Update 10-25-2022: a version of this article and "Habitat Atmospheres and Long-Term Health" (dated 1 Jan 2022), combined into one paper, was presented as a paper at the 2022 Mars Society convention at ASU in Tempe, AZ. It was well-received.
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I came up with the design analysis of suit and habitat
atmospheres posted in Ref. 1, and then
developed a simplified and organized spreadsheet model, to implement that design analysis procedure, all in one convenient place. This model uses a long-term hypoxia criterion
developed from data in Ref. 2 for the habitat,
and two short-term hypoxia criteria for the minimum-pressure suit, from pilot oxygen mask requirements. I developed a fire danger criterion for the
habitat out of oxygen concentration, per
its use in Arrhenius-type reaction-rate models. The “no pre-breathe” criterion
is NASA’s, via the USN.
The fully-compliant habitat and min-pressure suit atmosphere
values of Ref. 1 are now the default case in the spreadsheet model. This was reported in the Addendum to Ref.
1. I have since done two further
analyses, denoted “work case 1” and “work
case 2”, as their own worksheets in the
spreadsheet.
The default case at 0.45 atm and 45% oxygen
(by volume) in the habitat, produced a
recommendation well in excess of the long-term hypoxia criterion, even leaked down to 0.40 atm (some 11.111%
lower). It was compliant with the fire danger criterion, and produced a 3.031 psia pure-oxygen suit
proposal that is compliant with the fully-cognitive short-term hypoxia
criterion, even if leaked down by 10% on
pressure. This is the lowest suit
pressure that meets no pre-breathe. Anything
higher also requires no pre-breathe. This
is a very good combination, but I wanted
to see if I could do even better.
For “work case 1”, I
reduced the design (max) habitat pressure to 0.40 atm, and increased the oxygen to 50%, with a 10% pressure leak-down specified for
both suit and habitat. This still meets
the long-term hypoxia criterion for the habitat, even leaked down, and it still meets the fire danger criterion, by a very slightly better margin. But it produced a min pressure suit option
that failed to meet the fully-cognitive short term hypoxia criterion
entirely, and also failed to meet the
bare survival hypoxia criterion when leaked down.
I had to separately raise that suit pressure back up to
3.013 psia pure oxygen, before it met
the fully-cognitive short-term hypoxia criterion, even leaked down. This suit also needs no pre-breathe. Paired with the upgraded min suit
pressure, this is also a good
combination, although it wastes some
of the pre-breathe margin. I added a
separate suit upgrade calculation off to the right, in this worksheet.
So then
I ran “work case 2”. I started getting
acceptable suit pressures at about 0.43 atm habitat pressure, and I fully met the habitat long-term hypoxia
and fire danger criteria, at just about
43.5% oxygen. I had to hunt around a bit
on both habitat pressure and oxygen percentage,
before settling on these values.
They resulted in a min suit pressure that was just a bit lower than the
default case or “work case 1” at 2.975 psia,
but it still met the short-term fully-cognitive hypoxia criterion, even when leaked down 10%. This is the best combination I have
yet found. The separate suit
upgrade calculation is also in this worksheet,
but was not needed.
The
default case is Fig. 1, which is also
Fig. 9 in Ref. 1, “work case 1” is Fig.
2, and this best-version-yet “work case
2” is Fig. 3. The previously most
recent posting (prior to Ref. 1) about this subject is Ref. 3.
Spreadsheet Availability and Function
If you want a copy of the spreadsheet file, please contact me by email. As it says in the user instructions on the
worksheets I created, I recommend that
you keep these example cases unchanged as templates. Copy one of them to a fresh worksheet and do
your design analysis there.
If you copy “work case 1” or “work case 2”, you get the suit pressure rework calculations
as well, off to the right of the main
design analysis. That is only necessary
if your min suit pressure falls in a range that violates the short-term hypoxia
criteria. I did not put the
revised suit calculation block on the “default case” worksheet.
If you instead want to create your own calculations, just remember this critical point: to get wet in-lung oxygenation, you must first subtract-off the water
vapor partial pressure to get the total partial pressure of the breathing gas
inside the wet lungs. Only
after that is done do you get to apply the breathing gas volume percentages
to that total partial pressure of breathing gas in the lungs.
My calculations start with a proposed habitat atmosphere at
some dry total pressure, with a volume
percentage of oxygen in it, and also the
assumption that it is a two-gas mix of just oxygen and nitrogen. That produces the dry breathing gas partial
pressures of oxygen and nitrogen.
I reduce that total pressure by the vapor pressure of water
at human body temperature to find the partial pressures of the breathing gas in
the wet lungs, and apply the volume
percentages to that reduced value, to
get the partial pressures of oxygen and nitrogen in the wet lungs. The partial pressure of oxygen in the wet
lungs compares to the long-term hypoxia criterion of min 0.14 atm.
I do a molecular weight calculation to determine the mass
fraction of oxygen in the mix, which
multiplies the dry breathing gas density to produce the oxygen concentration as
mass per unit volume, for comparison to
the fire danger criterion of max 0.275 kg/m3, for warm dry sea level air at 77 F = 25 C.
The partial pressure of nitrogen in the dry habitat
atmosphere gets divided by the NASA/USN “no pre-breathe” factor of 1.2, to produce the minimum pure oxygen suit
pressure you can use, and still avoid a
pre-breathe time requirement. This gets
the vapor pressure of water subtracted to find the wet in-lung partial pressure
of oxygen. That gets compared to the
short-term hypoxia factors: min 0.12 atm
for full cognitive capability, and min 0.10
atm for bare survival. (Somewhere under
about 0.08 atm is the “certain death-by-hypoxia” point, although such exposure does take significant
time to injure or kill.)
