Re: [Phys-l] video

[John Mallinckrodt <ajm@csupomona.edu>]

Regarding:

> http://video.google.com/videoplay? 
> docid=-369888258105653405&q=space&total=301436&start=0&num=10&so=0&typ 
> e=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