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

摘要

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.