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How does a hobby weather balloon control its flight path? Just it just keep rising straight up vertically, always at the mercy of the winds, being swayed side to side?

Unlike a rocket/drone, it does not have an engine/motor that can be controlled remotely. So if I want the balloon to hover over a particular area and send me images (a particular section of a forest to watch for wildlife activity), how do I do it?

All weather balloons seem to be aimed towards gaining altitude and taking NASA like images, but is there a way to move a balloon horizontally and not just vertically

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    $\begingroup$ You can control a balloon horizontally but then we call it something else. $\endgroup$ – fooot Dec 17 '14 at 22:07
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An ordinary weather balloon cannot maneuver horizontally (unless an external force is applied to it) because it lacks the means to do that. It has only one purpose, to soar up to the altitude where the air pressure inside is more than outside and then burst.

If you want it to steer, you can add steering servos (as mentioned in this PDF). Of course this will add cost and complexity.

There are some websites for Balloon Trajectory Forecast, which might be helpful.

Only if Larry Walters had thought about this, things would have been different for him.

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Yes, I think a balloon can move horizontally the same way a cloud can (by wind).

if I want the balloon to hover over a particular area and send me images (a particular section of a forest to watch for wildlife activity), how do I do it?

I think I've got a simple answer to this one: Use a rope.

At least for a small balloon that's only 1 or 2 hundred feet up you could let it rise up like a kite and tie it off over your desired area. You might even be able to use a security camera wire to enable using a (relatively) cheap security camera, sending power & video up & down the wire, instead of a wireless camera. And you'll have the desirable ability to pull it back down to retrieve camera easily.

But, if you're thinking of using a giant weather balloon 1000+ feet in the air, I think that would create a hazard to aviation. [Does anyone know of any regulations or laws if that would be illegal anywhere? Canada/US/Europe?]

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A weather balloon is almost constantly moving horizontally. The only time it is not moving horizontally is when there is no wind and the balloon has no horizontal momentum (gained from rising through layers with horizontal winds). You cannot control this horizontal motion and the balloon is at the mercy of the wind.

If you want a platform that is in control of its position, you will need something that can provide its own thrust. A weather balloon is not going work for that application. A weather balloon is also not designed to hover, but to rise until it bursts somewhere around 100,000 ft.

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