"Erik Reuter" <[EMAIL PROTECTED]> wrote
If R=5km, m=4.85e-26, g=9.8, k=1.381e-23, T=300, and we note that
h must be in km, then
P/P0 = exp[ -0.115 h ] exp[ +1.15e-2 h^2 ] , h in km, R=5km, h <= R
For Rama, with R=8km,
P/P0 = exp[ -0.115 h ] exp[ +7.17e-3 h^2 ] , h in km, R=8km, h <= R
For the earth, the equivalent formula is quite similar (as David
predicted)
P/P0 = exp[ -0.115 h ] exp[ +1.81e-5 h^2] , h in km, h/6370 is small
Using these corrected formulae, my calculations for the pressures are
as follows. On Rama, the surface (i.e., rim) pressure comes to 462
mb, which is thin but doable. This is good.
The main problem is that the pressures calculated for Earth disagree
with the figures I have for a pilot's standard atmosphere. In areas
without clouds, the earth's actual atmosphere is best represented by a
dry adiabatic lapse rate, which gives a higher pressure than the
values calculated using Erik's formula.
At what altitude to clouds form in a spinning space habitat? Presume
it is built for humans' comfort. This means
The surface (i.e., rim) acceleration is 10 m/s^2,
the pressure is one bar,
the temperature is 20 degrees Celsius, and
the relative humidity is 50%.
Under these conditions on earth, the dewpoint is 10 degrees Celsius
(using the usual rule of thumb of a drop of 10 degrees being a
decrease of half in relative humidity; a detailed calculation done
using the calculator provided by
http://nimbo.wrh.noaa.gov/greatfalls/atmcalc.html
gives a dewpoint of 9.3 degrees Celsius and a wetbulb temperature of
13.9 degrees Celsius; but let's assume a dewpoint of 10 degrees).
With the usual assumptions of a dewpoint/temperature convergence of
8.2 or 8 deg C per km, the cloud bases occur at 1.2 km to 1.25 km or
about 4000 feet altitude.
Under the equivalent conditions, at what altitude do cloud bases occur
in a spinning space habitat?
Here calculations without the temperature information:
For a 5 km spinning space habitat
[This is the Emacs Lisp function I used. You can check the numbers.
I evaluate it in my mail buffer and then add table headers and such.]
(mapconcat
'(lambda (h)
"Calculate air pressures in a spinning space habitat, radius 5 km"
(format "%f \n"
(let ((e 2.718181828))
(* (expt e (* -0.115 h)) (expt e (* 0.0115 (* h h)))))))
'(0 1 2 3 4 5) " ")
Pressure
Altitude ratio
0.0 km 1.00 rim (i.e., `surface')
1.0 0.90
2.0 0.83
3.0 0.79
4.0 0.79
5.0 0.75 central spin axis
For Rama
(mapconcat
'(lambda (h)
"Calculate air pressures in Rama, radius 8 km"
(format "%f \n"
(let ((e 2.718181828))
(* (expt e (* -0.115 h)) (expt e (* 0.00717 (* h h)))))))
'(0 1 2 3 4 5 6 7 8) " ")
Pressure Pressure Calculated pressure
Altitude ratio given in
book
0.0 km 1.000 462 mb rim (i.e., `surface')
1.0 0.898 415
2.0 0.818 378
3.0 0.755 349
4.0 0.708 327
5.0 0.673 311
6.0 0.649 300 mb 300
7.0 0.635 294
8.0 0.631 291 central spin axis
(Calculated pressure is 462 times Pressure-ratio)
for Earth
(mapconcat
'(lambda (h)
"Calculate air pressures on Earth"
(format "%f \n"
(let ((e 2.718181828))
(* (expt e (* -0.115 h)) (expt e (* 0.0000181 (* h h)))))))
'(0 1 2 3 4 5 5.5 6 7 8) " ")
Pressure Standard
Altitude ratio atm (from one or other FAA handbook)
0.0 km 1.00 1013 mb Earth's surface
1.0 0.89 980
2.0 0.79 760
3.0 0.71 700
4.0 0.63
5.0 0.56
5.5 0.53 500
6.0 0.50
7.0 0.45
8.0 0.40
--
Robert J. Chassell Rattlesnake Enterprises
http://www.rattlesnake.com GnuPG Key ID: 004B4AC8
http://www.teak.cc [EMAIL PROTECTED]
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