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I can't find a reference of a working stratospheric balloon mounted with a compressor to control its altitude. Is there a big physical difficulty (such as compressor weight/power ratio, or power source availability) which prevents this, or just no one as an interest in it ?

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Frankly I don't see this as a physics question. I'm pretty sure that you are already on the trail of the engineering answer. –  dmckee Apr 22 '12 at 2:44
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The pump and power supply would add a great deal to the weight and cost compared to simply dumping the helium. And when it did descend how would you control where it landed? Most of the earth isn't very accesible.

Most stratospheric balloons are for weather observations - it's much easier to just dispose of them and their payload when they pass out of the region you are itnerested in rather than trying to retrieve them

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They are compressing their helium to descend.

When they descend (if they descend) they are going to a lower altitude with higher atmospheric pressure, which compresses the helium, so the balloon has smaller volume.

Helium balloons control their rate of ascent/descent by releasing ballast or valving off gas. Either way, the bouyancy of the helium in the envelope just balances the weight of the payload. As they go to a higher altitude where the air is thinner and has less pressure, the helium expands until it displaces the same weight of air as it did before. Same thing when it goes down.

Here is Felix Baumgartner's balloon when it's lifting off. Notice how little of the "bag" is occupied:

enter image description here

And here it is at 36km altitude:

enter image description here

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