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Firstly, this gif is not accurate unless the fan is really strong. Seemingly, even if the skateboarder is being propelled forward, the fan wouldn't blow a hard enough wind to cause this effect.

The concept of blowing your own sail really does have to do with conservation of momentum. In that very episode of Mythbusters you speak of, the sail was removed, the fan was spun around and the ship/boat was propelled forward much faster than with the fan facing into the sail (i.e. figure (1) is much faster than figure (2)).

The reason is really quite simple and can be explained with throwing a ball off a boat.

Suppose you are on a boat carrying a ball with total mass $m_{ball}+m_{boat}$ where $m_{boat}$ also takes into consideration your mass. Now if you throw the ball off the boat at velocity $v_{ball}$ then you and the boat will have momentum $m_{boat}v_{boat}=-m_{ball}v_{ball}$. This is analogous to the figure (1).

Now consider the case of figure (2). In this case, I throw the ball at the sail, it bounces off the sail and into the water behind me. Because the process is inelastic, the ball now leaves the boat with $v'_{ball} < v_{ball}$. Therefore my momentum is now $m_{boat}v_{boat} = -m_{ball}v'_{ball}$.

Now just replace the ball with air molecules and the analogy is complete. Therefore it will always be more efficient to spin the fan around and blow the fan in the opposite direction while forgetting the sail.

Hope this helps!

The concept of blowing your own sail really does have to do with conservation of momentum. In that very episode of Mythbusters you speak of, the sail was removed, the fan was spun around and the ship/boat was propelled forward much faster than with the fan facing into the sail (i.e. figure (1) is much faster than figure (2)).

The reason is really quite simple and can be explained with throwing a ball off a boat.

Suppose you are on a boat carrying a ball with total mass $m_{ball}+m_{boat}$ where $m_{boat}$ also takes into consideration your mass. Now if you throw the ball off the boat at velocity $v_{ball}$ then you and the boat will have momentum $m_{boat}v_{boat}=-m_{ball}v_{ball}$. This is analogous to the figure (1).

Now consider the case of figure (2). In this case, I throw the ball at the sail, it bounces off the sail and into the water behind me. Because the process is inelastic, the ball now leaves the boat with $v'_{ball} < v_{ball}$. Therefore my momentum is now $m_{boat}v_{boat} = -m_{ball}v'_{ball}$.

Now just replace the ball with air molecules and the analogy is complete. Therefore it will always be more efficient to spin the fan around and blow the fan in the opposite direction while forgetting the sail.

Hope this helps!

Firstly, this gif is not accurate unless the fan is really strong. Seemingly, even if the skateboarder is being propelled forward, the fan wouldn't blow a hard enough wind to cause this effect.

The concept of blowing your own sail really does have to do with conservation of momentum. In that very episode of Mythbusters you speak of, the sail was removed, the fan was spun around and the ship/boat was propelled forward much faster than with the fan facing into the sail (i.e. figure (1) is much faster than figure (2)).

The reason is really quite simple and can be explained with throwing a ball off a boat.

Suppose you are on a boat carrying a ball with total mass $m_{ball}+m_{boat}$ where $m_{boat}$ also takes into consideration your mass. Now if you throw the ball off the boat at velocity $v_{ball}$ then you and the boat with have momentum $m_{boat}v_{boat}=-m_{ball}v_{ball}$. This is analogous to the figure (1).

Now consider the case of figure (2). In this case, I throw the ball at the sail, it bounces off the sail and into the water behind me. Because the process is inelastic, the ball now leaves the boat with $v'_{ball} < v_{ball}$. Therefore my momentum is now $m_{boat}v_{boat} = -m_{ball}v'_{ball}$.

Now just replace the ball with air molecules and the analogy is complete. Therefore it will always be more efficient to spin the fan around and blow the fan in the opposite direction while forgetting the sail.

Hope this helps!

