Well I made a bit of a start on this one:
*Note 1 - Hideous rounding and significant figure liberties taken.
*Note 2 - Made assumptions to keep formulas simple. I’m good with spheres, not teardrops.
Found a formula for air density as a function of altitude:
d = 1.21 * exp(-height/8000)
Where d is in kg/m^3 and height is in meters. Dunno how accurate this is or how high it’s valid but it’s all I got.
This gives d for various altitudes as:
0.002337 kg/m^3 at 50km
0.0006698 kg/m^3 at 60km
0.0001919 kg/m^3 at 70km
0.00005499 kg/m^3 at 80km
The largest balloon on record that I could find mention of was 70 million cubic feet capacity built by Wintzen Research (they also launched a balloon to 49km back in 1972 so they seem to know their stuff).
Let’s assume for the sake of argument that at extremely high altitudes the balloon will be spherical (from photos I’ve seen this may be wrong but again it’s all I got and math for spheres is easy).
70 million cubic feet is a touch under 2 million cubic meters.
To “float”, the balloon will need to have (mass/volume) = air density at that altitude.
This gives critical masses of:
4600kg at 50km
1329kg at 60km
380kg at 70km
109kg at 80km
Let’s ignore the weight of the actual gas in the balloon and any non-envelope stuff (instrument package, gondola for those who want to ride along :-o, etc).
A sphere with a volume of 2 million cubic meters has a surface area of 76,356 square meters.
Our balloon envelope will have a mass/area found by dividing the critical mass (above) by the area (76,356 m^2), and then we can check this against known materials to see if we’ve got a chance.
I get the following:
1.43 grams/m^2 at 80km
4.98 grams/m^2 at 70km
17.4 grams/m^2 at 60km
60.2 grams/m^2 at 50km
I couldn’t find any definitive listing of masses for a good thin film polymer like Dupont Mylar, but some kite enthusiasts have a discussion board and mentioned that it’s commonly available in 20, 40 and 60 grams/m^2.
So, back of the envelope figuring, I’d say that 60km is probably achievable, although pretty darn challenging. Dunno about higher, it looks like the material will be hard to find - incredibly light yet rugged enough to survive the temperature and mechanical stresses.
Anyone care to sharpen this up a bit? Does anyone have better info on materials used?