Re: pressure vs. altitude

[William Valine <valine@galileo.physics.arizona.edu>]

Jason,

It is usually assumed that the atmosphere is in hydro-
static balance. This gives the relationship,

    dP/dz= -(rho)g   .

Then rho is elliminated with the use of the ideal gas
law applied to the atmosphere. This gives dP/dz in terms
of the pressure and temperature. Heights can be found
graphically or numerically if pressure and temperature
soundings are made. ( It can be seen that for an iso-
thermal atmosphere, dP/dz is proportional to -P and the
pressure falls off exponentially with height.)

For a (known or assumed) uniform lapse rate, 

    T=T0-(gamma)z,

z can also be found from measurements of P.
( Of course, if T0 and gamma are known, z can be found 
from measurements of temperature rather than measure-
ments of pressure.)

Bill Valine
 
On Mon, 25 May 1998, Jason Powell wrote:

> 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
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