Rigid vs Flexible structure

In previous models I supposed that the main structure will be flexible (like a balloon), and its flexibility will follow some kind of law (in my case that the manometric pressure depends on its radius according to the function 458*ln(1000*x+1) Pa ). Since such airship is much easier to build, there are many other issues that have to be considered; the modelization of the rubber will be always an approximation, and I also have to ensure that its radius won’t exceed some limit value (balloons burst when you inflate them too much).
So a rigid model, with constant (or even better, controllable) volume will be advantageous in some aspects. First of all it’s easier to control (height can be controlled with closed loop control systems that vary volume), it’s models will be more accurate (no strange functions of dubious realism) and the problem of burst is different (now manometric pressure must be checked to ensure that no extreme structural solicitations happen).

I also changed the friction model. Now it’s proportional to the air density and to the square of the velocity and radius. I adjusted the friction coefficient so that a common balloon (mass without helium is 3 grams and its diameter is 20 cm.) will rise at a constant speed of 3 m/s.

So, I modified the last script (and making some corrections that affect to the numeric results) and run it with the following initial conditions:

Total mass without helium:10 Kg.
Diameter (considering spherical shape): 3 m.
Initial height: 1 m.
Standard atmosphere.

To make easier the comparison between rigid and flexible models both results are plotted in the same graph.

After execution these are the results:

In X-axis it’s represented the time in hours. It’s shown that a constant height of 3300 m (10,000 ft.) will be achieved in less than 10 minutes. The lowest temperature is -7 ºC, not bad, since all electronics can work at -40 ºC.

In the flexible model the stationary height is much higher (16000 m.), and what is worse, the temperature at those heights are so low (-56 ºC) that the electronic devices won’t work.

To conclude, these two graphs represent the limit conditions in each case (difference of pressures in the case of a rigid model and diameter in the flexible one):