For those of us programming nerds that want to play with aerodynamics, I can't recommend AeroSandbox enough. While the code is pretty obviously written for people who know their way around aerodynamics and not so much around programming, it is remarkably powerful. You can do all sorts of aerodynamic simulations and is coupled with optimization libraries that allow you to do incredible aerodynamic optimizations. It comes included with some pretty powerful open weight neural network models that can do very accurate estimates of aerodynamic characteristics of airfoils in a fraction of the time that top tier heuristic solvers (like xfoil) can do (which are already several orders of magnitude faster than CFD solvers).
Ok that's long, one top line thing people tend to miss in these flying explanations is that airfoil shape isn't about some special sauce generating lift. A flat plate generates any amount of lift you want just fine. Airfoil design is about the ratio of lift to drag most importantly and then several more complex effects but NOT just generating lift. (stall speed, performance near and above the speed of sound, laminar/turbulent flow in different situations, what you can fit inside the wing, etc)
You can't escape momentum exchange. To generate an upward force, the airplane must exert a downward force on the air molecules.
An airfoil does this more efficiently than a flat plate, essentially using the top shape to create a low pressure area that sucks the air over the top downwards, imparting the downwards momentum, along with deflecting the air downward on the bottom surface. A flat plate pitched upwards "stalls" the air on the top surface, because the air has to travel forward some to fill the gap by the plate moving forward - so this creates a lot of drag as the plate is imparting more forward momentum on the air.
The issue is that to analyze lift using momentum, you have to do statisitcal math on a grid of space around the airfoil, which is super complex. So instead, we use concept of pressure with static and dynamic pressure differences creating lift, because it makes sense to most people learning this, which then all gets rolled up into a plot of lift coefficient vs angle of attack.
And as you dive deeper, you learn more analysis tools. For example, there is also another way to analyze performance of an airfoil more accurately, which is called vorticity. If you subtract the average velocity of the airflow around an airfoil, the vector field becomes a circle. In vector math, the total curl of the vector field is directly correlated to the effective lift an airfoil can produce. This method accounts for any shape of the airfoil.
Exactly. Airfoil is an optimization. There is a common misconception that planes wouldn't get off the ground if you didn't have airfoil. No, most of the lift (depends on the plane but in the ballpark of 80-90%) comes from the overall shape of the wings. ~20% is from leading edge airfoil deflection dynamics.
And if, say, airfoil was never discovered, we'd probably design the whole wing slightly differently to compensate for it, so the actual difference wouldn't even be 20%.
Airfoil is about as important as winglets, and planes fly without winglets just fine. But nobody points to winglets and says that's the crucial bit that makes the whole thing work.
Two ratios dominate aircraft design. Lift/Drag, Thrust/Weight
To get off the ground Lift > Weight, Thrust > Drag, or to simplify to stay aloft Lift = Weight, Thrust = Drag
Bigger engines weigh more.
To get off the ground you need an engine powerful enough to overcome the drag necessary to generate enough lift.
That is what enabled powered flight especially at the beginning. Wing design with a good enough lift to drag ratio and engine+propeller design that had a good enough thrust to drag ratio to come together for more lift than the aircraft weighed.
I was obsessed with fighter jets in my adolescence. My favorite plane was the F-15 Eagle; its thrust:weight ratio was greater than 1 -- meaning it could take off, point its nose straight up to vertical, and keep accelerating past mach 1. Amazing.
It is probably obvious, so obvious that no one starts with it? but it took me an absurdly long time to put together that an airplane lifts by moving air down.
Admittedly there is an amazing amount of fluid-dynamic subtly on top of this simple Newtonian problem. But I am surprised that almost no one starts with "An airplane produces lift by moving air down, for steady flight it needs to move exactly as much air mass down as the plane weighs. here are the engineering structures that are used to do this and some mathematical models used to calculate it"
That was what I was taught 30 years ago in university.
To be more precise, we defined or made a shorthand of this downward force W. Originally it stood for weight but we knew it was the downward force that must be counteracted by an upward force called L for lift. Lift by convention was always an upward force.
