Saturday, June 30, 2012

Atmosphere Models for Earth, Mars, and Titan

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


2 comments:

  1. Can I get more data points in textual form not as a rasterized image?

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  2. You can download my ref. 1 (Justus and Braun, "Atmospheric environments....") from NASA.gov/archive, just like I did. It's a pdf file, so it will be an image, but maybe it's a bit more legible and conventionally-formatted than my posting.

    GW

    ReplyDelete