Ultimate Terraformed Mars MARK V Milestone Release

[acrosome]

>> The most important one being the temperature dependence of the coefficient in front of the altitude in the exponent. In order to get a reasonable prediction, one has to assume a "standard atmosphere" where the temperature decreases by a certain amount per n meters of altitude.

Yes, I think that's the lapse rate, which I had mentioned.

Still, from what I've read the lapse rate has an effect on the order of single-digit-percent. I'm going for rough approximations, here. Heck, even if I'm off by 50% I could still argue for Nix Olympica.

So, why did Don leave? His reaction a couple of posts ago seemed kind of random. Obviously something was going on behind the scenes, or in another thread. (And I'm too lazy to chase down the posts...)

[t00fri]

>> The most important one being the temperature dependence of the coefficient in front of the altitude in the exponent. In order to get a reasonable prediction, one has to assume a "standard atmosphere" where the temperature decreases by a certain amount per n meters of altitude.

Yes, I think that's the lapse rate, which I had mentioned.

Whatever the "lapse" rate is supposed to mean, the temperature dependence of the exponent is a crucial effect and all but small!


Sorry, if I don't expand about Don's reasons for leaving.

Fridger

[acrosome]

Whatever the "lapse" rate is supposed to mean, the temperature dependence of the exponent is a crucial effect and all but small!

The lapse rate is the change in temperature with a given change in altitude. On Earth I think it averages 6.5C/1000m or so, but it is really variable depending upon the altitude range you're talking about. The more precise barometric formula looks like this:

P = Pb ( Tb / (Tb + Lb (h - hb)) ^ ((g * M)/(R * Lb))

where Lb is the lapse rate so, yes, it is in the exponent. Does that look familiar? It's hard to make it "look right" written out like that. It looks better on the wikipedia page.

All variables:
Pb = static pressure
Tb = standard temperature
Lb = lapse rate
R = universal gas constant
g = gravitational acceleration
M = molar mass of the atmoshpere
h = height above sea level
hb = height at bottom layer (a wierd empiric way to allow for differences in various layers of the atmosphere, including the lapse rate; I think this somehow incorporates the scale height, too, or maybe they are the same thing?; see the wikipedia page for an explaination)

I'm using terminology that I find in my brief reading so please forgive me if I'm using obscure or inappropriate definitions. I thus have no idea how to translate "lapse rate" into another term that you might be more familiar with. And my German is only suitable for ordering dinner and asking where to find a toilet, so your English is demonstrably far superior to my German, and I have NO IDEA what a comparable term would be in German. (Assuming that German is your native language.)

Anyway, since I didn't have data for hb for Mars I didn't use this formula- I used the simplified one.

But I will again note that when comparing the results from the simplified formula that I used to real data from Earth the correleation was great. Don seemed to be implying that average temperatures on his terraformed mars weren't too ridiculous, so for a rough estimate I thought that I could use the formula. The IMPORTANT point to be made, I think, is that:

1. Gravity is low, so gas tends to "stack high" instead of "compressing low".
2. Don wants a sea-level pressure of 2 atmospheres. Wow.

These combine to form a very high, thick air column- more so than Don thought, I suspect. (That's a LOT of gas, and another reason that I think a 2 bar goal is unrealistic.) As I said, even if I'm off by 50%, heck, there would still be enough air over Olymous Mons to haul snow up there.

I am a confesssed amateur. I'm just a science fiction Mars fanboy. You're a physicist. If I'm really that wrong, can you explain why in a little more detail? I have a science doctorate (granted it's an MD, not physics), so you needn't limit yourelf to simplistic explainations. Heck, if you can post a more accurate model, please do so. I'd be ecstatic. I'm really interested in figuring this out and, frankly, it's getting frustrating. I'd like to be able to estimate pressure at various altitudes on a terraformed Mars, given a notional "sea level" pressure.

[t00fri]

Whatever the "lapse" rate is supposed to mean, the temperature dependence of the exponent is a crucial effect and all but small!

The lapse rate is the change in temperature with a given change in altitude. On Earth I think it averages 6.5C/1000m or so, but it is really variable depending upon the altitude range you're talking about. The more precise barometric formula looks like this:

P = Pb ( Tb / (Tb + Lb (h - hb)) ^ ((g * M)/(R * Lb))

where Lb is the lapse rate so, yes, it is in the exponent. Does that look familiar? It's hard to make it "look right" written out like that. It looks better on the wikipedia page.

