Atmosphere Models for Earth, Mars, and Titan

Update 4-8-2024:  Should any readers want to learn how to do what I do (estimating performance of launch rockets or other space vehicles),   be aware that I have created a series of short courses in how to go about these analyses,  complete with effective tools for actually carrying it out.  These course materials are available for free from a drop box that can be accessed from the Mars Society’s “New Mars” forums,  located at http://newmars.com/forums/,  in the “Acheron labs” section,  “interplanetary transportation” topic,  and conversation thread titled “orbital mechanics class traditional”.  You may have scroll down past all the “sticky notes”. 

The first posting in that thread has a list of the classes available,  and these go far beyond just the two-body elementary orbital mechanics of ellipses.  There are the empirical corrections for losses to be covered,  approaches to use for estimating entry descent and landing on bodies with atmospheres,  and spreadsheet-based tools for estimating the performance of rocket engines and rocket vehicles.  The same thread has links to all the materials in the drop box. 

The New Mars forums would also welcome your participation.  Send an email to newmarsmember@gmail.com to find out how to join up.

A lot of the same information from those short courses is available scattered among the postings here.  There is a sort of “technical catalog” article that I try to main current.  It is titled “Lists of Some Articles by Topic Area”,  posted 21 October 2021.  There are categories for ramjet and closely-related,  aerothermodynamics and heat transfer,  rocket ballistics and rocket vehicle performance articles (of specific interest here),  asteroid defense articles,  space suits and atmospheres articles,  radiation hazard articles,  pulsejet articles,  articles about ethanol and ethanol blends in vehicles,  automotive care articles,  articles related to cactus eradication,  and articles related to towed decoys.  All of these are things that I really did. 

To access quickly any article on this site,  use the blog archive tool on the left.  All you need is the posting date and the title.  Click on the year,  then click on the month,  then click on the title if need be (such as if multiple articles were posted that month).  Visit the catalog article and just jot down those you want to go see.

Within any article,  you can see the figures enlarged,  by the expedient of just clicking on a figure.  You can scroll through all the figures at greatest resolution in an article that way,  although the figure numbers and titles are lacking.  There is an “X-out” top right that takes you right back to the article itself. 

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Update 6-5-2016:  this is one of the most popular articles on the entire website.  I hope this publicly-available information has proven useful to others.
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These data replace the previous post "Mars Atmosphere Model", dated 6-24-12, just below.

Atmosphere Models for Earth, Mars, and Titan GWJ 6-30-12

After perusing several links on the internet, I settled on a June 2007 paper by C. G. Justus and R. D. Braun (ref. 1), which contained rather realistic “typical” atmosphere data for Earth, Mars, Titan, Venus, and Saturn. For manned landings, Earth, Mars, and Titan are the only destinations of interest that have atmospheres. Justus is involved with the site-tailorable EarthGRAM and MarsGRAM models. On both Earth and Mars, site-specific atmosphere models can vary widely, which is what the –GRAM models calculate. For Titan, the Huygens descent probe data are really all we have.

The cited paper (ref. 1) has near-surface atmospheric composition, average molecular weight, and specific heat ratio data, for each world, reproduced here for the three destinations of interest. The report also gives an indication of atmospheric composition versus altitude for each world. For my purposes here, that devolves to an altitude limit above which the surface composition is no longer at all representative.

There are also recommendations for high-altitude average density criteria at which aero-braking and aero-capture apply. These are 4x10^-7 kg/m^3 and 2x10^-3 kg/m^3, respectively. Aero-braking refers to multi-pass atmospheric drag braking into a desired non-escape orbit, and aero-capture refers to one-pass atmospheric drag braking into a non-escape orbit.

For purposes of estimating when significant heating during entry begins, versus significant simple drag effects, the aero-capture altitude is the better measure. Simple drag effects “begin” closer to the aero-braking altitude cited. This is true for all three worlds covered by this document: Earth, Mars, and Titan. Only the relevant altitudes vary.

Earth

Earth’s atmosphere has been modeled in many different ways, all both site- and season-dependent. Some are well-known. These include the US 1962 standard atmosphere, the extended ICAO standard atmosphere, the US polar and cold atmospheres, and the US tropical and hot atmospheres. Some are not so well-known, such as the Max Ambient In-Flight and Min Ambient In-Flight days, given in older versions of the Pratt and Whitney vest-pocket aeronautical handbook. Only the ICAO model extends to 100-km altitudes. Continuum flow models are pretty much inapplicable above roughly 45 or 46 km, which corresponds to the aero-capture altitude.

