Friday, May 4, 2018

Some Thoughts on the Anniversary of the West Explosion

I wrote this article on 23 April,  2018.  A slightly-edited form of it appeared in the Waco "Tribune-Herald" on 26 April,  2018.  By way of disclosure,  I am on the board of contributors for that newspaper.  And a few years ago,  I worked in fire protection engineering,  which gave me much more than just a nodding familiarity with the various fire codes.

For those from out-of-state,  the "Trib" is the Waco,  Texas,  USA,  newspaper.  The agricultural plant in nearby West,  Texas,  caught fire and suffered an ammonium nitrate fertilizer explosion,  some 5 years ago.  Recovery from that devastation is now complete. And devastation it was.

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The 5 year anniversary of the West fertilizer plant explosion recently passed,  with excellent coverage on TV and in the newspaper regarding recovery since.  That recovery is now said to be complete,  and is a testimony to the people of West,  and to all who helped them.

Many things in life are a sort of “double-edged sword” that can either help you or hurt you.  Ammonium nitrate is one of those things.  It makes a wonderful fertilizer as a source of fixed nitrogen.  It is also a mass-detonable explosive in its pure form,  which is type 100-0-0 fertilizer,  something well-known from a long history of such explosions.

When combined with other fertilizer compounds as something other than 100-0-0 fertilizer,  the explosive risk goes away.  But there is still an enhanced fire danger,  as the ammonium nitrate decomposes when exposed to fire,  releasing oxygen into the fire.  That makes the fire very intense.

Now,  neat 100-0-0 ammonium nitrate fertilizer is hard to detonate,  requiring either the same sort of detonator as dynamite (just larger),  or confinement when decomposing in a fire.  Without confinement,  decomposing the material in a deliberate fire is actually the best way to dispose of mass quantities. 

The confinement comes from anything heavy resting on top of the fertilizer (including large amounts of the fertilizer itself,  as at Texas City),  or containing the fertilizer within some physical structure as it decomposes from the heat of a fire.  The fertilizer itself doesn’t burn,  it decomposes. It also melts and runs as a liquid down into any holes or spaces,  even floor drains.

In a building fire such as happened at the West fertilizer plant,  the confinement is generated by either (1) the burning building collapses down upon the decomposing fertilizer,  or (2) the melted fertilizer flows down a floor drain into a pipe.  Either will start the tremendous explosion. 

At the West fertilizer plant,  it was the building collapse that prompted the explosion.  This event actually happened after the majority of the stored fertilizer had already decomposed in the building fire.  Had it happened sooner,  much more of (perhaps all) the town of West would have been obliterated,  and the death toll would have been much,  much higher.

The way to positively prevent ammonium nitrate explosions is to positively prevent the building fire from collapsing the building in the first place.  Wooden structures,  feed,  and grain,  plus other building interior furnishings,  are all flammable:  fuel for the fire. 

In a new facility,  you simply eliminate all those materials from where ammonium nitrate is processed and stored.  But because the fertilizer is stored in paper bags,  there is still fuel next to the fertilizer that enhances the fire. 

So,  you fire-sprinkle the building according to the specific standards for fertilizer storage (and these already exist,  courtesy of the National Fire Protection Association).  There is no other way to be certain.

In an existing facility,  there are likely to be wooden floors,  wooden building structure,  wooden storage racks or pallets,  and perhaps even wooden handling and process equipment.  These are all flammable,  fuel for the fire.  That makes the fire-sprinkling of the building even more crucial,  plus it is prudent to seriously over-design the sprinkler system.

Most of these facilities now lie within the city limits of small towns all over Texas.  Many of them were outside the city limits when originally built,  putting them under county (or state) jurisdiction.  If there is no authorization for a county to impose the fire code standards upon these facilities,  then it is the Legislature’s job to authorize them to do so,  or else to make it a statewide mandate. 

And,  believe me,  they should do so!  There have been many of these explosions over the past century.  There is no excuse to let money trump public safety.  Official both in public service and in private organizations should be judged by how they prioritize public safety versus profit.

There is also the problem of urban sprawl.  As already mentioned,  towns grow toward and engulf these facilities.  Without thinking about the threat,  residences,  businesses,  and schools get built right next to facilities handling what amounts to a high explosive,  if mishandled. 

What that really means is that local officials need to understand the true nature of the threat from ammonium nitrate.  They need to zone around these facilities as their locations are annexed into the city,  to restrict development to a safe distance.  This has not been happening,  but ignorance should not be an excuse!

As for anhydrous ammonia,  it poses much less of an explosion hazard,  but something of a toxic gas release hazard,  even in a plant fire.  However,  there are standards for these,  too.  If applied,  the risks are reduced quite effectively.  Again,  this starts as a county or state requirement for rural construction,  and those same requirements should be applied by the cities as they engulf these facilities,  as well as proper zoning.

Citizens,  you render your judgements at the polls!

Tuesday, April 17, 2018

Reverse-Engineering the 2017 Version of the Spacex BFR

I visited the Spacex website in April 2018 and recovered from it the revised characteristics of the large BFR Mars vehicle,  as presented during 2017.  These characteristics are somewhat downsized from those in the 2016 presentation given in Guadalajara.  Thus this article supersedes the previous article posted on this site 10-23-17,  titled “Reverse Engineering the ITS/Second Stage of the Spacex BFR/ITS System”.  Both articles share the search keywords “launch”,  “Mars”,  and “space program”.  The older article has been updated to redirect readers here.

Data From the Spacex Website

What is listed includes a basic vehicle diameter of 9 meters (both first stage booster and second stage spacecraft),  a booster length of 58 m,  and a spacecraft length of 48 m.  The forward half of the crewed spacecraft includes an unpressurized cargo bay,  and over 825 cubic meters of pressurized space for the crew and passengers.  The rest is propellant tankage and engines. 

No data are given for the uncrewed cargo version,  but it appears quite similar overall,  with a giant clamshell door to open the entire space corresponding to the crewed vehicle’s unpressurized and pressurized payload spaces.

For the crewed vehicle,  payload mass is listed as 150 metric tons to low Earth orbit,  and the same on to Mars with refilling on-orbit.  Return payload (presumably from Mars) is listed as 50 tons,  with refilling done on Mars by in-situ propellant manufacture from local ice deposits and atmospheric carbon dioxide.  The cargo deliverable to orbit by the uncrewed cargo version is also said to be 150 tons.

The crewed spacecraft is listed as having an 85 ton inert structure weight.  Musk says the data right now actually say 75 tons,  but that always grows as development proceeds.  Propellant loadout in the tanks is 240 tons of liquid methane,  and 860 tons of liquid oxygen (1100 total),  both superchilled to a higher density than in normal usage.  The listed data imply similar numbers for the uncrewed cargo version.

Basic weight statements for the crewed vehicle (implied to operable either manned or unmanned by the mission planning) would then be as follows (all masses are metric tons):

Item                     at launch             ign. in LEO           ign. on Mars
Payload                150                         150                         50
Inert                      85                           85                           85
Dry                      235                         235                         135
Prop.                  1100                       1100                       1100
Ign.                    1335                       1335                       1235

 There are not enough data given to establish a weight statement for the first stage booster,  because no inert weight was given.  Only the gross takeoff mass (for 150 tons of payload) was given to be 4400 metric tons.  The inert fraction of the crewed spaceship is a bit over 6%.  Falcon-9 first stages seem to be just under 5%. 

On the assumption that the inert mass fraction of the BFR first stage is 5%,  given the 1335 ton max weight of the second stage,  then the first stage inert mass should be near 220 metric tons.  Under that assumption,  its weight statement would be approximately:

Payload (second stage at max)                   1335
Inert                                                              220
Dry                                                               1555
Propellant                                                    2845
Ignition                                                        4400

The first stage is listed as having some 31 sea level Raptor engines.  The second stage spacecraft is listed as having 2 sea level Raptor engines of high gimballing capacity,  and 4 vacuum Raptor engines of limited gimballing capacity.  The two versions differ only in the expansion bell size,  very much like the Merlin engines used on the Falcon 9 and Heavy. 

