I am currently making a survey of a world with a surface atmospheric pressure of 2.4 atmospheres. However, I would like to calculate how the pressure will change at different altitudes. And does world gravity affect how the pressure changes?
Google up "scale height" and "barometric formula". Read these links
http://en.wikipedia.org/wiki/Scale_height
http://en.wikipedia.org/wiki/Barometric_formula
As I am quite mathematically challenged I can't figure this out for myself, but if given a rather simple formula I can probably do the rest myself.
There isn't a 'simple' formula, there are actually three. The pressure at altitude will depend on temperature, gas mixture, and gravity. Here's all the math:
Pressure at altitude a, surface pressure P0, scale height H
P = 1/exp(z/H)×P0 = P0×exp(-z/H) = P0×e^-(z/H)
P = pressure at a given altitude z
P0 = pressure at reference level or "sea level"
z = altitude above sea level
H = scale height = RT/g = 8314.4 T/µg
µ = molecular weight of the atmosphere (air=28.964 g/mol)
R = gas constant = 8314.4/µ = (287 for breathable air, 296.8 for N2, 188.9 for CO2)
T = atmospheric temperature (in Kelvin)
g = surface gravity (in m/s²)
First, you need to know the mean molecular weight µ of the atmospheric mix. Good luck with that
Next, you need to know the gas constant R, it depends on composition = 8314.4/µ
With R, calculate the scale height H for the world. This is an atmospheric parameter that defines the altitude where the pressure is 1/e (36.8%) of the pressure at reference level.
Using scale height H, calculate altitude pressure P.
For breathable atmospheres, you can use 2.718282^-(a/8000/g) a in meters and g in earth gravities, and it'll be close enough.
