Mythbusters: Blow your own sail

[Intrastellar]

But imagine replacing the fan with a ballbearing gun, and the sail with a plate of steel. The ballbearings will rebound off the plate and escape to the rear of the vehicle, producing thrust. We don't normally consider air to have inertia, but if you get enough of it moving, it certainly will.

The plate of steal is connected to the ballbearing gun in the sail and fan example. When the ballbearing gun fires a ballbearing, the gun will get pushed back, and thus will the plate. When the forward moving ballbearing hits the backwards moving plate, they will both stop by momentum conservation.

Step one: ballbearing gets fired
gun+plate and ballbearing will have an equal and opposite momentum by momentum conservation

Step two: ballbearing hits the plate
since gun+plate and ballbearing have equal and opposite momentum, they will come to a halt when they collide, by momentum conservation

@A.T. : Is Dave's quoted post above the premise that you are defending ?

 

[jbriggs444]

The plate of steal is connected to the ballbearing gun in the sail and fan example. When the ballbearing gun fires a ballbearing, the gun will get pushed back, and thus will the plate. When the forward moving ballbearing hits the backwards moving plate, they will both stop by momentum conservation.

Momentum conservation permits a range of outcomes. This includes an outcome where the ball bearing stops dead at the plate (like a wad of putty) and an outcome where the ball bearing rebounds and gains a rearward velocity. If the collision is elastic then the putty-like outcome is forbidden and the rebounding outcome is assured.

 

[rcgldr]

This includes an outcome where the ball bearing stops dead at the plate (like a wad of putty) and an outcome where the ball bearing rebounds and gains a rearward velocity. If the collision is elastic then the putty-like outcome is forbidden and the rebounding outcome is assured.

To continue this analogy from AM's issue, the ball bearings are not on the boat, but sucked up from distance behind the boat, so ball bearings that float on the water.

 

[A.T.]

When the forward moving ballbearing hits the backwards moving plate, they will both stop by momentum conservation.

As jbriggs444 said, momentum conservation allows that the ball ends up moving backwards, while the boat ends up moving forward.

 

[A.T.]

To continue this analogy from AM's issue, the ball bearings are not on the boat, but sucked up from distance behind the boat, so ball bearings that float on the water.

What is "the issue" translated to this analogy? Here it is obvious that no "surrounding balls" need to be affected by the thrown balls for the boat to move forward.

 

[rcgldr]

To continue this analogy from AM's issue, the ball bearings are not on the boat, but sucked up from distance behind the boat, so ball bearings that float on the water.

What is "the issue" translated to this analogy? Here it is obvious that no "surrounding balls" need to be affected by the thrown balls for the boat to move forward.

AM's point is that the non-moving (wrt water) source of the thrown balls is at some fixed distance behind the boat (versus already on the moving boat). The balls are picked up from behind the boat (like the air beign sucked into the fan), and then thrown forwards at the sail (like the flow from the fan when it hits the sail). Since the videos prove this works, and since the center of mass of the system doesn't move, then "circulation" results in the balls (or air) being displaced backwards as the boat moves forwards. AM's issue is an explanation for this "circulation".

 

[A.T.]

then "circulation" results in the balls (or air) being displaced backwards as the boat moves forwards. AM's issue is an explanation for this "circulation".

If by "circulation" you mean that the used balls eventually end up behind their pick-up position, then I agree that it happens. And I think the analogy makes obvious why, without involving a greater mass by affecting surrounding balls.

 

[Andrew Mason]

The circulation is problem. This is due to the continuous operation of the fan. There is no question that a fan sucking in air from behind and compressing a volume of air behind the sail and then stopping and letting that compressed "blob" of air bounce backward will cause a net forward push on the boat. That results in a net rearward flow of air. But if the fan is continually drawing the same amount of air forward as is flowing backward, I am having difficulty seeing a net rearward flow of air. So I have to conclude that more air is moving backward than is moving forward. If the difference is large enough, the lower velocity but larger mass of air can carry more momentum (with considerably less flow energy).

I would suggest that the boat would get more forward momentum if they kept stopping and starting the fan. This is consistent with the fact that the forward impulse to the boat is realized only when the fan output is continually changing, being directed away to one side and then moved back directly behind the sail.

AM

 

[A.T.]

But if the fan is continually drawing the same amount of air forward as is flowing backward,

The amount moving forward is constant, while the amount moving backwards accumulates since the fan was switched on.

