Sunday, January 2, 2022

Refining Proposed Suit and Habitat Atmospheres

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)


Figure 2 – This Is the “Work Case 1” Worksheet,  Now In the Spreadsheet File (0.40 atm at 50% O2)


Figure 3 – This Is the “Work Case 2” Worksheet,  In the Spreadsheet,  and The Best Yet (0.43 atm 43.5%)


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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