# Mythbusters: Blow your own sail

#### Intrastellar

Gold Member
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

Homework Helper
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

Homework Helper
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

Homework Helper
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

Homework Helper
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

Homework Helper
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

Homework Helper
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

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#### 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.

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standing waves

#### CWatters

Homework Helper
Gold Member
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

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.

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#### A.T.

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

Homework Helper
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)...

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#### 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

Gold Member
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

Homework Helper
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.

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