And there are several entirely erroneous, or partially erroneous explanations,

and actually very few entirely correct explanations actually 'cause it's quite complicated.

[Brady] Well how do we know yours is going to be right?

Ah. It probably won't actually, in its entirety, but, well you shouldn't say that on video. [guffaw]

[Brady] Ha ha, where do you want to start?

Maybe we should start with some of the wrong explanations. So the classically

wrong explanation invokes a thing called the Bernoulli Effect, and says ok so you've got your aerofoil and it's flying through the air but let's think of

things in the reference frame of the aerofoil so we'll have that stationary and move the air streaming past it. And the classic

explanation has the air going above and below the wing and kind of joining up when it gets around the other side.

And of course there is more air kind of going higher and lower as well.

And the classically wrong explanation says, "so the air going over the aerofoil

has further to go than the air going under the aerofoil so in order to meet up with the air at the other end it

has to travel faster," and then there's this thing called The Bernoulli Effect

[which] basically says that when air is traveling faster, its pressure decreases and that's really just the

Conservation of Energy. That's really just saying that the energy of the air molecules is partly

in random motion, which creates pressure, partly in the streaming motion, and

in order to conserve energy, if you increase the amount of streaming energy, you decrease the amount of pressure energy.

So the pressure up here, [be]cause these air has got further to go than this air, it's traveling faster, [the] pressure is reduced,

therefore the pressure above the wing is lower than the pressure below the wing.

Pressure is just the force per unit area. That means that actually the force above the wing pushing down on the wing is less than

the force below pushing up and therefore the thing just rises. Which all sounds very plausible.

[Brady, incredulously:] But the Bernoulli Effect is a real thing!

Yes!

[Brady:] Is that not the Bernoulli Effect you just described?

That _is_ the Bernoulli Effect I just described. There are at least two flaws with this argument.

The fundamental one,

that I kind of slipped in there, is saying that the air meets up on the far end.

So there's no reason why, you know, when the air leaves from this end,

it doesn't kind of make an agreement with its pal here, that's it's gonna meet up when It gets to the other end.

There is no reason why the air traveling above should get to the far end at the same time as the air traveling below. In fact the air traveling above

travels so much faster, that it gets there *before* the air traveling below in reality.

So that's the first fallacious part of the argument, is that It has to travel faster to meet up

with its friend at the farther side of the journey past the airfoil.

[Brady] But professor, if you just said that in fact It gets there faster, doesn't that mean that we get like a Hyper-Bernoulli Effect?

You actually get more lift than that naive argument would predict. So there's a second argument which is sometimes put forward about why this can't be the

explanation, and this one's not quite so true, and the argument goes that if It were true,

then It wouldn't be possible for an aeroplane to fly upside down. Which of course they can. [Brady: yes] So here's our aeroplane,

here's our aeroplane flying upside down. If the previous argument was true (which to some extent, it is) [then] this aeroplane would just fly straight

into the ground, because the lift effect we were talking about before is now pulling it in this direction

instead of that direction. But of course the pilot has other things that they can alter, and in particular they can move the nose

of the plane up and down, which of course has the effect of moving the wing. And by changing the angle of attack, with the wing like

this, the airflow we were talking about before, there's a thing called the stagnation point, which is the point at which the air kind of

splits between either going above the wing or below the wing, and the stagnation point as you change the angle of attack in this

way moves downwards. The previous arguments still sort of holds because actually the air going above the

aerofoil is still going further than the air going below the aerofoil, so the Bernoulli type effects that we were talking about before still occur.

So the other argument goes:

that actually even when you're flying the right way up, you have a bit of an angle of attack, so the way you really

fly an aeroplane is with the aerofoil slightly tilted.

And the argument goes that the air essentially just

bounces off the underside of the wing, and heads on down this way

and you can see that the air molecules, through this process, have acquired a momentum downwards. And that means that the aerofoil will acquire a

momentum upwards just from Conservation of Momentum.

Brady: Yeah the plane's just being *battered* into the air.

It is, it's been pushed up by air bashing into it.

There are a couple of reasons why this is wrong.

What happens on the upper side of the aerofoil remember is that the air goes

over, and actually also ends up being bent downwards. The air traveling over the top of the wing, by acquiring downwards momentum,

means that It has to be transferring upwards momentum to the wing as well, and so in fact the air traveling over the wing is

also contributing to the lift. It actually contributes _more_ of the lift than the air [that's] going underneath

the aerofoil.

It really comes down to the fact that you can't really think about a gas like air as just a load of little ping-pong balls.

One easy way to think about that is if you were to,

to hold your hands up in front of your face and blow against it. [Whooshing sound as he blows]

The air actually hits your hand and then shoots out to the sides.

Now if you were just throwing ping pong balls at the wall that would never happen, right? They would just bounce straight back at you.

And It really is because

air as a gas behaves in a very different way from this collection of individual particles. You have to worry about the

interactions between the particles as well.

Which means that these kind of simple momentum conservation

ideas about how . . . an aeroplane can fly can't be the whole story.

Brady, incredulously: How does an aeroplane fly? [Guffaw]

Okay.

So.

The physics for this sort of goes back to Leonhard Euler in the 18th Century,

who came up with a set of things called the Euler Equations.

And the Euler Equations, you can write them down mathematically (it's all quite complicated) but actually physically what they're saying is that as air moves around

there are three conserved quantities you need to worry about. The mass is conserved, which it just says that molecules don't appear and disappear, that

they have to kind of flow continuously so you have Conservation of Mass.

Momentum is conserved.

Just from Newton's Laws,

which kind of goes to one of those slightly spurious explanations we were looking at,

and Energy is conserved.

Which of course is where the Bernoulli Law comes from,

and you need to conserve all three things at the same time.

And that's why neither of those previous

explanations can be the whole story, because each kind of borrows bits of the physics but doesn't do the whole thing at the same time

The way these three things behave together is really quite complicated, which is why you get these complicated flow patterns around

wings like this and you have to start worrying about effects like turbulence and those kinds of things. Although each of those

previous arguments kind of captures some aspect of what's going on, you really need to think about all three of them at the same time

and actually if you really want to do things properly, you have to worry about

viscosity effects, that If you've got one load of air traveling at a particular speed it'll tend to drag the next lot of air along

at a similar speed. It's very hard to have one lot of air going very quickly and the other lot not moving at all.

So you have these

viscosity effects that air kind of drags other bits of air around and if you want to put that in as well then you have

to take the Euler Equations and add this viscosity effect and then you end up with a thing called The Navier-Stokes Equations

which were only invented in the Nineteenth Century,

which are the full set of equations you really need to solve, to understand what's going on with it.

[Brady] What is going on with it?

So ok, so remember we're trying to do these three aspects and really we,

you know, you need to do Conservation of Mass, Conservation of Momentum, and Conservation of Energy, all at the same time.

So here's what's going on.

Here's our wing. The air above is kind of being squeezed together.

It's a little complicated to figure out exactly why, just because, you know if there were a wall up here it would kind of make

sense that actually suddenly it's being pushed into this narrower space and everything's being squeezed together. But there isn't, there's just a whole lot more

air up there. But again this comes out of the equations that the air ends up being squeezed in this way.

Because it's being squeezed into a tighter space but you've got the same amount of air,

remember the first of the things we have to conserve is mass. To get the same amount of air through

but in this squeezed region instead of this sort of wider region, it has to travel faster. So the air is Indeed

traveling faster above the wing than it is below the wing, so that part is true.

Not because it has to go further, just because the geometry of the obstruction here

squeezes the air together. It really is just the way the air flows around an obstruction like this, so it is traveling faster so that's

the Conservation of Mass. The air here is compressed, which means it's traveling faster, which means Bernoulli's Law,

Conservation of Energy, says that the pressure here is lower which means that the force downwards on the top of the wing is less than the

force upwards, and therefore that's the phenomenon of lift.

But then the last part, like if you think about it, the gas originally all flowed in like this, and by the end it's all flowing downwards like this.

So that the air has Indeed acquired a downwards momentum, and we have to conserve momentum.

You know if the air is now flowing downwards, being pushed downwards, that means that the wing is pushed upwards, and

so you can Indeed you think of this globally as a Conservation of Momentum effect that the air

globally acquires downwards momentum due to these various phenomena we've just been talking about, which means that the wing acquires an upwards momentum.

So you can see all three of these aspects all feed into the explanation.

The Conservation of Mass, the Conservation of Energy, and the Conservation of Momentum, and really

you can't extricate any one of them and say "that's the reason why!"

You really have to think about all three at the same time in order to understand the global phenomenon.

Brady: Between The Bernoulli one and the Conservation of Momentum one, which one is more important? Which like. . .

I don't think you can separate it out in that way. I think you really have to think about all three at the same time. Because the

physics equations you're solving, [you] really are solving for all three of these things at the same time. And if you were to fiddle with one

of them, that would affect the others.

So actually you can't say "Lift is being caused by Conservation of Momentum"

or "Lift is being caused by Conservation of Energy through the Bernoulli Effect." It really is the

combination of both of them together with the Conservation of Mass which is causing the effect.

Well I guess the last thing to say is that

reality is always more complicated

than any of these simple explanations, and actually if you really want to design a wing you have to do very complicated

hydrodynamic simulations in three dimensions because this is not a real wing, in fact, you know this is just a piece of cardboard,

and actually real wings are fundamentally three dimensional entities, and so for example, one of the other

aspects you have to worry about with a real wing is that it has an end. And at the end of It you

have all sorts of effects like vortices being shed off the end of the wing and what-have-you which actually have a

significant effect on the lift of the wing as well. So although as a physicist, this is the explanation, if you want the engineer's

explanation as to how a wing works, you really have to give an even more complicated story.

Brady: I mean you showed me a bunch of things at the start that you described as like the fallacies, and yet a lot of it ended

up being part of the final explanation.

So it felt like those fallacies were okay [Prof: Right], there were just other things at play as well.

That's true. No I agree and that's a fair reflection that actually you know, I

refer to them as fallacies but they are, I guess, "partial truths" would probably be a better explanation for them.

Brady: So the Bernoulli Effect does make planes fly.

[The] Bernoulli Effect does make planes fly. So does Conservation of Momentum.

So in some sense everyone's right, so maybe everyone should be happy.

. . . water. So i got over there

some water, which I'll go and collect and we'll go another 20 paces that way, and show you that the water will

extend the range even further.