Chapter 5 of 29 from Chris Hadfield

Rockets: Atmospheric Drag


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

Topics include: Atmospheric Drag

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

Topics include: Atmospheric Drag

Chris Hadfield

Chris Hadfield Teaches Space Exploration

In 28+ lessons, the former commander of the International Space Station teaches you the science of space exploration and what the future holds.

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Explore the unknown

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.

Learn about the past, present, and future of space exploration with astronaut Chris Hadfield.

Download the workbook for lesson recaps, assignments, and photocopies of handwritten notes that Chris took to space.

Upload videos to get feedback from the class. Chris will also answer select student questions.


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

Beautifully well done. Brought many insights into how challenging and courageous it is to be an astronaut.

that achieving impossible goals and dreams is actually not that impossible

Perfect ....lessons from the master. thank you so much.

Chris not only has the plethora of knowledge of being an astronaut but he is able to describe and explain his wonderful experiences in a fascinating way. The main lesson I will take from this class is Chris' advice about taking satisfaction from the journey leading to your dreams and not just the enjoyment you gain from achieving the goals themselves.


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.


So, now we get to the heart of things: Mathematics, the language of physics. It is wonderful to hear how the math actually works to explain the physical world. I'm hoping there's much more!

Jaden P.

I love hearing about the physics and math behind launching rockets into space. Super interesting!

Pedro C.

There must be a few methods to determine the drag coefficient for a particular vessel. It would be interesting to study them, whether mathematic methods and/or experimental methods. On the other hand, there must be some standart drag coeficients for a set of basic rocket designs. It would be useful to get them, perhaps a table.

Rob G.

"And there are thousands of those equations..." -- This was a fantastic mini-lecture. I'd love to hear another equation (or three!) being discussed this way by Chris. So informative!

Justin S.

I always wondered why the lunar modules looked so unsightly compared to the elegance of a typical rocket. Now I understand - no drag in space!


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...