About This Episode
How is energy different from matter? Neil deGrasse Tyson and comedian Chuck Nice break down what energy is and where it comes from, ancient theories about sight, and how wheels keep us moving. Explore physics, thermodynamics, and more!
What is energy? How did the idea of energy come to be? Learn about how early scientists thought about energy, kinetic versus potential energy, and how energy gets released. We discuss energy in food, fuel, bombs, and the sun. It is energy that built civilization, but will it also destroy it?
How did Greek mythology influence the stars? We explore the myth of Medusa and what it shows about ancient theories about sight. Learn about discovering the mechanism of sight in the golden age of Islam. Are there other examples of misconceptions about sight in mythology? We explore the constellation of Perseus, the head of Medusa, and the variable star that is her eye.
What part of a moving train is going backward while the train is going forwards? We delve into the physics of wheels and how they move us. Did you know that when you’re driving there is a part of your car that’s going 0 mph? Find out the physics that’s happening in your wheels. What part of the car is going twice the speed? Learn how the wheels of trains and different wheel shapes. Is there only one usable shape for a wheel?
Thanks to our Patrons Matt Smith, Matthew Tolbert, benjamin flanders, Nick Davis, Joseph, and Hemant Sudiwala for supporting us this week.
NOTE: StarTalk+ Patrons can watch or listen to this entire episode commercial-free.
Transcript
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Muchas gracias, you say.
Siempre de nada, I say.
What are you doing?
Chuck is smoking something.
I’m just saying.
I’m ready to talk about this all day.
Chuck is smoking.
But wait, there’s more.
Welcome to StarTalk, your place in the universe where science and pop culture collide.
StarTalk begins right now.
This is StarTalk, Things You Thought You Knew Edition.
So I was just thinking how much we take for granted about when we use the word energy.
And it has profound origins.
I mean, our understanding of energy has profound origins.
The brilliance of Isaac Newton, who discovered the laws of optics and gravity and motion and invented calculus, energy was not a fully developed concept in his time.
And so I just want to sort of spend a few minutes offering an appreciation or a triumph of the human intellect to figure out what the hell energy is and then how to manufacture it and exploit it.
I just want to spend a few minutes.
This is like a public service announcement for energy out there.
So energy is not a thing, right?
You can say a rock is a thing and you can point to it, or a planet is a thing, and energy is not a thing.
So it was delayed in our ability to understand what it was and how to think about it.
So we knew some things.
For example, when you had a cannon, back when cannons were like a popular tool in warfare, there were physicists at the time who said, hmm, I have a cannon ball and I have this gunpowder, and the cannon has made of iron, then I fire it.
And if I keep doing this, the cannon gets hotter and hotter.
But where’s that heat coming from?
So what is it?
And so in the urge to turn energy into a thing, early ideas was that there was energy was a fluid, was a thing.
That could move in and out of objects.
One of them they called it logiston.
Another one was caloric.
These were words invented to try to think about energy as a thing.
And it moves and it’s got to be somewhere.
And so a hot cannon had more of this in it than a cold cannon.
And so you had to start somewhere.
We were crawling before we even could walk.
And it wasn’t until we understood molecules and atoms and that we were able to say, and what role friction plays in this, we were able to say, hmm, so you can store energy in different ways.
And when you store it, it’s not manifesting itself.
It’s not saying, here I am, look, it’s not really doing that.
And when you’re storing it, no, the object is not in motion, no, the object is not, you know, is not all these things that it is when it’s manifesting.
So let’s take the simplest case, a roller coaster.
Right.
Every roller coaster, the first ascent is the highest.
Yeah.
So what’s going on?
So there you go, and you’re leaning back, and this thing cranks you up.
It is endowing you with energy, potential energy, stored energy, potential gravitational energy.
When you get to the top, you can calculate, because we have formulas for this, calculate how much gravitational energy it handed you.
So I don’t feel this energy.
I don’t know what you’re talking about.
Until I push you over that ledge, over the other side of that hill.
Then what happens is your potential energy starts converting to kinetic energy.
And it’s an exact trade-off.
An exact trade-off.
So all that energy they gave you at the top, now is returned with you speeding up as you descend.
And that is when the ham sandwich becomes actual vomit.
Okay, that’s a transformation of another kind, right?
So, and it’s this trade-off.
