Limits of inflatable structures

There are specifications including “Balloon Material Thickness Thou/Inch”, volume (m³), length (ft), width (ft).
For a balloon of 1 m³, length of 5.5 ft and width of 4 ft, thickness is 1 thou/inch.
For a balloon of 34 m³, length of 22 ft and width of 15 ft, thickness is 6 thou/inch.

Some very rough calculation based on usual statements: the surface area increases by the square, and the volume increases by the cube. The volume is counted only as a basis for estimation, without considering the mass of the helium contained.

The surface area increase would be between squared 22/5.5 (= 4²) and 15/4 (= 3.75²), let’s say squared square root of 15 = about 3.87². The thickness increases 6 times. Total of skin mass increase: 90.

The volume increase is 34. We will note that the cube root of 34 is 3.24, and not 1 m³ which is the volume of the smaller balloon between the two ones.This is likely due to the fact that the two blimps contain surfaces with very little volume (kite and keel) that can be clearly seen in the photo, said surfaces being taking account for the calculation of the length.

Thus, the volume of the balloon should increase to 3.87³ = 58. But 58 is still not 90. Even considering a real cubic volume scale for the balloon, we find that the increase in the mass of the skin remains higher, which gives 3.87 raised to the power of 3.325 = around 90.

We understand “why Blimp Technology Doesn’t Scale Up Well”, leaving the room to rigid airships.