I should also remark the laminar fluid boundary layer only is true for subsonic flight. When you go over Mach one, a permanent shock wave forms in front of the wing. This shock wave disrupts the laminar boundary layer. Lift is achieved by Newtonian breakdown of the air hitting the wings underside. This is why supersonic planes require fly by wire. As computers are constantly issuing commands to ailerons and rudder to prevent stall.
Exactly. Any kid who has stuck a flat hand out of the window of a car at speed knows how airplane wings work. You tilt your hand back and the wind pushes it up. Tilt it forward and the wind pushes it down. Everything else is an optimization.
Umm no, at zero degrees AoA as the first diagram on the page shows, a flat plate does not generate lift.
But nobody actually questions that a flat shape can generate lift; we all made paper planes as a kid.
But every airfoil has an equilibrium angle of attack (not always stable with velocity) where it generates zero lift. The chordal angle of attack is for convenience because it depends only on airfoil geometry and not ambient velocity, but it isn't a fundamental physical property of the airfoil.
If we treat the angle where zero lift is generated as the base angle for an airfoil, then all airfoils generate lift depending on their angle relative to that, including a flat plane. As the GP says, other properties are the dominant factor in airfoil geometry.
When introducing airfoils I think it is more useful to start from a plane than a traditional airfoil shape; the math and intuitions are much clearer from there.
And with steady level flight symmetrical airfoils are flown at an angle, a cambered airfoil shape being flown at 0 degrees angle of attack vs its chord line would be an unusual coincidence. Wings are mounted at a small angle relative to the direction of thrust and what one would define as a flat line on the fuselage.
Uncambered airfoils also don't generate lift at zero degrees. What constitutes "0" for curved airfoils is convenience. You want lift, you put a flat plate on an angle, anything fancier is for Lift/Drag, Thrust/Weight, etc.
There are about a million places incorrectly "explaining" that airfoils create lift because the top path is longer and this means the air has to go faster. A flat plate would not create lift in that case. The fact that paper airplanes obviously can fly somehow never stops people from repeating this.
He usually posts these brilliant explanations once or twice a year but nothing in 2025. I hope he finds the time to continue because the lessons are really really brilliantly told.
These are amazing illustrations, but I don't understand the emphasis on pressure differentials. That is not how wings generate lift. Due to attachment they deflect the flow, and the momentum change generates an upward force [1]. The practical point of understanding the flow over the wing is to keep that flow attached so that you can deflect it or reattach it if you get out of sorts.
The explanation you described is the greatly simplified "high school friendly" explanation. It's not wrong, per se, but it's incomplete.
Even your link explains: "The net fluid force is generated by the pressure acting over the entire surface of a closed body. The pressure varies around a body in a moving fluid because it is related to the fluid momentum (mass times velocity). The velocity varies around the body because of the flow deflection described above."
I.e. pressure differential is experienced as lift and is caused by the flow turning.
Explaining the actual cause of the flow turning and resulting lift (and why attachment is maintained along top surface) requires looking at fluid dynamics/navier-stokes including pressure differentials, viscosity etc. The pressure differentials allow a more comprehensive way of breaking down the forces at play.
He should have started his lecture with the chart shown at the 26 minute mark. Saying when we measure the pressures on the airfoil, we see high pressure at the front and bottom of the airfoil. Let me explain what is going on…
I found his explanation at the 13 minute mark to be hand wavy. He talked about flow turning and momentum change but just hand waved away why pressure is higher at the bottom of the wing.
You are correct in that the deflected airflow exerts an upward force on the wing (or at least a force with an upward component; there's also a backward component (called induced drag if my memory serves me well)).
The way the airflow exerts that force is through pressure differentials: air under the wing having higher pressure than the air above it.
Momentum change can describe physical interactions, and it's often easier to calculate things that way, but actual physical forces still exist, and can also be used to describe the same physical interactions.
This is so cool. I've become more interested in aerodynamics since I've started watching F1 and reading Adrian Newey's book. This is such a great post, especially the diagrams in the velocity section.