Design chamber pressure is listed as 250 bar,  with growth eventually anticipated to 300 bar.  The engines are said to be throttleable from 20% to 100% of rated thrust.  The given specific impulses (Isp) apply to 100% thrust at 250 bar,  and should decrease slightly as thrust is throttled down.  No data are given for that Isp reduction.  It is a relatively minor effect at this level of analysis,  and is ignored in my reverse-engineering analysis here.

Data as listed for the individual Raptor engines are as follows.  The sea level design data as presented do not report vacuum thrust,  but an exit diameter is given,  so that it may be calculated using sea level air pressure of 101.325 KPa.  I did this in my reverse-engineering analysis.  Only vacuum performance is listed for the vacuum design.  Listed data are for one engine. 

The data on the site claim a vacuum engine exit diameter too big to fit a 9 m diameter vehicle;  that has to be a typographical error!  Because the vacuum design is never operated with backpressure (excepting 6 mbar on Mars,  essentially negligible),  the lack of a reliable vacuum exit diameter does not impact my estimates.  

Version                                sea level                               vacuum
Vacuum Isp, s                     356                                         375
Vacuum thrust, KN          not given                                 1900
Sea level Isp, s                   330                                         not given
Sea level thrust, KN         1700                                         not given
Exit dia, m                           1.3                                        12.4 (typo !!!)

The presentation as given on the Spacex website does show the reentry sequence as currently envisioned at Mars.  This shows direct entry from an interplanetary trajectory,  with an entry interface speed up to about 7.5 km/s.  Initially the vehicle is flown inverted for downlift,  presumably to keep it from “bouncing off” the Martian atmosphere while traveling faster than Martian escape speed.  Later in the entry trajectory,  the vehicle rolls upright for uplift, in order to shape the trajectory. 

By the time the hypersonics are ending at about 0.7 km/s (local Mach 3) speeds,  the vehicle is within 4-5 km of the surface,  and climbing upward towards about 10 km altitude.  It reverses to tail first for the retropropulsive burn,  all the way to landing.  The presentation claims max 5 gees deceleration during entry sequence while hypersonic.

No data is given at all for the return entry at Earth.  Presumably,  this would also be direct from the interplanetary trajectory,  with entry interface speeds somewhere in the vicinity of 17 km/s.  This will be a very high-gee entry,  as return from the moon with Apollo was 11 gees at 11 km/s entry interface speed.  12-15 gees (or more) is nothing but a gut-feel guess.

The data on the site show 4 landing legs whose span is 3 or 4 times less than the length of the crewed second stage vehicle.  Cargo is lowered to the ground from the cargo bay door with a crane.  People would leave the vehicle by the same means,  and reverse the crane to return to it.

Organizing the Analysis

The Spacex website presentation claims refilling on orbit from uncrewed tanker vehicles.  The illustrations show variously 4 to 5 such tankers,  but no data are given.  Propellant transfer is by tail-to-tail docking,  with thruster-induced microgravity driving propellant flow from one vehicle to the other.  It is unclear whether the tanker is an unmanned crewed vehicle or the cargo vehicle,  and it is unclear whether propellant is loaded as cargo,  or is leftover in the tanks after flying to orbit with no payload.

The tanker performance problem is not analyzed here.  

The analyses here were made using simple rocket equation estimates modified with realistic “jigger factors” for gravity and drag losses.  Because of the long times in interplanetary flight with cryogenic propellants,  other “jigger factors” get included to account for boiloff effects and midcourse correction budgets.  And because retropropulsive landings must have a margin to adjust touchdown if obstacles are encountered,  yet another “jigger factor” must be included to model the need to hover and/or redirect touchdown laterally some distance away. 

For Earth launch with slender,  “clean” vehicle shapes,  something like 2.5% gravity loss and 2.5% drag loss provide realistic first estimates.  The two add to 5%,  which gets incorporated into a “jigger factor” of 1.05,  that multiplies the kinematic delta-vee requirement,  making it suitably larger to cover gravity and drag losses in the simple rocket equation.  At Mars,  gravity is weaker and the air much thinner,  so I reduce the gravity percentage by a factor of 0.384 (Mars surface gravity in gees),  and the drag percentage by a factor of 0.007 (Mars surface density ratioed to Earth standard).  In retropropulsion,  drag helps rather than hinders,  so the two percentages subtract instead of adding. 

I assumed a factor of 1.1 increase on the already “jigger-factored” propellant weight (out of the rocket equation for that burn) to include a “kitty” for minor midcourse corrections,  and the same for long-term propellant boiloff effects in transit.  I also assumed a hover/redirect factor of 1.5,  to multiply the same already-factored propellant weight,  during landing burns. 

These calculations can be made by hand,  but are very conveniently entered into a spreadsheet,  for rapid changes and refinements.  That is what I did for this analysis.  Its results were incorporated into a series of figures.

First Stage Problem

The first stage problem has but one payload,  a weight statement based on the 5% inert fraction assumption,  and suitable sea level and vacuum engine performance data for the sea level Raptor engine design.  The website presentation does not give any indication of the staging speed or altitude,  only depictions showing the trajectory bent over almost level by the time staging occurs. 

This is complicated by the need to fly the booster back to launch site,  and land it there,  very much like the Falcon-9 first stages.  Therefore,  beyond just reaching staging speed against realistic gravity and drag losses,  enough propellant must remain on board after staging,  for the stage (with no payload) to more-than-“kill” its flight velocity with a boostback burn,  ease the entry heating with a shock-penetrating entry burn,  and conduct the final touchdown burn. 

I made the “reasonable” guesses of allowing 0.99 km/s worth of delta-vee for the touchdown burn,  an arbitrary 0.10 km/s delta vee for the entry burn,  and a boostback delta-vee equal to,  or slightly exceeding,  the speed at staging.  I assumed staging altitude to be essentially in vacuum,  so that the average of the sea level and vacuum Isp’s could be used to represent average booster performance. 

Staging speed was an input assumed value,  since it was not specified in the presentations on the website.  I iteratively modified this value until the 3 flyback burns all had reasonable delta-vee values.  The boostback kinematic delta-vee is the staging speed.  It is figured for the ascent weight statement,  “jiggered” by factor 1.05,  and then plugged into the rocket equation for a mass ratio less than what the stage provides overall.  Dividing launch mass by that ratio gets the burnout mass,  and the difference is the ascent boost propellant mass burned to reach staging speed.

Deleting the payload mass (second stage) gives a new weight statement for booster inert and the mass of propellant still on board.  It corresponds to a certain delta-vee from the rocket equation,  “jigger-factored” down by 1.025,  since there is no drag outside the atmosphere.  Subtracting 0.99 km/s for the touchdown burn,  and 0.10 km/s for the entry burn,  leaves the delta-vee benefit available for the boostback burn.  I adjusted my assumed staging speed until my boostback delta-vee equaled or slightly exceeded this staging speed value. 

At launch,  the sea level thrust of the 31 sea level Raptor engines totals to 5375 metric tons-force (force in KN/9.805).  The website data lists 5400 tons of thrust,  close enough.  The thrust/weight ratio minus unity gives the kinematic acceleration straight upwards,  in gees.  At staging,  one must correct to vacuum thrust of the sea level engines,  and since the trajectory is nearly level,  the thrust/weight ratio is the pathwise kinematic acceleration in gees.  These values can be factored by the throttle percentage expressed as a fraction,  if needed.  I bounded the burnout accelerations by calculating values at 100% and 20% thrust.


Those results are summarized in Figure 1.

 Figure 1 – Results for the Booster Problem with Flyback Recovery

Going to Mars After Refilling in Earth Orbit

This is not quite straightforward,  because you cannot use all your propellant to go to Mars.  You must have enough propellant still on board after departure,  to enable the landing on Mars.  That means you analyze the Mars landing first,  and then the departure burn from Earth orbit. 

You have to analyze from dry tanks at touchdown on Mars back to the landing burn ignition conditions,  complete with Mars retropropulsion gravity/drag effects,  for the min propellant needed to land.  Then you scale that amount of propellant up with the hover/redirect factor on your delta-vee for a realistic propellant budget to land from the rocket equation.

