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Page 819
Clearly, the cost of the project is dominated by ammunition, and
the number of stations and rifles is reasonable, as is the amount
of activity, considered on a large industrial scale. The rifles
could be deployed at sea or in empty areas (e.g., military
reservations) where the noise of the shots and the fallback of
expended shells could be managed.
Balloon System
Consider a hydrogen balloon floating at 20 km, using the
Archimedes principle and noting that the density of hydrogen-gas is
one-fourteenth that of air:
md(isplaced) =
mg(as inside balloon) +
mb(alloon) + mp(ayload)
4/3pr3ro=4/3pr31/14ro + 4pr2Drrs(kin)
+ mp
mp=4/3pr3ro13/14-4pr2Drrs
=4pr3[13/(3x14)ro-(Dr/)/rs]
If
r = 100 m (radius of balloon)
ro =
88 g/m3 = 8.8 × 10-2 kg/m3 (density of air at 20 km)
Dr = 1 mm = 10-3 m (thickness of balloon skin)
ro =
1.15 g/cm3 (nylon) × 10-3 kg/g × [102 cm/m]3 = 1.15 × 103 kg/m3.
Then
mp = 1.26 × 107 (2.7 × 10-2 - 1.15 × 10-2)
= 1.26 × 105 (1.55)
= 1.95 × 105 
2 × 105
kg.
The mass of the balloon for a 1-mm thickness is
4pr2Drr = 12.6 × 104 × 10-3 × 1.15 × 103
= 1.26 × 1.15 × 105
× 10-3 × 103 kg
= 1.5 × 105 kg.
If the balloon is 2/3-mm-thick (assumed for convenience), its
mass from the previous computation is 1.5 × 105 kg and the mass of dust lifted, if a
50 percent efficiency factor is used to account for instruments,
dust dispenser, container, and so on (this is conservative), is
105 kg. Nylon of the appropriate
gauge for weaving into a 2/3-mm-thick fabric (1050 denier is about
0.3 mm) costs $2/lb = $4.4/kg. If this is tripled for fabric and
balloon manufacture
