Update 1-11-2022: revised Figures 1 and 2 to show correspondence of curve fit and criterion.
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I had originally intended to do this as an update to an
existing article (Ref. 1), but since
have changed my mind. This is different
enough to warrant being its own article.
The data and recommendations in Ref. 1 are based on
experiences for relatively short-term exposures, a few days or weeks similar to Apollo and
Skylab for habitat atmospheres, and a
few hours for low-pressure pure oxygen in space suits. Those results are based on the wet in-lung
inhaled oxygen partial pressure in the lung gases, set by concentrations available to pilots
flying aircraft, and there’s nothing
wrong with that approach for space suits!
But as it says in the article,
for very long-term exposures, and
especially for pregnancy and childbirth,
other constraints unknown to me then, may apply.
That is why in Ref. 1,
I recommended a general habitat atmosphere compatible with no
pre-breathe time getting into an oxygen suit,
and also compatible with no greater fire danger than in warm sea level
Earthly air. But at the same time, pregnant women and young children were
limited to a portion of the habitat that had another atmosphere more similar in
oxygen content to Earthly air, at a
higher pressure.
I have
recently run across some very pertinent information regarding long term
exposure risks, and pregnancy and
childbirth risks, for life at high
altitudes in Earthly air. These would
have a direct bearing on the atmospheric composition and pressure in any ship, space habitat, or any habitat upon some other celestial
body. I found this in an older issue of
AAAS’s journal “Science” (Ref. 2). It
deals with health investigations made in the Andes, up to altitudes of 5100 meters (16,700 feet).
What I do here is combine the Ref. 2 health vs altitude data
with my wet, in-lung oxygen partial
pressure calculation approach from Ref. 1,
using a standard atmosphere table to relate altitude to total
atmospheric pressure. The fire danger is based on the oxygen
concentration, expressed as mass per
unit volume, just as it was in Ref. 1.
Health vs Altitude Information From Ref. 2
The information in this reference is given in terms of
altitude above sea level, as it relates
to hypoxia effects upon humans living at high altitudes on Earth. Fundamentally, oxygen diffusion across the lung tissues from
the in-lung gases to the blood is driven by differences in oxygen partial
pressures between the lung gases and the blood.
That is why I converted the relevant altitudes to oxygen partial
pressures, but only after letting
water vapor displace some air inside the wet lungs (at human body
temperature).
There is also a carbon dioxide displacement effect, from the carbon dioxide diffusing out of the
blood into the lung spaces to be exhaled(see update 2-2-22 just below).
However, this effect is far
smaller than the water vapor displacement effect, by at least an order of magnitude! Thus it is safely ignorable for design
purposes. In contrast, the water vapor displacement effect is significant
at any pressure, but very much
more so at reduced breathing gas pressures,
precisely because the vapor pressure of the water depends on body
temperature, and just does not reduce
with reducing total pressure. It is
simply a bigger fraction at lower total atmospheric pressures.
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Update 2-2-22: Carbon dioxide
displacement turns out not to be as negligible as I originally thought, down in the dead-end blind spaces of the lung
alveoli. Further research turned up
something called the alveolar equation,
which estimates the average oxygen partial pressure in the alveoli, over the entire inhale-exhale cycle, allowing
for water displacement, carbon dioxide
displacement, oxygen diffusion into the
blood, and the dead-end space mixing
effect.
As it turns out, carbon dioxide partial pressure is held
essentially constant by the body up to about 2500 m elevation, prioritized over oxygen partial
pressure. Above that elevation, the body re-prioritizes maximizing oxygen
partial pressure over controlling carbon dioxide pressure. This leads to hyperventilation and
respiratory alkalosis, increasing severe
with increasing altitude above the critical 2500 m.
Most who use the alveolar equation to
size habitat and suit pressures use the “typical” carbon dioxide pressure from
below 2500 m as a constant, when above
2500 m it is most certainly not! Not
even close at severe conditions! This
leads to larger design values for habitat and suit pressures than are
necessary. Unfortunately, my researches also yielded no accepted model
for how carbon dioxide pressure varies in the alveoli for elevations above 2500
m, which would be reflected in the total
dry gas mixture breathing pressure.