Then you scale that realistic landing budget up with the boiloff factor and the midcourse factor to find the actual reserve propellant that you must still have on board after the departure burn.  That is what sets your weight statement for the departure burn. 

These results for the Mars landing are given in Figure 2.

 Figure 2 – Results of the Analysis of the Mars Landing

The departure burn from Earth orbit sees an Earth gravity loss,  but no drag loss.  The usable delta-vee from it adds to the Earth orbit velocity for a velocity Vdep at that Earth orbit location.  A little farther from Earth,  you figure a velocity-at-infinity as Vinf = (Vdep^2 + Vesc^2)^0.5.  Then you add Earth’s orbital speed to that value for the vehicle speed with respect to the sun Vwrt sun. 

For a min energy Hohmann-type transfer ellipse orbit there is a perigee velocity,  which varies with planetary positioning along their ellipses.  I used the worst case (highest) value.  The vehicle velocity with respect to the sun Vwrt sun,  minus the Hohmann transfer perigee speed Vper-HOH,  is the margin you have,  that might be used to fly a faster trajectory.  Hohmann transfer is about 8.5 months one way. 

These results for the departure from Earth orbit are given in Figure 3.

Figure 3 – Results for the Analysis of Departure from Earth Orbit

Returning From Mars

Very similarly to the trip outbound to Mars,  one must analyze first the landing on Earth,  to define the propellant needed to land there,  jigger that up for the transit,  and have that quantity in reserve after the Mars departure burn.  So you analyze the Earth landing first,  then the departure from Mars,  which is a direct ascent into the interplanetary trajectory.

I used the same basic end-of-hypersonics at 0.7 km/s (local Mach 3) as my kinematic definition of min landing delta-vee.  This just happens at higher altitude,  and in much thicker air,  on Earth.  Unlike Mars,  it is quite feasible to fall a long way in the transonic/low-supersonic flight speed range,  before reversing vehicle orientation to tail-first for the touchdown burn. 

You “jigger-up” this min delta vee by a gravity-drag factor (near 1 in retropropulsion on Earth) and by the hover/redirect factor (I used the same factor 1.5 for this).  That much larger delta-vee goes through the rocket equation for a mass ratio from dry tanks at touchdown.  This leads to a realistic landing propellant budget.  Then you factor that up for boiloff and midcourse,  to find the reserve propellant that must be on board after the Mars departure burn. 

The Earth landing results are given in Figure 4.

 Figure 4 – Results for the Earth Landing Analysis

This Earth landing propellant budget at Mars departure then adjusts the weight statement of the refilled craft upon Mars,  in addition to the stated reduction in return payload.    This is a direct departure:  the weight statement and choice of engines finds the ideal delta-vee,  adjusted downward by the Mars gravity-drag factor to a realistic delta-vee.  We are not stopping in Mars orbit,  this realistic delta-vee becomes the speed of the vehicle near Mars.  It is adjusted using Mars escape velocity to find the Vinf in the vicinity of Mars.  That is in turn subtracted from Mars’s orbital velocity to find the velocity with respect to the sun.  This is compared to the Hohmann min energy transfer orbit’s apogee velocity,  to determine any margin available for a faster trip home. 

These numbers indicate little or no potential for a fast return home.  The results are given in Figure 5. 


Figure 5 – Results of the Mars Departure Analysis

Conclusions

Using Spacex’s own data  plus some reasonable assumptions regarding gravity and drag losses,  and hover requirements for retropropulsive landings,  and for boiloff and midcourse budgets,  I calculated performances estimates,  for the big Spacex Mars vehicle as presented in 2017, that are not very far at all from what is claimed in their 2017 presentation. 

I show some potential for a slightly-faster trajectory to Mars than min energy Hohmann transfer.  I show very little,  essentially zero,  potential for a faster return trajectory from Mars,  compared to min energy Hohmann transfer. 

To get these data,  I had to assume that the inert mass fraction of the BFR first stage is 5%,  and I had to assume that the BFR stages at just about 2.55 km/s flight speed,  outside the sensible atmosphere,  and already almost level. 

I used the reported engine performance data for the sea level and vacuum forms of the Raptor engine,  operating at 250 bar chamber pressure at full thrust.  If the chamber pressure can be raised closer to 300 bar (as Spacex wants),  some of the faster-trip performance shortfalls ease.  I did not analyze these data to quantify that effect.

Gravity and drag loss effects upon ideal rocket equation delta vee are assumed at 2.5% each here on Earth,  and ratioed down by 0.384 for gravity,  and 0.007 for drag,  at Mars.  Propellant quantities coming from the rocket equation mass ratio and appropriate weight statements get ratioed by an assumed factor of 1.5 for retropropulsion hover/redirect effects,  by a factor of 1.1 for boiloff effects in transit,  and by a factor of 1.1 for budgeting midcourse correction propellant. 

To correct sea level thrust of a sea level Raptor engine to vacuum conditions,  add a force equal to the exit area multiplied by Earth sea level air pressure.  This does not affect rocket equation results,  but it does affect vehicle acceleration-capability calculations.  These help you choose which engines to burn,  and what levels of throttling to use.

Spacex has posted data for anticipated Mars entry from the interplanetary trajectory,  but not for Earth entry from the interplanetary trajectory.  It is peak entry deceleration gees during the return to Earth that is very probably the highest gee requirement for occupants to endure.  This is not something controllable with engine thrust,  as there is no propellant available to budget for this purpose. 

Earth entry deceleration from Mars (on a direct entry from the interplanetary trajectory) is quite likely to be far more severe than the Apollo 11-gee peak deceleration coming back from the moon at an entry interface speed of 11 km/s.  Coming back direct from Mars,  entry interface speed is likely to be in the vicinity of 17 km/s.  The crew simply must be very physically-fit to endure this.  This is a serious issue yet to be addressed in the Spacex presentations.

Landing stability of a relatively tall and narrow vehicle,  on unprepared rough ground on Mars,  is not addressed here.  This is another serious issue yet to be addressed in the Spacex presentations.

Update 4-18-18 artificial gravity

For Spacex’s mission plan with its BFR vehicle,  the health risk for high gee entry occurs at Earth return.  It cannot be avoided.  The occupants so exposed will have endured months-to-years of low Mars gravity (0.384 gee),  followed by about 8 to 8.5 months exposure to zero-gee on the transit home.  They are very unlikely to be physically fit for an 11+ gee entry,  even if Mars gravity is found to be fully therapeutic for microgravity diseases.   

The support for that assertion comes from years of orbital experiences at zero gee.  Astronauts exposed to zero gee for times on the order of 6 months to a year have proven to be fit enough to endure a 4 gee ride down from Earth orbit,  with an entry speed of 8 km/s.  We have absolutely nothing to point at,  to support the assumption that higher gee levels are safely endurable in that physical state!   Coming from Mars is a faster entry at about 17 km/s than from the moon,  and that was an 11 gee ride at 11 km/s.

Given that risk,  artificial gravity for at least the voyage home seems prudent.  This could possibly be accomplished by having two ships make the return voyage together.  Taking advantage of the refilling plans and procedures,  dock the two ships tail-to-tail during the long coasting transit.  Spin them up end-over-end with the attitude thrusters.  At the nominal 4 rpm spin limit,  near-Earth gee levels are obtained as shown in Figure 5. 


Figure 5 – Obtaining Spin Gravity in Two BFR Ships Docked Tail-to-Tail

The 4 rpm limit is a “fuzzy” limit.  If a very slightly-higher spin rate (maybe 4.6 or 4.7 rpm) is tolerable to the balance organs in the middle ear,   then very near full Earth gravity can be simulated in the occupied decks.  This is also shown in Figure 5 as the data in parentheses.  This is an artifact of the size of the BFR vehicle.  Achieved gee level is proportional to spin radius,  and to spin rate squared.  A nominal reference point is 1 gee at 56 m radius and 4 rpm.

There are two inconvenient design issues with this notion,  but they are not “show-stoppers”.  One is the reversed directions for up and down,  sitting on the landing legs versus spinning for artificial gravity.  What were floors become ceilings,  and vice versa.  All the interior equipment and appurtenances will have to be reversible physically,  or “double-ended” if not. 

