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
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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.


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This is absolutely a masterpiece. Thank you Chris for having shared your unique knowledge and your unique life journey.

The only way to learn is to learn from the best

This is my first master class. I am going to follow and learn from other teachers as well. But I am pretty sure Chris would be the best among all.

My favorite class to date. Inspirational, educational, and thought provoking. Chris Hadfield is super impressive!


Ian M.

As a parent, and with my kids in mind, this kind of explanation - this kind of MasterClass - is exactly what our youth need so they'll find STEM-related classes exciting, provoking, and call their name towards a career in these fields. I HATE math and yet I was captivated by the interrelationships of these variables and how they impact outcomes. Math and Science are cool! (that's from a marketing guy). Great job!

Yuri K.

Very good and simple explanation. May be it is necessary to add, that we can't go to a high altitude (where Rho is small) on very low speed - the beast named Gravity Drag will eat all our gas (fuel+oxidizer). That means. unfortunatelly, we cannot go too slow into a space through the atmosphere to lessen the Aerodynamic drag, because we will burn our gas just to keep the rocket not falling back to Earth. Merely keeping the whole weight of the Space Shuttle stack (some 2,000,000 kg / 4,500,000 lb) quite a lot of the side boosters (SRBs).

David B.

I’m having trouble downloading the PDFs. I keep getting this message AccessDeniedRequest has expired36002019-05-02T17:28:03Z2019-05-02T17:41:24ZFC5DF9673A69A655mbv4lBpebaoFaws5QsfF+ZjG1oopqM4hhoiiAq+BAcFvuo/Ex1S9btYm0UYyxRcSPv1LFqMMip4=

A fellow student

I'm having an issue opening the link at the bottom in the "Learn More" section. When I click on the link, the browser throws a "too many redirects error".

A fellow student

I like this class, cos this is the first class where I see any maths equation. Also, for sum reason I'm not able to download pdf version of all lessons I have already had. I have an error "Request has expired". ???? I payed my money and I hope I have something else rather than several videos with only one maths equation so far.

john K.

Doesn't the effect of gravity figure into the drag effect. Is it de minims in relation to the other forces?

Jim S.

I liked how he took one equation and could teach so much from it. It reminded me of when I was a starting graduate student too. I had an assistantship on an x-ray rocket experiment. The rockets were launched from White Sands and we had to know when we could open up the experiment to the sky. It was covered in mylar. If it opened too soon, it would burst. It was my first task and it was all about this equation too.

Sandra Solis

I was just speechless, with that strange feeling of when I was little, and something impressed me so much that I could not articulate a word, because the words collided with each other, and it took me time to assimilate it, Chris you are the most exemplary teacher to show someone something of which I never imagined could be real. "And you have to understand this, as if it was the alphabet," this equation. wow, it's too much, it's going from your hand walking, step by step, smiling excited from when you start to where you want to go, with that smile, almost childish, like when everything was really amazing, I was never a maths fan but finally life part of that, right? and maybe I never had the knowledge of it so close. Thank you.


It's all about the shape. This is just a constant wealth of information. There's something incredibly exciting about learning all of this. I love the stories. I could listen to them for hours. This is going to a long night because I can't stop watching this.

John H.

I definitely learned some new things about why launch trajectories are shaped the way they are.