Calculating Partial Pressure of Atmo

[Kilgs]

Been reading up on this and how to determine if the levels in an atmo are still decent for human breathing. I learned about partial pressure and the tolerable limits. Unfortunately, the only the calculators I can find are altitude based or scuba-diving based.

Anyone know where I can find a calc that allows me to input:

1. Total atmo pressure
2. Amount of Oxygen (% or Kp)

and get the partial pressure?

EDIT: May have found a decent equation for my purposes. Since 1 bar is roughly 1 atmo...

Using diving terms, partial pressure is calculated as:

partial pressure = (total absolute pressure) × (volume fraction of gas component)

For the component gas "i":

ppi = P × Fi

For example, at 50 metres (165 feet), the total absolute pressure is 6 bar (600 kPa) (i.e., 1 bar of atmospheric pressure + 5 bar of water pressure) and the partial pressures of the main components of air, oxygen 21% by volume and nitrogen 79% by volume are:

ppN2 = 6 bar × 0.79 = 4.7 bar absolute
ppO2 = 6 bar × 0.21 = 1.3 bar absolute

where:
ppi = partial pressure of gas component i
P = total pressure = P in the terms used in this article
Fi = volume fraction of gas component i
ppN2 = partial pressure of nitrogen
ppO2 = partial pressure of oxygen

----
Does this work for a quick/dirty solution? I realize altitude will change things but I'm not trying to be perfect, just don't want to be all wrong.

 

[Carlobrand]

As far as I know, that is the solution.

Altitude changes your total absolute pressure, but the percentage of oxygen doesn't change worth worrying about, not where there's air movement to keep things mixed. So, you can just recalculate for different altitudes if, for example, you want to know what the difference in partial pressure is for someone in Houston verses Denver.

 

[aramis]

As far as I know, that is the solution.

Altitude changes your total absolute pressure, but the percentage of oxygen doesn't change worth worrying about, not where there's air movement to keep things mixed. So, you can just recalculate for different altitudes if, for example, you want to know what the difference in partial pressure is for someone in Houston verses Denver.

The only case where it's likely to be different is when there's a layer that is isolated (due to predominant density sorting) and stable. Such as a SO2, CO2 or N2O layer. (All of which of which, in still air, sink.)

So, if you've got isolated rift valleys, or craters, without significant outflows, you can have an oxygen depleted fraction at relatively normal pressures.

One of the hazards vulcanologists face is a non-visible CO2 and SO2 rich layer in a caldera.

 

[Kilgs]

Great, thanks.

As a follow-up, any quick/dirty ways to determine pressure at altitudes on non-Earth objects or is that beyond our ken? If you have size, gravity, atmo, temperature and altitude...

 

[Carlobrand]

If you're using the standard IPP, the pressure at sea level - assuming there is a planetary ocean - is determined by the atmosphere code.

From CT Book 3, "Thin, standard, and dense atmospheres are breathable
without assistance." Ergo partial pressure of O2 is pretty close to 0.21, probably between 0.18 and 0.24. From there it depends entirely on you, with the note that it'd be unlikely to have a pure O2 atmosphere. You could have a thin atmosphere at half a bar with a really happy set of plants and algae pumping the local O2 up to 36%, for example.

Planetary atmosphere is 2D-7+size, so basically size +/- 5, which sets some very broad limits: a dense (8, 9) atmosphere won't occur on a size 2 or less world, an atmosphere too thin to breathe (i.e. very thin, trace, vacuum, <4) won't occur on a world of size 9 or larger.

You can use that to play with values a bit. A planet with a mostly metal core could be twice as dense as Earth, while a planet with a core bereft of metal could be 3/4 the density of Earth - with corresponding effects on the gravity field and therefore the atmosphere. That could be enough to explain a thick atmosphere on a smallish world or vice versa. However, Book 6 assigns surface gravities to smaller worlds that would let O2 escape rather easily from any world of about size 4 or smaller, given enough time. The only way to justify a Size-1 Standard-Atmosphere world is to invoke other properties that offset the low gravity - for example by suggesting the Size-1 Standard-Atmosphere world is a young and very volcanic world, outgassing actively to replace what is lost, and has an unusually vigorous plant population turning that outgassed CO2 into O2 to keep up your O2 levels.

In other words, you're not really going to be able to determine pressure by calculating from size. You'll have to put your Gamemaster hat on and just make a ruling based on the IPP because factors we'd just make up - like age, level of volcanic activity, and such - will play the bigger role in the resulting pressure.

I've considered looking at the UPP atmosphere code as describing O2 concentrations rather than atmospheric pressure. Consider: a world at half a bar could have a shirt-sleeve breathable atmosphere if the local algae and other flora were to keep the O2 percentage there above 36%. Conversely, an otherwise earthlike world with a 1-bar atmosphere might just present with an O2 percentage down around 10%. The other issue is slapping a compressor to your face isn't necessarily the best way to deliver more air to your lungs unless you've also got some abdominal support: beyond a certain differential, you risk damaging and collapsing your lungs. Saves me from trying to explain why the tiny world has an Earth-pressure atmosphere - it only needs a more O2 rich atmosphere. In that view, "thin" would be breathable but in the 18% range - about what you'd get in the Rockies - while "very thin" implies O2 levels in the danger range. I'd then replace the condensor with a concentrator; the smallest I've seen, at 0.8 kg, is not too much bigger than a Trav condensor.

