Erik Reuter <[EMAIL PROTECTED]>
The only way I know of to get a simple equation is to make a
couple approximations:
(1) The temperature of all the air is the same, 300K
(2) The air all rotates with the endcaps, speed proportional to
radial distance from center
The second approximation, or assumption, makes good sense. But the
first begs the question. Is the air temperature the same throughout
the spinning space habitat?
Think of a parcel of air near the axis. It cools and becomes denser
than the surrounding air. So it drops towards the rim. As it drops
its pressure increases. Does it not heat up? (As well as move
anti-spinward.)
Erik Reuter goes on to say:
Here is the corrected formula for the pressure in the habitat as a
function of height h:
P/P0 = exp[ - ( h / R )^2 / ( 2 k T / ( m g R ) ) ]
= exp[ - ( h / R )^2 / 3.45 ]
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 5.0)) ; radius of habitat
(expt e (- (/ (expt (/ h R) 2) 3.45))))))
'(0 1 2 3 4 5) " ")
Altitude Atm. Pressure for a spinning space habitat, radius 5 km
0.0 1.00 rim (i.e., `surface')
1.0 0.99
2.0 0.95
3.0 0.90
4.0 0.83
5.0 0.75 central spin axis
On earth, according to the standard tables, the pressure at 3 km (9800
feet) is 0.7 of an atmosphere. In this spinning space habitat, at 3
km it is 0.9 atm. So the pressure drop is less in the spinning space
habitat than on earth.
Indeed, according to this table, it would be possible for humans to
breath the air at the central spin axis; its pressure there, 3/4 of an
atmosphere, is about the same as on earth at an altitude of 2 km or
6500 ft.
Incidentally, according to Erik's formula, the pressure at the center
of a spinning space habitat with a radius 8 km, like Rama, would be
nearly 0.9 of the pressure at the rim.
But I still wonder what the standard temperature is? What is the
lapse rate? How much does temperature drop per kilometer of increased
altitude? How much does dew point drop?
--
Robert J. Chassell Rattlesnake Enterprises
http://www.rattlesnake.com GnuPG Key ID: 004B4AC8
http://www.teak.cc [EMAIL PROTECTED]
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