In Dr. Taylor's example, the standard atmosphere
is 29.92 inches of Hg and the pressure at altitude is 24.61 inches of Hg. (Note: Ambient air pressure, or barometric pressure, is commonly measured in inches of mercury, the element whose symbol is Hg).  Therefore, an additional pressure of:

 (1)       29.92 - 24.61 in. Hg = 5.31 in. of Hg

is required to bring the gage reading from some negative value (which is not seen on analog gages because of the physical stop on the needle) to a zero reading.  Since mercury is 13.6 times as dense as fresh water, this corresponds to:

 (2)        5.31 in. Hg => (5.31 * 13.6 / 12) = 6.0 FFW

                     = 5.9 FSW

This correction is added to the depth gage reading for all depths so that a new calculation for every depth (as implied by Dr. Taylor's note) is *not* required.

This calculation can be made even simpler in a way that does not require knowing the density of Hg (or even the number of inches in a foot).

If the pressure at altitude is known (in any units) and the pressure at sea level is known (in the same units), then the additive correction factor, in feet of seawater, is:

(3)          CF = (1 - Pal/Psl)*33.0 in FSW

      Where: CF is the correction factor to be added to the gage reading, in feet of seawater.
             Psl is the pressure at sea level.
             Pal is the pressure at altitude.

Note that this correction factor does not depend on the depth of the dive. The same correction factor is added to every depth at the same Pal.
Equation 3 is all that is needed and, since the only information required is the *ratio* of the pressure at altitude to that at sea level, the units of pressure can be anything!

(Note: It is a simple exercise to show that this is *exactly* equivalent to the lengthy calculation shown by Dr. Taylor.)

Since most depth gages and computers measure pressure in FSW (but check your computer manual) and since all dive tables are based on pressure in FSW, you simply add the correction computed by Equation 3 to the gage reading. If an estimate of the actual depth (that is, the distance from the surface) is required, convert the corrected gage reading from FSW to FFW by multiplying by the standard conversion factor of 1.026.

As an example, to answer Dr. Taylor's question: What does the depth gage read in 60 feet of FW when the ambient pressure is 24.61 in. Hg?  The correction factor that must be added to the gage reading is:

      CF = (1 - 24.61/29.92)*33 = 5.9 FSW

Since:  True Depth = Gage Reading + Correction Factor, the gage reading
is:

      GR = TD - CF

But, since the gage reads in FSW, the 60 foot depth must be converted to FSW, so that all units are equal, by dividing by 1.026.  Thus, the gage reading is:

      GR = 60/1.026 - 5.9 = 58.5 - 5.9 = 52.6 FSW

But most divers do not carry a barometer with them.  How can you know the pressure at altitude?  The answer is you don't.  However, for most purposes we can use a standard table of atmospheric pressure as a function of altitude such as that provided in the NOAA Diving Manual (1991 Edition, page 10-27).
 

         Altitude     Ratio of pressure at altitude
         (feet)       to pressure at sea level

             0         1.000
          1000         0.964
          2000         0.930
          3000         0.896
          4000         0.864
          5000         0.832
          6000         0.801
          7000         0.772
          8000         0.743
          9000         0.715
         10000         0.688


(Note: Always use the next higher altitude for all corrections.  That is, if diving at 5200 feet, use the pressure ratio for 6000 feet.)

Now we know how to correct our depth gage in order to determine our actual depth when diving at altitude.  But that is not enough!  There are three other factors to consider:

      1- 'Theoretical depth'
      2- Ascent rate
      3- Nitrogen status when arriving at altitude

Theoretical Depth:

When surfacing after a dive at altitude, the ambient nitrogen partial pressure is less than when surfacing from the same dive at sea level. Therefore, a correction must be applied to your dive profile to take this reduction in pressure into account.  It is easy to show that the so called 'theoretical depth' can be computed from the actual depth from:
 

(4)      TD = (Psl/Pal) * AD
 

      Where: TD is the theoretical depth
             AD is the actual depth

As an example, suppose you did a dive at an altitude of 2400 feet using a standard analog depth gage.  Rounding this altitude up to 3000 feet, the correction factor that must be added to the depth gage reading is, from Equation 3, (1 - 0.896)*33 = 3.4 FSW.  If the analog gage reads 50 FSW, then the true pressure at this depth is (using Equation 3) 50 + 3.4 = 53.4
FSW. Then, this pressure must be adjusted using Equation 4 to give the theoretical
depth of 53.4/0.896 = 59.6 FSW.

So your 50 foot dive (on your gage) became a 60 foot dive (for the purposes of your dive tables)!

Equations 3 and 4 can be combined into a single equation that provides both the gage correction and the theoretical depth adjustment into a single computation:

 (5)     TD = (Psl/Pal) * (DM + 33.0) - 33.0
 

      Where: TD is the 'theoretical depth' (that is, the depth that is
used in your dive tables) in FSW.
DM is the depth measured on you depth gage in FSW.

Ascent Rate

So Equation 5 is all you need, right?? Not quite.  You must also ascend more slowly when diving at altitude so that the rate of change of nitrogen partial pressure in your tissues at altitude is the same as the rate at sea level.  Simple enough:

 (6)        Ral  = (Pal/Psl) * Rsl
 

      Where: Ral is the ascent rate at altitude
             Rsl is the ascent rate at sea level
 

Nitrogen Status when Arriving at Altitude

So now we're done, right?  Well not quite.  If you have been at sea level for a substantial time (6 - 12 hours) and then drive to altitude, the nitrogen partial pressure in your tissues is greater than that in the surrounding air. In other words, it is just as if you have done a dive even though you haven't gotten wet yet!

This problem is not amenable to the kind of simple analyses above because it depends on the dive tables you use.  If you are using the PADI tables, you should count 2 letter groups for each thousand feet or fraction thereof. For example, if you drive to a mountain lake at an altitude of 3400 feet, you are an H diver before you hit the water.  Your 'surface interval'
begins when you arrive at altitude, so you can use the surface interval portion of your table to determine your letter group when you begin your dive.
 

SUMMARY

If you dive at altitude, there are four things you must be concerned
about:

      1- If you are using a standard analog depth gage, your gage won't read depth correctly and must be adjusted using Equation 3 or some equivalent.

      2- If you are not using an altitude-compensating computer, after you determine the actual depth, this must be converted to a 'theoretical depth' using Equation 4 or some equivalent.  This 'theoretical depth' is the depth used to compute your pressure group from your dive tables (always rounding up depth and time, of course).

         (Or you can use Equation 5 to combine gage correction a theoretical depth calculation in one step.)

      3- You must slow your ascent rate.  You can use Equation 6 or simply be safe and use 30 feet/minute.

      4- You must consider your nitrogen status when arriving at altitude.

Now, you see why almost everyone that dives at altitude uses a computer that makes all these corrections for them. However, a word of caution with regard to dive computers and altitude.  Read your instruction manual carefully.  Not all computers correct for all factors, some must be turned on only after arriving at altitude, and, for many, the manual is not clear.

Dive safe,
John Ware, Ph.D., PADI Master Instructor #56318


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