A Physics Prof Bet Me $10,000 I'm Wrong
I am here to sign a document betting $10,000 that my last video is, in fact, correct. This is the video in question. Some people may have missed it, but in this car, there is no motor, no batteries, no energy source, besides the wind itself. And the counterintuitive claim is that this car can maintain speeds faster than the wind that's pushing it. There is a physics professor at UCLA, who got in touch to say that he thought that I was wrong, that the explanation was wrong. You know, we went back and forth a little bit, and eventually I said, "Well, how about we bet $10,000? I can prove it to you. This vehicle really can go downwind faster than the wind." And to my surprise, he is taking me up on the bet.
Look, no one is perfect, but you have a much lower error rate than most people on YouTube, in YouTube Space.
Now, Professor Alex Kusenko wanted this wager and all related discourse to be public. In fact, he suggested we get a celebrity to witness the signing. So I asked Neil deGrasse Tyson, Bill Nye, and Sean Carroll to be our witnesses. And they graciously agreed.
And Alex, I just wanna say, I agree with everything you said about Veritasium. That generally I can watch it and not have to wonder, is he gonna mess up? How am I gonna—
No, he's brilliant, no, he's brilliant.
I'm excited about this bet because if I am wrong, then I wanna know. Like the whole point of the channel is to get to the truth. And that is, I think, why we're all here today. And I think, you know, this is a great chance to sort of see. I'm going to summarize Alex's main points in this video, but I'll put his full presentation here.
So let me first explain what I see in the video. In the video, the vehicle is operated in a gusty wind. Initially, you have the wind speed exceeding the car speed, but then the wind speed is not constant. The wind speed drops, and the car moves by inertia with deceleration for a while.
So, basically Alex thinks a gust pushes the car to a high speed. And then when the wind dies, the car is going faster than the wind momentarily, but it must be slowing down.
In fact, that will be my conclusion at the end of this presentation, that whenever you have velocity faster than the wind, I'll actually show you in an equation, the acceleration is negative. The second effect is that the wind in the video is measured at the height of about a meter or a meter and a half.
Now, due to interactions with the ground, there is a wind gradient. Wind travels slower, close to the ground, and then faster, higher up. Now, Alex estimated that the wind speed of the propeller might be 10 or 15% higher than at the tell-tale. So it's possible that the car could be moving slower than the wind at the propeller, and yet appear to be moving faster than the wind at the height of the tell-tale.
Now, I think that this is a small effect. However, in combination with the previous effect, it just can make this more frequent, okay. And that completes—
Alex, if I remember the video correctly, Derek reports that they've achieved up to 2.8 times wind speed. That feels much higher than what is possible here, unless the wind had picked up and then spontaneously sort of dropped.
Very, very good question. Okay, if you're going for the record, you probably will do many attempts. You will be sampling that gusty wind over, and over, and over until you set the record, right? That's how you set the record. And on one of those occasions, you will get a nice strong gust, which is three times the air that comes after it, okay? And that's when you will clock the record. And that's where that 2.8 factor will come in.
So what about the treadmill tests? These are conducted in still air. By moving the ground backwards, you're simulating a perfectly steady tailwind. And if you hold the car stationary on the treadmill, well, that's equivalent to the car going exactly wind speed. Now, if the car can move forward on the treadmill, that shows it can accelerate faster than the wind. But Alex had multiple explanations why these experiments don't actually show what they claim to show.
If you have this fluctuating speed of the treadmill, and then if a human just sort of steers it, it then can introduce unconsciously a bias towards the desired result.
So, would it any be that the guy with the spork is inducing the model craft to go across the lane now and then? And as you pointed out, I would go downhill now and then.
Yeah, I'm sure, I'm a hundred percent sure that the guy in the video doesn't do it on purpose, okay. However, you know, if he is expecting forward drift—
Yeah, oh he's trying.
Yeah, yeah absolutely, that's exactly, okay, so there you go.
In the absence of convincing experimental evidence, Alex turned to theoretical analyses, like one by MIT Aero Professor, Mark Drela. But here too, he found problems. His main concern is that the equation for net force includes the difference between the speeds of the car and the wind in the denominator, which seems to imply that when traveling exactly wind speed, you should get infinite force.
Now, here's the real danger. Because if Derek drives very close to the wind, that difference in speed goes to zero. If it's one millionth of one percent, that's like a nuclear bomb exploding behind him. Then Derek is definitely in trouble, right? So we need to find something to save Derek's life here. This is serious, right?
But dividing by zero, come on, you guys. I never looked at that.
