What is the air pressure near the center of a spinning O'Neil type
space habitat when the pressure at the rim is 1 atmosphere?
What is the equation that tells you the pressure?
On Earth, sea level air pressure averages approximately 1 bar
(1013.25 mb or 1 atmosphere) and decreases as the altitude increases.
At 5.5 km (18,000 feet), atmospheric pressure is about 0.5 bar.
Suppose you were to construct a spinning space habitat, perhaps by
melting, spinning, and putting an air bubble into a nickel-iron
asteroid. Presumably, you would shape the habitat so it is a
cyclinder that is wider than it is tall, for stability, with end caps
that bulge outwards, for strength.
Perhaps it looks somewhat like the following diagram, but with the end
caps bulging outwards, and with the incoming sun (reflected from
mirrors not shown) coming through the top window (marked by the ^ )
and reflected on to the surface from a central cone (marked by the |
and +):
_______^_______
/ \
| | |
| | |
| | |
\_______+_______/
<-- r -->
`r' is the radius of the habitat.
Suppose the habitat has a radius of 5 km
Then, to produce at the rim a 10 m/s^2 acceleration, approximately one
gravity, the habitat will need to spin once every 140 seconds.
Am I right about the spin? My membory is that A = v^2/r, where A is
the acceleration, equal to circumference/time-of-a-rotation, and v is
the tangential velocity of the rim.
------------
| 4 pi^2 r
Or, put another way, T = period-of-rotation = \ | ----------
\| A
(let ((pi 3.14159265359)
(r 5000)
(A 10))
(sqrt (/ (* 4 (expt pi 2) r) A)))
==> 140.496 seconds
Given this acceleration, and a pressure of 1 bar at the rim, what will
be the pressures at a distance from the center of 3 km (i.e. 2 km
altitude above the rim), at a distance from the center of 1 km, and at
the center itself? What is the equation?
Another question: At what rate do the temperatures and dew points
converge in a spinning space habitat?
In the Earth's atmosphere, when unstable, dry air rises, the
temperature/dew point spread converges at a rate of about 8.2 deg C
per km (4.4 deg F per 1000 ft). Thus, when the ambient temperature is
20 deg C and the relative humidity is 50%, clouds form at an altitude
of approximately 1300 meters, or approximately 4300 ft, using pilots'
rules of thumb for unstable air.
What happens in a spinning space habitat?
Again, assume that the ambient temperature at the surface (i.e., the
rim of the habitat) is 20 deg C or 293.15 kelvin or 68 deg F, the
pressure is 1 bar, the relative humidity is 50% (i.e., the dew point
is 9.3 C or 282.45 K).
Suppose a vent releases air with the same dew point as the ambient air
but a little warmer temperature.
Obviously, as the warmer air rises, it will head spinward. But will
it cool enough as it rises to form a cloud? If so, at what altitude
in the habitat?
Incidentally, right now, on earth, my outside temperature is
27.2 deg C (81 deg F) and the relative humidity 45%. The dew point
is 14.4 deg C (58 deg F) so by my convergence rate calculation,
the base of the clouds should be at 1500 meters or 5100 ft. According
to the automated measuring device at the local airport, the base of
clouds is at 1400 meters or 4600 ft, so the rule of thumb is not bad.
(I am taking these rules of thumb from an old, since replaced, US FAA
handbook. The stated convergence rates are not exactly consistent for
the two measuring systems: 4.4 deg F is 2.44 deg C, not 2.5 deg C.
So 4.4 deg F per 1000 ft should be 8 deg C per km. This puts the
bases of the clouds higher. On the other hand, when doing
calculations in the airplane, which meant doing them in your head, the
advice for people using the `English' system was to `divide by 4', not
4.4.)
Note that all these temperatures involve the `dew point', not the `wet
bulb' temperature. What is the difference between the two? Why does
the wet bulb temperature depend on pressure, but the dew point
temperature does not? Or does it really?
By the way, the USA Today website,
http://www.usatoday.com/weather/whumcalc.htm
says the altitude of cloud bases, in meters, can be calculated by
multiplying the temperature/dew point spread in deg C by 125. This
calculation gives high bases, like mine using 8 deg C per km.
(For deg F and feet, their multiplier is 222.)
--
Robert J. Chassell Rattlesnake Enterprises
http://www.rattlesnake.com GnuPG Key ID: 004B4AC8
http://www.teak.cc [EMAIL PROTECTED]
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