Welcome to Engineering with Rosie. I recently watched
Veritasium's video on the Blackbird vehicle. It's a strange looking thing that sort of resembles a wind turbine on a go
kart. It's powered by the wind, and yet it can travel faster than the wind. To summarize, in case you haven't seen that
video yet, there is a cart with a propeller on it, and it's traveling downwind, the wheels of the cart turn the
propeller, which creates thrust that pushes the car along. Now if you find that hard to believe, then you're not the
only one. A UCLA physics professor has actually bet Veritasium aka Derek 10,000 US dollars that traveling
downwind faster than the wind is not possible. There's a contract and everything. And the contract was witnessed by
Neil deGrasse Tyson, Bill Nye and Sean Carroll. So some pretty big names in science there. So when I watched the video for like a week afterwards, my
brain actually hurt as I grappled with the physics involved. And I wanted to make this video to share the extra steps
that I use to understand how it works. So for me, I never had a problem believing that it was
possible for such a cart to work, because I know that high performance sailboats tack both upwind and downwind much
faster than the wind. And not only can the sailboat sail faster than the wind, but its velocity component in the
direction of the wind can be much faster than the wind. I also know that there is an immense amount of power in the
wind, since I've worked in the wind energy industry for the last decade. I mean, a turbine the size of the propeller on
the cart could definitely easily generate enough power to run a go kart. So it didn't seem like a conceptual leap to
me. But what I didn't understand was how it worked, and why it
doesn't violate the laws of thermodynamics. So that's what I'm going to show you in this video, including a conceptual
design spreadsheet model that I made to play around with all the design parameters and see how they relate to each other. So I will start with explanations in words. And I will
gradually add mats to it as we progress. And I will put bookmarks in the description so you can use those to jump
around in the order that makes sense to you. And you will also find a bonus analogy at the very end. So keep watching
for that. Okay, I'm going to start with the cart already moving
because the way it works when it's just getting started is totally different to how it works when it gets some speed.
And I think that that adds extra confusion. So here's our cart already moving along the ground, there is
some wind moving in the same direction as the cart, the wheels are turning, they're connected to the propeller via a
chain. And that is causing the propeller to rotate. It is just a normal propeller design, like you'd see on a model
aeroplane or whatever, only it's a lot bigger. And the way that a propeller works is that when you rotate it, it
accelerates air through the rotor and generates a thrust force. So I'll get further into the aerodynamics and how the
thrust is created later. But conceptually, it basically pushes the air backwards. In
the same way as like, if you were riding a bike in traffic, you could push off a car's side mirror to make yourself go
faster. I wouldn't recommend that because drivers do get very angry when cyclists do stuff like that. But you can
imagine that even if the car is moving, you can move faster than the car by pushing off it. In the same way the
propeller can move faster than the air that it's pushing on. So the propeller's thrust pushes the car along. And as long
as the wheels don't slip on the ground, they will rotate as the cart moves forward. And since they're connected via a
chain to the propeller, they turn the propeller. So we have thrust from the propeller and moving the card forward, minus
some drag and frictional forces. And as long as we're getting enough power from the wheels to power the carts
forward motion, the wheels will keep turning the prop and the thrust for the prop makes the car go forward. So far, so good. Or, maybe not. Does this sound like I'm
saying the wheels power the prop and then the prop powers the wheels? So not quite. The wheels turn the prop but they
don't power it. Remember, the cart is not a closed system, the ground and/or the wind are moving by constantly. But
what about when they are traveling exactly at wind speed? So they see no relative wind speed at all? Well, at that point,
there's no motion of the cart relative to the wind, but there is motion relative to the ground. The wheels are
turning so the prop is turning. So it's generating thrust. It might help to think of it not being as wind powered, but
rather being powered by the difference between the wind speed and the ground speed. So at this point, you might be wondering, why don't the
wheels put more drive on the propeller than it needs to move forward? And this is a question that I need to answer with
maths and aerodynamics. So I will come back to that later. All right, so what about the energy balance? It's all well
and good to say that energy comes from the wind. But how? Since the wind's energy is due to the kinetic energy of all
the moving air particles, if we're extracting energy from the wind, the wind must slow down. But we also know that the
propeller works by accelerating air across the rotor, so it must speed up. It's a paradox! Except it's not, it's all
just a matter of perspective. From the perspective of someone standing on the ground, the air slows down across
the propeller. And from the perspective of the cart driver, the air speeds up across the propeller. And that sounds like
a paradox. But it's not. If we go through with some very simple numbers, we can show that there's nothing weird going
on here. So let's say I'm driving the car moving at 12 meters per
second relative to the ground, and I have a 10 meter per second tailwind relative to the ground. So I see a two meter
per second headwind, and the propeller accelerates air through its rotor to let's say, four meters per second. So