The density profile can be approximated between two specific altitudes as a simple exponential model dens(z) = dens(0)*exp(-z/Hd), where z is altitude, dens(0) is a curve fit parameter, and Hd is the density scale height. Average density scale height between those two altitudes is estimated by Hd = (z2 – z1)/ln(dens1/dens2). This is applicable to computations of max-deceleration, max-dynamic pressure, max heat rate flux, and max absorbed integral heat flux, all as functions of ballistic coefficient and entry velocity. Those effects I will explore in another posting.

The version reported here is an abbreviated table from the cited paper, and 6 plots, given as figures 1 through 6 below (at end of this article). They include the temperature profile, the pressure profile, the density profile, the speed-of-sound profile, the scale height profile, and a representation of the abbreviated table of values. It resembles the extended ICAO atmosphere model.

There is also a short table just below representing near-surface composition, properties, and scale height models. I interpolate the aero-brake altitude as 92.66 km, versus the aero-capture altitude as 46.72 km. Pressure data in are missing in the reported table and figure above the altitude at which composition varies significantly from surface values.

Table 1 – Earth Atmospheric Surface Parameters

for surface air composition 78.084% N2, 20.946% O2, Ar 9340 ppm, CO2 350 ppm, Ne 18.18 ppm, He 5.24 ppm, CH4 1.7 ppm, Kr 1.14 ppm, H2 0.55 ppm
usually near 1% water vapor

MW Cp/Cv
28.97 1.4

best fit 0-100 km
d(0)kg/m^3 = 1.226
Hd km = 7.256


Mars

The tables and figures are “representative” of Mars, knowing full well that variations there are more severe than on Earth. The data quoted herein are within about half an order of magnitude correct, versus a few percent for Earth. These data are given in figures 6-12 below, plus the following abbreviated table. I interpolate the aero-braking altitude as 94.55 km (comparable to Earth), and the aero-capture altitude as 23.82 km (much lower than on Earth). Pressure data are missing in the reported table and figure above the altitude at which composition varies significantly from surface values.

Table 2 – Mars Atmospheric Surface Parameters

for surface "air" composition CO2 95.32%, N2 2.7% , Ar 1.6%, O2 0.13%, CO 0.08%, H2O 210 ppm, NO 100 ppm, Ne 2.5 ppm, HDO 0.85 ppm, Kr 0.3 ppm, Xe 0.08 ppm

MW Cp/Cv
43.34 1.33

best fit 25-70 km
d(0)kg/m^3 = 0.03032
Hd km = 8.757


Titan

The tables and figures are based on Huygens descent probe data. They are the best we have. These data are given in figures 13-18 below, plus the following abbreviated table. I interpolate the aero-braking altitude as 637 km, and the aero-capture altitude as 192 km. Titan is unusual in having a far deeper atmosphere, of higher surface pressure and a lot higher density (because it is so cold there), than on Earth.


Table 3 – Titan Atmospheric Surface Parameters

for surface "air" composition N2 97.7%, CH4 2.3%

MW Cp/Cv
27.32 1.4

best fit 130-800 km
d(0)kg/m^3 = 0.1006
Hd km = 48.38


References:

1. “Atmospheric Environments for Entry, Descent, and Landing (EDL)”, C. G. Justus (NASA Marshall) and R. D. Braun (Georgia Tech), June, 2007.
2. “Atmospheric Models for Mars Aerocapture”, C. G. Justus, Aleta Duvall, V. W. Keller, no date except latest cited reference 2005.
3. “Mars Global Atmospheric Reference Model (MarsGRAM 2005) Applications for Mars Science Laboratory Mission Site Selection Processes”, H. L. Justh and C. G. Justus, no date except latest cited reference 2005.





