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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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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. –  DumpsterDoofus Feb 27 at 22:48
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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. –  DumpsterDoofus Feb 27 at 22:53
    
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. –  user2179817 Feb 27 at 23:00
    
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. –  OSE Feb 28 at 20:13

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

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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. –  fibonatic Apr 8 at 0:07

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