Impact of the thermo-mechanical behavior of elastomeric membrane on the flight dynamics of sounding balloons

Abstract

The following work deals with the coupling of a thermo-mechanical model (TMM) of elastomeric membranes of sounding balloons with a flight dynamics model (FDM) of the whole system composed of a sounding balloon and its gondola. This type of balloon, filled with Helium gas, is typically used for its low cost to conduct tests of space technologies in near-space conditions between 20 km and 40 km above sea level where low pressure of the order of millibar can be found. The coupling between the TMM and the FDM is held by the rate of expansion of the balloon. The rate of expansion depends on the mechanical state of the membrane given by the surrounding atmospheric conditions. The model is used to assess the burst altitude, the time of flight during the ascent and the impact velocity of the gondola at the final stage of the descent. A generic model of the atmospheric conditions provides the necessary aerodynamic parameters to describe the balloon ascent to its final altitude. Special attention is given to the balloon membrane as it is subjected to constant changes of pressure during the ascent. The TMM is built to include the details of the temperature-dependent stress–strain relation experienced by the elastomeric membrane as a function of altitude. Knowing its thermo-mechanical state during the flight allows predicting with greater accuracy the burst altitude and the flight duration than provided by a sole FDM. However, in a thorough effort to understand the limitation of the proposed TMM, its results are compared against those computed from classic hyperelastic models showing key differences. Nevertheless, these differences do not translate into any significant impact on the flight dynamics as shown in the comparison between simulation results and experimental data (time of flight, altitude versus time and impact velocity) obtained for three actual flights that occurred over the State of Guanajuato, Mexico, in 2015 (flight F1), 2016 (flight F2) and 2018 (flight F3). It is argued that the present thermo-mechanical flight dynamic model (TMFDM) can be applied to the fair estimation of the flight duration and the burst altitude with sufficient knowledge of the atmospheric conditions. The model can provide key information for the suborbital flight. Amongst these key information, the maximum altitude reached by the balloon is essential to estimate the impact velocity and subsequently to design reliable impact attenuators to ensure the physical integrity of the payload when the gondola touches the ground. The same information can also be used to determine the operating conditions of payloads in high altitudes. Additionally, the time of flight may be used to plan ahead of time the duration of the tests to be performed in a near-space environment.