It’s kind of sad IMO. Bartosz has made a ton of these super interesting and meticulously designed explainers. Something thrown together with AI is much more likely to be made by someone who doesn’t know what they’re talking about, and I’m worried that the sheer volume will crowd out actually quality content like this.
Don't think so, and we should stop spread damaging narrative like this. I'd say it's already able to imitate this kind of explainers(badly) thanks to his training data. All the subtle teaching nuances, effort, know-how and visual creativity that people like Bartosz Ciechanowski put on this kind of work is not reproducible if not statistically imitating it
Good rule of thumb: it should take less time to consume content than it does to create it.
I don’t know how long it takes Ciechanowski to create these explainers, probably a few months? It shows and it’s well worth spending your time reading through his content meticulously.
How long does it take for an LLM to crap out an equivalent explainer? 60 seconds? You should be spending less time than that reading it.
In order to be taken serious I feel like statements like this need to be qualified with who the claimant is imagining to be responsible for generating the anticipated output. The ‘A’ in AI isn’t for ‘autonomous’.
Bartosz Ciechanowski could generate an explainer like this using Claude today if he wanted to. But would he? If someone like him had the mind to do it then they could instead. But where’s it at? These types may hold themselves to a standard above this method. No shame in that.
I think it's actually already there. It's definitely possible to make these sorts of explainers with something like a Claude Code, you just have to spend a fair amount of time making sure that it's actually doing what you expect it to do. I think the biggest danger with something like a Claude Code is that you get something that looks functionally correct but that the details are suddenly wrong on. I wrote a little bit about this on my blog for some of the places that I've done visualizations actually, and I think it's remarkably easy to iterate on them now.
> Someone like Bartosz Ciechanowski is still operating at a level I can't touch. His work reflects years of accumulated craft and a visual intuition that I don't have.
Seems like you’re contradicting yourself a bit here- is it actually possible to make the sort of explainers from TFA, or is the author operating at a level you can’t touch?
It's been said before, but this prediction isn't amazing, imo.
I look forward to Bartosz's articles because they're rock-solid sources of information and the visualizations are both easy-to-understand and surprisingly light on performance. It's all shockingly digestible.
Honestly, as popular science writing goes, this is art as far as I'm concerned, and art is best when it comes from a place of passion and conviction, something AI will never be able to reproduce.
This is absolutely amazing.
For those of us programming nerds that want to play with aerodynamics, I can't recommend AeroSandbox enough. While the code is pretty obviously written for people who know their way around aerodynamics and not so much around programming, it is remarkably powerful. You can do all sorts of aerodynamic simulations and is coupled with optimization libraries that allow you to do incredible aerodynamic optimizations. It comes included with some pretty powerful open weight neural network models that can do very accurate estimates of aerodynamic characteristics of airfoils in a fraction of the time that top tier heuristic solvers (like xfoil) can do (which are already several orders of magnitude faster than CFD solvers).
https://github.com/peterdsharpe/AeroSandbox
Thank you for the kind words! :)
I say it every time it pops up; I’m a huge fan of ciechanow.ski!
They should receive an unlimited grant to produce educational content for the digital generation’s benefit.
Here's how you can help: https://www.patreon.com/ciechanowski
Ok that's long, one top line thing people tend to miss in these flying explanations is that airfoil shape isn't about some special sauce generating lift. A flat plate generates any amount of lift you want just fine. Airfoil design is about the ratio of lift to drag most importantly and then several more complex effects but NOT just generating lift. (stall speed, performance near and above the speed of sound, laminar/turbulent flow in different situations, what you can fit inside the wing, etc)
To be more specific,
You can't escape momentum exchange. To generate an upward force, the airplane must exert a downward force on the air molecules.
An airfoil does this more efficiently than a flat plate, essentially using the top shape to create a low pressure area that sucks the air over the top downwards, imparting the downwards momentum, along with deflecting the air downward on the bottom surface. A flat plate pitched upwards "stalls" the air on the top surface, because the air has to travel forward some to fill the gap by the plate moving forward - so this creates a lot of drag as the plate is imparting more forward momentum on the air.