Maybe it will help you to think about the ball analogy. If you throw the next ball when the previous ball bounces back, then there is only one ball moving forward. But there are many balls that bounced before and are still moving back.

 

[Andrew Mason]

The amount moving forward is constant, while the amount moving backwards accumulates since the fan was switched on.

Maybe it will help you to think about the ball analogy. If you throw the next ball when the previous ball bounces back, then there is only one ball moving forward. But there are many balls that bounced before and are still moving back.

How does the motion of the air after it leaves the sail affect the boat? The mass flow that causes a force on the boat (ie. at the fan and the sail) should be the only mass flow that is material to the motion of the boat, no? If the rearward mass flow at the sail is exactly equal and opposite to the forward mass flow on the fan, I don't see how you get forward momentum to the boat. That is why I am suggesting that the rearward mass flow is greater.

AM

 

[A.T.]

How does the motion of the air after it leaves the sail affect the boat?

It affects the center of mass of the whole system, which I thought was "your issue".

The mass flow that causes a force on the boat (ie. at the fan and the sail) should be the only mass flow that is material to the motion of the boat, no?

Mass flow doesn't "cause a force". The change in the air's momentum is related to the force on the boat.

If the rearward mass flow at the sail is exactly equal and opposite to the forward mass flow on the fan, I don't see how you get forward momentum to the boat.

See above. The mass flow rate at the sail can be the same as at the fan, but the change in momentum can still be greater, because the change in velocity is greater.

Please do the math instead of using flawed informal arguments. You are just confusing yourself.

 

[Andrew Mason]

Please do the math instead of using flawed informal arguments. You are just confusing yourself.

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

 

[A.T.]

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 $-v\Delta t\dot m$.

So after the first packet is through the fan, the boat is moving back.

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.

So after the second packet is through the fan, the boat doesn't move at all. That's already an improvement compared to moving back. Hmm... I wonder what happens after the third packet.

If not, perhaps you can explain where I am in error.

Nothing wrong so far. Please continue your analysis. The fan is still on.

 

[thankz]

standing waves

 

[CWatters]

Fan sends a mass of air Δtm ˙ \Delta t\dot m forward toward the sail at speed v. The (rearward) impulse to the boat from this is −vΔtm ˙ -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 2vΔtm ˙ 2v\Delta t\dot m for a net forward momentum of vΔtm ˙ v\Delta t\dot m. Now if the fan had stopped, you would be fine.

So what happens if the fan does stop and start...

Fan sends a mass of air Δtm ˙ \Delta t\dot m forward toward the sail at speed v. The (rearward) impulse to the boat from this is −vΔtm ˙ -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 2vΔtm ˙ 2v\Delta t\dot m for a net forward momentum of vΔtm ˙ v\Delta t\dot m. Now if the fan had stopped, you would be fine.

Fan stops
Fan starts

Fan sends a mass of air Δtm ˙ \Delta t\dot m forward toward the sail at speed v. The (rearward) impulse to the boat from this is −vΔtm ˙ -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 2vΔtm ˙ 2v\Delta t\dot m for a net forward momentum of vΔtm ˙ v\Delta t\dot m. Now if the fan had stopped, you would be fine.

Fan stops
Fan starts

Fan sends a mass of air Δtm ˙ \Delta t\dot m forward toward the sail at speed v. The (rearward) impulse to the boat from this is −vΔtm ˙ -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 2vΔtm ˙ 2v\Delta t\dot m for a net forward momentum of vΔtm ˙ v\Delta t\dot m. Now if the fan had stopped, you would be fine.

 

[georgir]

Whole thread is tl;dr
But blowing (moving air) obviously can provide propulsion - we even named the big fans that do it "propellers".

Adding a sail to the situation does not change much. A sail acts as kind of a mirror for the prodoced air stream, it can reverse its direction. But it is far from a perfect mirror. It does not catch the whole stream, and it does not really reverse its velocity, but mostly just stops it. So it will be much less effective than the propeller, so if you are telling me that their boat moved against the direction of the propeller and into the direction of the sail, you misunderstood something in the experiment. Such a result can only happen if the propeller is not horizontal, for example, but mainly blowing upwards, and the sail reflects the stream to be horizontal.

In any case ditching the sail and simply keeping the propeller, appropriately directed, would provide better results.

 

[A.T.]

Whole thread is tl;dr
But blowing (moving air) obviously can provide propulsion - we even named the big fans that do it "propellers".

