Calculation of the size of torus, filled with hydrogen, needed to suspend a Soyuz, fueled for lift off, in the Venusian atmosphere next to a cloud colony
Hydrogen is a slightly stronger lifting gas for Venus with denser CO2 atmosphere - and of course no concerns at all of combustion.
Hydrogen has a density of 0.0899 Kg/m3. and Carbon Dioxide, 1.977 kg/ m3, for air it is 1.205 kg / m3
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So a hydrogen balloon on Venus has lifting power of 1.8871 kg per m3, compared with 1.1151 kg / m3 on Earth
To counteract the mass of a fully fueled Soyuz - lift off mass lift off mass 308 metric tons (not sure of lift off mass for the latest TMA-M), then you would need 308,000/ 1.8871 = 163,213 m^3
That could be more than supplied by a torus filled with hydrogen with radius 50 meters and with the radius of the tube around 14 meters. Volume 193444 m3. Lifting capacity 365 tons.
Surface area 27634 m2, so if you had fabric weighing 1 kg / m2 that's 28 tons for the fabric
As a bonus, if we make the torus able to expand to a larger size, like a weather balloon, then it could lift the Soyuz high into the Venus atmosphere before take-off.
So for example, suppose it's a 100 meter radius balloon.
r = 100 m
V = 4188790 m3
A = 125664 m2
C = 628.319 m
works out at Max 2,094 tonnes total, and Max 16.5 kg per square meter of surface area.
Assuming 1 kg / m2 for the fabric, that's 126 tons of fabric
If you go up to a cloud nine like 1000 meter radius you get 2,094,395 tons total, and 165 kg per square meter of surface area.
r = 64 m
V = 1098070 m3
A = 51471.9 m2
C = 402.124 m
Max payload 549 tons. Max 10 kg per m2.
51 tons of fabric
For a smaller start up colony
r = 29 m
V = 102160 m3
A = 10568.3 m2
C = 182.212 m
Max payload 51 tons, Max 5 kg / m2.
11 tons of fabric.
(if you want to do more of these, the online Sphere Calculator may save a bit of time).