Refinements to the Aerodynamic Model of an Ascending Balloon

Trajectory simulations for high altitude scientific balloons have typically focused on the thermal balance of the system. The calculated upward force, or free lift, on the balloon was based on the density of the lifting gas and the density of the surrounding air. Aerodynamic models for calculating the ascent rate of the balloon were simple drag equations using a constant drag coefficient. The drag coefficient was adjusted in the model to allow general agreement with the total time to float from actual flight data. This generally results in predicted ascent rates that vary considerably from actual data at different points in the flight. In addition to the limitations of prediction of ascent rates on large balloons, observed ascent rates of very lightly loaded balloons have shown that there is a limit to ascent rate that is independent of the amount of initial free lift put in the balloon during inflation. In this paper, the authors will review previous work done on the aerodynamic modeling of ascending balloons and will present the results of a numerical study of the shapes of ascending balloons with the inclusion of an aerodynamic pressure distribution down the length of the balloon. Nomenclature A = balloon envelope surface area a = initial pressure head at the base of the balloon b = lifting gas buoyanc