(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.
