Hot Air Balloon Shape and Pressure Gradient Within the Envelope

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Discussion Overview

The discussion focuses on the mathematical modeling of the ideal teardrop shape for hot air balloons and the calculation of the pressure gradient within the balloon's envelope. It encompasses theoretical aspects of geometry and fluid dynamics as they relate to balloon design.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant expresses interest in the mathematical details required to calculate the ideal teardrop shape for a hot air balloon and seeks further information on the calculations involved.
  • The same participant inquires about the methods to calculate the pressure change from the top to the bottom of the balloon.
  • Another participant suggests contacting "K^2" for additional insights or expertise on the topic.
  • A later reply mentions a previous attempt to contact "K^2" and notes a successful attempt to repost the inquiry for broader benefit.
  • A link to a resource on the parametric equation for a teardrop curve is provided, which may assist in understanding the shape mathematically.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the specific mathematical methods or details needed for the calculations, and multiple avenues for obtaining information are suggested.

Contextual Notes

The discussion lacks specific mathematical assumptions or definitions that may be necessary for accurate calculations, and the scope of the inquiry into pressure gradients remains undefined.

Yachtsman
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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.
 
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Have you tried contacting "K^2" ?
 
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.
 

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