Re: pressure vs. altitude

["Dr. William Newbolt" <NewboltW@madison.acad.wlu.edu>]

> Date:          Mon, 25 May 1998 10:52:32 -0500
> Reply-to:      phys-l@mailer.uwf.edu
> From:          "Jason Powell" <fizzx@wi.net>
> To:            <PHYSHARE@lists.psu.edu>, <phys-l@atlantis.uwf.edu>,
>                <PHYSLRNR@IDBSU.IDBSU.EDU>, <phys-l@atlantis.uwf.edu>,
>                <tap-l@listserv.appstate.edu>
> Subject:       pressure vs. altitude

> Why is that when people learn your a physics head they
> immediately start asking you questions?  :-) At a local
> high power rocket launch this weekend I was asked a
> question that's got me stumped. A fellow is designing an
> onboard computer for his rockets that has a pressure
> sensor onboard.  He wants to know how to turn his pressure
> readings into altitude readings as the rocket is
> accelerating up, decelerating up, and returning back to
> earth via a chute. I know there is an answer to his
> question because I have an onboard computer (that I
> purchased) that uses an absolute pressure device. 
> According to the company it uses a logarithmic amp to
> accurately measure the nonlinear pressure vs altitude
> relationship.  After sensing a rapid 300' change it begins
> taking data and then captures max alt at the same time
> triggering a switch to deploy a drogue chute.  A second
> trigger then fires at 600' (user selectable) for the main
> chute. The only thing I can come up with is the old
> P2=P1+(p)gh which assumes the density is the same for any
> h and thus can't be used for gases.  I've looked through
> all my college and hs texts and have found nothing more
> detailed. Anyone know the answer or who to contact to get
> more info? TIA, Jason
> *********************************************************
> Jason (and Kim and Jacob) Powell Kenosha, WI Our Webpage: 
> http://www2.wi.net/~fizzx/ ==========================
> Physics Dept ZionBenton HS Zion, IL
> ========================== '96 Red Miata[PEP]...FIZZX 1
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As I remember it,  the pressure in an isothermal atmosphere 
varies as a negative exponential with altitude.  It goes 
something like:

			P  =  P0*exp(-Mgh/RT)

where P0 is the pressure at ground level, M is the mass of 
a mole of the gas ( I presume you need a weighted average 
of diatomic oxygen and diatomic nitrogen), g is the 
acceleration due to gravity,  h is the altitude,  R is the 
gas constant per mole, and T is the absolute temperature.  
Note that the atmosphere is not isothermal so that we need 
not expect perfect accuracy from this model.     WBN
Barlow Newbolt
Department of Physics and Engineering
Washington and Lee University
Lexington, VA 24450
Telephone and Phone Mail:  540-463-8881
Fax: 540-463-8884
e-mail: NewboltW@madison.acad.wlu.edu

"Prediction is very difficult, especially about the future."
                                          
                                          Neils Bohr