The inhaled wet in-lung oxygen
concentrations that I use are actually a part of the alveolar equation! They are thus quite accurate for what they really
are. Since my hypoxia criteria are based
on that definition, and not actual conditions
deep in the alveoli, then my calculation
procedure described here is also valid.
It is certainly more “accurate” than using the alveolar equation at
conditions above 2500 m, because of the inherent
uncertainty in the “correct” value of carbon dioxide pressure to use.
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The “Science” article uses chronic mountain sickness (CMS)
as the indicator for the relevant hypoxia effects. The common external symptoms are
dizziness, headaches, ringing ears,
sleep problems, breathlessness, palpitations,
fatigue, and (particularly) cyanosis. That cyanosis turns lips, gums,
and hands a purplish blue, easily
observed by the most casual observer.
Examined closer medically,
the hallmark of CMS was long thought to be a great proliferation of red
blood cells, to the point of making the
blood more viscous. This increase in
viscosity raises the blood pressure,
especially in the arteries leading from the heart to the lungs. It can also lead to enlargement of the left
ventricle of the heart, and thickening
of its walls, eventually causing heart failure.
For short-term exposures (measured in days or less), the treatment for hypoxia effects is supplemental
oxygen, followed quickly by a return to
lower altitudes. For long-term exposures
(measured in months or years), the only
treatment is relocation to low altitude,
but some of the damage may be permanent! According to the Ref. 2 article, it has been known since the Spanish first tried
to colonize the Andes in the 16th century, that the risks for eclampsia in pregnant women
are elevated at high altitudes. For the
unborn and newborn at those same high altitudes, the elevated risks are for low birth weight, and for premature birth. This problem of long term hypoxic exposure is
really quite serious!
All that stuff has been known for a while, but Ref. 2 also reveals some more recent
information: the increase in blood
viscosity that precipitates CMS does not correlate with only the proliferation
of red blood cells! Everybody
suffering hypoxia while living at high altitudes has more than the normal red
cell count. However, only some of them show the CMS symptoms. Exactly why this is true is not fully
understood yet, but there does seem to
be some genetic components to it. People
living at high altitudes in the Himalayas,
the Andes, and the mountains of
Ethiopia all show different responses.
The Ref. 2 science news article indicates there are no
CMS cases below 2500 meter altitudes,
which is 8200 feet. 8000
feet cabin altitude is now quite common in airliners, when only a few years ago 10,000 feet was
more common. One thing to investigate
would be the equivalent altitude for no CMS from the CMS case percentages
versus altitude. It should correlate
to the 8200 feet criterion rather closely.
In South America (the focus of the Ref. 2 article), a closer reading generates these data: In La Paz,
the capital of Bolivia, at 3600
meters = 11,800 feet, some 6 to 8% of
the large local population shows symptoms of CMS. In the central Andean town of Cerro de
Pasco, at 4300 meters = 14,100
feet, about 15% of those aged 30-39
showed CMS, while some 33% of those aged
50-59 showed CMS. (I simply misused
those percentages as the upper and lower bounds for that population at that elevation.) The article focused on the mining town of La
Rinconada, at 5100 meters = 16,700 feet! This is a town of 50,000 to 70,000
people, living and working under utterly
deplorable conditions. They show at
least 25% with CMS, and it may be a lot
higher. I arbitrarily used 50% as an
upper bound. It could be higher.
Figure 1 shows a plot of lower and upper bound percentages
of CMS as a function of wet in-lung partial pressure of oxygen. The “average” seems to strike the zero CMS
level at about 0.13 atm for this population.
Per Figure 2, this occurs at
about 9000 feet. Note that below 8200 feet
(2500 m) the expected CMS rate is zero,
and the wet in-lung oxygen partial pressure is 0.14 atm (or
higher). The correspondence between
these altitude criteria is very close indeed!
We can probably reliably use 0.14 atm wet in-lung oxygen partial
pressure as a hypoxia criterion, for
either CMS or reproductive effects.