Adding a sail to the situation does not change much. A sail acts as kind of a mirror for the prodoced air stream, it can reverse its direction. But it is far from a perfect mirror. It does not catch the whole stream, and it does not really reverse its velocity, but mostly just stops it. So it will be much less effective than the propeller,

Yes, it is inefficient, but can work.

so if you are telling me that their boat moved against the direction of the propeller and into the direction of the sail

Why don't you watch the videos for yourself, instead of relying on what we are telling you?

Such a result can only happen if the propeller is not horizontal, for example, but mainly blowing upwards, and the sail reflects the stream to be horizontal.

What do you see in the videos?

 

[rcgldr]

if the fan is continually drawing the same amount of air forward as is flowing backward ...

The amount moving forward is constant, while the amount moving backwards accumulates since the fan was switched on.

The amount of air moving forward also accumulates as over time, an increasingly longer column of air is shifting forwards to continously fill in the lower pressure zone being created by the fan, but update - much of that air flow well behind the boat will have a vertical component as well as a horizontal component, but I don't know how the direction of flow varies versus distance behind the boat. Since the center of mass of the boat and air is not moving, then the continously backwards flow must be greater than the continously forward flow, despite the velocity differences in the immediate vincity of the sail boat, so that the center of mass of the affected air moves backwards as the boat moves forwards. At some point behind the boat, part of the backwards flow will circulate into the forwards flow, but the net flow has to be backwards as the boat moves forwards.

(Wondering how I got sucked into this thread)...

 

[A.T.]

At some point behind the boat, part of the backwards flow will circulate into the forwards flow.

It might even cause a hurricane on the other side of the globe, but I don't think this is important for understanding how this works.

 

[georgir]

I guess I should have seen it coming... it really doesn't matter if the sail isn't too good at reversing the stream velocity, all that's needed is for it to stop most of it from going forward and reverse just enough of it.

This still does not change the fact that using a sail is less efficient than just a propeller directed towards the back. So even if blowing in your own sail "works", it is still more stupid than just blowing backwards.

 

[Mark Harder]

Yes, Andrew. I think you are on the right track. There's a control experiment that would eliminate the complications introduced by the rearward component of air entering the fan. Use a rocket instead of the fan to generate a highly directional flow of gases onto the sail. The source of the flow, including the fuel, would be contained in the boat so no flow of external matter (air) is involved. Would such a vehicle go forward, backward or nowhere?

 

[A.T.]

it really doesn't matter if the sail isn't too good at reversing the stream velocity, all that's needed is for it to stop most of it from going forward and reverse just enough of it.

Exactly.

 

[A.T.]

Yes, Andrew. I think you are on the right track.

He isn't just on the right track, in post #62 he has already shown mathematically that the boat can gain forward momentum. His then stated conclusion to the opposite reminds me of the DDWFTTW discussions, where people just couldn't accept something counter-intuitive to them, despite mathematical and practical proof. And "people" includes several physics professors here.

http://en.wikipedia.org/wiki/Blackbird_(land_yacht)

 

[Andrew Mason]

He isn't just on the right track, in post #62 he has already shown mathematically that the boat can gain forward momentum. His then stated conclusion to the opposite reminds me of the DDWFTTW discussions, where people just couldn't accept something counter-intuitive to them, despite mathematical and practical proof. And "people" includes several physics professors here.

http://en.wikipedia.org/wiki/Blackbird_(land_yacht)

It is more a matter of figuring out what is actually happening. So long as there is a net movement of air rearward, the boat can experience a forward force on the sail. That is all I am saying. This is not based on intuition. It is based on the application of the law of conservation of momentum.

If the fan is pointed directly at the sail so that it builds up higher pressure behind sail it transfers potential (PV) energy into the air behind the sail. If the fan were to stop, thereby reducing its forward pressure on that air, the higher than ambient internal pressure in that mass of air behind the sail would then result in rearward movement of that air and the boat would be pushed forward (conservation of momentum). That is, I think, what is happening in the Mythbusters video. That is why, I think, the boat is pushed forward only when the direction of the airflow from the fan is moved to the side. I also think that the rear movement of air involves a larger mass of air than was moved forward, which I have explained.

AM

 

[A.T.]

the boat can experience a forward force on the sail.

That is totally trivial. The discussion was about the net force on the boat, not just on the sail.

That is why, I think, the boat is pushed forward only when the direction of the airflow from the fan is moved to the side.

So what happens in the video where the fan always points the same way?

I also think that the rear movement of air involves a larger mass of air than was moved forward, which I have explained.

Sure, but that doesn't necessitate a greater flow rate at the sail than at the fan, as your own analysis in post #62 shows.