And it goes back and forth as you go up hills and down.
If you go up a shorter hill than the first one, okay, you have enough energy to reach the top of that hill.
Because you started out with way more energy than that at an even higher hill.
You’re going to lose some energy to friction, okay?
So, in other words, you can’t ascend back to a hill exactly the same height that you started in, okay?
Some energy will go to friction.
And when you lose energy to friction, that makes heat, okay?
That’s the source of heat when you lose energy.
All right, so that’s why the engine of your car gets hot, okay?
Not all the energy that you started with got transferred to the motion of the car.
The losses went to friction, the friction heated your engine, your engine gets hot, okay?
So in a roller coaster, you’re converting gravitational potential energy to kinetic energy and back and forth and back and forth and back and forth.
And if they designed it right, the frictional energy that you lose, okay, you don’t go up higher and higher.
The hills you go over have to get lower and lower.
And there’s the last one, then you come in for the stop.
Right.
So they gave you the energy when you started at the top of that hill.
So that’s gravitational potential energy becoming kinetic energy.
That’s what’s going on there.
And like I said, if you go back up a shorter hill, you’ll slow down.
Because some of that kinetic energy is giving back to you so you can have another little lump of potential energy to take the next hill that comes after that.
All right, so that’s easy.
We’ve had roller coasters forever.
You could have imagined them forever ago.
But it’s more complicated, or a little more physics involved, if you want to say this molecule has energy.
A molecule?
Well, how am I going to get the energy out of the molecule?
Just sit in there.
Oh, well, you can in one case burn it.
Burn the molecule, okay?
Why is it that you can throw a log in the fire and the log is room temperature, you put in the fire, then the fire ignites the log and the log keeps burning?
There’s chemical potential energy in the molecules of the log.
Where did that energy come from?
Where did the log get that energy, Chuck?
You tell me right now.
The log is from its molecules.
It was storing…
Where did its molecules get their energy?
Okay, let me think about this.
Oh, from their atoms?
What did the log used to be?
No, it used to be a tree.
A tree?
How does a tree get energy?
From the sun.
Thank you.
Thank you.
The sun builds molecules that contain stored energy.
So that’s why wood burns.
Because it has stored chemical energy given to it by the sun.
Look at that.
And it’s just sitting there, minding its own business.
But that’s why fires in homes are so deadly.
Because there’s all this potential energy stored in the molecules of organic matter, wood, if your house is made of wood, so that the whole thing burns, converting the chemical energy into thermal energy.
So much of our lives is the conversion of energy of one form into another.
And what happens while that’s going on?
So other forms of energy.
There’s energy in the nucleus of an atom.
You split the nucleus and take it out.
We make bombs doing that.
So we turn nuclear energy into the kinetic energy of an explosion to do damage to things in warfare.
That’s nuclear.
Or chemical energy.
Some chemicals will give you their energy not slowly, like a slowly burning log, they’ll give it to you catastrophically.
And we call those bombs.
Or a firecracker.
Catastrophically.
The energy goes to break apart the firecracker, goes into the sound that it makes, the shockwave, all of that.
So our lives and everything we do is nothing but a ballet of the conversion of energy from one form into another.
So when we consume food that has calories, a one-for-one definition of calorie is energy.
So you eat food that has…
You look at the calorie content.
That’s how much energy it has.
So then you consume it.
You need energy to live, to move, your heart beats.
All this requires energy.
You’re getting it from the calories of the food you eat.
So what happens if you consume more calories than you need?
Your body says, store that.
So it creates chemical potential energy in the form of fat.
And it stores it away.
I’m not fat.
I’m just filled with potential.
What are you talking about?
You see this?
This is potential.
I am potentially Michael B.
Jordan.
I am potentially Michael B.
Jordan.
That’s the potential.
My six pack is just beneath the potential.
It’s just beneath the potential.
You don’t even know what you can have.
And by the way, that conversion of your body’s calories to your energy is not perfectly efficient.
So what happens to that excess energy that’s not converted?
That’s the inefficiency of your body.
We are an engine of sorts.
It’s inefficient.
So that inefficiency gets converted to heat.
So your body heats up when you exercise.
It’s a consequence of the inefficiency of your body.
But your body loves that because now it’s part of your temperature regulating system.
But I’m just saying, when you exercise, your body heats up.