It is entirely acceptable to find a habitat atmosphere at somewhat
lower pressure and slightly higher oxygen than my best recommendation (“work
case 2”), that meets long-term hypoxia
and fire danger criteria, yet the
resulting minimum pure oxygen suit pressure fails to meet the short-term
hypoxia criteria (that is exactly that happened in my “work case 1”).
That minimum suit pressure is just a lower bound on what you
can design your suits to have. You can
always design your suits to a higher pressure than this lower bound, to meet the hypoxia criteria. They will always then satisfy the “no
pre-breathe” criterion. That is exactly
what I did in “work case 1”, and it is
precisely why I added the suit pressure redesign block out to the right of the
main calculation block.
References
#1. G. W. Johnson,
“Habitat Atmospheres and Long-Term Health”, posted 1-1-2022 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).
#3. G. W. Johnson, “Suit and Habitat Atmospheres 2018”, posted 16 March 2018 to http://exrocketman.blogspot.com
Figure 1 – Default Case is Best Case From Ref. 1 (0.45 atm
at 45% O2)
Addendum: “Rule of 43” for Habitat and Suit Atmospheres
Here’s a design combination that is really easy to
remember, and yet gets just about as
good an answer as the fully optimized form.
The optimum case had a habitat atmosphere that was 43.5% oxygen at 0.43
atm pressure. It produced a minimum
oxygen suit pressure of 2.975 psia. The
habitat satisfied the fire danger criterion,
and the long-term hypoxia criterion,
even leaked down 10%. The suit
met the no pre-breathe time requirement, and the fully-cognitive short-term hypoxia
criterion, even when leaked down
10%. It would be more easy-to-wear as a
gas balloon design than current NASA suits,
by far! It would be even more
feasible and easy-to-build as an MCP suit than what Dr. Webb did in the
1960’s.
The “rule of 43” case gets very similar results, but is far easier to remember. It uses a habitat atmosphere that is 43%
oxygen at 0.43 atm pressure (both “43”).
It meets the fire danger criterion,
and meets the long-term hypoxia criterion if leaked down no more than
9.5% (it just barely fails at 10%). The
min suit pressure for no pre-breathe time comes out just a tad higher at 3.002
psia pure oxygen, and meets the
short-term fully-cognitive hypoxia criterion at 10% leaked-down. Like the optimum case, this would be far easier to wear as a as
balloon suit, and far easier to build as
an MCP suit.
Figure 4 is the “rule of 43” combination, and Figure 3 above is the optimum combination
that I found earlier. These were done
with the spreadsheet tool I developed, and
in just a matter of less than an hour,
iterating through several possibilities where the atm of pressure and
the oxygen percentage were the same numbers.
Figure 4 --
“Rule-Of-43” Design Case At 0.43 Atm Pressure And 43% Oxygen
These two cases are so close, that I see very little difference between
them. If the objective of “something
easy to remember” is as important as I have been told it is, then this “rule of 43” design is the one you
really want. Its no pre-breathe min suit
pressure is very slightly higher, and
its habitat pressure leak-down percentage isn’t quite the full 10%, but that doesn’t really matter. Both are in the very same ballpark, with the differences out in the decimal
places.
The main point here is to get into that ballpark, so as to reduce the min suit pressure for no
pre-breathe way below NASA practice, so
that easier-to-wear gas balloon suits become feasible, and that even easier-to-build MCP suits
become possible. These suit pressures
are quite adequate, but are far below
what NASA and its favored contractors have been using (3 psia vs over-4.2 psia).
You find out how adequate these lower suit pressures really
are, once you generalize the health and
oxygen mask altitude criteria to wet in-lung oxygen partial pressures. You need that generalization of those
criteria, in order to extend them correctly
to lower pressures and higher oxygen percentages, than those of Earthly air. You also need a fire danger criterion cast in
the mass/volume chemical concentration format.
And, you need suit short-term
hypoxia criteria based on Earthly use of oxygen masks for pilots at high altitudes.
Utter-Minimum Suit Pure Oxygen Pressures
I used the “work case 2” suit upgrade calculation block to
investigate just how low a suit pressure was safe, using the short-term hypoxia criteria. Remember,
a wet in-lung oxygen partial pressure of 0.12 atm supports a fully-cognitive
wearer. 0.10 atm supports survival
without full cognition: the wearer may
well be somewhat nonfunctional mentally.
Figure 5 is what I get if I require the fully-cognitive hypoxia
criterion to the suit in the 10% leaked-down state. Figure 6 is what I get if I only require the
fully-cognitive hypoxia criterion to the design pressure; leaked down 10%, it fails fully cognitive, but still satisfies bare survival. The lesson here is that suit pressures as low
as 2.675 psia will be quite adequate for fully-cognitive wearers. 2.407 psia will save life, even if the wearer is mentally not fully functional.
Figure 5 – Min Suit For Fully-Cognitive When Leaked-Down 10%
Figure 6 – Min Suit For Fully-Cognitive Only At Design
Pressure
A word of caution:
these utter-minimum pressure suit designs cannot be used
indiscriminately with the two long-term habitat atmospheres identified so far
(0.43 atm and 43.5% O2, and the “rule of
43” design with 0.43 atm and 43% O2).
The utter-minimum pressure designs violate the min suit pressure specs
for no pre-breathe time, because the
ratio of habitat nitrogen partial pressure to suit design pressure exceeds the 1.200
criterion.
I include these utter-minimum suit design specs here, to show what is actually feasible for adequate life
support and mental functionality in pure oxygen suit designs, when those designs are independent of
a habitat pressure that must meet a long-term hypoxia criterion (for the safety
of pregnant women and unborn/newborn children).
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