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*From*: John Mallinckrodt <ajm@csupomona.edu>*Date*: Tue, 1 Apr 2008 11:47:36 -0700

I should have mentioned that it's fun to use the spreadsheet to explore other situations. For instance, if you "jump" from 100 km (I'm not sure how you do that practically speaking!), drag is completely inconsequential for the first two minutes and you reach speeds around 3.6 km/s. Shortly thereafter you essentially hit a brick wall at about 25 km and experience more than 4 g's. At about the 2.5 minute mark you're down to an altitude of 15 km and only slightly exceeding the local terminal velocity moving at about 200 m/ s. From there on you simply continue to slow down gradually as the density increases causing the local terminal velocity to decrease.

John Mallinckrodt

Cal Poly Pomona

On Apr 1, 2008, at 11:10 AM, John Mallinckrodt wrote:

Regarding:

http://video.google.com/videoplay?

docid=-369888258105653405&q=space&total=301436&start=0&num=10&so=0&ty p

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

**References**:**[Phys-l] video***From:*"Anthony Lapinski" <Anthony_Lapinski@pds.org>

**Re: [Phys-l] video***From:*Brian Whatcott <betwys1@sbcglobal.net>

**Re: [Phys-l] video***From:*John Mallinckrodt <ajm@csupomona.edu>

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