In the same way you drive a car, the car heats up.
In the same way the wheels and the tracks of a roller coaster are actually getting hot because of the inefficiencies of the conversion, because there’s inefficiencies in every conversion of energy from one form to another.
So the only point of this is just to say, so much of what we do and how we live involves the clever conversion of energy from one form to another.
Nuclear energy, chemical energy, which is molecular.
We have kinetic energy, gravitational energy.
All of this comes together, and our ability to exploit that in the service of civilization is one of the great triumphs of physics, especially 19th century physics, where they figured out, oh my gosh, look what we can do.
Another quick one, just look at a locomotive.
What’s going on there?
Well, the locomotive, I don’t know if you remember, they have to fill up from water tanks every now and then.
Well, what does the water do?
Well, a locomotive burns either coal or wood, and it heats a…
So that’s the chemical energy.
It heats a vat of water, so it gets the stored chemical energy of the wood into the active thermal energy of the vibrating water molecules.
They then evaporate, creating pressure for the steam to then move wheels to have the locomotive go forward.
Oh, my gosh.
And that all started with solar energy that made the wood or the coal, that made the fire, that made the boiling water, that made the pressure, that moved the wheels.
All of this is a triumph of our understanding of energy.
Now, what you just said there, I can hear Exxon going, listen, guys, we’re actually solar energy.
We got…
Ultimately, guys, this is solar energy, okay?
fossil fuels started as solar energy.
This is true.
This is true.
It reminds me of this bumper sticker.
It says, no nukes, right?
From the anti-nuke movement.
And then the O in the no is an image of the sun.
It says no nukes.
I know what they mean.
They want you to do solar energy, but the sun makes its energy with nukes.
Just make that clear here.
That’s how it started that way.
So anyhow, I just thought I’d put all that out there.
And just to enhance our appreciation for what energy does for us and how being clever has enabled us to build civilization on the exploitation of converting energy from one form into another.
Yeah, it has built civilization, and ultimately it will destroy.
On that happy note!
Chuck, thank you!
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I’m Joel Cherico and I make pottery.
You can see my pottery on my website cosmicmugs.com.
Cosmic Mugs, art that lets you taste the universe every day.
And I support StarTalk on Patreon.
This is StarTalk with Neil deGrasse Tyson.
Thanks for watching.
I don’t want to see her, nor that.
If she ever said to me, look here, I’m like, no.
Not looking.
No, I’m not looking.
She may look here.
Yeah, she makes eye contact with you, you turn to stone.
She’s famously in the night sky.
She’s immortalized.
The severed head of Medusa is immortalized, held by the Perseus.
Perseus is a constellation in the sky.
And there’s a star called Algol, which is a variable star.
It changes its brightness over relatively short periods of time.
That’s why we call them variable stars.
And the eye of the severed head is Algol.
So this is Medusa, like, looking at you.
It’s pretty fun.
And of course, Perseus was the hero in the story with Andromeda, who is the daughter of Cassiopeia.
And she was, I don’t remember why, oh, Cassiopeia said she was more beautiful than the sea nymphs.
And then out of punishment, they took her daughter and strapped her to the cliffs for the sea monster.
Perseus comes to save her.
He has to slay Medusa, all right?
And so he does it by looking at her, but through the reflection of his shield, okay?
And that way it’s not a direct sight line.
I can’t believe she fell for that.
And backs up to it and slays her backwards, right?
That was pretty cool.
And it cuts off her head and puts it in a sack.
Perseus is in the sky, rides on the back to go save Andromeda by showing the severed head of Medusa to the Kraken.
And the Kraken turns to stone and then crumbles away because he’s too big to be stone, right?
I gotta say, that’s a big chance that Perseus took that the severed head would still be able to do its thing.
Good guess.
Yeah, rather than just with closed eyelids, right?
You have to pry open the eyelids with toothpicks.
Exactly, because, you know, a lot of times, you know, he had to make sure she died with her eyes open, probably from the surprise, the surprise of falling for that stupid trick of looking at her through a shield.
So she died with her eyes like, I can’t believe that I fell for this.
Like…
Is that what she sounds like?
That’s Medusa.
I can’t believe I fell for this stupid trick.
Okay, so all of them are in the night sky.
We got Medromeda, Medusa, Cassiopeia.