The issue is that to analyze lift using momentum, you have to do statisitcal math on a grid of space around the airfoil, which is super complex. So instead, we use concept of pressure with static and dynamic pressure differences creating lift, because it makes sense to most people learning this, which then all gets rolled up into a plot of lift coefficient vs angle of attack.
And as you dive deeper, you learn more analysis tools. For example, there is also another way to analyze performance of an airfoil more accurately, which is called vorticity. If you subtract the average velocity of the airflow around an airfoil, the vector field becomes a circle. In vector math, the total curl of the vector field is directly correlated to the effective lift an airfoil can produce. This method accounts for any shape of the airfoil.
But under the hood its all momentum.
Nearly everything you wrote here is inspired by reality and mostly incorrect.
Exactly. Airfoil is an optimization. There is a common misconception that planes wouldn't get off the ground if you didn't have airfoil. No, most of the lift (depends on the plane but in the ballpark of 80-90%) comes from the overall shape of the wings. ~20% is from leading edge airfoil deflection dynamics.
And if, say, airfoil was never discovered, we'd probably design the whole wing slightly differently to compensate for it, so the actual difference wouldn't even be 20%.
Airfoil is about as important as winglets, and planes fly without winglets just fine. But nobody points to winglets and says that's the crucial bit that makes the whole thing work.
Two ratios dominate aircraft design. Lift/Drag, Thrust/Weight
To get off the ground Lift > Weight, Thrust > Drag, or to simplify to stay aloft Lift = Weight, Thrust = Drag
Bigger engines weigh more.
To get off the ground you need an engine powerful enough to overcome the drag necessary to generate enough lift.
That is what enabled powered flight especially at the beginning. Wing design with a good enough lift to drag ratio and engine+propeller design that had a good enough thrust to drag ratio to come together for more lift than the aircraft weighed.
I was obsessed with fighter jets in my adolescence. My favorite plane was the F-15 Eagle; its thrust:weight ratio was greater than 1 -- meaning it could take off, point its nose straight up to vertical, and keep accelerating past mach 1. Amazing.
The F-15C (and the F-16), yes.
The F-15E was a different story, which I remember from flamewars at flightsim forums over how slow of a climber it was :)
It is probably obvious, so obvious that no one starts with it? but it took me an absurdly long time to put together that an airplane lifts by moving air down.
Admittedly there is an amazing amount of fluid-dynamic subtly on top of this simple Newtonian problem. But I am surprised that almost no one starts with "An airplane produces lift by moving air down, for steady flight it needs to move exactly as much air mass down as the plane weighs. here are the engineering structures that are used to do this and some mathematical models used to calculate it"
That was what I was taught 30 years ago in university.
To be more precise, we defined or made a shorthand of this downward force W. Originally it stood for weight but we knew it was the downward force that must be counteracted by an upward force called L for lift. Lift by convention was always an upward force.
These are conventions taught and used.
I should also remark the laminar fluid boundary layer only is true for subsonic flight. When you go over Mach one, a permanent shock wave forms in front of the wing. This shock wave disrupts the laminar boundary layer. Lift is achieved by Newtonian breakdown of the air hitting the wings underside. This is why supersonic planes require fly by wire. As computers are constantly issuing commands to ailerons and rudder to prevent stall.
Exactly. Any kid who has stuck a flat hand out of the window of a car at speed knows how airplane wings work. You tilt your hand back and the wind pushes it up. Tilt it forward and the wind pushes it down. Everything else is an optimization.
Was gonna say where is the debate of bernouli vs. AoA/pforce (p-factor), scatter blast shotgun hitting bottom of wing
There is an interactive simulation on the page with a simple plane showing exactly this.
Umm no, at zero degrees AoA as the first diagram on the page shows, a flat plate does not generate lift. But nobody actually questions that a flat shape can generate lift; we all made paper planes as a kid.
But every airfoil has an equilibrium angle of attack (not always stable with velocity) where it generates zero lift. The chordal angle of attack is for convenience because it depends only on airfoil geometry and not ambient velocity, but it isn't a fundamental physical property of the airfoil.