Figure 1 – Abbreviated Earth Atmosphere Table


Figure 2 – Earth Atmosphere Temperature Profile


Figure 3 – Earth Atmosphere Pressure Profile


Figure 4 – Earth Atmosphere Density Profile


Figure 5 – Earth Atmosphere Speed of Sound Profile


Figure 6 – Earth Atmosphere Density Scale Height Profile


Figure 7 – Abbreviated Mars Atmosphere Table


Figure 8 – Mars Atmosphere Temperature Profile


Figure 9 – Mars Atmosphere Pressure Profile


Figure 10 – Mars Atmosphere Density Profile


Figure 11 – Mars Atmosphere Speed of Sound Profile


Figure 12 – Mars Atmosphere Density Scale Height Profile


Figure 13 – Abbreviated Titan Atmosphere Table


Figure 14 – Titan Atmosphere Temperature Profile


Figure 15 – Titan Atmosphere Pressure Profile


Figure 16 – Titan Atmosphere Density Profile


Figure 17 – Titan Atmosphere Speed of Sound Profile


Figure 18 – Titan Atmosphere Density Scale Height Profile

Mars Atmosphere Model

The NASA Glenn Research Center (Glenn RC) has published online a model of the properties of the Martian atmosphere.  It was based on measurements made by the Mars Global Surveyor in 1996.  The basic model comprises a temperature profile with two lapse rates (one below 7 km and the other above 7 km),  and a single exponential fit of pressure versus altitude.  Density is computed from these profiles. 

These Glenn RC data are available in either metric or US customary units at:  

http://www.grc.nasa.gov/WWW/k-12/airplane/atmosmrm.html   (metric)

http://www.grc.nasa.gov/WWW/k-12/airplane/atmosmre.html  (US customary)

One problem with this model is extending the upper zone lapse rate to very high altitudes.  Above about 115 km,  this model predicts temperatures below absolute zero (0 degrees K,  -273.15 degrees C).   I “corrected” that by limiting the extreme altitude temperatures to a constant 4 degrees K (-269.1 degrees C) as indicated in Figure 1.  But,  I do not believe this profile is anywhere near correct at altitudes around 100 km,  because the temperature profile in the extended ICAO atmosphere model for Earth does not tend to very cold temperatures at very high altitudes.  It actually goes very hot.

UPDATE 6-30-12:  there are far better models to use,  such as MarsGRAM.  Do not use this one!  There is a published paper "Atmospheric Environments for Entry,  Descent,  and Landing (EDL)" by Justus and Braun that has better temperature profiles for Mars and other destinations.  It also has a scale height-based way of approximating density,  and some 1956-vintage back-of-the-envelope entry hypersonics relations.  These are likely within half an order of magnitude of the correct design conditions.  In future postings,  I will elaborate a better "typical model" for the atmosphere of Mars,  and what kinds of vehicles might land large payloads through it.     

SECOND UPDATE 9-25-12:  The Justus and Braun atmosphere models (more than just Mars) and 1956-vintage entry hypersonics model,  I have examined,  updated,  and posted as usable "how-to" articles posted just above.  For atmospheres,  see "Atmosphere Models for Earth,  Mars,  and Titan" dated  6-30-12.  For the entry hypersonics models,  see "'Back of the Envelope' Entry Model",  dated 7-14-12.  Those two have what you need,  in all likelihood. 

Nevertheless,  using the “corrected” Glenn RC temperature profile and the Glenn RC pressure profile (Figure 2) to a peak altitude of 200 km,  I computed a density profile  vs altitude (Figure 3),  and a speed-of-sound profile (Figure 4).   This speed of sound was based on pure CO₂ at a molecular weight of 44.01,  and a specific heat ratio (γ) of 1.300.  It shows ridiculously-low values around 100 km,  precisely because the predicted temperatures are ridiculously low. 

It is known from experience on Earth that “re-entry begins” around 90 km altitude.   It is a little difficult to quantify why that might be so.  The density in the ICAO atmosphere at 90 km is about 3.213 x 10^-6 kg/m³.   The corresponding mean free path length between air molecules is about 3 cm.  Above 90 km,  the molecular weight departs from 28.966,  reflecting a change in composition.   Aerodynamically,  this is most definitely free molecule flow,  probably best represented by some modified Newtonian flow model.  Accordingly,  I calculated a Newtonian stagnation pressure (P_stag) of 2 mbar at 90 km,  and 7905 m/s velocity,  which is Earth’s surface circular orbit velocity.  Actual entry speeds from real orbits are not much different from that value at all. 

