Balloon neutral buoyancy + an interesting idea

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Medula_O
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Hi,
I'm trying to achieve neutral buoyancy with a sounding balloon (a large latex balloon).
Is there a certain weight/helium ratio that will make it afloat at 10km/20km etc (tyhe balloon bursting altitude is ~38km)
One idea that I had was to attach another balloon, which is mostly empty.
When the 1st, full balloon, bursts at 38km, the 2nd balloon will already be inflated to some degree (can be calculated of course).
But, what happens now ? How heigh can this 2nd balloon climb ? Can IT reach equilibrium ? Isn't this the same problem, or above that height there is something else that will limit its climb ?

More technical data on the balloon:
Launch diameter: 2.2 meters, with 4.97 cubic meters of helium.
Bursting diameter: 13 meters, at ~38km.

Thanks.
 
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Hi Medula,
Your plan sounds feasible, but I always thought sounding balloons had a valve that opened when pressure inside exceeded a given value - that way they simply don't burst but just vent the gas when they hit a certain altitude. Similar ways of controlling volume using pressure valves or automatic valves might be employed as well, such as a solenoid valve that opens for so long then locks shut to allow the balloon to burst, or a valve that maintains pressure for so long, then opens completely to allow the package to return to Earth.