## / Can you blow your own?

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Mythbusters, can you blow your own sail? For anyone who doesn't want to watch it. Big fan on a boat, sail set perpendicular to the fan. Boat goes forward.

I can't see how this can work. Any explanations using up to A level physics/maths please without using the word "reflected".

Andy

The air gets reflected.
In reply to ablackett: I saw this and it p155ed me off. Just turn the propellor round people! If you had that much capacity for wind generation you wouldn't direct it at a sail! The wind gets reflected though ;)

It would work if the boat was on a conveyor belt.

E
>
> It would work if the boat was on a conveyor belt.

River?

> I can't see how this can work.

I thought it was pretty obvious, you are still adding energy into the system to make the boat move.

In this case powering the fan.

Yup exactly. Not sure why it would surprise.

The air is reflected is not really the way to think about it IMHO. It's just forces. No different to usual sailing except this time the wind is being created by converting power driving the fan.

Thought this was going to be a sexual skills post....
In reply to A Game of Chance: me too, and no I can't, so I still go out now and again.

Each time it "works", it seems that the sail is at a slight angle. Proper sails don't get their greatest effect from drag, but rather from the "lift" they produce. Generally, they form themselves into an aerofoil shape, and a component of the force is going in the right direction to push it forward. I suspect that when it does work, they are managing to produce some lift (which, on a properly designed aerofoil is many times greater than the drag).

I put a health warning on this though - I've not thought it through completely, so there could be some gaping hole in my argument. I agree with you though, a truly simplified model, with a big fan blowing directly perpendicular on a flat sail, should make a lot of noise and do not a lot else. Actually, if you look at their main example of it "working" on the full scale model, they're making about 3 mph, if they turned the fan round I reckon they'd make 50mph or so. Is that small enough to say that it's negligible?

Tim
In reply to Epic Ebdon: Thanks. I was starting to think I must have missed something obvious.

I have failed to draw a force diagram I am happy with so was thinking that perhaps I don't understand what is going on. But if feels to me like it shouldn't do anything unless, like you say there is some kind of lift.

It would be interesting to see what could be achieved with a proper sail mounted so it blew across the boat.

I think you are on the right track here.

When the sail bends forward (and the fan is pointing slightly up if you notice) wind is escaping out of the top of the sail producing a force down and forward and the boat moves because force has a forward vector. I suspect that if the "boat" was on a set of scales, they would read slightly higher the more fan speed is added due to the downward vector of the force.

Simple explanation:

Imagine having the fan facing backwards, and no sail. The boat would go forwards because you are pushing air backwards.
Now imagine turning the fan round so it points forwards, but using a length of ducting to take the air from the front of the fan and put it out over the back of the boat. It will work the same way (but much less efficient).
Now replace the ducting with a big hemispherical bowl. You blow the fan into the middle of it, and it re-directs the air backwards. Much like the ducting, but even less efficient.
Finally replace the big bowl shape with a sail that's floppy enough to take the shape of the bowl when you blow in the middle and voila!

Another way of looking at it is that the force on the fan due to the air it's chucking forwards is exactly balanced by the force on the sail as it stops the air.
But the air is not magically destroyed when it hits the sail. It goes all over the place. If you take the average direction and speed (strictly the integral over all space of air mass times vector velocity) of all that air, and it is backwards, then it's pushing the boat forwards.
>
> Simple explanation:
>

> Now imagine turning the fan round so it points forwards, but using a length of ducting to take the air from the front of the fan and put it out over the back of the boat. It will work the same way (but much less efficient).

Are you sure about this? I reckon it would go nowhere as the net acceleration of the air is zero.
> (In reply to Jack B)
>
> Another way of looking at it is that the force on the fan due to the air it's chucking forwards is exactly balanced by the force on the sail as it stops the air.

Now I know for a fact that isn't true because all of the air isn't stopped.

The fan is moving the air. It has a pitch, which basically means if it is not fastened down, one full turn will "screw" it x distance through the air. Since it is fixed to the boat, essentially that amount of air gets moved (think of the "screwed" area being a cylinder of air). Now I have not seen the video, so I have no idea which way the fan is blowing.

