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The flight simulation of airships and hot air balloons usually considers the envelope geometry as a fixed shape, whose volume is eventually reduced by ballonets. However, the dynamic pressure or helium leaks in airships, and the release of air to allow descent in hot air balloons can significantly change the shape of the envelope leading to potential dangerous situations. In fact, in case of semi-rigid and non-rigid airships a reduction in envelope internal pressure can reduce the envelope bending stiffness leading to the loss of the typical axial-symmetric shape. For hot air balloons thing goes even worse since the lost of internal pressure can lead to the collapsing of the balloon shape to a sort of vertically stretched geometry (similar to a torch) which is not able to sustain the attached basket and its payload.