Mythbusters: Blow your own sail

[rcgldr]

You have to compare the final momentum of the air, to the initial momentum zero momentum of the air. Not to some intermediate state where the air has already been accelerated. Whatever the air does in between is irrelevant. If at the end the air leaves the sail with backwards momentum, then it has gained backwards momentum from the boat and the boat has gained forwards momentum.

Consider the air and the boat as a closed system. Even though the air gains backwards momentum, it could appear that the mass of the air is being shifted forwards by the interaction of fan and sail, but the center of mass of the system doesn't move since there are no external forces, so some form of circulation occurs where the mass of the affected air is shifted backwards while the mass of the boat is shifted forwards.

 

[A.T.]

But the final momentum of the air includes the forward moving air moving through the fan.

No. The final state of the air is leaving the sail backwards. That's where it's interaction with the boat ends, so that's the momentum that has to be compared to the the initial zero momentum.

 

[A.T.]

it could appear that the mass of the air is being shifted forwards by the interaction of fan and sail

What matters for the force on the boat is the change of the air's momentum, not of the air's position. The air starts with zero momentum and ends up with backwards momentum, so the boat receives forward momentum.

the affected air is shifted backwards

Yes obviously, since the air receives backwards momentum.

 

[Andrew Mason]

What matters for the force on the boat is the change of the air's momentum, not of the air's position. The air starts with zero momentum and ends up with backwards momentum, so the boat receives forward momentum.

So where does the air flow through the fan get its forward momentum from, if not from the fan? You seem to be deliberately omitting the rearward force on the fan from this air flow.

AM

 

[A.T.]

You seem to be deliberately omitting the rearward force on the fan from this air flow.

You seem to be deliberately ignoring my post #17 where I compare the forces on the fan and sail.

Also note that you don't have to care about the individual interactions, if you know that the net effect of them all is giving the air backwards momentum. It then follows from momentum conservation that the net force on the boat is forwards.

 

[Andrew Mason]

You seem to be deliberately ignoring my post #17 where I compare the forces on the fan and sail.

No, I agree with that. I am just pointing out that for a steady-state system that is providing continuous forward net force on the boat, a net mass of air has to be moving backward relative to the boat. I am suggesting that the only way this can occur is if the rate of rearward mass flow is greater than the rate of forward mass flow passing through the fan. Since the rearward speed of the air coming off the sail is going to be less than the speed of the air entering the fan, I am suggesting that a greater mass of air moves backward in a given time period $\Delta t$ than is moving forward (through the fan) in the same period.

AM

 

[A.T.]

I am just pointing out that for a steady-state system that is providing continuous forward net force on the boat, a net mass of air has to be moving backward relative to the boat.

If everything started from rest, then yes.

I am suggesting that the only way this can occur is if the rate of rearward mass flow is greater than the rate of forward mass flow passing through the fan.

If by "rearward mass flow" you mean the flow rate at the sail, then no, it doesn't have to be greater than the flow rate at the fan.

Since the rearward speed of the air coming off the sail is going to be less than the speed of the air entering the fan, I am suggesting that a greater mass of air moves backward in a given time period Δt\Delta t than is moving forward (through the fan) in the same period.

Yes, there is a greater mass of air moving back, than forward. But this doesn't require a faster flow rate at the sail. Note that the amount if air moving forward between fan and sail is approximately constant, while the amount of air moving back accumulates over time, as air is released with backwards momentum from the sail.

 

[paddywwoof]

the simplest way of thinking about it, as you say, is as a black box where you don't worry about what's happening inside. All that matters is the net flow around the box. For the box to experience a forward force the air must be experiencing a backward force and have net flow in that direction.

Traditionally (i.e. approximately) 'free' fans suck fluid from all around them (i.e. you can't really suck directionally) but blow directionally. However putting a sail in the way of the fan's exhaust effectively guarantees that the net outflow is in any direction but forward. i.e. the air is sucked in from pretty well all directions but it leaves mainly sideways but with a slight rearward component.

 

[Carno Raar]

I don't understand why this is a "thing".

If I blow air or water out a pipe for propulsion, and I bend the pipe into a U, it's obvious and easy to demonstrate that I will reverse direction. So the stuff hits the sail and the sail acts like a pipe bend. Either I am missing something vital or the sail is just confusing some people because sails do that (people don't believe we can sail upwind or sail at higher than the wind speed).

I am guessing that Mythbusters having to angle the fan to move is an issue of directional control because their boat has no keel (this type of boat is designed for swamps (very calm, shallow water) and is flat bottomed with no projections under the hull.

A mechanically propelled ship can rely on small fins sticking out the side for stability control (like a missile) but a sailboat experiences some quite extreme forces from the wind on the sail and needs a keel both for stability and to "grip" the water for propulsion when the wind is offset to the desired direction of travel. You may also have to lean out over the side to maintain its balance, like in Andrew Mason's avatar picture. Anyway if you'd only asked a sailor, he would have told you why a keel-less sailboat is moving in a small circle instead of forwards :-)

I don't know why aircraft jet can't reverse thrust indefinitely. I guess it's to do with breaking the deflector or not being designed to move backwards. Boats with marine waterjets can certainly reverse until they run out of fuel or break something, by deploying a "reversing bucket" over the jet nozzle.

 

[A.T.]

If I blow air or water out a pipe for propulsion, and I bend the pipe into a U, it's obvious and easy to demonstrate that I will reverse direction.

Exactly. And the mass flow rate at the bend is the same as at the propeller in the pipe. With an open system (no pipe) there is obviously diffusion of the flow, but that is in no way required for the concept to work.

I don't know why aircraft jet can't reverse thrust indefinitely.

Who says they can't?

 

[Carno Raar]

Who says they can't?

It's some technical limitation on the plane or its engines, and not anything to do with new physics. No need to panic! :-)

 

[A.T.]

It's some technical limitation on the plane or its engines

Any references on that?

 

[Carno Raar]

Any references on that?

I'm not a pilot (unless you count the time I flipped a catamaran yacht) so I just Googled it. Google found a post on a pilot's forum explaining why a particular airliner can't reverse thrust below 60 knots. http://www.pprune.org/tech-log/438954-question-reverse-thrust.html#post6168002

 

[A.T.]

Google found a post on a pilot's forum explaining why a particular airliner can't reverse thrust below 60 knots. http://www.pprune.org/tech-log/438954-question-reverse-thrust.html#post6168002

Here the quote:

The primary reason for stowing reversers below eighty knots or so is that as the aircraft slows, the potential for exhaust gas re-ingestion increases, as well as the potential for reverse flow gasses to cause or permit foreign object ingestion. Direction to stow reversers is there to protect the engine. Ingestion of exhuast by products can cause a flameout, and some engines aren't very stable in deep reverse at slow speeds; they may compressor stall and flame-out on their own. Reverse thrust isn't very effective at low speeds, and offers little advantage.

So it's not like they can't do it, but more that it is being avoided, because it creates some risks.

 

[rcgldr]

I don't know why aircraft jet can't reverse thrust indefinitely. I guess it's to do with breaking the deflector or not being designed to move backwards.

Earlier in this thread I mentioned that at some airports the terminals are blast tolerant, and commercial jets can optionally use reverse thrust to back away from the terminal.

 

[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.