[Derek] Alex performed his own analysis and found no such divide by zero problems. In fact, he found there's no way for the car to accelerate at, or above wind speed.
The acceleration of this craft is negative. So when we, you know, so it's possible to move the craft faster than the wind, but it's not possible to move it at zero acceleration which would be needed to maintain constant speed.
[Derek] That is basically where we left it.
That is right.
Okay, thank you, thank you, Neil. Thank you very much.
Thanks guys, thanks Neil.
So now it was up to me to convince Professor Kusenko that Blackbird really can go faster than the wind. When I posted about it on Twitter, Alice Zhang, who runs Chinese Veritasium, said, "I think you lost Derek. I'm 80% on Alex's side now." What's amazing to me is that neither one of them had seen my attempts to replicate the treadmill experiments. For the first video, I asked my friend and YouTube maker, Xyla Foxlin, to make a model downwind cart.
All right. (wheels screeching) (laughing)
[Man] Oh, no!
Version one ended in failure, but Xyla was undeterred, coming back in a couple of days with version two.
Is it feeling like it's gonna...?
Unlike these models, most of her projects actually work. She is determined. So maybe this tells us something about whether you can actually go faster than the wind downwind. What was clear to me is that I didn't do a good enough job in the first video, explaining how Blackbird works and providing convincing evidence that it can really go faster than the wind in a sustained way. In my defense, I thought the concept was well enough established. Way back in 1969, Andrew Bauer built the first successful downwind cart. And he did it to settle a friendly wager with Aero Engineer, Apolo Smith. The bet was inspired by a claim in a student's paper from 20 years earlier. Now, Rick Cavallaro, the builder of Blackbird, was completely unaware of all this until after he built his cart. But other analyses have been published under names like the push-me pull-you boat. So I didn't honestly think anyone would doubt the vehicle's operation, much less bet me $10,000. But clearly, there is a need for a deeper explanation. So I want to do that now by responding to the points Alex raised.
So first, let's deal with wind gradient. I mean, why didn't we measure the speed of the wind higher up? Well, the answer is because it's already been done. They mounted tell-tales on fishing poles out to the sides of the propeller and even above it. Now, although the lowest tell-tale flips back first, all of the tell-tales do eventually flip backwards showing that every part of the vehicle is going faster than the wind. Could this be because of a big wind gust that pushed the car up to high speed and then the wind died? I don't think so. Even though I didn't have a speedometer in the car for my runs, someone on Twitter pointed out that we could use the rotation of the back wheel to determine the speed from the video footage. This shows that even after the tell-tale flips backwards, the car keeps accelerating. Another thing I want to point out is that if wind gradient or gusts were the reason that the car travels faster than the wind, well, you'd expect the tell-tale to jump around or at least not point straight back at me. But it consistently does for over 30 seconds until I had to hit the brakes to avoid crashing into parked vehicles. But if that's not enough for you, when Blackbird achieved its record speed of 27.7 miles per hour in a 10 mile per hour tailwind, it was still accelerating. And we know this because there were multiple GPS units in the car and wind speeds which were measured at the height of the propeller at multiple locations. The highlighted section shows the ten-second measurement period over which the record was set. Also, in 2013, the U.S. Physics Olympiad Semifinal Exam asked questions about Blackbird. Like, can it go faster than the wind downwind and upwind? The solution says both modes are possible. And with sufficiently low energy loss, any speed is possible. Now, I'll admit that the evidence I showed in the first video was not definitive when gusts or gradients could have explained the observations. But now that you've seen this evidence, are you convinced that Blackbird can go downwind faster than the wind without slowing down? Well, Professor Kusenko was not convinced.