Second bit, the sail. As mentioned, they work as an aerofoil. Which is to say, like a planes wing. The shapes makes the air move at a different speed above than what goes under, which creates a low pressure above. This then "sucks" the wing up, and the rest of the plane follows the wings. The boat sail uses the same idea, except instead of "sucking" the boat up, it pulls it forward instead.

All that mythbusters are doing is using the fan to get the air moving initially and keep it moving. Normally this is what the wind would do, they are simply using the fan to create the same effect.

To the pedants - my descriptions, as requested, are very simplified. I can get more info on fans etc if wanted, but I know little about aerofoils, so that is pretty much as far as I can go without some serious studying To be fair, I am a ships engineer (hence knowledge of fans, which are the same as propellers) so I have never really needed to know much about wings :P

> Are you sure about this? I reckon it would go nowhere as the net acceleration of the air is zero.

If we assume the fan magically creates the air, then the only moving air is that going through the ducting and over the back. So if you think of the boat as a black box then it only has air coming out of it, imparting a force by newtons 3rd law.

But the fan doesn't magically create the air, it sucks it in. It's intake isn't the same as it's exhaust though (or you're right, the boat wouldn't move). Lets assume the exhaust is a cylindrical column of air, so it's all going in the same direction and all the momentum counts. Now lets assume that the intake takes air evenly from a hemisphere behind the fan. Some of the air comes from directly behind, so has a momentum which is the same as when it leaves. Some comes from the sides, so air sucked in from the left cancels out air sucked in from the right. Thus the backward-thrust from the intake is less than the thrust from the exhaust. In the example of a hemisphere in and a cylinder out it's less by a factor of almost 3 (I can prove that if you want, but don't want to get too sidetracked.

> Now I know for a fact that isn't true because all of the air isn't stopped.

As long as all the air ends up going where it should, you can analyse the problem in a series of steps. What I meant was you can think of it in three stages (four including the air going into the fan, which I was ignoring before)
1) the air is sucked into the fan, this pushes backwards by about 1/3 mv
2) the air is chucked forwards, this pushes backwards by mv
3) the air is stopped by the sail, this pushes forwards by mv
4) the air is chucked outwards and back, this pushes forwards by hopefully more than 1/3 mv

The air doesn't really stop, it's just a way of breaking it down and analysing it in bits.

PS. Are you happy with the ideas of integration as a way of adding up little bits of air? If so, that might be an easier way for me to explain.
> PS. Are you happy with the ideas of integration as a way of adding up little bits of air?

He's a maths teacher... so probably not!

I don't know what all the fuss is about:

Imagine standing on a boat and throwing a ball forwards so it bounces off a wall and flies back off the back of the boat. It has backwards momentum, so boat has forwards momentum to conserve total momentum. Same thing with air particles.
Another point to remember, a sailing boat can actually continue sailing even when the wind has dropped, as it's own movement essentially creates a wind. This is kinda like coming at the matter from the opposite end of the problem.

Again, this is not my area of expertise (yacht sailor would probably know a bit more) just I can remember hearing a commentator telling us about this effect whilst watching a sailing event during the olympics!!

You are forgetting about the keel, the keel generates a portion of "lift" through the water and hence forward motion when the sail is acting against it. Bermuda rigged fin keel boats are at their fastest at about 90deg to the breeze.

I think you've over complicated the sail element.

F=ma explains how a sail boat moves when positioned directly down wind.

Bernoulli principle explains how a sail boat can move forward into the wind. As you way - because the airflow over the front of the sail is faster than the flow over the back of the sail, thus creating a pressure difference which moves the boat forward.

However, the fan in a boat experiment is more like the former and not the latter.

You know, now I consider what "perpendicular" means, I quite agree!!

I simply assumed it would be similar to sailing into the wind, teach me to read the bloody post eh!!
>

> 1) the air is sucked into the fan, this pushes backwards by about 1/3 mv
> 2) the air is chucked forwards, this pushes backwards by mv
> 3) the air is stopped by the sail, this pushes forwards by mv
> 4) the air is chucked outwards and back, this pushes forwards by hopefully more than 1/3 mv

I could imagine integrating all the bits of air to get the answer 1/3 mv, but will trust you on the numbers.

Understand all this now I hadn't allowed for force (1) and force (4) above. It all comes down to if (4) is bigger than (1), which depends on the how bouncy the air/sail is.

