Looking for an equation related to lifting force of air

[Paranemertes]

Hello,

I've been wondering for a while now how hot air balloonists figured out how big their balloons needed to be to lift themselves, the basket,the balloon itself, ect. Is there an equation that would tell me how much lifting force I could get out of x amount of air at x temperature, what volume that would take up, and maybe the pressure?

Thanks!

 

[Paranemertes]

Well did some research and found this very helpful document, if anyone else is wondering about this, here you go:

https://www.brisbanehotairballooning.com.au/media/BalloonPhysics.pdf

 

[MrMatt2532]

I didn't read the document, but you can construct a basic model just by knowing two forces: the bouyancy force and the weight force.

(mass_basket+mass_balloon+mass_air_in_balloon)*g = Volume_balloon*g*density_surrounding_air

This equation would be for if the balloon were not accelerating up or down.

 

[Paranemertes]

Yep, that is very similar to what this fine gentleman derived. Thanks!