This is an approach I am thinking of for an alternative to ion propulsion for making silent drones.
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$\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$– Community BotJun 24, 2022 at 15:58
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In theory, but a sail will be far less efficient than a balloon. A hot air balloon works because the hot air in the balloon is less dense than the surrounding air, making the balloon buoyant. As long as there is a density difference, the balloon rises.
Using a sail instead of a balloon uses the updraft of the rising heated air, but then just throws away most of the benefit by letting the heated air escape. You'd be better off containing the heated air and continuing to benefit from the density difference, rather than getting a one-time impulse. By using a sail instead of a balloon, the heated air is still rising in the same way, it's just not carrying you along with it for the most part. It's a bit like winding up a rubber band helicopter propeller, and then just letting go of it shortly after takeoff - you expended energy to make something rise, but then aren't actually using it to lift your payload.
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$\begingroup$ A heated coil would be limited by the battery. Since it is joule heating hypothetically you could pretty efficiently convert the energy of a battery to heat, but batteries compared to burning fuel have limited energy density. Gasoline for example has about 100 times the energy density of a lithium battery. But as @Nuclear Hoagie points out, once you are buoyant it might help. Although you would probably be at the mercy of the wind. $\endgroup$– UVphotonJun 24, 2022 at 15:59