The other is the solar panel fans that Spacex shows for powering these vehicles with electricity.  The presentations show them deployed near the tail of the vehicle while in space (free fall).  These will have to be strong enough to deploy properly,  and stay in position,  while exposed to low levels of effective gravity while spinning.  As shown in Figure 5,  these levels of gravity will be less than lunar gravity.  Capture of solar energy for conversion to electricity will usually be intermittent,  at the spin rate.

These are design inconveniences,  to be sure.  But in comparison to losing occupants due to heart failure at high entry gee,  just minutes from returning to Earth,  these are minor inconveniences.  I am fond of reminding people that “there is nothing as expensive as a dead crew”. 

Update 4-19-18 landing stability etc:

Landing stability on Mars is associated with overturning issues,  landing pad penetration into soil,  and the perturbing dynamics of trying to land among rocks.  There are also issues with the jet blast flinging debris where it is not wanted,  although these only arise with subsequent ships landing near the first ship or any other structures or equipment already there. 

From an analysis standpoint,  there are static effects and dynamic effects.  From a mission standpoint,  there is a landing at low weight,  and a takeoff at high weight.  For the takeoff,  there are few,  if any dynamic effects to worry about.

Landing Statics

This topic divides into static overturn stability,  and the soil bearing pressure underneath the landing leg pads.  Static overturn stability simply requires that the weight vector fall within the polygon defined by the landing pads,  no matter how off-angle the ship sits,  such as on inclined ground.  As shown in Figure 6 below,  this isn’t much of an issue for inclinations oriented directly toward a pad,  as illustrated. 

The center of gravity position in the figure is only a guess,  but a realistic one.  The span pad-to-pad is only a guess,  but also a realistic one.  The ground could incline some 18 degrees directly toward a pad,  and still be stable,  as shown in the figure.   If the inclination is directly between two pads,  the lateral distance is 70% of the value shown,  for a max inclination angle of about 13 degrees.

13 degrees is a rather steep local slope on terrain chosen to be flat.  We can conclude that the otherwise tall BFR spaceship is at relatively lower risk of simple static overturn,  as long as small localized hazards like a pad coming down in a dry stream gully can be avoided.  That might be very challenging to satisfy in a robotic landing,  though.  Hopefully the available stroke in each landing leg exceeds the roughly 2 m shown in the figure.  That should take care of most of the localized roughness hazards.  Stroke rate capability should be comparable to ship speed just as it touches down.

At landing,  with the full 150 ton payload and 85 tons of inert,  the ship at “dry tanks” masses 235 metric tons.  If the landing is “perfect” and does not use any of the hover/redirect allowance built into the propellant budget,  there might still be something like 53 tons of propellant on board at touchdown,  bringing the as-landed mass to 288 tons as a maximum.  At Mars 0.384 gee,  the corresponding weight on the landing legs is 1084 KN. 

If evenly distributed among the 4 landing legs,  and if the total pad area is 10 sq.m as shown in the figure,  then the bearing pressure exerted upon the soil after landing is 108-109 KPa.  If all the propellant is used,  the bearing pressure is the lesser 88.5 KPa shown in the figure. 

The figure shows typical soil bearing pressure capabilities for two soils that might be like soils that could be encountered on the plains of Mars.  One is soft fine sand,  like many deserts with sand dunes on Earth,  capable of from 100-200 Kpa.  The other is more like desert hardpan on Earth,  with lots of gravel mixed into coarse sand and relatively-compacted:  some 380-480 KPa.  Excluding dynamic effects,  even the soft fine sand seems capable of supporting the low weight of the as-landed ship.

Landing Dynamics

If there is some inclination,  it will tend to throw some of the ship’s weight toward the downslope pad or pads.  Landing impact dynamics could possibly double the static forces on a short transient.  If we double the static bearing pressures,  this should typically “cover” the landing impact dynamics and any small inclination effects.  For a ship with residual propellants on board,  the doubled static bearing pressures are in the 220 KPa class. 

That rules out soft fine sand by considerable margin.  Any landing site must be desert hardpan or better in terms of soil bearing strength,  or else the landing pads had better total far more than 10 square meters of bearing area (something difficult to achieve).  Thus it would pay to select a landing site already visited by an earlier probe or rover,  whose visit could verify soil type and estimated strength. 

Once the equipment is in place to prepare hard-paved landing sites ahead of time,  this restriction loosens.

About the worst conceivable landing dynamics event is for one pad to touch down on a boulder,  and then slip off during the touchdown,  leaving the vehicle temporarily unsupported on that side.  If that happens to be downslope,  the vehicle will start to topple that way,  while the leg strokes to reach the actual surface. 

If one assumes a realistic 5 degree local slope down toward the pad that hits and slips off a 1 m boulder,  then for the max landed weight of 1084 KN (as calculated above),  a side force at the center of gravity of about 95 KN acts to topple the vehicle.  This is on an effective moment arm of 22 m,  using the surface as the coordinate reference.  That torque is 2090 KN-m = 2.09 million N-m.

Approximating the vehicle as a solid bar 48 m long of mass 288 metric tons,  its moment of inertia is roughly (1/12) m L^2 = 55.3 million kg-sq.m.  The resulting angular acceleration is something like 0.0378 rad/sq.sec or 2.16 deg/sq.sec. 

Ignoring the recovering stroke rate of the slipped leg,  the vehicle could rotate through about 5 degrees for that pad to actually strike the real surface.  Adding the inclination of 5 degrees,  that’s 10 degrees out-of-plumb,  within the 18 degree limit for one pad directly downslope,  and also within the limit for two pads downslope. 

Now,  in this transient as the slipped pad hit surface,  the vehicle is already moving,  and is going to take time to stop moving once the pad is on solid ground to resist.  Crudely speaking,  the time for the pad to strike the surface is near 2.15 sec,  and the ship will be moving at about 4.6 deg/s.  The pad support force has to stop this motion in its 1 remaining m of stroke. 

That pad force will be in the neighborhood of 279 KN,  just ratioed from the disturbing force by the ratio of moment arms,  and acting upon about 2.5 sq.m for one pad.  The vehicle will move another 5 degrees during this deceleration transient.

At the end of this transient,  the vehicle is about 15 degrees out-of-plumb,  dangerously close to the 18 degree limit directly toward 1 pad,  and beyond the 13 degree limit directly between two pads.  The bearing pressure under the pad exerting the restoring force is in the neighborhood of 112 KPa plus the allocated static weight pressure for the vehicle at rest (109 KPa):  a total near 221 KPa. 

From an inclination standpoint during this transient,  the vehicle is dangerously close to toppling over,  even if the soil is infinitely strong and hard.  If the soil resembles packed coarse sand with gravel,  it is theoretically strong enough to resist serious compaction under the pad exerting the restoring force,  but whatever compaction does occur allows the vehicle to incline just that much more.  If the soil resembles more soft fine sand in strength,  the restoring pad will inevitably dig in,  without being able to exert enough restoring force,  and so the vehicle will indeed topple over and be destroyed. 

The toppling risk is high if a pad strikes an obstruction of any significant size (in this example,  a boulder 1 m in dimension).  Things of this size are difficult to observe by remote sensing from orbit.  The risk situation is quite similar to the boulder field encountered during the Apollo 11 moon landing,  and requires a hover and redirect action away from the threat.

The BFR vehicle obviously needs some sort of “see-and-avoid” capability at touchdown.  This would be direct vision with a human pilot,  or something very sophisticated indeed built-in for a robotic landing.  If the vehicle were not so tall,  the moment arm of the disturbing force would not amplify the toppling effect so much.  That is why the Apollo LM and all the Mars landers have had a height/span ratio under 1.   That number is 3+ for this vehicle.


Figure 6 – Data to Support Statics and Dynamic Calculations

Takeoff Statics (Only)

At takeoff,  payload is reduced to 50 tons,  inert is the same 85 tons,  and the refilled propellant load is the maximum 1100 metric tons.  The vehicle mass at takeoff is then 1235 metric tons.  At Mars 0.384 gee,  the vehicle weight is near 4650 KN.  Evenly distributed onto a nominal total of 10 sq.m of pad area,  the exerted bearing pressure is 465 KPa.

