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Science & Technology

Rockets: Atmospheric Drag

Chris Hadfield

Lesson time 6:41 min

Chris breaks down the equation for drag and shows how rockets are designed to overcome the biggest hurdle of launching into space—the atmosphere.

Chris Hadfield
Teaches Space Exploration
The former commander of the International Space Station teaches you the science of space exploration and what the future holds.
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The essence of you being an astronaut is the ability to leave Earth, the ability to fly a rocket through our atmosphere and get into orbit or beyond. But flying a rocket through the atmosphere is the hardest part. It's the most dangerous part of a space flight. And the reason is because of the equation for drag, unfortunately, which is 1/2 rho v squared S-- 1/2 rho v squared S. It sounds maybe complicated or it maybe sounds deceptively simple, but to push yourself through the atmosphere-- because to stay in orbit, you have to be going 5 miles a second, 8 kilometers a second, 17 and 1/2 thousand miles an hour, 25 times the speed of sound. That's how fast you have to go to orbit the world. Those speeds are incredible. How do you get through the atmosphere and accelerate out fast enough that you can successfully stay coasting in orbit from then on? And the main impediment to doing that is to shoulder your way through the drag of the atmosphere. When you're driving a car down the highway, I'm sure at some point in your life you've stuck your hand out the window, maybe when you were a kid in the backseat, and you stuck your hand out the window. And if you're going slowly, it's kind of fun. You can feel the air. You can fly your hand. But if the car gets going faster, it becomes pretty hard just to stick your hand out there. And if you stick your hand out at highway speed, you know, your hand will get whipped right back. If you're on board a spaceship coming through the atmosphere, you stick your hand out the window, it's going to break your arm and burn your arm off. That's how much drag there is at that high speed. And it's because of the equation 1/2 rho v squared S. So let's just think about that. The 1/2 we can sort of ignore. That's just to make the math right. But rho is an ancient alphabet symbol for density. How thick is the air? Down here, close to the ocean with all the air up above me, the air is pretty thick. The higher you get, the thinner the air gets. So as you go up, rho, density, gets less. S-- rho v squared S-- S is just a matter of area, like inches by inches or meters by meters. It's really how big is your ship. What type of blunt object-- you know, if you measured my hand, you know, it's got this width by this height. That would give you the area, which would be S. The S of my hand is whatever that is, 4 inches by 3 inches, 12, we'll say, square inches. That's the S of my hand pushing through the atmosphere. If I could make by hand like this, it'll go through the atmosphere a lot easier because the S is a lot smaller. If my hand is the size of a house, it's going to be really hard to push through the atmosphere. So it helps you think about what you're trying to do with your rocket ship, that rho, the density, is getting less as you go up. And S, the size of your ship, is a really big, important factor, the cross-sectional size. But v squared, that's the big surprising part. v is just your velocity or your spe...

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Impossible things happen. At age nine, Chris Hadfield knew he wanted to go to space. He eventually went there three times, becoming a commander of the International Space Station. In his MasterClass, Chris teaches you what it takes to explore space and what the future holds for humans in the final frontier. Learn about the science of space travel, life as an astronaut, and how flying in space will forever change the way you think about living on Earth.


Students give MasterClass an average rating of 4.7 out of 5 stars.

Incredible! Amazing! Life changing Master Class. Thank you Chris

Through this class, I have learned what it takes to be an Astronaut, and seeing someone who had the same dream making. This has given me a whole new light on things in my life and my future. I am glad I finally took this class

Chis Hadfield is a hero and this masterclass is his gift to all of us. Thank you.

very intresting how he goes int detail about every little thing and he is very inticing


Bernardo F.

Didn't know this equation, but it's beautiful how it works and how astronauts have used it in their advantage. I hope you to explain the rocket equation as well.

Jos J.

So, does it matter which measurement system you are using for S? And if so, which should I be using? Thanks in advance!

Janice G.

I start the morning watching these clips. What a shot of adrenaline. And this lesson strikes me as a perfect metaphor for the challenge of writing--moving into the creative realm and the flow requires shouldering your way through a terrific 'atmospheric drag' until you come out on the other side, and then you're timeless and weightless. So cool, Mr. Hadfield. Thanks so much.

Mário Filipe P.

Great explanation of one of the million things engineers have to take into consideration when building a rocket ship, and the challenge it presents from the moment you launch until you get to orbit. I will forever remember your words that the atmosphere would "break your arm, and burn your arm off" every time I put my arm out of the window of my car now!

A fellow student

I think that for simplicity the drag coefficient was taken out of the equation (coefficient that depends on geometry). Nonetheless, a very precise explanation. Thank's Chris!


It's crazy how Chris boils it down to something the average person could understand.

Mary R.

Brilliant! Making a complicated explanation so clear and fascinating to follow.

Bob C.

My first Masterclass. My first segment. The best piece of story-telling I have ever witnessed. Worth the price of admission. They can't all be this good, surely. Thank you. I have now travelled to space.

Maddie W.

I love this video because it explains mathematical concepts in a way that is interesting and accessible to everyone. It really illustrates the relationship between math and science and how that translates into real scenarios like rocket launches. This is exactly the kind of education we need to inspire interest in STEM careers.

Duarte G.

Just a doubt The S, area, on the equation is the part of the ship that you see when you look it from the top, right? If that's correct why does it has to be pointy why not just the same area, but flat?