I was thinking of the system as being like bullets being fired and embedding themselves in a block of wood (sail), it is more like bullets being fired and bouncing off the sail, which obviously gives more momentum to the sail.

Thanks Jack.

To everyone who said "I can't see what the fuss is about", you either have a much better grasp of physics than me or much worse, but I really don't know which!

PS. It turns out, if I now understand this, that the air reflecting (bouncing) off the sail is actually why this happens so I retract my initial banning of the word reflect.

Tchuh.

I mean, really. Tchuh!

Amateur trolls, you'll never catch up ;-)

> But the fan doesn't magically create the air, it sucks it in. It's intake isn't the same as it's exhaust though (or you're right, the boat wouldn't move).

But the intake must be the same as the exhaust - you have the same mass flow front and back, otherwise you very quickly get a load of backed up air or a vacuum in the fan.

Lets assume the exhaust is a cylindrical column of air, so it's all going in the same direction and all the momentum counts. Now lets assume that the intake takes air evenly from a hemisphere behind the fan. Some of the air comes from directly behind, so has a momentum which is the same as when it leaves. Some comes from the sides, so air sucked in from the left cancels out air sucked in from the right. Thus the backward-thrust from the intake is less than the thrust from the exhaust.

You are overcomplicating it. You're right that the sideways momentums "cancel each other out" leaving you with no sideways force on the fan. Talking about force from the inlet and outlet isn't necessary (and doesn't really make much sense). In the end, the rotating blades of the fan impart a force on the air molecules, causing a rate of change of momentum (dp/dt). It's just this rate of change of momentum that's important, as that's our force.

> 1) the air is sucked into the fan, this pushes backwards by about 1/3 mv
> 2) the air is chucked forwards, this pushes backwards by mv

The units here make me slightly nervous (mass x velocity is a momentum, not a force), but even if is the mass flow, rather than just mass, then you've got to be double counting.

I totally understand that normally the velocity at the inlet to a fan seems much less than the velocity at the outlet, and you're right, this is because the air is sucked in from a hemisphere, but comes out in more of a beam shape. However, the mass flow is the same, and if you stick that fan in a long tunnel, the speed before the fan, and the speed after the fan are the same (assuming no massive pressure differences, or cross sectional area differences). It's how most open circuit wind tunnels work, you use the fan to "suck" rather than "blow" air through the wind tunnel - you achieve the same speed, but with much less turbulence.

Tim

> I was thinking of the system as being like bullets being fired and embedding themselves in a block of wood (sail), it is more like bullets being fired and bouncing off the sail, which obviously gives more momentum to the sail.

Me too! And was chin scratching. I suspect Robert Durran is bang on the money. It depends on the properties of the sail (and the fan), I guess.

Tim

> (In reply to Jack B)
> [...]
>
> But the intake must be the same as the exhaust - you have the same mass flow front and back, otherwise you very quickly get a load of backed up air or a vacuum in the fan.

The mass flow is the same, what I meant was the geometry (and thus force imparted) will be different.

> The units here make me slightly nervous (mass x velocity is a momentum, not a force), but even if is the mass flow, rather than just mass, then you've got to be double counting.

mv is also an impulse. I was considering the impulse given by a 'chunk' of air, purely to try and simplify the maths I had to type. Perhaps I should have just tagged 'per second' onto everything and used force instead of impulse.

> You are overcomplicating it. You're right that the sideways momentums "cancel each other out" leaving you with no sideways force on the fan. Talking about force from the inlet and outlet isn't necessary (and doesn't really make much sense). In the end, the rotating blades of the fan impart a force on the air molecules, causing a rate of change of momentum (dp/dt). It's just this rate of change of momentum that's important, as that's our force.
>
I'm a physicist, overcomplicating things is what we do. Ultimately talking about force at the inlet and outlet makes sense if you think of the fan as a black box and you just integrate over some surface enclosing it to get the impulse it's imparting to the air, and thus that the air imparts to it.
I chose that approach rather than thinking about what happens at the fan blades because that's actually horribly complicated if you get into it. The (small) pressure difference across the blade becomes important, and the maths becomes horrific. By integrating over a surface 'far enough' from the fan you can have the same air pressure everywhere you are doing the integral.
>
>
> I totally understand that normally the velocity at the inlet to a fan seems much less than the velocity at the outlet, and you're right, this is because the air is sucked in from a hemisphere, but comes out in more of a beam shape. However, the mass flow is the same, and if you stick that fan in a long tunnel, the speed before the fan, and the speed after the fan are the same (assuming no massive pressure differences, or cross sectional area differences). It's how most open circuit wind tunnels work, you use the fan to "suck" rather than "blow" air through the wind tunnel - you achieve the same speed, but with much less turbulence.