If we treat the angle where zero lift is generated as the base angle for an airfoil, then all airfoils generate lift depending on their angle relative to that, including a flat plane. As the GP says, other properties are the dominant factor in airfoil geometry.
When introducing airfoils I think it is more useful to start from a plane than a traditional airfoil shape; the math and intuitions are much clearer from there.
And with steady level flight symmetrical airfoils are flown at an angle, a cambered airfoil shape being flown at 0 degrees angle of attack vs its chord line would be an unusual coincidence. Wings are mounted at a small angle relative to the direction of thrust and what one would define as a flat line on the fuselage.
Uncambered airfoils also don't generate lift at zero degrees. What constitutes "0" for curved airfoils is convenience. You want lift, you put a flat plate on an angle, anything fancier is for Lift/Drag, Thrust/Weight, etc.
Paper airplanes do not have barndoor wings, though. Most of them have stepped camber through the way they are folded.
It's not finished but I started writing this to clarify: https://entropicthoughts.com/paper-airplane-aerodynamic-stab...
Scroll down to "trim and angle of attack".
(I hope there's nothing embarrassing in there. It's an old, early draft.)
There are about a million places incorrectly "explaining" that airfoils create lift because the top path is longer and this means the air has to go faster. A flat plate would not create lift in that case. The fact that paper airplanes obviously can fly somehow never stops people from repeating this.
HERE WE GO AGAIN...
https://news.ycombinator.com/item?id=39526057
Thanks! Macroexpanded:
Airfoil - https://news.ycombinator.com/item?id=39526057 - Feb 2024 (296 comments)
He usually posts these brilliant explanations once or twice a year but nothing in 2025. I hope he finds the time to continue because the lessons are really really brilliantly told.
These are amazing illustrations, but I don't understand the emphasis on pressure differentials. That is not how wings generate lift. Due to attachment they deflect the flow, and the momentum change generates an upward force [1]. The practical point of understanding the flow over the wing is to keep that flow attached so that you can deflect it or reattach it if you get out of sorts.
1. https://www.grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/a...
The explanation you described is the greatly simplified "high school friendly" explanation. It's not wrong, per se, but it's incomplete.
Even your link explains: "The net fluid force is generated by the pressure acting over the entire surface of a closed body. The pressure varies around a body in a moving fluid because it is related to the fluid momentum (mass times velocity). The velocity varies around the body because of the flow deflection described above."
I.e. pressure differential is experienced as lift and is caused by the flow turning.
Explaining the actual cause of the flow turning and resulting lift (and why attachment is maintained along top surface) requires looking at fluid dynamics/navier-stokes including pressure differentials, viscosity etc. The pressure differentials allow a more comprehensive way of breaking down the forces at play.
I like this video for a more comprehensive understanding without getting too in the weeds with the math: https://www.youtube.com/watch?v=aa2kBZAoXg0
He should have started his lecture with the chart shown at the 26 minute mark. Saying when we measure the pressures on the airfoil, we see high pressure at the front and bottom of the airfoil. Let me explain what is going on…
I found his explanation at the 13 minute mark to be hand wavy. He talked about flow turning and momentum change but just hand waved away why pressure is higher at the bottom of the wing.
You are correct in that the deflected airflow exerts an upward force on the wing (or at least a force with an upward component; there's also a backward component (called induced drag if my memory serves me well)).
The way the airflow exerts that force is through pressure differentials: air under the wing having higher pressure than the air above it.
Momentum change can describe physical interactions, and it's often easier to calculate things that way, but actual physical forces still exist, and can also be used to describe the same physical interactions.
That's the missing course for the first year of any Aerospace Engineering faculty.
Should be (2024).
I was excited for a moment, and wondered why the RSS feed didn't work, but later realized that the article is from 2024.
Oh man. This guy. His work is simply some of the best explanation content I have ever seen
This is so cool. I've become more interested in aerodynamics since I've started watching F1 and reading Adrian Newey's book. This is such a great post, especially the diagrams in the velocity section.