Firstly, this gif is not accurate unless the fan is really strong. Seemingly, even if the skateboarder is being propelled forward, the fan wouldn't blow a hard enough wind to cause this effect.

The concept of blowing your own sail really does have to do with conservation of momentum. In that very episode of Mythbusters you speak of, the sail was removed, the fan was spun around and the ship/boat was propelled forward much faster than with the fan facing into the sail (i.e. figure (1) is much faster than figure (2)).

The reason is really quite simple and can be explained with throwing a ball off a boat.

Suppose you are on a boat carrying a ball with total mass $m_{ball}+m_{boat}$ where $m_{boat}$ also takes into consideration your mass. Now if you throw the ball off the boat at velocity $v_{ball}$ then you and the boat will have momentum $m_{boat}v_{boat}=-m_{ball}v_{ball}$. This is analogous to the figure (1).

Now consider the case of figure (2). In this case, I throw the ball at the sail, it bounces off the sail and into the water behind me. Because the process is inelastic, the ball now leaves the boat with $v'_{ball} < v_{ball}$. Therefore my momentum is now $m_{boat}v_{boat} = -m_{ball}v'_{ball}$.

Now just replace the ball with air molecules and the analogy is complete. Therefore it will always be more efficient to spin the fan around and blow the fan in the opposite direction while forgetting the sail.

Hope this helps!

Firstly, this gif is not accurate unless the fan is really strong. Seemingly, even if the skateboarder is being propelled forward, the fan wouldn't blow a hard enough wind to cause this effect.

The concept of blowing your own sail really does have to do with conservation of momentum. In that very episode of Mythbusters you speak of, the sail was removed, the fan was spun around and the ship/boat was propelled forward much faster than with the fan facing into the sail (i.e. figure (1) is much faster than figure (2)).

The reason is really quite simple and can be explained with throwing a ball off a boat.

Suppose you are on a boat carrying a ball with total mass $m_{ball}+m_{boat}$ where $m_{boat}$ also takes into consideration your mass. Now if you throw the boat off the boat at velocity $v_{ball}$ then you and the boat with have momentum $m_{boat}v_{boat}=-m_{ball}v_{ball}$. This is analogous to the figure (1).

Now consider the case of figure (2). In this case, I throw the ball at the sail, it bounces off the sail and into the water behind me. Because the process is inelastic, the ball now leaves the boat with $v'_{ball} < v_{ball}$. Therefore my momentum is now $m_{boat}v_{boat} = -m_{ball}v'_{ball}$.

Now just replace the ball with air molecules and the analogy is complete. Therefore it will always be more efficient to spin the fan around and blow the fan in the opposite direction while forgetting the sail.

Hope this helps!

Firstly, this gif is not accurate unless the fan is really strong. Seemingly, even if the skateboarder is being propelled forward, the fan wouldn't blow a hard enough wind to cause this effect.

The concept of blowing your own sail really does have to do with conservation of momentum. In that very episode of Mythbusters you speak of, the sail was removed, the fan was spun around and the ship/boat was propelled forward much faster than with the fan facing into the sail (i.e. figure (1) is much faster than figure (2)).

The reason is really quite simple and can be explained with throwing a ball off a boat.

Suppose you are on a boat carrying a ball with total mass $m_{ball}+m_{boat}$ where $m_{boat}$ also takes into consideration your mass. Now if you throw the ball off the boat at velocity $v_{ball}$ then you and the boat with have momentum $m_{boat}v_{boat}=-m_{ball}v_{ball}$. This is analogous to the figure (1).

Now consider the case of figure (2). In this case, I throw the ball at the sail, it bounces off the sail and into the water behind me. Because the process is inelastic, the ball now leaves the boat with $v'_{ball} < v_{ball}$. Therefore my momentum is now $m_{boat}v_{boat} = -m_{ball}v'_{ball}$.

Now just replace the ball with air molecules and the analogy is complete. Therefore it will always be more efficient to spin the fan around and blow the fan in the opposite direction while forgetting the sail.

Hope this helps!