Re: [Phys-l] video

["Robert Cohen" <Robert.Cohen@po-box.esu.edu>]

Neat spreadsheet.

Not that it would make much of a difference, but your value of g should
probably be less than 9.8 and the initial height (according to the
Wikipedia article) was 31,330 m, not 30,000 m.

I think the biggest error, though, might have to do with the density
profile.  A scale height of 7km probably underestimates the density
through most of the atmosphere, leading to smaller drag values than
appropriate.

[The US standard atmosphere surface density is 1.225kg/m3, which
decreases your density profile but not so much to counteract the error
associated with your scale height]

There is also integration error.

I haven't redone the integration, though, to see if incorporating these
things explains the 153 vs. 276 second difference.

----------------------------------------------------------
Robert A. Cohen, Department of Physics, East Stroudsburg University 
570.422.3428   rcohen@po-box.esu.edu    http://www.esu.edu/~bbq 

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu 
> [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf 
> Of John Mallinckrodt
> Sent: Tuesday, April 01, 2008 2:11 PM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] video
>
> 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
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