Computation of Buckling Pressure of Pumpkin Balloons

This paper is concerned with the elastic buckling of pumpkin-shaped balloon structures. Pumpkin balloons, currently being used in the NASA Ultra-Long Duration Ballooning (ULDB) Program, consist of stiff meridional tendons that constrain a thin, highly curved plastic surface. The present study exploits the high degree of symmetry of this design by adopting a newly developed, closed form expression of a symmetry-adapted coordinate system for structures with n-fold symmetry, which provides the tangent stiffness matrix in a very efficient block-diagonal form. The critical buckling pressure of balloons with different properties are computed. It is found that for any chosen balloon there is a power law relation between the critical pressure and the number of lobes. The change in the powerlaw coefficients is used to study the sensitivity of different balloons to design parameters such as the shape of the lobe cutting pattern and the elastic properties of the membrane and tendons.