All variables:
Pb = static pressure
Tb = standard temperature
Lb = lapse rate
R = universal gas constant
g = gravitational acceleration
M = molar mass of the atmoshpere
h = height above sea level
hb = height at bottom layer (a wierd empiric way to allow for differences in various layers of the atmosphere, including the lapse rate; I think this somehow incorporates the scale height, too, or maybe they are the same thing?; see the wikipedia page for an explaination)

I'm using terminology that I find in my brief reading so please forgive me if I'm using obscure or inappropriate definitions. I thus have no idea how to translate "lapse rate" into another term that you might be more familiar with. And my German is only suitable for ordering dinner and asking where to find a toilet, so your English is demonstrably far superior to my German, and I have NO IDEA what a comparable term would be in German. (Assuming that German is your native language.)

Anyway, since I didn't have data for hb for Mars I didn't use this formula- I used the simplified one.

But I will again note that when comparing the results from the simplified formula that I used to real data from Earth the correleation was great. Don seemed to be implying that average temperatures on his terraformed mars weren't too ridiculous, so for a rough estimate I thought that I could use the formula. The IMPORTANT point to be made, I think, is that:

1. Gravity is low, so gas tends to "stack high" instead of "compressing low".
2. Don wants a sea-level pressure of 2 atmospheres. Wow.

These combine to form a very high, thick air column- more so than Don thought, I suspect. (That's a LOT of gas, and another reason that I think a 2 bar goal is unrealistic.) As I said, even if I'm off by 50%, heck, there would still be enough air over Olymous Mons to haul snow up there.

I am a confesssed amateur. I'm just a science fiction Mars fanboy. You're a physicist. If I'm really that wrong, can you explain why in a little more detail? I have a science doctorate (granted it's an MD, not physics), so you needn't limit yourelf to simplistic explainations. Heck, if you can post a more accurate model, please do so. I'd be ecstatic. I'm really interested in figuring this out and, frankly, it's getting frustrating. I'd like to be able to estimate pressure at various altitudes on a terraformed Mars, given a notional "sea level" pressure.

Hi acrosome,

that all looks quite sensible and I certainly have no principal objections against applying the barometric formula to Mars. However the values of the parameters will be quite different, since the Mars atmosphere is quite different from the one on Earth.

The derivation of the barometric formula holds quite generally for a ball of gas surrounding a solid body of a certain mass and radius. The crucial assumption is however that the atmospheric gas behaves strictly like an ideal gas (as defined in thermodynamics). For example, if there is humidity in the atmosphere, such a gas ceases to be "ideal".

Sorry, from your first post, it rather looked as if you had heard about that formula only quite recently without having "digested" yet the various hidden pitfalls . But I completely agree with your above, more recent comments (from consulting Wikipedia?).

While my scientific working language is actually English, I have never heard before of the English term lapse rate in this context. Anyway, it's the appropriate quantity to consider and means nothing but the (negative) gradient of temperature T with altitude z

[tex]-\frac{d\,T}{d\,z}[/tex].

For an accurate application of the formula to Mars, a detailed knowledge of the temperature dependence with altitude is required. I am almost certain that such data must exist somewhere. Unfortunately, I have no idea, where, but probably it's even publicly available in the net...That's essentially all one would need along with a typical value of the surface pressure.

Fridger

[acrosome]

Sorry- it has been a while...

Yes, the "lapse rate" thing is -dT/dz, as you mentioned. I'm sure it is hidden in the other formula I posted. And, yes, I looked all this stuff up on Wikipedia. This is definitely out of my field, but I have a science background, so I understand how apparently minor points can snow ball.

But, as I've said, I'm just looking for very rough estimates, here. Thanks for letting me know I'm not misusing this formula in some sophomoric fashion. I assumed that the atmospheric composition would be pretty close to Earth's- after all, it has to be breathable. And since it would be rather difficult to produce an awful lot of, say, argon or xenon I assumed that a lot of the filler gas would be nitrogen. So, a nitrogen-oxygen atmosphere. Perhaps a bit more of other noble gases, with a smaller oxygen fraction, as I think I recall Don was implying.

Anyway, I figured it would at least be reasonably close.

And no gas at workable temperatures acts even remotely like an ideal gas, yet so many atmospheric formula assume they are ideal!- so I don't feel particularly guilty about this one.

Anyway, by very rough estimates, I propose that the great volcanoes would be snow-capped. They do not "stick out of the atmosphere" given the parameters Don is using: a sea-level of about -2000m from the datum (which looks like roughly where Don has set it) and sea-level atmospheric pressure of 2 bar. I will go farther and say that the top of Olympus wound probably be breathable within these parameters.

Personally, I still maintain that a sea-level pressure of 1 bar is both more realistic (if any of this can be considered realistic) and less problematic.

[eburacum45]

Eeeh!
I vaguely remember the adiabatic lapse rate concept from my college years
http://en.wikipedia.org/wiki/Lapse_rate ... lapse_rate
but that was upwards of thirty-two years ago; apart from a fascination with convection clouds, all that stuff has been forgotten now.