The soil upon which it rests had better not be similar to fine soft sand,  or the landing legs will sink deeply into the soil as propellant is loaded. 

This could lead to landing leg damage as the ship launches,  or even prevent its launch,  given the high extraction forces trying to pull out deeply-embedded pads.  If the soil properties vary on a 5 m scale,  the legs could embed unevenly.  That could risk toppling over with propellants on board,  leading to a huge explosion.

If the soil resembles gravel embedded in packed coarse sand,  the static bearing pressure at launch falls within the range of soil bearing strengths,  before the safety factor of 2 is applied.  That means it is very likely that the pads will sink a bit into the soil,  although not likely enough to run the embedding risk.  If the soil properties vary on a 5 m scale,  this sink-in will be uneven,  adding to the vehicle inclination. 

Given those outcomes,  it would be wise to design larger pads on the landing legs,  or use more than the 4 legs depicted in the website presentations.   This size and shape of vehicle is more safely operated from a very level,  hard-paved pad,  or from level,  flat solid rock. 

I do recommend using the coarse sand/gravel soil strength as representative of the sand/rock mix we see on Mars.  The minimum Earthly strength of that material is about 380 KPa,  with around 480 KPa as the max strength.  I also recommend using at least a factor of 2 upon exerted pad pressures to model inclination and sudden-impact effects on landing.  Best practice would apply that to takeoff as well,  although perhaps a factor nearer 1.1 might be adequate. 

The landing leg and pad depictions on the website are very generic and lack detail.  I don’t believe this part of the vehicle has yet received much in the way of design attention.  I presumed 10 sq.m of pad area,  and it is really not enough.  This part of the design needs such attention,  as it will be difficult to incorporate 14+ sq.m of flat pad area on the ends of 4 landing legs,  and still stow these away successfully for hypersonic entry aerobrake events.  If circular,  that 14 sq.m of pad area corresponds to pads about 2.1 m in diameter.  Even my 10 sq.m analysis implies circular pads 1.8 m diameter.

Debris Flung By Jet Blast

The force exerted on the surface by the rocket streams as the vehicle touches down is just about equal to the engine thrust.  At landing on Mars,  this would be the vacuum thrust of two sea level Raptor engines.  This is about 3670 KN.  It would be exerted over an area on the ground comparable to the exit area of the engines,  or maybe a little more.  That would be something in the vicinity of 3 sq.m.  That effective average pressure is near 1220 KPa. 

That pressure is so far above the soil bearing strength,  even for coarse sand with gravel,  that the sand will get flung as a supersonic sandstorm,  and rocks of substantial size are going to get torn loose and flung with considerable force,  albeit at a rather low launch angle. 

For a 10 cm rock,  the cross section area is about 0.00785 sq.m.  The jet blast pressure acting on that area produces a force in the vicinity of 9.6 KN.  At specific gravity 2.5,  such a rock should mass something in the vicinity of 1.3 kg,  and on Mars would weigh something like 4.9N.  The force to weight ratio is huge at nearly 2000 to 1. 

Using impulse and momentum,  with a wild-guessed action time on the order of 0.01 sec,  the thrown velocity of this rock would be on the order of 75 m/s.  If the elevation angle were 10 degrees,  the range at which the rock comes down would be around 0.5 km.  These crude estimates could easily be too conservative. 

Loss of a Ship Leading to Explosion

If a ship should topple over and explode,  or crash and explode,  large debris will be flung with incredible force.  Based partly on half the speed of the military fragment impact tests,  the velocity of such debris might be in the vicinity of 1.2 km/s.  It will leave the scene at all elevation angles from zero to straight up.  In the low gravity on Mars, such debris flung at 45 degrees will travel over 350 km.

It will be almost impossible to protect from debris flung nearly vertically,  which will come down close to the site.  It would be possible to intercept the low-angle debris with an earthen embankment bulldozed around the landing pad.  That might protect neighboring ships on adjacent pads,  or base buildings erected nearby,  acting as a shadow shield.  Based on what I have seen published about the base to eventually be constructed with these BFR ships,  I don’t think this issue has yet been considered at all.  Yet,  such an explosion is inevitable over the long haul,  even if very rare. 

Conclusions and Recommendations

It is probably too late in the design process to adjust vehicle length and diameter to a shorter,  fatter proportion.  That means the landing pads must exceed about 14 sq.m total area in actual contact with the ground,  if my soil strength estimates have any reality at all.

I strongly recommend to Spacex that they start looking closely at these issues of landing and takeoff statics,  and the landing dynamics.  From what has been published so far,  I have to conclude that they have not addressed these particular issues in any detail,  yet. 

I would definitely,  and very strongly,  recommend that BFR landing sites be at least 1 km away (preferably 2+ km) from other grounded ships or any other structures or equipment,  to mitigate the flung rock hazard.  This would be true until such time as hard paved landing pads can be constructed.  “Hard” means materials with compressive and shear strengths both exceeding about 1500 KPa = 1.5 MPa.  Such will automatically satisfy needed bearing strength.

I would also recommend to Spacex that they begin considering the possible effects of a ship explosion upon adjacent ships,  base buildings,  and other nearby equipment.  Berms around hard-paved pads are highly recommended.  Such high-velocity debris will travel a long way in Mars’s low gravity,  and some of these pieces will be quite large.   Such events may actually be exceedingly rare,  but the results are unacceptably catastrophic,  no matter how rare.  Probability x cost is NOT the way to judge this.

Update 4-21-18 speculations on the tanker issue:

This update presents very speculative numbers I ran trying to understand the tanker vehicle issue.  This includes both the design of the tanker,  and how many are needed to fully refill a crewed BFR second stage vehicle in Earth orbit. 

Spacex presents on its website estimated weights data for the crewed vehicle,  and not for the cargo-only unmanned vehicle (or the tanker).  The implication is that the cargo vehicle overall characteristics are similar to the crewed vehicle.  There is no clue given as to the identity or characteristics of the tanker. 

It would make sense that the same engine section and propellant tank section would be used in both (or all three),  just with different forward section structures,  although with the same heat shield.  That is the “justification” for using the same inert weights,  propellant weights,  and payload weights for crewed and cargo vehicles in the original portion of this article.  In particular,  the inert weights are likely not to be the same,  although they are likely to be crudely similar.

Here in this update,  I extend that inert weight assumption to any potential third configuration that would serve as a dedicated tanker.  It would have additional tanks holding 150 tons of propellant mounted in the forward section,  and plumbed into the other tanks.  The other competing idea is to fly a crewed BFR unmanned,  or a cargo BFR,  but both with zero payload on board.  If fully loaded with propellant in the tanks,  either of these would arrive on orbit with considerable unused propellant beyond the landing budget (effectively the “tanker load”).

All the assumptions and engine performance data are the same as I already used in the original portion of this article.  The same basic mission analysis consideration applies:  hold enough propellant in reserve to land.  The difference here is that the landing is made with zero payload on board,  which reduces the necessary budget for landing propellant.  Plus,  no budgets need be maintained for long-term boiloff effects, or for deep space midcourse maneuvers.  Thus the reduced figure of 32.6 tons of landing propellant will suffice to land at zero payload,  even with factor 1.5 on the landing delta-vee to cover any “hover and redirect” effects. 


Similar to what I did in the original portion of the article,  we start with the landing to determine that landing propellant budget.  With all three designs sharing the same overall weight statement,  all three then share the same dry-tanks weight at landing,  and thus the same landing propellant budget.   Then we apply that reserve to each of the three tanker configuration candidates to determine how much deliverable propellant they can provide on orbit.  Assumptions are shown in Figure 7,  results in Figure 8.

