Linear theory of optimum hot air balloon performance – application to Titan

Abstract

Abstract We develop a simple theory for hot air balloon performance with fixed thermal power and linear heat transfer to the environment, applicable to low-temperature situations such as Titan’s atmosphere. The theory results in a closed-form solution and it is shown that an optimum balloon diameter exists – the maximum payload is achieved when the envelope mass and payload mass are equal. It is also shown simply that the floating mass for a given power has a stronger sensitivity to heat transfer coefficient than to the envelope specific mass. A hot air balloon on Titan with a ~2kW heat source could loft a theoretical maximum payload of ~195kg or ~100kg with appropriate margins.