 

[Andrew Mason]

That is totally trivial. The discussion was about the net force on the boat, not just on the sail.

If the fan is simply maintaining greater than ambient pressure on the sail, the flow rate forward through the fan would be reduced due to that increased pressure. It would have to pull in only enough air to replace the amount of spillage from the sides of the sail. I think we agree, and the experiment agrees, that this does not produce forward momentum.

When the fan is directed to the side, the pressurized volume of air between the fan and sail would be pushed backward from the sail and the sail and boat pushed forward. Whether that will be greater than the forward flow through the fan at that point is difficult to say without some measurements. That is why I suggest turning the fan off. But it does appear to be enough to cause a bit of forward momentum even with the fan on.

Better still would be to have the fan push air into a balloon, build up the pressure and then turn the fan off letting the air in the balloon shoot backward. That is essentially how a jet engine operates, except that it draws air in from in front so it can operate continuously.

So what happens in the video where the fan always points the same way?

The boat doesn't move.

AM

 

[A.T.]

If the fan is simply maintaining greater than ambient pressure on the sail, the flow rate forward through the fan would be reduced due to that increased pressure. It would have to pull in only enough air to replace the amount of spillage from the sides of the sail. I think we agree, and the experiment agrees, that this does not produce forward momentum.

No. Neither me, nor the experiment, nor your own math agrees with that conclusion.

So what happens in the video where the fan always points the same way?

The boat doesn't move.

I'm talking about the controlled experiment on the table, not the MB video. Can't you see the embedded video above? Try clicking on the link below:

www.youtube.com/watch?v=0CrXvOKPymk&t=71

 

[Andrew Mason]

No. Neither me, nor the experiment, nor your own math agrees with that conclusion.

The premise is that the only air that is escaping is the air moving sideways due to the higher pressure between the fan and the sail. Are you suggesting that air moving sideways off the sail imparts forward momentum?

I'm talking about the controlled experiment on the table, not the MB video. Can't you see the embedded video above? Try clicking on the link below:

www.youtube.com/watch?v=0CrXvOKPymk&t=71

Ok. That is a very interesting demonstration. It does not appear that there is a net rearward flow of air there. There may be some very subtle effects due to turbulence at the sail edges. Fluid dynamics can be rather complicated. I would want to experiment with different sail and fan configurations. So I don't have an explanation at the moment but I will think about it.

AM

 

[A.T.]

The premise is that the only air that is escaping is the air moving sideways

That premise is flawed. The sail is not a flat surface, but has the upper/lower edges bent backwards, so the air leaving the sail across those edges has backwards momentum.

Ok. That is a very interesting demonstration. It does not appear that there is a net rearward flow of air there.

Of course there is, for the same reason as stated above.

 

[Andrew Mason]

Of course there is, for the same reason as stated above.

You may be right, but my point was that it is not apparent. A smoke trail might help to see if your theory that air is actually flowing backward off that sail is correct.

Perhaps you understand exactly how an airplane wing provides lift. I don't. There are several theories and still a lot of controversy over the physics of flight. See this, for example. Regardless of how the wing does it, it appears from principles of physics that in order to impart upward force, there has to be a net downward movement of air around the wing. This situation is a bit different than an airplane wing, but I think the same basic principle applies. I would be interested in hearing any comments you or others may have.

AM

 

[A.T.]

A smoke trail might help to see if your theory that air is actually flowing backward off that sail is correct.

How else do you expect it to flow along the sail, other than parallel to the surface?

Regardless of how the wing does it, it appears from principles of physics that in order to impart upward force, there has to be a net downward movement of air around the wing.

Yes, there is, but Bernoulli also applies. There is no contradiction between the two, so the debates are pointless. Look at the countless old threads on this.

 

[Carno Raar]

You may be right, but my point was that it is not apparent. A smoke trail might help to see if your theory that air is actually flowing backward off that sail is correct.

Perhaps you understand exactly how an airplane wing provides lift. I don't. There are several theories and still a lot of controversy over the physics of flight. See this, for example. Regardless of how the wing does it, it appears from principles of physics that in order to impart upward force, there has to be a net downward movement of air around the wing. This situation is a bit different than an airplane wing, but I think the same basic principle applies. I would be interested in hearing any comments you or others may have.

AM

Wat? No. We undertstand how airplane wings work. That article just discusses methods for simulating it. Edit: This is quite clearly stated near the start of the post.

How else do you expect it to flow along the sail, other than parallel to the surface?