 Figure 7 – Assumptions Made to Model the Tanker Problem Two Ways

Figure 8 – Results Obtained Modeling the Tanker Problem Two Ways


Applicable overall weight statements (metric tons) are:

                                crewed                 cargo                     ded. tanker
inert                      85                           85                           85 (#1)
payload                0 (#3)                    0 (#3)                    150 (#2)
b.o.                        85                           85                           235
propellant           1100                       1100                       1100
ign                          1185                       1185                       1335

notes:  
#1. incl extra tanks
#2. payload is propellant
#3. capable of 150 tons, flown here at 0

The resulting as-flown weight statements are:

                                Crewed                cargo                     ded.tanker
Ign                          1185                       1185                       1335
Asc.prop              925.6                     925.6                     1042.8
b.o.                        259.4                     259.4                     292.2
less del.prop      141.8                     141.8                     174.6 (#1)
land.ign.               117.6                     117.6                     117.6
land.prop            32.6                        32.6                        32.6
b.o. (inert)          85                           85                           85

notes:
#1. 141.8 left in main tanks excl. landing prop.
#1. 24.6 left in main tanks excl. land.,  plus 150 in payload tanks

The “dedicated tanker” configuration with extra tanks holding 150 tons in the forward section is the most efficient tanker of the three candidates.  It takes 6.3 of these to completely refill a crewed BFR vehicle in low Earth orbit,  using that 150 tons plus the excess in the main tanks beyond the landing budget.  The downside of this design is a third configuration to account fir in manufacturing.  It wouldn’t take much design refinement to eliminate the “.3” and get to 6 tanker flights. The target is 183-184 tons delivered to low Earth orbit.  The design (as crude as it is) delivers 175.

Provided that the crewed and cargo vehicles share the same inert masses,  then if flown at zero payload,  they arrive with enough excess propellant in the main tanks beyond the landing budget,  to enable complete refilling of a crewed vehicle in low Earth orbit,  if flown some 7.8 times.  This approach is less efficient from a number of flights standpoint,  but allows the advantage of having to account for only two configurations in the manufacturing effort.  It is probably not possible to get enough design refinement to eliminate the “.8” and get to 7 tanker flights.  8 flights is likely realistic.

The “real” numbers are going to be different,  once revealed by Spacex,  because these configurations will not all share the same inert weight as was assumed here.  The “flown-at-zero-payload” potential is close enough to the “dedicated tanker” potential that perhaps Spacex should investigate this possibility closer,  before “freezing” the crewed and cargo designs,  in spite of the inefficiency of flying with such large volumes of empty space on board.

Note also in the results figure that gee loads have been held to very tolerable values with very simple choices of engines and throttle settings.  In particular,  the landing settings have been chosen to enable either a 1-engine or 2-engine touchdown from the very same point in the descent trajectory.  You plan on flying as 2-engine,  but if one fails to ignite,  you just immediately double the thrust setting on the remaining engine.  The throttle margins are there to support that.

Friday, March 16, 2018

Suit and Habitat Atmospheres 2018

This article takes on the best available information regarding selection of pure oxygen space suit pressure levels,  and how they relate to space habitation atmosphere composition and fire dangers.  The previous related articles posted on this site all share the same basic methodologies and calculation methods. 

The fundamental methodology here is to calculate both atmospheres and design criteria in terms of the wet in-lung partial pressure of oxygen,  which in turn is what actually drives the diffusion of oxygen across the lung tissues into the blood. 

In the earlier articles,  there were unresolved issues with “pre-breathe” (decompression) criteria,  and with fire danger criteria,  that have since been resolved or sidestepped.  This article brings,  as a new item,  a “leak-down” suit pressure factor,  and also brings additional supporting data for the selected suit pressures,  which are lower than is typical of NASA practice today.  Lower pressures make space suits more comfortable to wear,  and easier to design.

Lists of the previous articles follow.  The most recent,  superseded by this one are:

“A Better Version of the MCP Space Suit?” 11-23-2017
“Suits and Atmospheres for Space” 2-15-2016

Those two in turn superseded these earlier articles:

Space Suit and Habitat Atmospheres” 11-17-2014
“On Orbit Repair and Assembly Facility” 2-11-2014
“Fundamental Design Criteria for Alternative Space Suit Approaches” 1-21-2011

The best way to find any of these is to use the date/title navigation tool at the left.  Click on the desired year,  then on the desired month.  If the article is not top of the list (in view),  click on its title. 

To view any or all of the figures enlarged,  click on any of the figures.  You may then scroll through all of them in enlarged format.  Once done,  you can return to the article by “X-ing-out” of the enlarged figures screen. 

Another way is to find one,  then click on the “space program” keyword.  Then you will see only those articles with that search keyword,  which these all share.  An alternative keyword is “space suit”,  but I’m not sure that all of them share this search keyword.  The more recent ones do,  for sure.

Wet In-Lung Oxygenation is Not the Oxygen Content of What You Breathe

Atmospheric pressure is easily determined versus altitude using published atmosphere tables.  It doesn’t vary much from model to model.  The model used here is the US 1962 Standard Day,  which for altitudes up to about 65,000 feet,  is identical to the ICAO Standard Day. 

Air composition is fairly standard as follows.  It is oxygen,  diluted with mostly nitrogen.  The largest trace ingredient is argon.  Whether given as fractions or percentages,  these compositions are usually given in volume format,  which is also molar.  True “synthetic air” is the two-gas mix of oxygen and nitrogen,  at the same oxygen content as real air.  Other ratios are also feasible,  for different purposes.  The standard air oxygen content used for this article is 0.20946 = 20.946% by volume.

Gas                      Vol %
Oxygen                20.95
Nitrogen              78.09
Argon                   0.93
Carbon dioxide   0.03 (older figure,  has since risen to 0.04)
Trace gases         0.018 or less

These figures are for dry air (no humidity).  The presence of water vapor displaces dry air,  so that the total of their pressures adds to the atmospheric pressure.  The water of interest here is that within the lungs,  with liquid moisture present at body temperature.  If one assumes the vapor is in equilibrium with the warm liquid,  then the vapor pressure in the lungs is the standard steam table value at body temperature:

                Pvap = 47.07 mm Hg = 0.061934 atm 
at T = 37.0 C = 98.6 F (human body temperature)

The oxygen partial pressure in the dry air is the dry air pressure multiplied by the volume fraction of oxygen.  In the atmosphere tables,  the pressure ratio to standard sea level pressure is numerically equal to the altitude pressure in atm.  Dry air oxygen partial pressure,  atm,  is thus 0.20946 * (P/PSL).

In Figure 1,  oxygen partial pressure in the dry air is plotted versus a wide range of altitudes.  To calculate wet in-lung oxygen partial pressure,  you reduce the dry air pressure by the water vapor pressure,  then apply the oxygen fraction to that reduced value.  Both are plotted in Figure 1.  The difference between then becomes increasingly significant as altitude increases,  because water vapor pressure depends on only body temperature,  and is thus an ever-larger portion of the atmospheric pressure as altitude increases.

There are several notes added to the figure.  First is that US Navy pilots are required to start using supplemental oxygen when they exceed 5000 feet altitude.  Second is that USAF pilots,  and FAA civilian pilots,  must use supplemental oxygen when above 10,000 feet.  In the civilian case,  this is coupled with a time limit,  so that oxygen is not required if above 10,000 feet,  until the time is exceeded.  But oxygen is always required if above 14,000 feet.

Also shown on the figure is the usual airliner cabin pressure altitude practice,  which is 10,000 to about 15,000 feet equivalent.  The 10,000 foot condition is rather close to the elevation of the city of Leadville,  Colorado (USA).  The 15,000 foot condition is rather close to the elevation of the city of Daocheng,  Sichuan (China).  La Paz,  Bolivia,  is not shown,  but has an elevation in the middle of the cabin pressure altitude range,  at 13,323 feet.  These are all cities where people live perfectly normal lives.

Equivalent wet in-lung oxygen partial pressure is also shown in the figure as the arrows A and B for the effects of a (vented) supplemental oxygen mask at 40,000 feet,  and at 45,000 feet,  respectively.   These masks seem quite adequate for long flight times at 40,000 feet,  for which wet in-lung oxygen falls in the cabin pressure altitude range at just about 12,000 foot equivalent.  They are recommended only for short exposures at 45,000 feet,  which seems about equivalent to 20,000 feet.  Only a few genetically-adapted herders live and work at this altitude,  in the Andes and the Himalayas.  