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Update 2-2-22: Note also that the
2500 m elevation for onset of CMS corresponds exactly to the elevation
at which the body deprioritizes carbon dioxide pressure in favor of maximizing
oxygen pressure in the blood, per the
supporting science behind the alveolar equation. This is the biological mechanism that also supports
using the inhaled oxygen partial pressure (with water vapor displacement) as
both the measure, and the criterion
(that being the 0.14 atm partial pressure).
--------
Figure 1 --
Occurrence of CMS vs Wet In-Lung Partial Pressure of Oxygen (Andes) UPDATED
Figure 2 – Wet In-Lung Partial Pressure of Oxygen vs
Altitude UPDATED
For purposes of this article, let us use 0.14 atm wet in-lung partial
pressure of oxygen as the long-term limitation on a single habitat atmosphere
composition and pressure for all residents,
including pregnant women and the unborn/newborn. We will see what suit pressures and fire
dangers result from this. It pays to be
conservative, because of the long-term
risks.
Habitat Atmosphere
To do this in the most straightforward way, I made total habitat breathing gas pressure (in
atmospheres) and habitat oxygen content (percent by volume) inputs. This is for a two-gas mix of oxygen and
nitrogen. From these data, using 0.06193 atm as the vapor pressure of
water at human body temperature, I
computed partial pressures of oxygen and nitrogen in the dry breathing gas, the displaced partial pressure of breathing
gas in the (wet) lungs, and the wet
in-lung partial pressure of oxygen. That
procedure is intended to address the long-term hypoxia exposure issue, for which we just determined the safe wet
in-lung oxygen partial pressure needs to equal or exceed 0.14 atm.
Running numbers to see trends, I started at standard day sea level
conditions, with a two-gas “synthetic
air” at 20.946 volume % oxygen. I
corrected air density at 1 atm to 77 F living temperature (which is where the
0.275 kg/m3 concentration came from). Then I reduced the total synthetic air
pressure by 0.1 atm increments down to 0.4 atm,
for a wet in-lung oxygen partial pressure about half the min value
needed. Then I raised the oxygen
percentage to 40%, getting very nearly
the desired wet in-lung partial pressure desired. 0.4 atm at 40% oxygen is not quite adequate
long term.
From that 0.4 atm - 40% oxygen point, I then looked at 0.45 atm – 40% oxygen, 0.45 atm – 45% oxygen, and 0.40 atm – 45% oxygen, in order to “bound the problem”. Note that this bounded problem is not
unique: one could use lower pressure and
higher oxygen percentage, and still meet
the wet in-lung criterion. Such choices
might trip the fire danger limit,
though.
Fire Danger
I computed the molecular weight of the synthetic air as the
sum of the volume percents of the gases times their molecular weights, and then from this and the input volume
percent oxygen, the mass percent oxygen
(as MWO2 * vol%O2 / MWsyn.air). I used
the habitat pressure and temperature to correct the sea level standard density
of air in kg/m3, and then
multiplied that by the mass percent oxygen,
to compute the oxygen concentration in kg/m3. That looks at the fire danger issue, for which the oxygen concentration should be
under the warm sea level air criterion of 0.275 kg/m3.
Min Suit Pressure
From the partial pressure of nitrogen in the habitat
atmosphere, reducing that by a factor of
1.2 is the “no pre-breathe” criterion for minimum pure-oxygen suit
pressure. At the higher habitat
pressures nearer 1 atm with real synthetic air,
this produces ridiculously-large min suit pressures! But as the habitat total pressure dropped
near 0.4 atm, and the oxygen percentage
increased (driving down nitrogen even further),
the min suit pressures became quite attractive. Higher suit pressures are compatible
with no pre-breathe time, but not suit
pressures lower than this computed minimum. I also computed wet in-lung oxygen partial
pressure for that min suit pressure, and
for 10% leaked-down.