In the Mars atmosphere model presented here,  I computed an Earth / 90 km-equivalent density of 3.213x10^-6 kg/m³ at about 140 km on Mars.   I computed an equivalent P_stag = 2mbar for Mars at 122.2 km,  using a Mars surface circular orbit velocity of 3636 m/s,  and a profile I generated (Figure 5). 

I personally have no way to compute mean free path on Mars.   So,  based on either density,  or Newtonian P_stag,  re-entry should start a little higher up on Mars:  somewhere near 120-140 km,  versus about 90 km on Earth.  This value is comparable,  so there is some confidence in this assertion. 

Now,  in Earth’s atmosphere,  one starts to lose the applicability of the continuum flow model somewhere around 150,000 feet (45-46 km).  That density is around 1.48x10^-3 kg/m³,  and the corresponding mean free path is around 0.1 mm.  These data are available in many references;  the one I used was the CRC Handbook of Chemistry and Physics,  53^rd Edition,  1972-1973,  pages F171-F174.

In the Glenn RC model for Mars,  that same density occurs at roughly 28 km altitude.   Accordingly,  I would use some sort of Newtonian flow model for altitudes above 28 km,  and the continuum flow model below that altitude.  This choice is also speed-dependent,  however.   In any event,  I am not sure this is a model adequate for predicting hypersonic drag during high-altitude re-entry.  The temperatures “look too low” up there.   The computed Mach numbers will be all wrong. 

On the other hand,  for the final supersonics and chute-deployment phases,  somewhere below roughly 28 km altitudes,  this model is probably pretty good. 

Figure 1 – NASA Glenn RC Temperature Profile Model, Limited to 4 K Minimum

Figure 2—NASA Glenn RC Pressure Profile

Figure 3 – Density Profile Based on NASA Glenn RC Model

Figure 4 – Speed of Sound Profile Based on NASA Glenn RC Model

Figure 5 – Newtonian-Flow Stagnation Pressure Profile at Constant Circular Orbit Velocity

Quote from MSNBC news Monday 6-21-12:

"Taliban commander in Pakistan’s tribal belt says that the U.S.-funded vaccinations for tens of thousands of children would be outlawed until drone attacks stop."

Observation:

These bastards are now hiding behind diapers,  not just skirts.  They're really afraid of drone strikes.

Conclusion:

Strike more,  not less.  Lots and lots and lots more.  The world will be a much better place once they're dead.  Don't stop until they are. 

Corollary:

Most of the societies that tolerate groups like this in their midst will be afflicted with really nasty and evil violence,  until they learn better than to tolerate this nonsense. Until then,  they are not civilizable into fit company.  For anybody. 

Kudos to the Chinese

My congratulations to the Chinese for their launch of Shenzou-9 with 3 aboard,  including their first woman astronaut.  Their manned spaceflight record seems pretty good so far.  We'll soon see if the docking goes well,  along with their first cut at space station-like operations.  Best wishes and Godspeed.

GW

Pressurizable Domed Habitat Structures

The image is a diagram of a spherical-segment membrane-type pressure dome structure, such as might be used on Mars to pressurize acreage for agriculture in a future colony.

The membrane is a uniform tensile stress tension-field structure, tied to a retention ring buried below grade in the surface. The "blowout load" on ring diameter is balanced by the weight of the ring structure, which is in compression in bulk, but locally tension where the membrane ties to it. The tension stress in the membrane is proportional to the spherical radius, and to the net pressure differential across the membrane.

The membrane itself ought not to be a single layer. The material needs to let some visible and some UV light through for photosynthesis, but must be proof against UV damage over time. (This pretty much rules out all known polymers.) Access to that layer actually holding the gas pressure must be unimpeded from below, in order to repair meteroid punctures, which will occur. That's a basic safety thing.

The retention ring would be reinforced concrete if it were built on Earth. Concrete as we know it won't set in the cold on Mars, so I suggest "icecrete". That's a composite of water ice as the matrix, sand,  and rounded-by-tumbling rocks as the aggregate, and steel (or other comparably stiff) reinforcing bar. You mix the aggregate up with liquid water, pour into forms containing the reinforcement bars, and let it freeze. It either must be coated or buried to prevent sublimation of the ice.

One should note that the weight per unit circumference of the retention ring scales with diameter of the ring (and its cross section area), whereas the "blowout" load scales as ring diameter squared. For any given collection of materials, there will be a maximum size that can be practically built. This is because the increases in the retention ring cross section area cannot make up the discrepancy between the ring diameter and ring diameter squared factors.

