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If I need to fly a drone in strong winds, how can I stabilize it? Should I use accelerometers and gyroscopes to keep it steady? Or should I just use some flight technique under such circumstances?

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    $\begingroup$ Flying the drone under strong winds is not an easy task. I expect you don't refer to things like these spaceref.com/news/viewpr.html?pid=47749. Anyway, a very careful control is the most necessary in this kind of conditions, not loads of apparatus. $\endgroup$ – galtor Mar 14 '16 at 21:41
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In controls this is known as disturbance rejection. In order to sustain your motion in the presence of high winds you need the controller to be as responsive as possible, and an accelerometer would help. A fast loop rate will also help.

You also have to deal with the nonlinearities of thrust, drag, weight, and lift. Depending on the design of your drone, you might be able to "point it into the wind" to get some additional lift. But the dynamics of this are very difficult.

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