I am interested in the math involved to calculate the ideal natural teardrop shape for a hot air balloon. I want to learn the details of what is involved to calculate this accurately. I read this https://www.physicsforums.com/showthread.php?t=658802 which was a really nice start, but it unfortunately did not get into the details of how this is calculated. Regarding the pressure gradient within the balloon, I'm curious how to calculate the pressure change from the top to the bottom, and the math involved in calculating the shape. I appreciate the help. Thank you.