Results
I chose as the design value 0.45 atm total habitat
pressure (which is 6.6132 psia) at 45% oxygen by volume (which is 2.9759 psia
partial pressure of oxygen and 3.6373 psia partial pressure of nitrogen). That is very similar to, but not exactly the same, as the habitat mix of Ref. 1. This selection resulted in a wet in-lung
oxygen partial pressure of 0.1746 atm,
which far exceeds the adopted 0.14 atm long-term exposure criterion. Even with a leak-down to 0.40 atm, the wet in-lung oxygen is still 0.1521
atm, which significantly exceeds the
criterion. As long as long-term hypoxia
is avoided this way, there should be no
troubles with CMS, or with pregnancy and
birth beyond the “normal occurrence” rates.
The computed oxygen concentration at 0.45 atm – 45% oxygen
is 0.257 kg/m3, which is
under the 0.275 fire danger criterion.
Leaked down to 0.40 atm – 45% oxygen,
it is only 0.228 kg/m3.
The fire danger is similar to,
but very slightly less than, that
of sea level warm Earthly air.
The minimum pure oxygen suit pressure for the 0.45 atm
– 45% oxygen design point is quite attractive at 3.031 psia (157 mmHg), although that is slightly higher than the
suits explored in Ref. 1, which met
short-term hypoxia exposure criteria. Any
suit pressure at or above this value meets the no pre-breathe criterion for the
selected design habitat atmosphere. This
is well below current NASA suit pressures,
and is still quite similar to the lowest altitude-equivalent suit
recommended in Ref. 1 (2.945 psia = 152 mmHg).
That suit had a wet in-lung partial pressure of oxygen of 0.1385
atm, almost meeting the long-term
hypoxia criterion adopted here.
In the event of suit leak-down, there is still sufficient wet in-lung oxygen
partial pressure to avoid short-term hypoxia effects, as already explored in Ref. 1. There is no pre-breathe or decompression time
needed to go from an oxygen suit back to the habitat atmosphere, even if leaked down 10%.
See the data table in Figure 3, for all the habitat atmosphere numbers run
for this study.
Figure 3 – Spreadsheet Image of Numbers Run for this Study
Recommended Suit Design Criteria to Match
The minimum-pressure altitude-equivalent suit design, per the methods of Ref. 1, is 7.72 kft (2350 m) altitude, for which the pure oxygen suit pressure is 0.20625
atm = 3.031 psia = 157 mmHg. The resulting
wet in-lung oxygen partial pressure actually meets the long-term hypoxia
criterion at 0.144 atm vs the 0.140 criterion.
If leaked down 10%, the suit
pressure is still 0.1856 atm = 2.728 psia = 141 mmHg. That wet in-lung partial pressure of oxygen
is 0.1237 atm, which corresponds to
Earthly air at 11.36 kft (3460 m). This
is still quite safe for short exposures,
as explored in Ref. 1. See Figure
4.
Figure 4 – Min Suit Pressure Data for No Pre-Breathe Time
Conclusions
(see also Fig. 5, 6, and 7):
#1. Use
a long term habitat (or ship) atmosphere of 0.45 atm (6.61 psia) at 45% oxygen
by volume, in a simple two-gas
composition with nitrogen. This
atmosphere is safe from a fire danger standpoint, and more-than-meets the wet in-lung oxygen
partial pressure criterion to avoid long term hypoxia effects, like CMS.
Presumably, this also avoids
aggravating complications of pregnancy and childbirth beyond the normal
occurrence rates. It is still safe,
even if leaked-down to 0.40 atm at that
same 45% oxygen.
#2. The
minimum pure-oxygen suit pressure that does not incur a requirement for
pre-breathe time with this habitat atmosphere,
is only 0.20625 atm = 3.031 psia.
This is a 7.72 kft altitude-equivalent design, and is no worse than 11.36 kft equivalent
when leaked-down 10%. Any pure-oxygen
suit design with that pressure or higher, is free of the pre-breathe time requirement, and meets the long-term hypoxia criterion. It does not meet that criterion if
leaked-down 10%, although such exposures
should be quite short, thus doing no
permanent harm.
