# Ascension rate of balloon

1. Jun 12, 2010

### Imustthink

How do I find the accelerating ascension rate of my helium balloon?
Ignore factors such as the increase of volume as it ascends, temperature, wind etc.
I just want the basic ascension rate of ideal non changing conditions.

rho_f Outside air density - I think typical air density is this - 1.2 kg/m^3

v Volume - 179.59438 m^3

m Mass - 90.7184 kg

g Earth's gravity - 9.80665 m/s^2

Through some research I have been given this formula but am not sure if its the correct one or how to compute it.

a = g*(rho_f * V - m)/(rho_f*V + m)

http://en.wikipedia.org/wiki/Buoyancy#Beyond_Archimedes_Principle

Last edited: Jun 12, 2010
2. Jun 12, 2010

### Phrak

For a non-accelerating ascent, the upward force of buoyancy will be balanced by a downward force due to air friction.

3. Jun 12, 2010

### Imustthink

(edited) I meant the accelerating rate, sorry

4. Jun 12, 2010

### Phrak

OK. Use the T=ρfVg-mg equation from your Wikipedia article to find the initial upward force.

The initial acceleration is then, ai=T/m.

5. Jun 12, 2010

### Imustthink

So if I did this correctly the answer is: 13.490311 m/s^2 ?

6. Jun 12, 2010

### Phrak

7. Jun 12, 2010

### Imustthink

Giga-thanks!

8. Jun 12, 2010

### Imustthink

How would I find the constant non accelerating ascent due to air friction? haha

9. Jun 13, 2010

### Phrak

Under Mechanical Engineering there's a Aerospace Engineering subfolder. I take it this balloon would take the shape of a teardrop, flattened on the nose, with a lot of wrinkles. I'm not touching that one.