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I was trying to figure out how to calculate an ascent rate of a helium balloon, and I thought to calculate it's buoyant force $F_b$, subtract it from the gravitational force $mg$, and find some kind of effective $g$; call it $g_e$. Obviously, this value is negative.

The 'iffy' point was where I took that value, made it positive, and put it in the terminal velocity formula (modelling the balloon as a sphere), instead of $g$. Despite getting fairly decent results, I wasn't sure how physically correct using that formula was. According to this website, the drag formula for fluids work for slow moving objects (slower than I'm assuming ~5m, hence why I didn't use it).

Side note: According to a research paper I found, up to ~35km, balloons ascend at more or less a constant rate. Not strictly relevant, but it gives context as to why I want to find its terminal velocity.

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    $\begingroup$ does the volume of your balloon increase with high or does it stay constant? $\endgroup$
    – trula
    Sep 6, 2021 at 14:18
  • $\begingroup$ The volume increases $\endgroup$
    – yolo
    Sep 6, 2021 at 14:51
  • $\begingroup$ @trula would that matter since the velocity is (apparently) constant at every instant? $\endgroup$
    – yolo
    Sep 6, 2021 at 14:51

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It would mattet since the buoyant force depends of the volume, it stays constant only if the balloon expands at higher altitudes. And since the sum of all forces should be zero for constant velocity it matters.

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