The reason why I’m saying all this is there’s a whole set of legends that derive from the expectation that when you look at someone or anything that you’re sending out some beam of energy or information or light, as though seeing was an active aspect of what it is to obtain information.
Right.
So I see you because I’m going out there and I’m getting you and bringing you back in to my head.
Right.
Right.
So that is not how seeing works.
And this was not established until about 1300 years ago in the Middle East, in what we call the Golden Age of Islam, Alhazen, occasionally referred to as Alhazen, both of those I think are legitimate names for him, one of the great scientists of the era, an early scientist in the history of scientists, kept good notes, had hypotheses of how things worked.
He looked at a cow eyeball, saw a lens, saw that you can make an image on the back of the eyeball, and he deduced that the act of sight is 100% passive.
All reception.
All reception.
So you can’t just give someone the Google eyes and have them say, oh, I feel someone’s looking at me.
People will still say that.
But all experiments show that, no, you cannot tell if you do it in a controlled setting.
You cannot tell when someone’s looking at you, okay?
Unless you’re in the subway.
Because sometimes you’re in the subway and you just get that feeling that comes up the back of your neck and you turn and there is some creepy person staring at you.
And they don’t turn away.
They will not.
That’s how you know you’re in New York.
Any other place, you look at somebody and they look away like, oh, shoot, I was staring at them.
They look sheepish about having been caught.
Yeah, well, I can’t believe I was staring.
In New York, you turn at them and they’re just like, that’s right, I’m going to kill you.
Don’t scare people from the New York City subways.
That’s not what…
Here’s my point.
Anytime you turn around because you think someone’s staring at you and they are staring at you, you have not recorded the thousands of times people were also staring at you and you didn’t turn around to notice.
This is when you do the control setting, this is the case.
It’s just an interesting fact.
The Bible story is about, who was it that turned back and she became a pillar of salt?
Lot’s wife.
She observed the destruction of Sodom and they were told, whatever you do, do not look back.
And so she violated the directive, looked back at the destruction and turned to stone in doing so.
Okay.
So that case, that might not be her sending out a signal from her eyeball.
So that sounds like a more legit consequence of this relative to Medusa looking at you, her eyes light up and then you turn to stone.
So it’s an interesting history how there can be mythologies that rise up around physiological misconceptions that make for interesting stories.
And people used to be thought of as dying of a broken heart, all right?
Maybe it was an actual heart attack, all right?
But then, you know, there…
It was bacon.
It was bacon.
But Francis Bacon?
Or bacon?
No, it was just bacon.
The bacon-y.
That’s just like he died of a broken heart.
No, no, that’s called cholesterol.
That’s called cholesterol.
The man had bacon with every single meal.
And you know, you can’t do it.
You don’t want to take away the romance of dying of a broken heart.
That’s all.
No.
So it’s just fun.
So I don’t object to misconceptions if you have no better explanation at the time.
And it becomes part of a sort of our cultural sense of the world.
This is the richness and the depth of history that we experience as a culture.
Who knows what they’ll be saying about…
You know, here’s the problem with that, though.
Someone of your particular acuity can say that.
Can say, this is part of the wondrous romance of life.
Charming elements of our past.
The charming elements of life that we’re able…
Because you’re a person who understands the scientific method.
You’re somebody who believes in data and empiricism, both, okay?
But the problem with that, that charming, that wonder, that these idiosyncratic things that happen, that we attribute meaning to them, you know that we’re attributing that meaning.
We are affixing meaning to those things.
They don’t really have meaning.
The problem is, there are a bunch of dumbasses who actually believe, they believe this.
There’s no excuse, once we’ve learned how all this works, there’s no excuse to continue to think it’s true.
And that’s what you’re talking about.
The people who are delayed in their acceptance of objective realities.
And I’m with you there.
But I’m not going to judge people from long ago on today’s standards.
I’m going to say…
No, no.
You got me.
I got to give it to you there.
They’re perfectly acceptable.
They had no other information.
So therefore, boom, I get it.
Exactly.
And right on down to those who imagine that someone had an epileptic seizure were being invaded by the devil.
And so you go get the priest and they do the holy water.
And then they come out of these symptoms.
The seizure is over.
The 20-minute seizure ends.
It just ended because how far away is the church?
500 years ago.
It’s like two blocks away.
Just in time for the priest to get there.
So we’re trying to make sense of the world.
