■ FIGURE 2
Air Pressure
(Standard Atmosphere Mars)
100000
90000
80000
Altitude (feet)
70000
60000
50000
40000
30000
20000
10000
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3. 5 4.0 4. 5 5.0 5. 5 6.0 6. 5 7.0
Pressure (mb)
is a mathematical model describing
the average Martian atmosphere as a
function of altitude. According to the
webpage (listed in the sidebar), the
atmospheric pressure of the Martian
Standard Atmosphere is calculated by
the following equation,
P = 14. 62 x e(-0.00003 X H)
where
P is pressure in pounds per square
foot (PSF)
H is the height in feet
■ FIGURE 3
Air Temperature
(Standard Atmosphere Mars)
Personally, I prefer millibars of
pressure and feet of altitude. (That
sound you just heard was that of an SI
purest having a minor heart attack after
reading that last sentence.) The atmospheric temperature of the Martian
Standard Atmosphere is calculated by:
100000
90000
80000
Altitude (feet)
70000
60000
50000
40000
30000
20000
10000
0
-140 -130 -120 -110 - 100
T = - 25. 68 - 0.000548 x H
(below 22,960 feet)
T = 10. 34 - 0.001217 x H
(above 22,960 feet)
where
T is the temperature in degrees
Fahrenheit
H is the height in feet
- 90 - 80 - 70 - 60 - 50 - 40 - 30 - 20
Temperature (*F)
Therefore, the volume required to
displace 40 grams of a CO2
atmosphere at Martian temperature and
pressure is no longer 22. 4 liters but,
22. 4 liters * (259/273) * (1013/7) or
3,076 liters (108.6 cubic feet).
To lift our 10. 6 pound Earth
payload (which is the balloon and
payload weight), our astronauts will
need to fill the balloon to a volume of
13,066 cubic feet. This is equivalent to
a spherical balloon with a radius of
14. 6 feet or a diameter of 29.2 feet.
This is well within the capabilities of a
3,000 gram balloon which can inflate
to a diameter of 42. 6 feet before
bursting. But before we can actually
launch the balloon, the astronauts
will need to add a little extra helium
92 March 2006
to generate a positive lift. However,
we’ll ignore that for this article since
the additional volume is small
compared to the initial volume of the
balloon. Now let’s have our astronauts release the balloon and watch it
climb into the morning skies of Mars.
ATMOSPHERIC
STRUCTURE AND
MAXIMUM BALLOON
ALTITUDE
At the NASA Glenn Research
Center (GRC) website, I found the
equations describing the air temperature and pressure of the Martian
Standard Atmosphere (MSA). The MSA
These equations were developed
by the observations of the Mars
Global Surveyor, a spacecraft that is
still functioning in orbit around Mars.
Figures 2 and 3 show charts of air
pressure and temperature on Mars as
a function of altitude that I generated
from these equations.
Both air pressure and air temperature will affect the volume of the
balloon. So in my spreadsheet, I
combined the effects of pressure and
temperature into a new column that
calculates the volume of the balloon
in ratio to its initial volume on the
surface. Figure 4 shows the chart from
that column in the spreadsheet.
In these charts, I assumed the
temperature and pressure of the
helium inside the balloon will be
the same as the temperature and
pressure of the atmosphere outside
the balloon. You’ll note from the chart
that the volume of the balloon begins
