Rigid multi-cell structure. The definitive choice?

I’ve seen that NASA has built two balloon prototypes to explore Venus and Titan. Since these two bodies have such different environments, two different design considerations must be carried for each one.

The main issue in Venus (about the design of the balloon structure) is the highly corrosive atmosphere. Since the mission is not expected to last for much time (few Earth days), autonomy and gas leakages are not the main concerns.

The other balloon, intended to explore Titan, is much more similar to this project. Since it will go beyond Saturn, the mission is expected to one year or more. Of course issues like communications and automated decision making algorithms must be carefully designed. What attracted most my attention was the solutions they proposed for increase the lifting properties of the craft.
As in Titan temperatures are about 80-90 K, common materials to prevent gas leakages designed for Earth conditions are not applicable, and in those cryogenic temperatures the lost rate is much bigger than in Earth. So, the device will obtain hydrogen from chemical reactions of the methane widely available in Titan’s atmosphere.

After reading the papers related to those two projects, and since in Earth ambient conditions are not so hard –but in high layers of atmosphere are UV degradation and temperatures of 223 K-, many of the solutions proposed are not directly applicable to this model. Nevertheless, they talked about Mylar supper pressure balloons (rigid structure) used in meteorological observation, which have flown for 744 days.

That gave me the idea of the following design, in order to decrease gas leaks and tensions in the rubber.

Let’s study the performance of a rigid model. Unlike in a flexible model, here the pressure difference must be taken into account. But despite in flexible models pressure differences should not be dramatically high, in the upper layers of the atmosphere outside pressure is very low, the rubber must elongate too much, eventually provoking burst or (which is quite sure) a sudden drop in gas-containing properties.
In addition, a rigid model would be much easier to control in height.

If we calculate the tension that a spherical shaped balloon must bear, we get something like:

This means that the tension supported by the rubber is proportional to the radius of the balloon.

So, maybe there’s a way to reduce the radius of the balloon, but without limiting the gas volume it contains.

Let’s take the following rigid device. It’s composed of an outer spherical structure filled with many small cells (imagine that like a ‘rigid’ balloon filled with smaller ‘rigid’ balloons).

If we make some numbers we can get some interesting information:

The first conclusion is that the radius of the global structure grows with the cube root of the number of cells. This means that in order to decrease the radius of the cells a 50% the number of cells must be increased a 800%.
The good point on that is that the bigger the number of cells is, the better the structure will bear bursts and gas leaks.

But, of course, that also would increase the total surface of the balloon, and hence it’s weight. But would that be limiting?

Assuming a density of boPET film with a thickness of 30 μm of 0.042 Kg/m², we get:

To estimate magnitude orders (which is what I’ve been doing the whole post) let’s suppose a constant difference of density between helium and air of 1 g/m3.

Let’s assume, also, a diameter of 5 m., and the required number of cells to make the small radius equals to 0.5 m. That results in 1000 cells, and the lifting force (expressed in kg.) would be 30 Kg, in contrast to the 60 Kg. of the single-cell structure.

In conclusion, the most suitable design for the balloon (attending to gas leakage, pin holes resistance and reduction of stress) is a multi-cell rigid structure.