On Mon, Jul 14, 2003 at 10:23:53AM +0000, Robert J. Chassell wrote: > 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.
For earth, that is not just "my" formula -- as I said, one of my textbooks gives p/p0 = exp[ -h/hc] and they do a curve fit to experimental data to find that hc = 8.5km. And they show a graph of curve fit and experimental data, and the fit looks pretty good. You don't say how much lower the formula is compared to the data you are looking at. The curve fit in my textbook looks to have less than 5% error, and it may be better than that (it is hard to read the graph very precisely). What accuracy were you expecting? > 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. That link doesn't give any formulas. I looked at the Javascript and it is full of "magic numbers". I'm not sure how those algorithms were derived, but they certainly do not appear to be straightforward physical formulas. With such a complicated system, so much depends on the assumptions and approximations that are made. This is not fundamental physics -- it is a highly applied branch of science. If you don't make assumptions that are valid for the system being modeled, the results will be nonsense. Not having studied atmospheric science myself, I don't know the assumptions that were made to come up with these results. Do you? > 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 > Above one km, it seems the error is less than 5%. I consider that not too bad given the simplicity of the formula and assumptions that were used, compared to the actual atmosphere. Is it surprising to you that the formula is a little off (10%) near the surface? I can think of many reasons why the assumptions made in deriving the formula don't hold exactly near the surface. It seems to me that you are expecting to calculate all of these parameters from first principles of physics, but it also appears to me that the actual numbers used in practice that you quote are not derived from fundamental physics alone, but also have some phenomenological constants ("fudge factors") included to make the formulas better fit actual measured data. This is not unusual when modeling such a complex system. Of course, it makes it difficult to calculate the corresponding values for a habitat, since we don't have any experimental data to fit to. -- "Erik Reuter" <[EMAIL PROTECTED]> http://www.erikreuter.net/ _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