the air is accelerated from two to four meters per second. And so as a result, there will be a thrust force. From my
reference point in the car, it's all very easy to understand. But now let's step outside the cart onto the
ground. So now we feel a tailwind of 10 meters per second. And we see the cart moving away at 12 meters per second
relative to us. So we need to subtract that 12 meters per second from what the cart driver experiences to translate it
to what we're seeing. So the car driver's two meters per second headwind minus the 12 meters per second cart speed is
a 10 meters per second tailwind like we expect. And the cart driver's four meters per second air behind the prop minus 12
meters per second is an eight meters per second tailwind. Slower than the wind on the other side of the cart, because
some energy has been extracted. From either frame, the wind was accelerated two meters per second to the left. So it's
accelerated by two meters per second in the cart frame, but decelerated by two meters per second in the ground frame. We
get more thrust from the prop, then we imposed drag on the wheels since the wheels are moving over the ground faster
than the prop is moving through the air. Just like a lever, we trade a small force over a large distance - the wheels
moving over the ground - for a larger force over a smaller distance - the prop moving through the air. So that is the
energy balance part. The paradox is simply Galilean relativity. Alright, so in the previous sections, I assumed the cart is
already moving. But of course, in reality, the cart starts off stationary and has to somehow get up to speed. And the
way that happens is totally different to the way that it accelerates beyond the speed of the tailwind. So when the
cart is at rest, it has a 10 meter per second tailwind behind it, and that wind pushes on it and gets it moving.
It's just like riding a bike with the wind behind you, it'll push you along, even if you're not pedaling. But you'll
never go faster than the wind this way, because the faster you go, the less wind there is from your perspective. So once the wheels are turning, the propeller starts turning
but not from the force of the wind on the blades as if it were a wind turbine. Instead of taking incoming wind and
converting it to rotation like a wind turbine does, it takes rotation from the wheels and converts it to faster wind out
the back. Any time the wheels are turning, the prop is turning... unless the chain falls off. And if the prop is
turning, it's accelerating air behind it and generating thrust. So once the car and its propeller are traveling
close to the speed of wind, it's no longer pushed by the wind on its back, it gets turned by the wheels. And then the
speed that the propeller sees - its relative wind speed - is mostly from its rotational speed, which can be much faster
than the wind. This doesn't happen all at once. As we hit the wind speed,
the torque from the prop increases gradually from the moment that we'll start turning and the relative wind flows over
the propeller and create a lift force. If the blades are 2.4 meters long and rotating at just 1.1 revolutions per second,
then the blade tips are moving at 17.2 meters per second, which is 62 kilometers an hour or 38 miles per hour. So the
blade sees a very fast wind speed. And furthermore, the lift force that's created by air moving over the airfoil is much
stronger than the drag force that pushed the back of the cart at the start. So this is really similar to the reason
why modern wind turbines generate a lot more power than the old fashioned ones. Okay, let's talk more about how a propeller works. A
propeller is just like a rotating airplane wing or a rotating sailboat as we saw in the original video. When air
flows over a profile at an angle, it causes high pressure on the bottom and low pressure on the top, which results in a
lift force acting perpendicular to the airflow and a drag force acting parallel. And for small angles of attack, the
lift force is much larger than the drag force. The lift force depends on the shape of the airfoil, the angle of
attack and the relative or apparent wind speed, that's the airflow from their perspective of the airfoil. To find the relative wind speed for a cruising aeroplane,
you would need to add the wind speed and direction to the aeroplanes own speed and direction. And the angle of attack
is just the angle of the wing relative to the airflow. The lift force lifts the plane perpendicular to the relative
airflow, and the drag force slows it parallel to the relative airflow. So now let's take this same analysis on to the propeller,
which is slightly more complicated because it's rotating. So the tip of the propeller is like a wing, but it's
constrained to rotate around an axis. So it sees relative wind that's a combination of the wind that the cart sees,
and also the speed due to its own rotation. The lift force created by that propeller has a component that pushes the
cart along - a thrust force - and a component that wants to slow the rotation a torque. That's the force that needs to
be provided by the wheels turning. Okay, are you still with me? Now I'm going to take you
through some maths and a spreadsheet model that I made to go through a realistic, uh, a kind of realistic conceptual
design. So the propeller blade has a complicated geometry, it's twisted and tapered. But we can simplify the analysis
by splitting it into a lot of small pieces. Each piece is small enough that the pitch and chord don't change much over
any given piece. This is a blade element method. And it's not 100% accurate, because I'm ignoring things like the
inflow, so we're going to overestimate the thrust of it. But it is a really great way to visualize what's going on. So we calculate the apparent wind speed and angle, the lift
and drag forces in each section. When you add all these up, you get the thrust force for the whole propeller, and we
need to multiply the tangential force by the radius to get the torque components, which will add up to the total
