Atmospheric Density - Equation to Model from Sea Level to 200km

[ZachWeiner]

Hey, does anyone have an equation that roughly models atmospheric density from sea level to about 200 km up?

 

[Phrak]

There's not much of an equation for atmospheric pressure that's simple. If you have a CRC handbook you could look up a few values. You should know, as well, that it's quit variable at higher altitudes, dependent on solar activity.

 

[aniketp]

Hi ZachWeiner,
Pressure at a height "h" is given by :
P=(Patm)*e^(-Mgh/RT) [Patm is the pressure at sea level]
And D=PM/RT
But there is an assumption that T is const. this formula will only enable you to calculate the density roughly. So do not use it if you want accurate answers.

 

[Phrak]

Hi ZachWeiner,
Pressure at a height "h" is given by :
P=(Patm)*e^(-Mgh/RT) [Patm is the pressure at sea level]
And D=PM/RT
But there is an assumption that T is const. this formula will only enable you to calculate the density roughly. So do not use it if you want accurate answers.

I have no excuse for it, but in response to this question, I actually tried an exponential curve of pressure vs. height, and fit it to two points of data; sea level and 100 Km. It was off by 28% at 50 Km. Very disappointing.

To get a decent curve fit, P = P0 * exp(ah^3 + bh^2 + h) might do it.

 

[James3849]

what do you need to model it for? pretty much any fluid mechanics text will tell you in a table at the back.

lol.. if u really want to model it, put all the numbers into excel and graph it

 

[nucleus]

There are more than one standard atmosphere, US and ICAO, to name two. They have limitations, such as assuming zero RH, but they give some indication of how temperature and pressure decreases with altitude. Regardless here are some formulas you can enter into your calculator.
http://mtp.jpl.nasa.gov/notes/altitude/StdAtmos1976.html
http://en.wikipedia.org/wiki/Atmospheric_pressure
http://en.wikipedia.org/wiki/Barometric_formula