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I'm trying to model the ascent of a helium filled weather balloon from 0km to 25km altitude. The plan is to eventually use a python script to calculate the time taken to reach 25km. However, I don't really know where to start.

I have worked out an expression for acceleration in terms of the balloons volume and the density of surrounding air. I now need to find an way of calculating the volume at a given altitude such that I can model the acceleration throughout the ascent.

So if anyone could help me with this I would greatly appreciate it.

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    $\begingroup$ Why would you want to do this on a computer? Haven't people been launching weather balloons for nearly a hundred years? Aren't there hundreds of books which detail this kind of thing based on experimentally-observed launch characteristics? Wouldn't altitude vs. time be the very first thing that would be easy to access by consulting the literature? Why waste time trying to write a computer program that will most likely give inaccurate results when exact experimental data is available? I have no at-sci background, but it seems like an hour of literature search could save weeks of programming. $\endgroup$
    – DumpsterDoofus
    Commented Feb 27, 2014 at 22:48
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    $\begingroup$ Again, I'm not saying this is a bad question, it's certainly a legitimate mathematical modeling question, but from an engineering perspective it seems like it'd be far more effective (and accurate) to consult known weather balloon characteristics. $\endgroup$
    – DumpsterDoofus
    Commented Feb 27, 2014 at 22:53
  • $\begingroup$ Hi, the reason I'm doing it is because it's a problem that I've been set at university, I know it won't be particularly accurate, it's just more about thinking how one could solve a problem like this. $\endgroup$
    – user2179817
    Commented Feb 27, 2014 at 23:00
  • $\begingroup$ On a related note: there are a few websites that take a starting location and predict the path of a weather balloon based on the daily weather forecast. See for instance this one. I've launched 2 weather balloons using these calculators for planning purposes and they are reasonably accurate. Final location was within 30 miles or so of prediction. $\endgroup$
    – OSE
    Commented Feb 28, 2014 at 20:13

2 Answers 2

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Both temperature and pressure variation with altitude are given here on page 2. You can use the ideal gas law to get the volume with altitude from these.

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  • $\begingroup$ But this does not yet explain the what drag force the balloon will experience. Especially at the beginning when it isn't fully inflated. Later on I think you could use the drag coefficient of a sphere. I would expect that the balloon will be going near terminal velocity. So this might simplify the problem, but you can test this by using the acceleration instead and integrate twice. $\endgroup$
    – fibonatic
    Commented Apr 8, 2014 at 0:07
  • $\begingroup$ Is it only for me or is the URL showing a incorrect page? $\endgroup$
    – Harshdeep Chhabra
    Commented Jun 20, 2023 at 14:16
  • $\begingroup$ @HarshdeepChhabra: I updated the link. $\endgroup$
    – Ross Millikan
    Commented Jun 20, 2023 at 16:22
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This is actually a very complex problem. Adiabatic expansion cooling, balanced by radiant and convection heat transfer, determines the super temperature by which finally you can apply the ideal gas law to get volume (and then diameter). And then there are the aerodynamics of drag with the drag coefficient changing with Reynolds Number (balloons just happen to fly in the middle of the transition zone between high and low drag). For latex balloons where the optical properties keep changing as the film stretches (a/e ratio, translucence), and the drag transitions, there seems to be a perfect balance resulting in a near-constant rate of ascent. Quite remarkable.

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