QUOTE (Greg Hullender @ Jan 5 2008, 07:21 PM)
Why so pessimistic? I took Wikipedia's figures for a "normal" hot air balloon .....
max operating temperature of 120 C (393 K).
.......
Mass of the balloon vs. volume enclosed goes up as the 2/3 power, so a large balloon (100,000 m^3) could carry an amazing 8 tons!
......
As usual, I may have a math error somewhere, but my first cut at this suggests it doesn't look bad at all.
Not a math error; but we are in a very different physical parameter regime.
Terrestrial hot air balloons are peak_T limited (the sealant degrades above 120C). Propane burners
(operated at a low duty cycle) have plenty of power.
Unlike a buoyant gas balloon (where you can just make the envelope bigger to get the volume=r^3,
area=r^2 scaling) you can't just make a hot air balloon bigger, as this increases the area over which
it loses heat, so for a given power you can only sustain a lower temperature, so you need more volume, so....
Turns out nobody (as far as I know) has considered this analytically until this year, since it is such a different
situation from Earth. I have a paper in review at the Aeronautical Journal where I derive an approximate analytic
solution (where the heat transfer is linear with temperature, more true for Titan/Jupiter than Earth...)
for a 2kW power source (1 MMRTG) at 1 bar on Jupiter, assuming heat transfer coefficient of
1 Wm-2K-1 (I bet it is higher for Jupiter, actually, so a worse situation) and a 0.1 kgm-2 envelope
you are able to float 0.07 kg of payload. My wristwatch (which has a pressure sensor and compass!)
would pretty much be it.
On Earth you could float just under 2kg - my laptop.
On Titan (ok at 1.4 bar, so cheating a little bit) you can float 270kg - me and a couple of friends!
High molecular weight and low temperatures are what buy you hot air balloon performance.
(These are all absolute maximum values - practical designs would be a factor of two lower).
Terrestrial hot air balloons are basically sporty - high manoeuvrability (and small envelope size
to facilitate launch/packaging in trailer) at the expense of low mass/power performance.
One last aside - the reviewers of my Titan balloon paper (just out in the January 2008 Journal of
the British Interplanetary Society - www.bis-spaceflight.com) noted that the Daedalus interstellar
probe study long ago proposed reactor-powered Jovian hot-air balloons to do the propellant mining
for the probe....
Ralph