Thursday, January 27, 2022

The Vaccinations Really Do Work!

These plots are data recently published in the New York Times,  complete with attributions to sources.  They are real data,  and they make liars out of those who claim the vaccinations do no good!  Look for yourself. 

Case rate data are in Figure 1.  Hospitalization rate data are in Figure 2.  Death rate data are in Figure 3.  These are recent enough that the Omicron variant dominates,  but the Delta variant is still out there. 

The attribution for Figure 1 is:  “Data is age adjusted. Recent data may be incomplete.  Sources: New York City Department of Health, Washington Department of Health”

The attribution for Figure 2 is:  “Data is age adjusted. Recent data may be incomplete. Sources: New York City Department of Health, Washington Department of Health”

The attribution for Figure 3 is:  “Data is age adjusted. Recent data may be incomplete. Sources: New York City Department of Health, Washington Department of Health”

So,  dear readers,  if your sources have been lying to you about the effectiveness of the vaccines and boosters,  then what else have they been lying about to you? 

Makes you wonder. 


Figure 1 – Case Rate Data


Figure 2 – Hospitalization Rate Data


Figure 3 – Death Rate Data



Thursday, January 20, 2022

A Question For Readers

Here is a question for my readers who are particularly interested in the space travel stuff that I do.  Would you be interested in participating with others of like mind,  working on these kinds of ideas?  If so,  you might visit,  or even join,  the community that is on the New Mars forums,  part of the Mars Society’s efforts. 

That link is http://newmars.com/forums/

I am a frequent contributor there,  and we on those forums are looking for more folks interested in trying to contribute toward any possible viable ideas.  Give it a try.  Let me know here what you think,  if you go visit there.  Please use the comment option here.  I only remove obvious spam. 

GW 

Wednesday, January 19, 2022

Pertinent Funny

This one speaks for itself,  but is pertinent to so many things I see going on.  Enjoy.  My wife found this for me somewhere on her Facebook.  



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). 


Saturday, January 1, 2022

Habitat Atmospheres and Long-Term Health

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.  Howeveronly 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).

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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/m3The 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