And so I don’t, you know, I’m okay with that.
It’s so funny you use that as an example because I think it’s a great example because we can actually see the brain now.
We can see the activity of the brain and exactly what is happening in the brain that causes this epileptic fit.
So we’re not seeing the devil.
What we’re seeing is a neurosynaptic breakdown or malfunction.
And so, you know, where did the devil go?
If you want to still believe that.
Fine, in the face of science, just don’t lead any science agencies that allocate research funding.
We’re going to play a job for you in a society.
Yes.
I got a fast one for you.
Alrighty.
This one is going to be about wheels.
Okay, I’m going to say, I’ll say a bit pedestrian for you.
So, did you know that if you’re driving down the road, pick a speed, 60 miles an hour.
Okay, whatever, sorry.
You got to bump that up by about 25 miles.
And now we’re talking.
At whatever speed you’re going, there is a part of your car that is going forward at zero miles per hour.
At all times.
All right, this already got interesting.
Because I have no idea what you’re talking about right now.
There’s another part of your car that’s going forward at twice that speed.
At every moment.
All right.
Okay, you ready?
Okay, are you seated?
Okay, here we go.
It’s all happening in your wheels.
So, the part of the wheel at any moment…
Contact with the pavement is not moving at all.
That’s right.
No, if your car were skidding, then the part of the wheel in contact with the road would be moving forward.
At the rate you’re skidding forward.
But that’s why you’re moving forward!
It’s why you’re moving forward.
It’s why you’re moving forward!
Because part of the wheel is not moving at all.
Because if it were, you’d be spinning in place!
You’d be spinning in place.
Correct!
By the way, okay.
Now, you know what, man?
You did it again!
I’m just saying.
First of all, this is what I’m going to do right now.
I’m going to publicly apologize to you for all that shit I was thinking.
Before I began.
Let me tell you something.
I was thinking some stuff.
I’m going to apologize to you right now.
Because you were like, alright, Chuck.
We’re going to talk about wheels.
I’m like, this brother-in-law’s his damn mind.
We’re going to talk about wheels.
Seriously.
But you didn’t.
Go ahead.
Let’s go for it.
Let’s keep going.
The center of the wheel which is…
Okay, it’s spinning.
But the exact center is going forward at the same speed the car is.
Absolutely.
The top of the wheel is going forward at twice the speed of the car.
Twice the speed of the car.
At twice the speed.
Because notice, if the chassis of the car is moving at the speed of the car, obviously, the top of the wheel is moving faster than the chassis.
It’s moving past the top of the wheel well.
The wheel well, the top of the wheel well, is going forward at your speed, at your speedometer speed.
The top of the wheel is going faster than that to come around to the bottom so that it’s not moving at all.
That’s…
If you run the math on that, you get zero at the bottom, the speed of the car in the middle of the wheel, and twice the speed of the car at the top of the wheel.
And so this is the geometry, the math and the physics of an axeled wheel on any moving vehicle.
What are you doing?
Chuck is smoking something.
I’m just saying.
I’m ready to talk about this all day.
Chuck is smoking.
But wait, there’s more.
That’s awesome.
That is awesome.
But wait, there’s more.
Because I’m picturing a dot on the wheel and a dot at the chassis.
And then it comes up.
It has to go faster than the top.
Faster.
It has to go faster.
Than the top of the wheel well.
So it can come around.
Correct.
Now think of the wheel that’s on a train.
Okay?
The train wheels are different, right?
They’re different from car wheels, obviously.
So there’s the metal flat part that touches the metal rails.
But then there’s another part that’s like an outer…
Outer…
Where should I use that?
It’s like a coupler.
There’s an outer part that extends outside of the track.
Right.
Can you picture this?
It’s not just rolling on a track.
It’s like a lip.
Like a lip on the wheel itself.
It’s a lip that extends outside of the track, which enables the train to stay on the track.
Otherwise it will just drive off, right?
So these lips that are exterior to the wheels keep the train aligned on the track.
Right.
But here’s what’s interesting.
They dip below the contact point of the wheel and the rail.
Correct.
By a little bit.
But whatever it is, they dip below.
Alright.
Well, if the top of your wheel is going twice the speed, the center of the wheel is going the speed, the bottom of the wheel is going zero, anything lower than the bottom of the wheel is moving backwards.
