I figured out some of the values relating to Rama; the air is thin
and the acceleration figures are not consistent with other claims.
Erik Reuter <[EMAIL PROTECTED]> wrote:
Rama had a radius of about 8km. They entered near the axis and
began descending in spacesuits. After descending 2km, they found
the pressure was about 300millibars. Not enough to breathe,
although Mercer briefly sniffed the air, but he put his helmet
back on afterwards. Gravity was 0.1 earth gravities at that
point. Slightly below that, they were able to breathe the
atmosphere. The surface gravity was 0.6 earth gravities. I didn't
see a mention of the pressure at the surface.
Let's reverse engineer:
* Find the spin rate, when given the radius and surface acceleration
------------
| 4 pi^2 r
T = period-of-rotation = \ | ----------
\| A
or
(let ((pi 3.14159265359)
(r 8000)
(A 6))
(sqrt (/ (* 4 (expt pi 2) r) A)))
==> 229.43 seconds
or nearly four minutes per revolution.
* Find air pressures, when given the radius, surface
acceleration, and the air pressure at an altitude;
P = P0 exp[ - ( h / R )^2 / ( 2 k T / ( m g R ) ) ]
P0 exp[ - ( h / R )^2 / 3.45 ]
>From Erik:
Rama had a radius of about 8km. After descending 2km, they found
the pressure was about 300 millibars.
So to make a table, evaluate:
(mapconcat
'(lambda (h)
"Calculate air pressures in a spinning space habitat"
(format "%f \n"
(let ((e 2.718181828)
(R 8.0)) ; radius of habitat
(expt e (- (/ (expt (/ h R) 2) 3.45))))))
'(0 1 2 3 4 5 6 7 8) " ")
Pressure Pressure Calculated pressure
Altitude ratio given in
book
0.0 1.000 353 rim (i.e., `surface')
1.0 0.995 351
2.0 0.982 347
3.0 0.960 339
4.0 0.930 328
5.0 0.892 315
6.0 0.850 300 mb 300
7.0 0.801 283
8.0 0.748 264 central spin axis
(Calculated pressure is 353 times Pressure-ratio)
* Does the acceleration fit the other info consistently?
According to Erik, at an altitude of 6 km (i.e., 2 km from the
spin axis), the acceleration was 1 m/s^2
Knowing that A = v^2/r, where A is the acceleration and v is the
tangential velocity of the rim, equal to
circumference/time-of-a-rotation.
Since v = (2 pi r)/T, A = (4 pi^2 r)/T^2 and r =(A T^2)/(4 pi^2)
(let ((pi 3.14159265359)
(r 2000)
(T 229.43))
(/ (* 4 (expt pi 2) r) (expt T 2)))
==> 1.5 m/s^2, which does not fit.
For an acceleration of 1/10 gravity, the distance from the axis must be
(let ((pi 3.14159265359)
(A 1.0)
(T 229.43))
(/ (* A (expt T 2)) (* 4 (expt pi 2))))
==> 1.3 km
and the altitude from the rim must be 6.7 km at which point
the pressure is
(* 353
(let ((e 2.718181828)
(R 8.0)) ; radius of habitat
(expt e (- (/ (expt (/ 6.7 R) 2) 3.45)))))
==> 288 mb
which is equivalent to about 8800 meters on the Earth
or the height of Mt. Everest.
* Can the humans breath?
Humans have a hard time breathing a standard Earthly air
mix when the pressure is less than about 40% of sea level,
or less than about 400 mb. This is equivalent to an
altitude of 6500 meters (21000 ft) on Earth. However,
people can survive breathing natural air that is as thin as
the top of Mt. Everest, approx 285 mb, but that takes
acclimatization.
--
Robert J. Chassell Rattlesnake Enterprises
http://www.rattlesnake.com GnuPG Key ID: 004B4AC8
http://www.teak.cc [EMAIL PROTECTED]
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