One should also note that the shear stirrups in the ring "beam" are also the tensile connections between the membrane and the circumferential reinforcing bars inside the ring. Those stirrups ought to "loop" at least some of those circumferential bars, as shown in the image. I do not know the details of connecting these stirrups to the membrane, but I do think there ought to be a lot of these stirrups (i.e., the spacing is very close).

I do not have any actual design numbers available. But these are the fundamental structural and safety design criteria.

Have fun .....

GW

UPDATE 1-26-13:  See also "Aboveground Mars Houses" dated 1-26-13 for a pressurized building concept that is much closer to an in-hand,  practical technology.  

Deceleration by Drag Devices (and More) on Mars

The “classic” landing scenario on Mars dates all the way back to Viking in 1976. After hypersonic entry is done, the vehicles “pops out” at around Mach 2.5, ready for ribbon chute deployment of one type or another. On Earth, that’s up around 40,000 feet (13 km); on Mars, it’s substantially closer to the surface. That’s because, even with the lower gravity, the thin “air” of Mars is far less effective as a hypersonic entry decelerator.

This hypersonic decelerator effect is more-or-less proportional to density, and to speed squared during entry. Entry speeds on Mars are less than those on Earth, due to the lower gravity. But, “air” densities are very, very far lower. The density effect “outweighs” the gravity effect by quite a lot.

Once the chutes are out, it becomes a simple drag-to-weight ratio question, all other things being equal. On Earth, densities are far higher, but so is weight. The surface density on Mars varies with temperature, but is around 0.6% of that here. These densities reduce essentially with atmospheric scale height, but the overall density argument still applies.

The surface gravity on Mars is 38% of that here. Drag/weight for a chute then scales as density/gravity, for 0.6%/38% = about 2%. So chutes are simply far less effective as decelerators on Mars, as measured in the same velocity range, from about Mach 2.5 to impact.

Drag/weight for a parachute system varies directly proportional to chute blockage area, drag coefficient, air density, and velocity squared, and inversely with load weight. Kinematically, we’d like the terminal velocity of a chute-and-load system on Mars to be similar to that here, around 20-30 mph (30-50 kph). That leaves only density and weight, which ratio at about 2% for mars. See Figure 1 below.

In other words, for the same kinematic effect, the payload retarded by a chute on Mars can be about 2% of what we would expect for the same size chute on Earth. (It can be more if you can accept a higher terminal velocity, except that on Mars, you cannot. You are already too close to the surface when the atmospheric entry hypersonics are over.)

For ribbon chutes, which work at moderate supersonic Mach numbers all the way down subsonic, the drag coefficient is in the range of 1 to 1.5 and is a function of Mach number, peaking near Mach 1.1-ish. It is not substantially different with ballutes, or any other inflated structures. To get the drag to support the load at a reasonable terminal velocity, the decelerator must be around 50 times larger on Mars than on Earth. This is one real whopper of a landing design problem!

The only way out of this dilemma that I see, is a combination of aero decelerator braking, and rocket retro thrust braking, done simultaneously. That is something we have not yet attempted on Mars.

But, it is something “we” (but not all of “us”) have attempted here on Earth: parachute extraction of battle tanks from aircraft, followed by parachute descent, and last-second rocket braking to a touchdown, parachute still attached. The Russians did this, somewhere around 1960. It does offer a way to make aero-decelerators more effective, at the expense of extra rocket fuel and hardware.

Here’s another thought: augment the hypersonic aero-braking with rocket retro thrust during atmospheric entry. Once that is over, deploy aerodynamic decelerators, but maintain rocket retro thrust. Increase rocket braking thrust sharply for the final last seconds to touchdown. The main problem is axial retro plume aerodynamic stability, which can induce control moments on the craft beyond its capability to cope. Nozzle cant angle might help resolve that, however. See Figure 2 below.

There are many questions and problems with this overall retro-thrust concept, but it actually does offer a possible way to land very large payloads on Mars, assisted by aero drag retardation. See Figure 3 (added as an update 6-10-12).

Figure 1 – How Aero-Decelerators Work

Figure 2 – Stability Problems with Hypersonic Retro Thrust Might Be solved by Cant Angle

Figure 3 - Combined Chute and Rocket Braking