# Mythbusters: Blow your own sail

#### A.T.

It has to impart backward momentum to a larger mass of air than is flowing out of the fan.
No, it does not have to be a larger mass, if the change in velocity is greater. See post #17.

You will notice in the film that it only provided forward net force if they kept changing the fan's direction.
Watch the other film:

#### rcgldr

Homework Helper
... it does not have to be a larger mass, if the change in velocity is greater.
The change in velocity explains the difference in forces at the fan and at the sail resulting in a net forwards force. The other issue is that momentum is conserved, the air, boat, (and the water) can be considered a closed system. If the sail boat is moving forwards, then the net air flow has to be backwards.

#### A.T.

The change in velocity explains the difference in forces at the fan and at the sail resulting in a net forwards force. The other issue is that momentum is conserved,
That's the same issue, not another issue. The net force is there because momentum has to be conserved.

If the sail boat is moving forwards, then the net air flow has to be backwards.
Yes, so?

#### rcgldr

Homework Helper
If the sail boat is moving forwards, then the net air flow has to be backwards.
So AM is wondering how that happens, when the backwards velocity of the air off the sail is less than the forwards velocity of flow feeding into the fan (this is an assumption, but seems reasonable). My guess is that the backwards flow involves more air due to the flow originating from the fan affecting the surrounding air, increasing the amount of air reflected off the sail.

#### A.T.

So AM is wondering how that happens, when the backwards velocity of the air off the sail is less than the forwards velocity of flow feeding into the fan (this is an assumption, but seems reasonable).
If you want to get the net airflow created by the boat as a whole, then you have to compare the velocity of the air off the sail, with the initial velocity of the air before it was affected by the boat at all. With the boat at rest, this initial air velocity is zero, so any backflow from the sail means a net backflow, and thus a net forward force.

#### Andrew Mason

Homework Helper
If you want to get the net airflow created by the boat as a whole, then you have to compare the velocity of the air off the sail, with the initial velocity of the air before it was affected by the boat at all. With the boat at rest, this initial air velocity is zero, so any backflow from the sail means a net backflow, and thus a net forward force.
What about the rearward force on the fan, which is connected to the boat? If the same amount of air is moving forward into the fan as is moving backward from the sail, the backward moving air has to be moving faster. I am saying that can't happen. However, if there is much more air moving backward - even though it may be moving backward more slowly than the air that is moving forward into the fan - it can carry more momentum.

If the fan simply builds up a higher pressure behind the sail and the releases it suddenly (by changing the direction of the fan output or just stopping the fan) the fan transfers energy to a large mass of air (pressure x volume = energy) and then sends that mass rearward. That, it seems to me, is what is happening here.

AM

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#### A.T.

the backward moving air has to be moving faster.
Faster than zero, which was the velocity of the air before it was affected by the boat in any way. This net difference in the air's momentum determines the net force on the boat.

#### Andrew Mason

Homework Helper
Faster than zero, which was the velocity of the air before it was affected by the boat in any way. This net difference in the air's momentum determines the net force on the boat.
At any given moment you have air moving forward into the fan. Unless you have more air moving backward at a slower speed than the air that is being sucked into the fan, you will have a net movement of air forward and the boat moving forward. That is what I am trying to avoid. The only way I can see that it can be done is if you have a much larger mass of air moving backward at a speed that is slower than the forward moving air but carrying more rearward momentum (due to the larger mass) using much less energy than the output of the fan.

AM

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#### A.T.

At any given moment you have air moving ....
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.

#### Andrew Mason

Homework Helper
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.
Ok. I agree. But the final momentum of the air includes the forward moving air moving through the fan.

AM

#### rcgldr

Homework Helper
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

Homework Helper
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

Homework Helper
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

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#### 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.

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?

#### 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:
SNS3Guppy said:
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

Homework Helper
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.

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