This is true, but the hemisphere thing is crucial to making this work. If the fan sucked in air in a 'beam' from behind it, the boat wouldn't move (or would move backwards). The boat only moves forwards if the air reflected off the sail has more backwards momentum than the air sucked into the fan has forwards momentum.
It is important that while the mass flow is the same both sides, and the speed (averaged over all the air) is the same both sides, the velocity (averaged over all the air) is less on the intake side.

Either way, I think Mr Blackett has got his head around it now...
> Lets assume the exhaust is a cylindrical column of air, so it's all going in the same direction and all the momentum counts. Now lets assume that the intake takes air evenly from a hemisphere behind the fan.

Forgetting sails for a moment.... are you saying that a propellor mounted in a long cylindrical tube, mounted on the back of a boat pointing backwards, wouldn't make the boat go forewards?
> (In reply to Epic Ebdon)
> [...]
>
> Forgetting sails for a moment.... are you saying that a propellor mounted in a long cylindrical tube, mounted on the back of a boat pointing backwards, wouldn't make the boat go forewards?

Hmmm like the ducted fan or turbofan! we all know those don't work.
> (In reply to Epic Ebdon)
> [...]
>
> Forgetting sails for a moment.... are you saying that a propellor mounted in a long cylindrical tube, mounted on the back of a boat pointing backwards, wouldn't make the boat go forewards?

You appear to be describing what is essentially a water jet?? Though to work properly, you would need to add a venturi. And possibly the add the water as well, but I think you get my point...........

Erm... You seem to be quoting me, but replying to Tim...
But anyway, I don't think either of us said that.

> (In reply to Robert Durran)
>
> Erm... You seem to be quoting me, but replying to Tim...
> But anyway, I don't think either of us said that.

Sorry. I may have misunderstood. But I just don't see the need for this hemisphere thing; the air is still accelerated from rest with or without it.

If the sail was not there at all wouldn't the fan would move backwards even faster.

Surely it is just a backwards travelling swamp boat with a daft sail in the way.

What am I missing?

Let us assume the air is moving much faster than the boat.
You turn on the fan, and at first it does accelerate the air from rest.
Soon however, it has taken all the air that was at rest, and chucked to towards the sail. More air must flow in to replace the air that was there.
This air is being sucked in, and exerts a reaction force on the thing that is doing the sucking.
The hemisphere thing is me trying to explain why the reaction force can be less than a full mv per second. It must be less than that if the boat is to move, as that's the most you can get from air coming off the sail.

You are missing that with the correct sail geometry, it can go forwards, not backwards.

The sail basically acts as a big inefficient thrust reverser.

Ah, maybe I didn't get that far in the video.
> (In reply to Robert Durran)
> This air is being sucked in, and exerts a reaction force on the thing that is doing the sucking.

Your "sucking" is just part of the acceleration of more air from rest and your reaction force just part of the force tending to push the boat backwards.

> The hemisphere thing is me trying to explain why the reaction force can be less than a full mv per second.

It can't be (Newton 3)

> It must be less than that if the boat is to move, as that's the most you can get from air coming off the sail.

No. If some of the air is reflected off the sail you can get more than mv (up to an ideal 2mv with total reflection with no loss of energy).

> (In reply to Jack B)
> [...]
>
> Sorry. I may have misunderstood. But I just don't see the need for this hemisphere thing; the air is still accelerated from rest with or without it.

Exactly, the accelerated from rest thing is the only thing that's relevant to this question. Sucking over hemispheres is just an interesting aside - why you can blow out a candle, but can't suck it out.

And I'm not going to dispute that ducted fans work - but that wasn't a quote from me

Tim