Thus wet in-lung oxygen partial pressures equivalent to 15,000 feet or lower are quite consistent with standard high-altitude flying practices. 

 Figure 1 – Wet In-Lung Oxygen from Atmospheric Air,  as a Function of Altitude

The calculation for the two supplemental oxygen mask points was a little different.  The calculated curves and some notes are given in Figure 2.  The big assumption was that 100% dry oxygen was in the mask,  at the altitude atmospheric pressure.  Offsetting this down by the vapor pressure gives the wet in-lung oxygen partial pressure,  as given in the figure. 

The assumption about 100% oxygen inside the mask is probably pretty good at the higher altitudes,  and probably not so good at lower altitudes.  The pressure drop from the supply to the mask is high enough to ensure choked flow somewhere in the equipment,  so that the delivered oxygen massflow is fixed,  and thus independent of the delivered density conditions in the mask. 

The delivered density is lower at high altitudes,  which for the same massflow is larger volume flow.  If that volume flow is large enough,  it overwhelms the effects of imperfect sealing of the mask to the face,  and of the diluting effect of the exhaled gases.  At those conditions,  the mask is filled with very nearly pure oxygen.  This would certainly be the case at the highest altitudes for which the mask is considered effective.  Those would be long exposures at 40,000 feet,  and short exposures as high as 45,000 feet.  Military flying practice requires pressure breathing equipment above those altitudes;  effectively,  some kind of pressure suit.

It is these wet in-lung oxygen partial pressures from the supplemental oxygen mask at 40,000 and 45,000 feet that was the objective here.  Those are the points A and B in Figure 1 above.  The possible error at low altitudes is irrelevant to the discussions here.

Figure 2 – Wet In-Lung Oxygen from a Vented Pure-Oxygen Mask,  as a Function of Altitude

How to Use Altitude Equivalence for Oxygen Suit Pressure Selection

Figures 3 and 4 show this process for two slightly-different suit design pressures.  You start with an assumed design altitude in Earthly air (for which you can also figure its dry oxygen partial pressure if you want,  but we don’t use that in this calculation),  and offset the ambient pressure down by the water vapor pressure,  to the wet in-lung dry air partial pressure.  Use the oxygen fraction against the dry air partial pressure to calculate the wet in-lung oxygen partial pressure.  Use this wet in-lung oxygen partial pressure as the wet in-lung result to be obtained by your suit.  Add to it the water vapor pressure,  and that is your dry oxygen suit pressure at design conditions. 

Then,  ratio-down that suit pressure by your leak-down margin factor (in this case 1.10) to the min tolerable dry sit pressure.  Offset that down by the water vapor pressure to obtain the min tolerable wet in-lung oxygen partial pressure.  This needs to fall in an acceptable range (generally that defined by the wet in-lung oxygen partial pressure at cabin pressure altitudes,  or 10,000-to-15,000 feet equivalent). 

Now,  divide that min tolerable wet in-lung partial pressure of oxygen by the volume fraction of oxygen in dry air,  to obtain the wet in-lung partial pressure of dry air.  Add to that the water vapor pressure to obtain the Earthly dry air pressure at altitude.  Reverse the table lookup to determine the equivalent altitude for your min tolerable leak-down condition.  If you did this right,  it will fall in the 10,000 to 15,000 foot range of acceptable cabin pressure altitudes. 

Figure 3 does this for an 8700 foot equivalent suit design at 0.2004 atm = 2.945 psia that leaks down by factor 1.10 to a 12,000 foot equivalent design at 0.1822 atm = 2.678 psia.  Figure 4 does this for a 10,000 foot equivalent suit design at 0.1930 atm = 2.836 psia that leaks down by 1.10 to an equivalent 13,300 foot design at 0.1755 atm = 2.579 psia.  Both fall within the cabin pressure altitude range or lower,  for acceptable wet in-lung oxygen partial pressures,  considered adequate for pilots.  The 13,300 foot condition is also equivalent to the major city of La Paz,  Bolivia,  to which tourists acclimatize very quickly.   

Either design,  or an even-higher pressure design,  are all quite acceptable for life support and fully-functional human cognition in a space suit.  The lower pressures allow easier suit design,  and more comfortable suits.  So,  unless there is an overriding need for higher pressures,  these lower pressure designs are to be preferred. 
 

 
 Figure 4 – Relating Design and Leaked-Down Suit Oxygenation to Equivalent Air at Altitude:  10/13.3 kft

Relating Suit Design Pressure to Two-Gas Habitat Atmospheres:  Fire Danger and Pre-Breathe Criteria

There are two issues that relate oxygen suit pressure to the pressure and composition of a two-gas habitat atmosphere.  One is the “pre-breathe” factor,  the other is the enhanced fire danger posed by a too-oxygen-enriched atmosphere. 

The pre-breathe factor used by NASA was originally developed for the US Navy,  for oxygen-nitrogen two-gas mixtures.  If in the dry habitat atmosphere the partial pressure of nitrogen is at or below factor 1.20 times the pure oxygen suit pressure,  then no decompression time is needed breathing pure oxygen to blow off the nitrogen in the blood.  That decompression time is the “pre-breathe time”. 

As an example,  for a two-gas oxygen-nitrogen atmosphere at 1 atm pressure and 20.946% oxygen by volume (“synthetic air” at 1 atm),  the nitrogen partial pressure is 0.79054 atm.  For a pure oxygen suit at 3.8-4.2 psia,  the dry oxygen partial pressure is 0.2586-.2858 atm.  The ratio of nitrogen to suit oxygen pressures is 3.057-2.766.  This range of values far exceeds the 1.20 criterion,  so significant hours of pre-breathe time are required.  This is pretty much current NASA practice at the ISS (space station).

In the earlier articles,  it was unknown to me whether that factor of 1.2 applied to individual dilution gas partial pressures,  or to the aggregate sum of their partial pressures.  I still do not know,  but I sidestepped that issue entirely by only considering two-gas mixtures of oxygen and nitrogen here. 

It is also fairly obvious that reducing habitat atmosphere pressure reduces the dilution gas partial pressure,  thus reducing its ratio to suit oxygen pressure.  It is also fairly obvious that increasing the oxygen fraction of the habitat atmosphere also reduces the ratio.  Thus,  reduced habitat atmosphere pressures at higher-than-Earthly oxygen content seems to be indicated for lowering or eliminating pre-breathe times. 

However,  increasing oxygen content runs afoul of enhanced fire danger.  I have read of two ways to judge the fire danger.  One is that the percent (by volume) oxygen for air pressures near 1 atm should be under 30% at most,  and preferably nearer the 20.946% of ordinary air. 

Percent oxygen is independent of total pressure,  but partial pressure of oxygen is not.  The second way to judge the danger is a limit on oxygen partial pressure,  limited to about sea level Earth normal. 

After thinking about this,  I realized that the enhanced fire danger resulting from the enhanced oxygen is really faster chemical reaction rates,  leading to very much-accelerated phenomena and enhanced energy release rates.  For an overall empirical model of a fuel-air chemical reaction rate,  a second-order two-component one-step Arrhenius model is often used:

Rate = k Cf^r Co^(n-r) exp[Ea/RT] 
where n ~ 2 and r ~ 1, 
with Cf and Co measured as mass/vol

That suggests the real criterion might be the oxygen concentration Co,  expressed in mass per unit volume units.  If this concentration were no worse than that of Earthly air,  then the fire reaction rates should be unaccelerated relative to those seen in Earthly air.  Both volume fraction oxygen and atmosphere pressure get into this concentration calculation. 

The volume fractions of the two gases,  and their molecular weights,  give you the molecular weight of the synthetic air mix:

                MW-O2 * vol frac O2 + MW-N2 * vol frac N2 = MW-air * 1

The molecular weight ratio and volume fraction of O2 give you the mass fraction of the air that is oxygen:

                (MW-O2 / MW-air) * vol frac O2 = mass frac O2

Because the pressure ratio to standard pressure P/Pstd is numerically the pressure in atm,  you can use the habitat pressure expressed this way,  and its temperature,  to correct standard air density to habitat atmosphere conditions.  The ignores the difference between the synthetic air and actual air,  but that is trivial:

                Dens-hab = density-std * (P/Pstd) * (Tstd/Thab)

Multiplying habitat density by the mass fraction of oxygen gives you the oxygen concentration:

                C-O2 = dens-hab * mass frac O2  (suggested units kg/cu.m)

For Earthly air at sea level pressure and standard temperature,  the density is 1.225 kg/cu.m,  and the concentration of oxygen is 0.275 kg/cu.m.  If the habitat oxygen concentration is that value or less,  the fire reaction speeds and energy release rates should be as slow (or slower) than on Earth.

