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Consider a boat with one sail and a fan fixed on the boat's deck. The fan is blowing air into the sail. If the fan is strong enough, will the boat move?

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Generally the intake of the fan gathers air from all directions, perhaps not equally but at least in a very broad distribution. In contrast, the outflow is much more unidirectional. So, the fan imparts net momentum to the air. With no sail, the force on the boat will be in the opposite direction as the fan points. A sail could redirect the moving air, changing the direction of this force. But it would be easier just to reorient the fan.

Edit in response to OP comment

One can imagine a “sail” that would redirect the flow by 180 degrees (it might look like half a cylinder). This would result in a net force in the same direction the fan points, so in this sense it is possible to sail “downwind”.

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  • $\begingroup$ Thanks for your answer, I get your point, but will the force induced by the sail will be enough to compensate the force induced from the fan and makes the boat moves forward ? $\endgroup$
    – Velobos
    Jul 19, 2021 at 20:04
  • $\begingroup$ I have added an edit to address this question. $\endgroup$
    – Ben51
    Jul 19, 2021 at 20:17
  • $\begingroup$ Relevant Mythbusters segment: youtube.com/watch?v=uKXMTzMQWjo $\endgroup$
    – notovny
    Jul 19, 2021 at 20:22
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    $\begingroup$ This video demonstrates three variations in a minute and a half. $\endgroup$
    – M. Enns
    Jul 19, 2021 at 20:39
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A fan mounted on a boat can make the boat move.

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It works best without a "sail" messing up the air flow, but if the sail merely re-directs the airflow without introducing too much turbulence, then there's no reason why it should not work.

It probably will work best if the fan and the sail are oriented such that the air flow is directed astern, and directly in-line with the boat's keel.

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