 

[Kilgs]

I'm not using Traveller so I have a bit more detail in my planetary entries. The entries and details are coming from Astrosynthesis.

 

[lspitz]

Whoops, I'm a little late finding this, but FWIW, here are the physics of breathable atmospheres:

Humans require at least 8 kPa (80 mbar) of oxygen. They can tolerate up to 54 kPa (540 mbar) before oxygen toxicity sets in. These are the lower and upper limits of human respiration for oxygen, and are independent of the total atmospheric pressure.

These figures are for the effective partial pressure of oxygen in the lungs, so they don't relate directly to the partial pressure of O2 in the atmosphere either. Air in the lungs is almost instantly saturated with water vapor, which displaces 6 kPa (60 mbar) of the inhaled gas mix at human body temperature. To figure out how much oxygen is actually available for metabolism, use the following equation:

pO2 (inspired) = fO2 * (Patm - 6), where:

pO2 (inspired) is the effective partial pressure of oxygen in the lungs (in kPa)
fO2 is the fraction of the unmodified atmosphere that is molecular oxygen (0 to 1)
Patm is the total atmosphere pressure in kPa

If you prefer to work with pO2 and Patm in millibars, use the same equation, but subtract 60 rather than 6.

You can see that the difference between the oxygen content of the atmosphere and the oxygen content of the gas mix in the lungs isn't very big at high pressures, but becomes significant at low pressures.

As for pressure dropoff with altitude, it's a function of surface gravity and temperature. The scale height H of an atmosphere is defined as the point above the reference altitude (sea level, if applicable, otherwise the mean altitude datum) where pressure falls to 1/e of its reference level. On Earth, at 288K and 1 G, this is about 8400 meters. I'm ignoring the average molecular weight here, because most breathable gas mixes are going to be in same ballpark as Earth in terms of average MW.

If z is the altitude in meters, Pz = P0 * e^(-z/H), where P0 is the pressure at the reference altitude, e is the base of natural logarithms (~2.71828), and H is the scale height in meters.

H varies inversely with the surface gravity (in gees) and directly with the temperature (in Kelvins). (It also varies inversely with the molecular weight, and in fact each gas has its own scale height, but see the discussion of the tropopause below.) E.g., a planet at 288K with a surface gravity of 0.5 gee and an Earthlike atmosphere has a scale height of 16,800 meters; a planet at 144K and a surface gravity of 1 gee with an Earthlike atmosphere has a scale height of 4200 m. Low temperatures compact the atmosphere; high temperatures expand it. Planets with weak gravity have deep atmospheres where the pressure falls off slowly with altitude; planets with strong gravity have shallow atmospheres where the pressure drops off rapidly.

As an interesting mathematical side note, if a planet's entire atmosphere could be compressed uniformly to the reference pressure, it would occupy exactly one scale height.

Below the tropopause, the atmosphere is thoroughly mixed by weather processes and gases don't separate by molecular weight. For various complicated reasons, the tropopause will occur where the pressure equals about 10 kPa, 100 mbar, or 0.1 standard atmosphere, across a wide range of gas mixes. For pressure calculation purposes, the scale height below the tropopause can be treated as if the whole atmosphere is composed of a single hypothetical gas of the average molecular weight of the mix.

You can get local, transient accumulation of heavy gases near the surface in special situations, like near volcanic vents, but these are very transient indeed and require a constant input of fresh gas to counteract mixing and dilution. Still, they can persist long enough to get unwary volcanologists in trouble.

Sorry, that's a bit wordy, but the topic does require some explanation if you want to understand the relationships between atmospheric pressure, oxygen content, altitude, and human respiration.

 

[aramis]

Ispitz, it looks like you're ignoring temperature and pre-inhalation relative humidity in the name of simplicity. I've been places where the temperature difference was zero and the relative humidity was in the upper 90's - I'm reasonably certain your 60mBar difference isn't going to happen then.

 

[lspitz]

Ispitz, it looks like you're ignoring temperature and pre-inhalation relative humidity in the name of simplicity. I've been places where the temperature difference was zero and the relative humidity was in the upper 90's - I'm reasonably certain your 60mBar difference isn't going to happen then.

You're right, there won't be much of a water vapor saturation difference under conditions of high heat and humidity. But the oxygen content of the air has *already* been lowered in that case, external to your body, by Mother Nature.

E.g., extreme case, if you're at sea level and 50C in 100% humidity (which is ~120 mbar water vapor at that temperature) on Earth, you are breathing in air that contains only 0.2*(1000-120) or 176 mbar oxygen. No further displacement of oxygen will occur when you inhale. If the air had been 50C and completely dry, it would saturate with water vapor inside your lungs and you'd end up effectively breathing 0.2*(1000-60), or 188 mbar oxygen, because your body temperature would control the saturation level (60 mbar).

The bottom line for human physiology is that for the purposes of breathing, it doesn't matter whether the air has become saturated with the maximum amount of water vapor inside or outside the lungs. Either way, the oxygen has been displaced and isn't available for respiration.

Really, the only place I would pay much attention to this effect is for a thin, borderline breathable atmosphere, where the amount of oxygen available is low to begin with, and is on the same order of magnitude as the vapor pressure of water at 312K.