So I wanna explain how the car works so clearly that no one, not even the professor, can doubt what's going on. The first thing to know is that the propeller doesn't work like most people think. It's not working like a windmill. It doesn't turn the way the tailwind is pushing it. Instead, it turns in the opposite direction, working like a fan to push air backwards. This fan is powered by the wheels, which are connected to the propeller by a bike chain. So at wind speed, the car can keep accelerating because the wheels turn the fan, which blows air back, generating forward thrust. Now the big question is, to drive the fan, there must be a backwards force on the wheels, which tends to slow them down. So why isn't this force bigger than the thrust from the propeller causing the car to slow down overall? Well, the answer is the wheels are going so much faster over the ground than the propeller is moving through the air. So the thrust force can actually be larger. I'm gonna do an analysis in the frame of reference of the car. And the important equation to know is, power equals force times velocity. So at the wheels, power is input into the system by the ground moving underneath the car. The power generated is the force of the ground on the wheels times the velocity of the car. At the propeller, work is done on the air, as the propeller pushes it backwards. The power out equals the force of the prop on the air, times the speed of the car, minus the speed of the wind. The prop is going slower through the air due to the tailwind. And if we assume no losses, then the power in at the wheels equals the power out at the propeller. From this equation, we can see that the force at the propeller will be greater than the force at the wheels. And since the propeller is pushing air back, the air applies an equal and opposite force forward on the prop. This is the thrust force, which will be greater than the backwards force on the wheels. So this car works like a lever or a pulley by applying a small force to the wheels over a larger distance, the propeller can apply a larger force over a smaller distance. This is just like when you're riding a bike going uphill; you move the pedals fast, but with smaller force, to make the wheels move slower over the ground, but with a bigger force. But now we've run into the divide by zero problem that Professor Kusenko warned us about. When the speed of the car is exactly equal to the speed of the wind, it seems like the propeller can provide infinite force. That can't be right, can it? I mean, is our analysis flawed? The answer is no, for two reasons. First of all, this is exactly what you'd expect theoretically, with any lever or pulley. If one arm of the lever is zero, then you can lift an infinite weight with any amount of force on the other side. The catch is, its displacement will be zero. But second of all, in practice, there is a propeller efficiency term that is ill-defined when the propeller is not moving through the air.
There's a better formula for the prop proficiency, which is well-defined in the zero speed limit. It makes an algebraic mess, but it's perfectly well-defined.
And then the divide by zero problem is eliminated. But that equation makes the problem look more complicated than it actually is. You don't actually need aerodynamics. Here, I have a little cart with a big wheel that rolls on two smaller spools. And what I'm gonna show is that when you have two media moving relative to one another, well then if this car is in contact with both media, it can actually move faster than their relative velocity. So as I push the board to the right, you can see that the car goes down the board faster than the board is moving. If you look carefully, you'll see that the big wheel isn't turning the way that the board is pushing it. It's actually rotating in the opposite direction. That's just like the propeller on Blackbird, which pushes back against the air, and that's how it's able to go faster than the wind downwind.
Now you can build one of these cars for yourself at home, or you can build a model downwind cart. I told you, Xyla was determined.
Yeah, I'm gonna make the claim on camera. I like, I think it's gonna work this time. We're changing the propeller.
It has to work before we get kicked out of the treadmill store. (laughing) (motors roaring) (chuckling)
[Derek] Does it work?
It totally works.
[Derek] Amazing.
Oh my god, it's so good.
Her fourth version of the cart works spectacularly and it was designed to be replicated by anyone using just a 3D printer and a simple list of materials. She explains how to build it with more detail on the engineering process on a video over on her channel. So go check it out.
Now, Professor Kusenko has now conceded the bet, and he transferred $10,000 to me. So I wanna thank him for being a man of honor, and changing his mind in light of the evidence I presented, which is really not easy to do, especially in a public debate like this one. Now I do not wanna keep the money. I wanna invest it in science communication. So I'm holding a one-minute video competition. I'll be awarding cash prizes to the top three videos that explain a counterintuitive STEM concept. I'll put some details down in the description.
What I love about science is that disagreements are not problems. They are opportunities for everyone to learn something. I learned a lot more about Blackbird aerodynamics, and gear ratios than I knew before. I also learned that I should go into more depth in my videos. I should make the evidence overwhelmingly convincing and put in some equations toward the end for those who want that level of detail.
I wanna thank everyone involved in making this video: Neil deGrasse Tyson, Bill Nye, Sean Carroll, Mark Drela, Professor Kusenko, and Xyla Foxlin, but especially Rick Cavallaro, the inventor and creator of Blackbird. He was a fountain of information, a constant source of support, and the man leading the charge to help people understand this area of physics for the past 15 years.
Let's hope this video puts the issue to rest once and for all. (electronics buzzing)
The Blackbird craft all started with a brain teaser. And this video sponsor, Brilliant, offers you a daily problem to solve every day, like this one about gear ratios. If the first gear spins 10 times per second, at what rate does the final gear spin? Now I did this problem the hard way, but my wife figured out how to do it the easy way. And that's what brain teasers are great for. They get you thinking about the world, and they give you insights into problems you might think you already understand.
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For viewers of this channel, Brilliant is offering 20% off an annual subscription to the first 200 people to sign up. Just go to Brilliant.org/Veritasium. I will put that link down in the description. So, I wanna thank Brilliant for supporting Veritasium, and I wanna thank you for watching.