I really like this pure-math way of looking at airfoil behavior: https://complex-analysis.com/content/joukowsky_airfoil.html
Where can I find more articles where things are explained in this manner?
The author of the Airfoil article has made several similar tutorials on various topics:
https://ciechanow.ski/archives/
For machine learning, Distill.pub has some excellent hands-on tutorials. For example, here's one on momentum:
https://distill.pub/2017/momentum/
https://explorabl.es collects various
https://ncase.me/projects/
And going kinda meta, learning about the principles:
https://worrydream.com/LadderOfAbstraction/
https://vimeo.com/906418692
https://ciechanow.ski/archives/
I wish there was an infinite number of blogs that where this good.
Bartosz Ciechanowski, the gift that keeps on giving.
Nit: paragraphs in footer are misordered.
wait what? this is goood!
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[dead]
I was just thinking the other day about how AI will pretty soon be able to create this kind of explainers on everything quite quickly.
Amazing times!
It’s kind of sad IMO. Bartosz has made a ton of these super interesting and meticulously designed explainers. Something thrown together with AI is much more likely to be made by someone who doesn’t know what they’re talking about, and I’m worried that the sheer volume will crowd out actually quality content like this.
> and I’m worried that the sheer volume will crowd out actually quality content like this.
It's a valid fear.
Don't think so, and we should stop spread damaging narrative like this. I'd say it's already able to imitate this kind of explainers(badly) thanks to his training data. All the subtle teaching nuances, effort, know-how and visual creativity that people like Bartosz Ciechanowski put on this kind of work is not reproducible if not statistically imitating it
And the usual corollary: Not just thanks to his training data, but because training data of that kind and for this kind of topic - still - exists.
Exactly and him not publishing any new post in 2025 makes me wonder...
Good rule of thumb: it should take less time to consume content than it does to create it.
I don’t know how long it takes Ciechanowski to create these explainers, probably a few months? It shows and it’s well worth spending your time reading through his content meticulously.
How long does it take for an LLM to crap out an equivalent explainer? 60 seconds? You should be spending less time than that reading it.
In order to be taken serious I feel like statements like this need to be qualified with who the claimant is imagining to be responsible for generating the anticipated output. The ‘A’ in AI isn’t for ‘autonomous’.
Bartosz Ciechanowski could generate an explainer like this using Claude today if he wanted to. But would he? If someone like him had the mind to do it then they could instead. But where’s it at? These types may hold themselves to a standard above this method. No shame in that.
Haven't people been saying this since 2023? Yet to see AI build this kind of stuff "quite quickly".
I think it's actually already there. It's definitely possible to make these sorts of explainers with something like a Claude Code, you just have to spend a fair amount of time making sure that it's actually doing what you expect it to do. I think the biggest danger with something like a Claude Code is that you get something that looks functionally correct but that the details are suddenly wrong on. I wrote a little bit about this on my blog for some of the places that I've done visualizations actually, and I think it's remarkably easy to iterate on them now.
https://estsauver.com/blog/scaling-visualizations
> Someone like Bartosz Ciechanowski is still operating at a level I can't touch. His work reflects years of accumulated craft and a visual intuition that I don't have.
Seems like you’re contradicting yourself a bit here- is it actually possible to make the sort of explainers from TFA, or is the author operating at a level you can’t touch?
Hey, that's a pretty great article! Thanks for sharing.
(I hope you don't get downvoted by Chichanowski's fanboys. Sad to see people being against innovation, on this site of all places.)
I think it's only a matter of time, AI history has been a cycle of "yeah, but it will never do this", then literal weeks later it does it, lol.
We should think about how each part of the iteration cycle you describe can be improved. This is definitely a problem that can be solved!
It's been said before, but this prediction isn't amazing, imo.
I look forward to Bartosz's articles because they're rock-solid sources of information and the visualizations are both easy-to-understand and surprisingly light on performance. It's all shockingly digestible.
Honestly, as popular science writing goes, this is art as far as I'm concerned, and art is best when it comes from a place of passion and conviction, something AI will never be able to reproduce.