Nuts & Volts

NEAR SPACE
Altitude (feet)
100000
90000
80000
70000
60000
50000
40000
30000
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0
line to the resulting chart and had
Excel determine a sufficiently accurate
equation for the standard atmosphere
of Titan (see Figures 6 and 7).
One thing you’ll notice about
these charts is that the atmosphere
on Titan becomes thinner more slowly
with altitude than it does on Earth
(check the sidebar for more information).
This is due to Titan’s lower
gravity, which is something like 16%
of Earth’s gravity. The rate at which an
atmosphere becomes less dense with
increasing altitude is referred to as
the atmosphere’s scale height.
The atmospheric pressure on the
surface of Titan is 50% greater than on
Earth, or 1,500 mb. The air temperature
is 96 Kelvins, or right at the
temperature that nitrogen liquefies.
The composition of the Titan atmosphere
is around 90% nitrogen and
10% trace gasses, like methane. But
I’ll stick with a 100% nitrogen atmosphere
to keep the calculations simple.
The mass of a mole of nitrogen
(N 2 ) is 28 grams. So a mole of helium
displaces 24 grams of atmospheric
mass. At a surface temperature of 96
Kelvins and pressure of 1,500 mb, I
calculate that 5.3 liters of helium gas
will displace 24 grams of nitrogen. To
lift the 10.6 pound payload (the mass
of the balloon and near spacecraft)
will require a balloon with a volume
of 1,063 liters or 37.5 cubic feet. This
implies that a 3,000 gram weather
balloon can expand 1,079 times larger
before bursting!
In the chart in Figure 8, you can
Balloon Volume (Titan)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Expansion (ratio)
■ FIGURE 8. Titan’s thick atmosphere
prevents a weather balloon from
expanding as much as Earth’s thinner
atmosphere, so the balloon will rise to
a higher altitude before bursting.
see that to climb to an altitude of
100,000 feet above the surface of
Titan, the balloon will only expand 4.5
times (compare this to 100 times on
Earth). So the maximum volume of
the balloon will only need to be 169
cubic feet. A balloon this small is
lighter in weight than a 3,000 gram
balloon and if we use the smaller
balloon, less helium will be needed to
begin with.
Indeed, we may find it difficult to
prevent the balloon from rising too
high in the Titanian atmosphere. Our
balloon could easily spend the
majority of its flight above the smoggy
clouds enshrouding Titan. This
would be great for an atmospheric
sounding, but it would be a disaster
for a mapping mission. NV
REFERENCES
Geology of Mars
www.lukew.com/marsgeo/
aeolian.html
Mars Atmosphere Model
www.grc.nasa.gov/www/k-12/air
plane/atmosmre.html
Titan Meteorology
www.astro.uni-bonn.de/~dwe/dweid/
Pathfinder Weather Data
mars.sgi.com/ops/asimet.html
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March 2006 95