torque. So I have tried to roughly copy the Blackbird design here,
at the time that it set its record of 2.8 times wind speed. I have the actual propeller design, and I estimated the
other relevant parameters. So there are a lot of parameters here. And you can definitely tweak them to get a really wide
variety of results. So I don't want you to think that I'm trying to say that this spreadsheet models proves that the
cart design works, it only kind of shows how it works, and what happens when we change various aspects of the design or
the conditions a little bit. So when we take a look at a single section, about three
quarters of the way along the blade, you can see that the relative wind speed that the aerofoil sees is much faster
than the tail wind. And the lift force is much, much, much larger than the drag force because we're using a really nice
aerodynamic profile. And even the component of the lift force in the direction to push the car along - the thrust
component - is a lot bigger than the component that's trying to slow the blades rotation - the torque component. That's
the part that needs to come from the wheels. So with these conditions, my very simple model gives a gives
me a balance between the power from the prop and everything that's slowing it down, including the drag from the wheels,
which is what we would expect if the car is at its max speed. If there was excess power from the prop, we would
speed up. And if there isn't enough power, then we'd slow down. Or actually, we would never have even gotten to that
speed. If we increase the cart speed, the rotational speed
increases, and the relative wind speed moves closer to the direction of rotation, decreasing the angle of attack. So we
need to twist the blade to get the angle of attack more similar to what it was at the slower cart speed. And that
does increase the thrust compared to the slow moving cart. However, it also increases the drag and now we don't have
enough thrust from the wheels to power the prop and overcome the drag. If we could reduce the drag by decreasing the
frontal area say we could increase our maximum speed. All right, so now let's slow down to wind speed. So we have
zero headwind, but the prop is still rotating, because the wheels are. Now the airflow the propeller sees is entirely
from its rotation. We need to twist the blade back the other way so the angle of attack gives us good performance. And
you can see that even with zero tailwind or headwind we still have power from the propeller to accelerate the car.
There's nothing weird about that. It's just like an aeroplanes propeller being used to get the plane started
from stationary. In that case, the motor will make their propeller turn and in our case we have the chain connected
to the wheels which are turning because the car is moving. Okay, and now finally slower again to half of the wind
speed. Now most of the power to accelerate the cart comes from the drag force of the tailwind pushing on the cart. The
propeller is still generating thrust but not much. So those were the analyses that I used to understand the
problem. But I have noticed that different people find different explanations useful. So if none of this work for
you, then I suggest that you take a look at this presentation that the designer Rick Cavallaro made, where he
runs through a whole bunch of other analogies. I have been kind of embarrassingly obsessed with this problem over the
last few weeks. I think it's a bit similar to that physics brain teaser: If you have a jet plane on a treadmill that's
moving the exact same speed as the plane's wheels can it ever takeoff? But in my opinion, the downwind faster than the wind
brainteaser is way cooler, because you can actually just make it to resolve the problem. So I want to give a huge
thank you to Rick Cavallaro the Great for not just coming up with this design and tirelessly defending it on the
internet, but especially because he actually followed through and made the thing. So I think you can learn a lot from these kinds of fun
engineering problems. And if you are interested in that sort of thing, then check out this video where I made a
functioning wind turbine out of gingerbread. Please comment if you've got another video idea for me. And if you want to
become part of their Engineering with Rosie community and help shape the future direction of the channel, then you can
join us on Patreon. I've also got lots of other videos about more mainstream renewable energy technologies on my channel.
So take a look at them. And I'll see you in the next one. Okay, so here is your bonus analogy, which didn't really fit
in the main video, but I wanted to include it anyway. Did you notice that when the car was going faster, we needed to
increase the pitch of the propeller and when it was going slower we needed to decrease it? This reminded me of another
way that you can think of a propeller. So instead of thinking of it like an aeroplane wing, like we just did, we
can think of it like a screw. When you screw into a wall, your hand moves a lot more than the screw does. But it takes
a smaller force from your hand than it would to you know, just press the screw into the wall. If you increase the
pitch on the screw, you'll travel further into the wall with each turn, but it will be harder and vice versa. So a
propeller does something similar. It's easy to visualize if you imagine the propeller working in say hard butter instead
of air. Since the butter is so thick, that propeller won't slip and the propeller just acts like a lever to turn a
small force over a large distance into a large force over a small distance. So that's what happens as long as it's not
slipping. But now imagine the butter a little bit softer. And when you turn the propeller you'll get some slip between
the propeller and the butter. So each time we'll move the propeller a little bit less than pure geometry would
suggest. That's how it is with a propeller in air. Each tur of the prop moves forwards a certain amount due to the geom
try and that maximum theoretical value is reduced by the am unt of
