Calculating Balloon Range and Altitude

[KJ4EPE]

I feel kinda stupid asking this, since I have a bachelor's degree in physics. But, here it goes: I'm doing a thought experiment on my own (i.e., not a homework problem) for a hypothetical vacuum airship. I've determined the following quantities:

V_displaced = 15 m^3
m = 13.5 kg
F_net = F_buoyancy - Weight = 44.0 N upwards
a = 3.26 m/s^2 upwards
I'm assuming that winds are calm (i.e. v_wind = 0), and I've not factored in how pressure and density change over altitude.

Again, I feel like a dunderhead for asking this, but using these quantities, how can I calculate range and altitude? All the equations I know involve the use of initial velocity, but the only forces acting on the airship are gravity and the buoyant force.

 

[KJ4EPE]

Okay, I thought about it some more, and I realized: I will need to factor in the change of pressure and density, because the maximum altitude is when the buoyant force is equal to the weight. Duh. Now I'm off to figure that out.

 

[dingpud]

Are you still working on this? Remember that for a conventional "weather balloon", the material is latex which will allow the lifting gas to expand and expand until the balloon bursts. If you have a determined enevelope which won't expand over a predetermined volume, that's going to be your max altitude...I think...