Mythbusters: Blow your own sail

[A.T.]

because a boat is always easier to move forward.

That is completely irrelevant. Different drag between forwards and backwards movment cannot move the boat or determine whether it moves forwards or backwards.

Also my problem with the air inertia theory is that all the reverse force being generated by the fan is directly used to push the boat aft mechanically without transmission loss.

The exact same force is being given to the air. But the transmission losses must be huge!

The relevant force is that on the sail, which is greater than the one used to accelerate the air, because the air's momentum is partially reversed by the sail, not just canceled.

 

[Rippetherocker]

That is completely irrelevant. Different drag between forwards and backwards movment cannot move the boat or determine whether it moves forwards or backwards.The relevant force is that on the sail, which is greater than the one used to accelerate the air, because the air's momentum is partially reversed by the sail, not just canceled.

So the force being experienced by the sail is more than that being supplied by the fan? I am sorry if I seem stupid.

As to the matter of the trim- I work on ships and can assure you that boat design and trim have a substantial effect on speed. Given an equal force a vessel will move forward much more easily

 

[A.T.]

So the force being experienced by the sail is more than that being supplied by the fan?

Yes

Given an equal force a vessel will move forward much more easily

It's not about which way it would move faster if it was pushed that way. It's about whether that combination of fan & sail can push it forwards at all.

 

[Carno Raar]

Like most vessels the boat would have a trim by stern i.e. lower in the water at aft. If the same force is applied to both directions the boat will have a resultant force slightly in the forward direction because a boat is always easier to move forward.

Trim by stern is more a powerboat thing. On a sailing vessel, the wind hitting the sail from behind will naturally pivot the boat about its centre of mass and push the bow (front) of the boat down. An aggressively handled sailboat is very wet: you get green water coming in over the bow all the time. Your objective is to find the optimum balance between sail area and not becoming a submarine.

I find the mythbusters airboat interesting in that it crosses over between sails and mechanical propulsion. All I can tell you about it is that without a keel and being unable to pivot the propeller due to the need to blow its own sail, it's not going to have any significant directional control, and will be very hard to keep moving in anythign except small, random circles.

 

[cjl]

Ok. Here is the math. Let's assume a perfectly elastic rebound of the air from the sail, which is the best you can do.

Fan sends a mass of air $\Delta t\dot m$ forward toward the sail at speed v. The (rearward) impulse to the boat from this is $-v\Delta t\dot m$. This same mass of air strikes the sail and bounces off the sail at -v imparting a forward momentum of $2v\Delta t\dot m$ for a net forward momentum of $v\Delta t\dot m$. Now if the fan had stopped, you would be fine. But it doesn't stop. It keeps pushing air forward. So, meanwhile, the fan has scooped another packet of air and is sending it forward at speed v creating another (rearward) impulse of $-v\Delta t\dot m$. Net impulse = 0.

It might be easier to see with balls being scooped up and flung at the sail and bouncing back off the sail. So long as there is another ball that has been propelled toward the sail for every ball that is striking the sail, the net impulse to the boat will be 0. If not, perhaps you can explain where I am in error.

AM

Why did your analysis have 2 parcels of air pass through the fan, but only one of the two hit the sail? Steady state, the rate of mass hitting the sail is going to be the same as the rate of it passing through the fan, so as long as the $\Delta V$ of the airflow off the sail is larger than through the fan, it will (steady state) experience a net forward force. This just requires that the air rebound with some nonzero velocity on average off the sail. For example, if the fan is blowing air at some volumetric flow rate Q, the force the fan will feel (negative sign since force is to the rear of the boat) is simply going to be

$F_{fan} = -QV\rho$

where V is the exit velocity of the fan (I'm assuming the boat isn't moving and is in still air). If this air then rebounds off the sail on average at 0.05V in the rearward direction, the change in velocity at the sail will be 1.05V, so the force the sail will experience will be

$F_{sail} = 1.05QV\rho$

If these are both attached to the same craft, the craft will feel an overall net force of

$F_{fan} + F_{sail} = 1.05QV\rho - QV\rho = 0.05QV\rho$

Note that even though the rebound speed is very small compared to the fan exit speed, this net force is positive, indicating the boat will (very inefficiently) progress forwards.

 

[A.T.]

All I can tell you about it is that without a keel and being unable to pivot the propeller due to the need to blow its own sail, it's not going to have any significant directional control, and will be very hard to keep moving in anythign except small, random circles.

You could pivot or deform the sail to steer. But given that this is a completely inefficient propulsion scheme, it's rather pointless.

 

[Carno Raar]

You could pivot or deform the sail to steer. But given that this is a completely inefficient propulsion scheme, it's rather pointless.

I don't disagree but I was more discussing the inability to control your direction of travel, and not the ease with which you can rotate the boat by any number of means. A sailboat without a keel is worse than an ice skate without a blade. As you note by your comment on propulsion efficiency, the key is applying overwhelming amounts power in the desired direction.

 

[A.T.]

Most complete video investigation of this topic I saw so far: