(clattering)
- Why am I doing this?
- I think I can explain what's going on here.
Yes, it's me, Matt Parker.
Don't panic, Steve Mould will be back in a moment.
In fact, I've got a framed picture of Steve here,
in case you miss him too much.
Steve and I have this ongoing video challenge system
until we get to a million subscribers,
which at the time of recording has not happened yet.
So it was my turn to challenge Steve.
And I saw the video that Derek made on Veritasium
about a ridiculous contraption, which could go faster
than the wind in the direction of the wind.
Along the way, Derek mentioned that a sailing boat
can do a similar thing, but not directly downwind.
And Derek did a bit of a hand wavy,
oh, you know, angles, aerofoils.
Back to the main story.
And I thought, you know what,
I want an intuitive explanation for how this works.
I want someone who's gonna make a ridiculous model
to help me understand what's going on.
So I've challenged Steve Mould to do exactly that.
- We'll get into this ridiculous contraption in a second.
But first, let's take a really naive
look at how sailing might work.
I've positioned this sail so it's perpendicular
to the direction of travel of this boat.
And it's facing me, I'm the wind in this scenario.
So, when I blow the wind pushes on the sail.
And that pushes the boat forwards.
That's pretty straightforward.
And, actually, in this configuration the sailboat
can't travel faster than the wind,
which is why by the way, Derek's contraption
is so remarkable in his video.
This particular configuration of sail
and boat isn't desperately useful.
Like, how often is it that the place
you want to go happens to also be
the direction that the wind is blowing.
What if you wanted to travel
in this direction relative to the wind?
Well, all you have to do is turn the boat
into the direction you want to travel
while maintaining the orientation of the sail.
Seems to work quite well.
But it's actually a flawed approach.
The more you turn the boat, the less well it works.
Let's look at the extreme case
where you want to travel perpendicular to the wind.
The wind doesn't propel the boat forward at all.
It simply tries to push it over.
What you do instead in this scenario
is angle the sail at about 45 degrees.
And there you go, we can just about get the boat
to go in the direction that we want it to.
To be fair, it's also going a little bit in the direction
of the wind, which we don't want to happen.
That's because it's a toy boat.
And I'll get to the details of why in a minute.
But for now, let's assume that it works perfectly
and only went in this direction.
It's worth looking at this particular configuration
in more detail to see what's going on.
Here's a simplified diagram of the sailboat.
You can tell when I do my own graphics, can't you?
Because they're so good.
So, the sail deflects the air like this.
Actually it deflects the air on the far side of the sail
as well because of the Coanda effect,
which we won't go into detail here.
But the point is the air has changed direction
by the time it's finished interacting with the sail.
An object only changes direction when it feels a force.
If this is the original direction,
and this is the new direction,
then the force must be in this direction.
Okay, so that force is coming from the sail.
The sail is pushing the wind into a new direction.
But every action has an equal and opposite reaction.
So the sail feels a force as well in the opposite direction.
And of course, that pushes on the whole boat.
This force is called lift, by the way,
the same force that's generated by an airplane wing.
The word lift is a bit confusing in this context.
Like, in the context of a plane,
the plane is being lifted up
against gravity in the upwards direction.
But lift here is happening in the horizontal plane.
So it's a confusing word, but it's the same thing.
So, why doesn't the boat move in that direction?
Well, it's because of the shape of the boat underwater.
The parts of the boat that's underwater is long and thin.
And, look, when I put my hand in water it's intuitive
to see that it's hard to move my hand side to side.
It meets lots of resistance from the water.
And it's easier to move my hand backwards and forwards
because there's less resistance in that direction.
And it's the same with boats.
The resistance to sideways motion isn't absolute.
In fact, in the case of our toy boat
there's quite a bit of sideways motion because the shape
of the boat underwater isn't very long and thin.
But for real sailboats it's negligible.
We're gonna assume it's zero.
So, we can take this force vector
and break it into components
in this direction and this direction.
This direction has no effect
because of the resistance of the water.
But there is a component in this direction,
so we expect the boat to travel in that direction.
The same is true on land, by the way.
Land yachting, or sand yachting,
or land sailing is where you use wheels on land.
The wheels present resistance to sideways motion,
but reduce resistance in the backwards and forwards motion.
I've created a physical model in that vein,
which I hope will explain why sailboats
can travel faster than the wind.
So, look, the wind comes in from here.
It pushes on the sail, and it pushes the boat,
we can call it a boat, can't we, in this direction here.
So, what is the theoretical maximum speed of this boat?
Let's assume that there's no resistance.
That's a ridiculous assumption,
but it's useful for our understanding here.
Well, the maximum speed of the boat is the speed
at which the sail exactly misses the incoming air.
Let me explain what I mean by that.
Imagine you've got a packet of air coming in at this speed.
And the boat is moving at just the right speed
that the sail exactly misses that packet of air.
The packet of air is unaffected
by the sail at this precise speed.
For completeness, here's a whole load of packets
of air failing to be affected by that sail
because the boat is moving at just the right speed.
Actually, there's something confusing
about this graphic, isn't there?
I think it's sort of an optical illusion actually.
If the boat were going any slower
that packet of air would be deflected slightly.
So the boat would increase in speed
until it reached that magic speed.
Again, this is all assuming that there's no resistance.
With the sail at 45 degrees like this,
the speed of the wind and the speed
of the boat are actually the same.
Look, by the time that packet of air has traveled
this distance the boat has traveled this distance.
They match when the sail is at 45 degrees.
But what if we changed the angle
of the sail so it's like this?
There's actually now too much friction
between my hands and the sail.
So I'm gonna switch to this stick
with a wheel configuration.
It's pretty high tech over here.
So, now in the time it takes for this packet of air
to move this distance the sailboat has moved this distance.
It's actually traveling faster than the wind.
And, remember, if the boat were going any slower
than that it would be deflecting the air.
And there would be a reaction force speeding the boat up.
At this point you might think,
well, why don't we angle the sail
so it's really, really close to the direction of travel?
That way we could go much faster than the speed of the wind.
Well, there's a trade-off and you can see it here.
Look, when the sail is really close to the direction
of travel, the component of the lift force
in that direction is really small.
So it would take a long time to reach that top speed.
And, actually, that's only true
in a world with no resistance.
In a world where there is resistance,
which is to say the real world,
the ship wouldn't be able to get up
much speed before the drag force
exactly cancels out that meagre component
of the lift force in the forward direction.
So, in practical terms there's
an optimum angle for the sail.
And, actually, that's part
of the skill of being a good sailor.
I can also use this model to show how it's possible
to travel against the direction of the wind.
But first, I just want to talk about the shape
of the sail compared to this model that I've used.
We talked about how a sail generates lift
in the same way as an airplane wing.
And an airplane wing tends to have
this cross-sectional shape.
It doesn't have to be that shape.
Planes can fly with a wing shaped like this,
angled into the direction of travel.
It's just that for complicated aerodynamic reasons
this is a more efficient shape.
The same thing is going on
between my model and real sailboats.
My model is this flat surface.
Well, sailboats act more like
that curved profile of an airplane wing.
So, how can you sail into the wind?
Well, you can't sail directly into the wind,
but you can sail a little off from directly.
I'll just show you with the model.
So, the wind is coming in this direction.
We want to travel in this direction.
We angle the sail like this.
And there you go, the boat moves forwards.
This isn't exactly how the sail
would be positioned in reality.
Because in this model I'm making the force vector be
in the same direction as the direction of the wind.
But the vector in a real sailboat
is based on the change of direction of the wind.
But it's the same basic idea.
Actually, you can travel directly into the wind.
You just have to take a zigzag path.
And that's called tacking.
There is another way to explain
how you can sail faster than the wind.
And maybe it's the explanation that you've heard.
For me, it's not very intuitive.
But I will type it out in the pinned comment.
Because that's likely where we're gonna talk about it?
If you haven't seen Derek's video yet,
it really is remarkable.
The link is in the card and the description.
Don't forget to stick around to the end of this video
for some more chat with Matt Parker.
- You know that feeling when
you're presented with a new puzzle.
And you go, ooh, ooh, hmm.
You start to think about the ways
that you're gonna solve this thing?
I remember getting that feeling when I first saw a Sudoku.
But here's the thing about the sponsor
of this video, Brilliant.
It's a website and an app that basically gives you
that feeling every time you pick it up.
It's a new puzzle or a new problem that you gotta solve.
Every time you look at it you go, ooh, oh.
Brilliant is actually a learning platform.
It's designed on this principle that the best way
to learn something is by doing it for yourself.
So, you work through these puzzles and problems.
They've got courses on broad topics like mechanics or logic.
But you can take deep dives into subjects
like cryptocurrency or quantum computing.
And actually, they've got a good search function as well.
So if you're ever thinking, you know what,
I'd like to learn more about a particular thing.
For example, after watching this video,
actually, I do want to know about how lift works on a wing.
You could search for Bernoulli, for example.
And start investigating that stuff through puzzles.
Because it's an app as well as a website,
I actually get on brilliant just before going to sleep.
Like a lot of people might scroll
through social media in bed or read a book, not me.
If you're the sort of person who sees a new puzzle and goes,
hmm, oh, interesting, I recommend you check out Brilliant.
If you go to my special URL you can check it out
for free, no strings attached.
Go to brilliant.org/stevemould.
The link is also in the description.
So, check out Brilliant today.
- That was good, I'm convinced.
When you were pushing it with your hand,
and it was the hand pushing that was then just moving
the sail out of the way, I was like I don't know.
But then the argument about when you're at the wind speed,
if it was going faster or slower,
the sail would speed up or slow down to match.
I was like, okay.
- That is critical because in the model
the force vector is always just the direction
of the wind, which isn't really true.
- Yeah, it's the deflection of the wind, yeah.
- Yeah, so I fixed that. (chuckles)
- Is it like everything with lift, where there's a bunch
of Bernoulli fans who are now a bit emotional?
- Yeah, I think that you can explain lift
in terms of Newton or in terms of Bernoulli.
In fact, I'll link to a video, might be
a Veritasium video actually, thinking about it.
- Classic Derek. - I mean.
- I'm prepared to sign off on what you've done.
In fact, I'm prepared to now move on
to the next challenge I'm gonna give you.
- Oh, no, because I've reached a million now.
- Yeah, you've reached a million, right,
it's not exclusive, right, I need to reach a million.
- That's the end, we did it!
- Well, no, you've done it.
So there's no point me doing another video
on my channel to encourage people to subscribe
to you because you're at a million.
- Which face has been better
at getting to a million subscribers?
You need this face on your channel.
Here's the challenge, right?
It was on Reddit, and I saw this thing.
It was this power cord, and it was stuck.
The power bit couldn't get through
this hole underneath this handle.
and the person does a loop thing.
And then the handle goes through, and it all comes out.
- Actually it sounds a lot like the kind of thing
you would find on brilliant.org.
You're like, huh, I think
I will go to bed and think about this.
- I hope you're not being sarcastic
about the sponsor of my video, brilliant.org.
- No, I was not, I'm a big fan of brilliant.org
- It's just sort of your baseline voice is quite sarcastic.
- My resting sarcasm voice, yeah, I accept that.
I will come back to you with
an explanation of the power cord thing.