Hot Air Balloon Fiesta

As I was looking through my old pictures from my semester off-campus in Santa Fe, New Mexico last fall, I came across shots of the Albuquerque Hot Air Balloon Festival that takes place every October. Hundreds of balloons take flight each day for two weeks, often with unique and fun shapes. How do big balloons filled with air take flight? Using buoyant force! This force occurs when a fluid exerts a force that opposes gravity. Normally, the buoyant force of the air displaced is not big enough to cause a balloon to rise. However, we can increase this force by decreasing the density of the air inside the balloon by heating it. As heat is added, the air molecule have more energy and therefore move more, taking up more space. Because air pressure is kept the same, the balloon will not be crushed by the air outside. Since more dense fluids sink and less dense fluids float, the less dense air inside the balloon will create a force upward towards air with the same density.

F buoyant - F gravity = Negative = Net force towards ground = sink or not leave ground
F buoyant - F gravity = 0 No movement in y direction
F buoyant - F gravity = Positive = Net force towards sky = float

Average mass of balloon = 600. kg
Average mass of heated air inside balloon = 2500 kg
Average volume of balloon =2800 m cubed
Density of air unheated = 1.225 kg/m cubed

F gravity = (600.+2500)(9.81)=30,400 N
F buoyant needed to generate lift = 30,500 N = (rho)(V)(g) = (rho)(2800)(9.81)
Density of air needed to generate lift = 1.11 kg/m cubed