Hot Air Balloon Shape and Pressure Gradient Within the Envelope

[Yachtsman]

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.

 

[CWatters]

Have you tried contacting "K^2" ?

 

[Yachtsman]

for some reason last night when I tried it did not let me email K^2, but now today it will. I must have been tired when I wrote my posted my note. What I did was to just repost what I wrote into that thread so that others can benefit from any response.

 

[256bits]

The parametric equation for a teardrop curve
http://mathworld.wolfram.com/TeardropCurve.html