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I don't know if takeoff would be the right term, but the wing should generate lift with any headwind.

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    $\begingroup$ That works only if the aircraft is somehow prevented from getting blown away. The concept of kite-flying applies. $\endgroup$ – Cpt Reynolds Mar 25 '18 at 15:42
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It could, but eventually drag would cause the ultralight to start moving in the same direction as the wind and it would lose any apparent forward airspeed.

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  • $\begingroup$ And if you tow it to the ground so it doesn’t move too much with the wind you have a kite. $\endgroup$ – Florian Mar 26 '18 at 22:40
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A wing will produce lift when exposed to a headwind. And yes, if the wind is strong enough, a properly tethered airplane, ultralight or not, will 'become unstuck'.

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    $\begingroup$ Even a tethered A380 could become "unstuck" with the right wind. The OP didn't mention tethering though. $\endgroup$ – Mike Sowsun Mar 25 '18 at 14:32
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The ultralight could takeoff with a strong enough headwind, but would be blown away in the process. This would not only be..ahem...very dangerous, but would cause the ultralight to lose a lot of airspeed. If it were tethered to the ground, it would fly like a kite. The wind would pick it up, and the strings or rope would prevent it from losing control or flying away.

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