Yes, there is, but Bernoulli also applies. There is no contradiction between the two, so the debates are pointless. Look at the countless old threads on this.

As an example of this, look at the telltales on a sailboat. These are the little bits of string or tape attached to the sail that indicate airflow over the sail. Under some circumstances the telltales will reverse, showing you have reverse airflow over the sail (the wind loops around like a vortex). Obviously this is bad.

 

[A.T.]

As an example of this, look at the telltales on a sailboat.

That's not a good example for the mechanism discussed here, because the flow relative to that sail boat is uniform on a much larger scale, than the size of the sail.

In contrast, the flow generated by the fan here is much smaller than the sail they used. In particular it doesn't extend to the edges, so the air can flow parallel the sail surface at the edges. This wouldn't work if the fan was bigger than the sail.

 

[Carno Raar]

Rather than nice parallel airflow (edit: along the sail) you likely have massive turbulence, similar to a stalled plane wing.

@AT: Don't get me wrong though. I am not saying this boat does not work. It does and I can see you understand why.

 

[A.T.]

Rather than nice parallel airflow (edit: along the sail) you likely have massive turbulence, similar to a stalled plane wing.

A stalled wing is another bad example, for the same reason I explained in post #83.

 

[Carno Raar]

Are we at least agreed there is turbulence? I don't remember the video. Was it a square sail powered from behind? In that case look at the side edges and see if they are flapping randomly or if there is smooth laminar flow over them. I'd be astonished if the sides weren't flapping about like mad.

 

[A.T.]

Are we at least agreed there is turbulence?

That is almost trivially true. Nobody claims that this is perfectly laminar flow, but it can be directed enough to work.

 

[Vespa71]

The amount of air moving forward also accumulates as over time, an increasingly longer column of air is shifting forwards to continously fill in the lower pressure zone being created by the fan, but update - much of that air flow well behind the boat will have a vertical component as well as a horizontal component, but I don't know how the direction of flow varies versus distance behind the boat. Since the center of mass of the boat and air is not moving, then the continously backwards flow must be greater than the continously forward flow, despite the velocity differences in the immediate vincity of the sail boat, so that the center of mass of the affected air moves backwards as the boat moves forwards. At some point behind the boat, part of the backwards flow will circulate into the forwards flow, but the net flow has to be backwards as the boat moves forwards.

(Wondering how I got sucked into this thread)...

Last time we discussed this, we weren't allowed to say suck... I probably missed the train here, but I'll post anyway.

I just wan't to agree to rcgldr and Andrew Mason's statements that there are forces that pulls the boat backwards. There is a low pressure volume behind the boat, caused by the propeller, causing the boat to move towards it. Also (and I think this is a different force-dynamics) the propeller accelerates a directed mass of air closely behind the propeller, that "sucks" the boat backwards. Both of these forces are small though, compared to the (inefficient) propeller-sail-thrust.

The reason why suction is small, is that it is wrong to assume that air going into the propeller comes from behind the boat. It comes from everywhere. That's why Newton is not violated. Shortly behind the propeller, airflow is unidirectionally forwards, but then the direction dissipates. The low pressure volume behind the boat is filled with air from all directions. The thrust sum from the propeller-sail- system, however, has one direction, forwards.

Imagine a vacuum-cleaner. Pointing the pipe, without attachments, forwards, what is the experienced pulling force to holding the pipe, with a 2000 watt motor? And imagine a similar power leaf blower...

Thrust is directional, suction not so much. That, and Newton's laws, explains the result i MB.

Alternative solution: Say the sail reflects backwards the same molecules of air back into the propeller, and it cycles. There is an outer hemisphere of air moving from the sail to the propeller, filled with a forwards flow from the propeller to the sail. This system would also move the boat forwards, as air from this system would friction surrounding air producing a net forward motion. Like a paddle steamer.

Vespa71P.S. This device baffles me: http://demolab.phys.virginia.edu/demos/demos.asp?Demos=H&Subject=1&Demo=1H10.20#subtopic They must have deliberately designed it to prove some mistaken point. Note the rigid flat sail.

 

[A.T.]

It comes from everywhere. That's why Newton is not violated.

What matters for Newton is how the prop and sail change the momentum of the air, not where it came from to the prop.

Say the sail reflects backwards the same molecules of air back into the propeller, and it cycles.

That doesn't help, but makes it less efficient.

 

[Rippetherocker]

This thread is so long! So did a unanimous answer reveal itself?

My two badly damaged cents-

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.

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!

Or am I mad??

 

[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: