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Re: [Phys-l] video



Robert,

As you note, none of those things will make any significant difference in the results, but I found this at http://tinyurl.com/ 6kkta :

Kittinger floated to 102,800 feet (31,333 meters) in Excelsior III, an open gondola adorned with a paper license plate that his five- year-old son had cut out of a cereal box. Protected against the subzero temperatures by layers of clothes and a pressure suit--he experienced air temperatures as low as minus 94 degrees Fahrenheit (minus 70 degrees Celsius)--and loaded down with gear that almost doubled his weight, he climbed to his maximum altitude in one hour and 31 minutes even though at 43,000 feet (13,106 meters) he began experiencing severe pain in his right hand caused by a failure in his pressure glove and could have scrubbed the mission. He remained at peak altitude for about 12 minutes; then he stepped out of his gondola into the darkness of space. After falling for 13 seconds, his six-foot (1.8-meter) canopy parachute opened and stabilized his fall, preventing the flat spin that could have killed him. Only four minutes and 36 seconds more were needed to bring him down to about 17,500 feet (5,334 meters) where his regular 28-foot (8.5- meter) parachute opened, allowing him to float the rest of the way to Earth. His descent set another record for the longest parachute freefall.


and this at http://tinyurl.com/2y95a4 :

... Shortly before zero hour, 5:30 a.m., he staggered from the van. his 165-lb. frame laden with 155 lbs. of clothing and equipment ...


The only significant deal here is the 2.5 m^2 parachute reportedly deployed early in the fall.

So, using the updated values

mass = 145 kg (see above)
drag coef = .8 (better reflecting a parachute?)
area = 2.5 m^2 (1.8 m parachute deployed early in fall)
surface density = 1.225 kg/m^3 (reflecting better standard values)
scale height = 7500 m (better agreement w/ Brian's figures at high alts)
init speed = 0 m/s
init altitude = 31,300 m (closer to correct value)
g = 9.76 m/s^2 (~average value over 30 km, *really* big deal)

I now find good agreement with the fall time (I get 262 s to 5330 m as opposed to the reported 276 s) at the cost of a significant discrepancy in the top speed (I get ~730 km/hr as opposed to the reported 990 km/hr). I can tweak the fall time easily by adjusting the drag coefficient or putting in the larger densities at lower altitudes that Brian W. reports, but I don't see any way to get anything like a top speed of 990 km/hr with that parachute deployed that early in the fall. Let me open it between 45 and 60 seconds and I can reproduce the reported values pretty nicely.

John Mallinckrodt
Cal Poly Pomona

On Apr 1, 2008, at 4:40 PM, Robert Cohen wrote:

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&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