That’s right.
Going in reverse.
It’s going reverse.
So for any train, there are parts of that train that are moving backwards on the track at all times.
That’s pretty wild.
Just picture that.
There’s the wheel rolling.
The part that’s below the contact point is moving backwards.
It actually lands in a place behind where it started.
That means it moved backwards.
That’s right.
That’s insane.
So I just thought I’d put that out there.
I know.
It’s nothing deeper than that.
The next time I tie up a woman and put her on the tracks, I’m going to let her know that you’re going to learn something.
Is this what you do, Chuck?
As I twirl my mustache.
Now, here’s something interesting.
Are you ready?
So that means there’s a part of your car that’s going at all speeds from zero up to twice the speed of the car.
Correct?
That’s right.
So imagine this.
Imagine attaching some device to your wheel that sends out a microwave signal and you can adjust it up or down.
From the center of the wheel to the outer rim.
Or from the center of the wheel to the bottom.
Sends out a microwave signal that will report a speed of your car at any speed you choose.
So, the police officer is there with the radar gun with the return signal that’s going 30 miles an hour even though you’re going 60.
Yes, so they’ll get the reflected signal off of your car, right?
But if you can override that with a more powerful signal sent from your wheels, you can broadcast any speed you choose down to zero.
If it’s attached to the wheel.
Right, which is the…
That’s the speed I’m choosing, by the way.
Well, you can’t do zero because they know you’re lying.
Well, that’s…
Any place between the center of the wheel and the bottom…
Bottom of the wheel.
You can broadcast a speed of that spinning wheel at any speed less than your actual driving speed.
But to configure this would be really weird and how to make that happen because it has to be moving with the tire.
I don’t know how you would design the engineering of that, but it’s just something to think about because there’s always a part of your car that’s going everywhere from the speed of your car down to zero and up to twice the speed of the car.
Well, maybe, you know, when the cop pulls you over, you can just tell him, I don’t know what speed you recorded, but I don’t know.
You should have been looking at the bottom of my wheels.
Yeah, that will work in court.
So that’s all I have to say about wheels.
That was pretty damn good.
I mean, sorry, pardon my language.
That was pretty doggone good.
Completely surprised.
Taken aback by this one.
Yeah, and there’s another kind of wheel, which is the shape of the object that rotates within a winkle engine.
So if you imagine an equilateral triangle, but curve the corners of it and make the sides a little bit convex, right?
I had a Mazda once.
Oh, you did?
Was it with a winkle engine?
So that shape, interestingly, the distance from the bottom to the top remains the same no matter how it’s oriented.
So if you roll it along the…
I made one of these shapes.
In fact, I don’t have one with me here.
We might have to do another explainer.
We used to call them spirographs when I was a kid.
Okay, yeah, so they’re related.
They’re related, right?
They’re related geometry to it.
So if you take a plank and place it on top of one of these triangular shapes and roll it, the plank will be absolutely steady, even though it looks like the thing is bobbing up and down.
It’s because there’s no central axle to it.
Right.
Okay, we think a wheel that gives you a smooth ride needs one central axle because a wheel is the same distance to each point on the rim.
You can design a shape where the top is always the same distance from the bottom, even though the center is moving in your Spirographian sort of way.
So I actually built one of these when I was a kid in Woodshop in seventh grade, and I don’t think it’s with me here.
That is why.
It’s in a closet somewhere.
I’m going to have to dig it up, and we’ll do another one.
Just fun things to do with a Wankel engine.
Nice.
Yeah, it’s an unfortunate name, but yeah.
I know, right?
It’s a little weird.
It is a little weird.
But it’s one of the many engines that have been developed over the years to convert chemical energy into kinetic energy.
So maybe we’ll do it.
I know.
We’ll do an explainer just on engines and the history of engines.
Why they differ from each other and where they’re headed.
That’s a good one.
That is a good one.
Now you know that part of your car ain’t moving at all.
But don’t use that as the excuse when you get pulled over.
That’s it.
That’s it.
Or don’t experiment with how the cop will react if you give that as an excuse.
Right.
You don’t want to experiment.
We got to call it quits there on StarTalks, Things You Thought You Knew Edition.
Chuck, always good to have you.
I’m Neil deGrasse Tyson, your personal astrophysicist.
As always, I bid you goodbye.


