Re: [Phys-l] video

[Brian Whatcott <betwys1@sbcglobal.net>]

At 12:10 PM 4/1/2008, John M.,   you wrote:
> Regarding:
    <http://video.google.com/videoplay?docid=369888258105653405&q=space&total=301436&start=0&num=10&so=0&type=search&plindex=0>



> Brian wrote:
>
> > An interesting challenge. If one descends at the local speed of
> > sound, what is the maximum g felt for a standard atmosphere
> > profile, and for how long?
>
> That (or a slight modification of  that) is a fun challenge.  Of
> course, the answer to the posed question is that, *if* you are free-
> falling (except for drag) *at* the local speed of sound, then your
> deceleration will be maximum at an altitude of zero where the density
> is largest.  For reasonable estimates of mass, cross sectional area,
> and drag coefficient you'll get 20 to 30 g's, so I suggest not trying
> that experiment!
>
> More interesting is the question, "If you jump at a large altitude
> and reach high velocities before encountering substantial atmospheric
> drag, what is your maximum subsequent deceleration."  So I threw
> together a spreadsheet (see <http://www.csupomona.edu/~ajm/special/
> kittinger.xls>) that models the motion of a falling object through an
> exponential atmosphere and subject to dynamic drag.
>
> In the case of Kittinger I used
>
> mass = 100 kg
> drag coef = .7
> area = .7 m^2
> surface density = 1.3 kg/m^3
> scale height = 7000 m
> init speed = 0 m/s
> init altitude = 30,000 m
> g = 9.8 m/s^2
>
> I found that the speed topped out at 1000 m/s (~1% error from the
> quoted value in the film) about 45 seconds after jumping and at an
> altitude of about 22 km.  I also found that the maximum deceleration
> was ~4.0 m/s^2 (subjecting Kittinger to ~1.4 g's) and occurred one
> minute after jumping at an altitude of about 18 km.
>
> Now, according to Wikipedia,
 <http://en.wikipedia.org/wiki/Joseph_Kittinger> ,
>  Kittinger fell for 276 seconds before opening his
> parachute at an altitude of 5500 m.  My spreadsheet indicates that he
> would have reached that altitude in ~153 seconds.   So the Wikipedia
> value doesn't seem very likely to me unless his drogue chute a) had a
> pretty substantial effect and b) was only deployed *after* reaching
> the maximum speed and I guess that might be pretty likely.
>
> John Mallinckrodt
> Cal Poly Pomona

Interesting response.
It is just possible that the folks at Wikipedia were accounting for
the atmospheric temperature lapse rate, which puts the density as
 high as 20% more than your values at some points in the descent.

It brings up an interesting point: it would not do for different
altimeter makers to model the atmoshpheric according to their
own lights -
as little as 500 ft difference could be crucial on some reduced
 separation paths across the Atlantic - accordingly, they all
adhere to a mid-latitudes model promulgated by ICAO,
which gives numbers like
0.01842 kg m-3 at 30 km
0.08891             at  20 km
0.41351             at  10 km
0.73643            at    5 km
1.2250               at mean sea  level.

Brian Whatcott    Altus OK    Eureka!