Figure 5 – Summary of Conclusions
Figure 6 – How the Habitat Atmosphere Fares Versus the Long-Term
Hypoxia Criterion
Figure 7 – How the Min Suit Fares Versus the Short-Term
Hypoxia Criteria
Post Scriptum
Where the short-term hypoxia criteria came from is more of a
judgement call. It is based on varying military
and civilian oxygen mask requitements for pilots, and on some high-altitude human
populations. Pilots require full
cognitive abilities. Somewhere between
where the USAF and the FAA require supplemental oxygen regardless of
circumstances, is that criterion. For our purposes, that is around 0.12 atm wet in-lung partial
pressure of oxygen, and it also matches
what obtains at the highest altitude for which a vented pure oxygen mask is
effective for more than a single handful of minutes.
For bare survival with cognitive impairment after several
minutes to an hour or so, the rare max
cabin altitude of 15,000 feet will serve well enough. That is about 0.10 atm wet in-lung partial
pressure of oxygen. You could go to
20,000 feet equivalent at 0.08 atm wet in-lung partial pressure of oxygen and
still survive, but most lowlanders will
be unconscious at this condition. There
are some acclimatized and genetically-adapted herders in the Andes who spend
parts of their days up there, but even they
return to lower altitudes at night.
This is shown in Figure 8,
along with the so-called Armstrong limit, where the water vapor in the lungs displaces
all of the air or oxygen you are trying to breathe. That is the so-called “vacuum death
point”. Actually, the real hypoxia death point is lower, somewhere in the 50-60,000 foot range. Some jet pilots have reached 50,000 feet with
only an oxygen mask, but they were only
there for mere seconds.
Figure 8 – Data From Which the Short-Term Hypoxia Criteria
Were Obtained
References
#1. G. W. Johnson,
“Suit and Habitat Atmospheres 2018”,
posted 16 March 2018 to http://exrocketman.blogspot.com
#2. Martin Enserink,
“Hypoxia City”, a science news
article published in the journal magazine “Science”, volume 365, Issue 6458,
dated 13 September 2019, as
published by the American Association for the Advancement of Science (AAAS).
Addendum:
Since completing the write-up of these design sizing
analyses, I have created a
well-organized spreadsheet that does these calculations quickly, all in one place. This allows iterative fine-tuning of the
pressure and oxygen percentage selections for the habitat atmosphere, while concurrently monitoring the long-term
hypoxia criterion, the fire danger
criterion, and the adequacy of the min
suit pressure value in terms of short-term hypoxia criteria.
One should note that the main difference between this min
suit pressure sizing procedure, and that
used in Ref. 1, is that the suit is
determined directly from the nitrogen partial pressure in the habitat
atmosphere. At mixture, the max value of habitat pressure produces
the max value of nitrogen partial pressure,
and that determines the max value of minimum suit pressure required for
no pre-breathe requirement. The Ref. 1 method used an independent
altitude-equivalent way of setting suit pressure, which in turn added another level of
iteration to the habitat atmosphere design process.
Also slightly different from Ref. 1, I have added a leak-down option for the
habitat pressure. For a short
transient, it is OK to violate the
long-term hypoxia criterion in the leaked-down state. But,
if you set the habitat design (max) pressure and leak-down percentage
such that the long-term hypoxia criterion is satisfied, even in the leaked-down state, then you have relieved yourself of the need
for fine pressure control. You
then have a range of long-term acceptable pressures, all at the same oxygen-nitrogen mixture.
Figure 9 shows an image of the new spreadsheet design
analysis tool. User inputs are
highlighted yellow. There are only 4 of
them: habitat pressure, habitat oxygen percentage by volume, the percent habitat pressure leak-down, and the percent suit pressure leak-down. All the rest is automatic. Significant items or outputs are highlighted
blue or green. The user instructions are
on the worksheet. Contact me by email if
you want a copy.
It is recommended that the default design analysis worksheet
be maintained as-is. Simply copy and
paste it into a fresh worksheet to do your own design analysis. That way,
if you screw up a cell formula,
you have the original available to restore it. The default input data correspond to this
article’s design analysis. The
odd-looking habitat leak-down percentage is that which produces exactly the
leaked-down habitat pressure used in that analysis.
Figure 9 – Image of Spreadsheet Design Analysis For Habitat
and Suit Atmospheres