Now,  using exactly the pre-breathe limit factor of 1.20,  you want your habitat atmosphere to equal the selected value of suit dry oxygen pressure,  and so the habitat nitrogen pressure is 1.2 times that oxygen pressure.  That is the inherently-high oxygen volume fraction of 1/(1 + 1.2) = 0.4545,  but the atmospheric pressures being considered here are well below sea level. 

For a range of suit oxygen pressures from about 0.13 atm up to about 0.24 atm,  habitat pressures vary strongly,  and so does oxygen concentration.  This is shown in Figure 5.  The note regarding “synthetic air” refers to a synthetic Earthly air,  at 20.946% oxygen,  with the remainder all nitrogen.  The habitat atmospheres considered here all have more oxygen content and less nitrogen content than a true synthetic Earthly air. 

Referring again to Figure 5,  the derived habitat atmospheres as a function of oxygen suit pressure reach the Earthly oxygen concentration limit of 0.275 kg/cu.m at a suit pressure of 0.2165 atm,  and a habitat atmosphere pressure of 0.4663 atm.  That’s your upper limit for fire reaction rates equal to Earthly rates at sea level.  It corresponds to a suit pressure lower than current practices,  and 45.45% oxygen by volume in the habitat two-gas mix. 

Note in Figure 5 that the volume percent-as-fire-criteria is always violated,  while in this pressure range,  the partial-pressure-of-oxygen criterion is satisfied until you get very close to the concentration criterion limit.   Yet,  it is these two items working together that actually determine the concentration-driven reaction rates in the fire chemistry.  Thus it is oxygen concentration that is the real fire danger criterion,  and it should not exceed sea level Earthly values,  for fires not to exceed familiar Earthly rates.  By this criterion,  you may actually have a slightly-higher suit pressure than by the partial pressure criterion.  But you may not lower it without triggering pre-breathe time requirements. 

Figure 5 – Comparing Fire Danger Criteria from Increased Oxygen Content

In view of that result,  what you really want to do is identify a minimum suit pressure design that you want to accommodate,  and use it to set your habitat atmosphere.  That way,  for that suit,  and for any higher pressure designs,  you will not trigger any pre-breathe time.  This is based on the design pressure,  not the factor-1.10 leaked-down pressure.  This is shown in Figure 6 for two candidate designs:  the 8.7 kft equivalent “A”,  and the 10 kft equivalent “B”,  with the habitat atmosphere “set” by the lower-pressure 10 kft equivalent design.  Both the 1.10 leak-down and 1.20 pre-breathe factors were applied. 

Doing this produced the results tabulated in the figure:  all the pre-breathe factors were at,  or under,  1.20,  all the way up to (and beyond) the “limit” suit design pressure of 0.2165 atm.   There is nothing about this selection which precludes suit pressures as high as current practice!

Note that the factor 1.10 leak-down points are also shown.  Decompression down to them is not an issue;  you will only be recompressing from them up to habitat pressure. 
 
 Figure 6 – Relating Oxygen Suit Pressures to Habitat Synthetic Air Compositions Subject to Fire Safety

Final Results:

These were calculated with a spreadsheet,  and are given in Figure 7.  The habitat atmosphere data is given in the upper part,  and the data for the A and B suit designs (design and leaked-down)in the lower part,  along with the “limit” suit design (at design only).  Bear in mind that the habitat atmosphere is a two-gas oxygen-nitrogen mix set at 45.45% volume percent oxygen,  it is fixed.  Bear also in mind that still-higher suit pressures,  are also compatible with this. 

Figure 7 gives suit and habitat pressures in a variety of measurement units for a variety of readers.  Note that the wet-in-lung partial pressure of oxygen in the habitat atmosphere is identical to that from the min-pressure design suit (the 10 kft B design).  This fell within the cabin pressure altitude range considered adequate for a pilot’s cognition (10,000 feet,  actually). 

The habitat atmosphere is 0.4242 atm (6.420 psia),  and 45.45% oxygen,  the rest nitrogen.  The lowest compatible (no pre-breathe required) oxygen suit pressure is 0.1930 atm (2.836 psia),  substantially lower than current NASA practice (3.8-4.2 psia).  Lower-pressure suits might require pre-breathe time,  but no higher-pressure suit would require any. 

This lowest compatible-pressure suit (at 146.7 mm Hg) is also substantially reduced from the 1968-vintage experiments of Dr. Paul Webb with his mechanical counterpressure (MCP) designs based on stretchable fabrics.  His experiments back then used about 170-190 mm Hg as the suit pressure. 

Under the conditions proposed here,  such MCP designs are far more feasible.  And,  conventional full pressure suits are far more comfortable,  and easier to design.

Finally,  the habitat atmosphere calculates to have (at 25 C = 77 F) an oxygen concentration of 0.245 kg/cu.m (per Figure 6 above),  which is less that Earthly air at sea level pressure (0.275 kg/c.m).  The fire danger in this habitat atmosphere should be no worse than Earthly sea level air,  and might actually be slightly reduced,  in spite of the high oxygen percentage. 


Figure 7 – Results for Recommended Suit Pressures and Recommended Habitat Synthetic Air

Final Comments

What I propose here is a low-pressure habitat atmosphere enriched in oxygen content,  yet safe enough in terms of fire danger,  while not requiring any pre-breathe time for pure oxygen space suits of suit pressure far lower than current practice.  Both the habitat and the min-pressure suit design maintain the wet in-lung oxygen partial pressure of Earthly air at an elevation of 10,000 feet,  considered by most authorities as quite adequate for pilot-level cognition.  There is no reason that explorer-type astronauts cannot make use of this in vehicles and space stations located anywhere in the solar system. 

Colonist-astronauts are different:  there are decades of exposure,  not just months or years,  and there are the inherent (and so far unknown) risks of pregnancy and child development.  For that situation,  I recommend that we “dance with who brung us”:  we evolved in Earthly-air at elevations from sea level to around 15,000 feet. 

We are genetically adapted to that.  So use it. 

I would recommend real synthetic air (20.946% by volume oxygen,  the rest nitrogen),  at an equivalent pressure altitude not to exceed about 10,000 feet. You will always have pre-breathe time to contend with,  when decompressing down to a relatively low-pressure oxygen suit.  Recognize that,  and just deal with it.

A suggestion for “dealing with it”: 

Those parts of the colony where pregnant women and young children might be,  should have oxygen-nitrogen at 20.946% oxygen,  and no less than the 10.11 psia that is equivalent to 10,000 feet elevation (0.1441 atm partial pressure of oxygen,  0.5437 atm partial pressure of nitrogen).  That’s 0.1311 atm wet in-lung partial pressure of oxygen, same as the min-pressure suit design. 

Other parts of the colony could use the 45.45% oxygen mix at 6.24 psia (0.1930 atm partial pressure of oxygen,  0.2316 atm partial pressure of nitrogen).  People using suits outside could decompress from the 45%/6.24 psia blend without any pre-breathe time.  That’s also 0.1311 atm wet in-lung partial pressure of oxygen,  same as the min-pressure suit. 

Everybody gets the same wet in-lung oxygen partial pressure,  whether in the habitat with synthetic air at 10.11 psia, the enriched blend at 6.24 psia,  or the min-pressure suit design at 2.84 psia.  There’s no pre-breathe time for decompressing to any higher-pressure suit designs,  although there would for yet-lower pressure designs. 

Whether any pre-breathe decompression time is needed going from the higher-pressure portion of the colony to the lower-pressure portion is something still unknown to me.  But the change is rather modest,  so any such decompression time should also be modest.

If any readers actually know that answer,  please weigh in with your comments!