# Using the terminal velocity formula for a helium balloon?

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.

• does the volume of your balloon increase with high or does it stay constant? Commented Sep 6, 2021 at 14:18
• The volume increases
– yolo
Commented Sep 6, 2021 at 14:51
• @trula would that matter since the velocity is (apparently) constant at every instant?
– yolo
Commented Sep 6, 2021 at 14:51
• You can calculate terminal velocity from balance : $F_b-mg=F_{\text{drag}}$, solve for $v_{term}$ in drag expression. Commented May 25, 2023 at 11:17