Hot air balloons have quite a bit of science behind them. Since they were first thought out, aeronautical engineering has helped. While it has not always been referred to as such, the modern terms help define more what they are.
Hot air balloons are crafted with meticulous specifications, that help it not only stay in the air, but provide a safe ride for those who are in the basket. WIth the use of helium, and the science of weight, air, and flight, aeronautical engineering has helped to make leaps and bounds to the study of hot air balloons.
Aeronautical engineering has the primary function of working with the development and crafting of aircrafts. This would include the hot air balloon. As each craft that goes into the air has specific safety requirements and functions, aeronautic engineers use their knowledge of atmospheric pressure and temperature to ensure that the aircrafts are safe to use. As hot air balloons are a form of aircraft, they fall into the category for aeronautical engineering.