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)
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.
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. 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.
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.
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).
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.
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.
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.
Momentum change is literally the same thing as a force. That makes what you said nonsensical. The first thing physics students are taught is that F=ma, which is F=dp/dt.
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[ 2.2 ms ] story [ 69.6 ms ] threadAirfoil - https://news.ycombinator.com/item?id=39526057 - Feb 2024 (296 comments)
Amazing times!
And going kinda meta, learning about the principles:
https://worrydream.com/LadderOfAbstraction/
https://vimeo.com/906418692
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"
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.
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.
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
They should receive an unlimited grant to produce educational content for the digital generation’s benefit.
1. https://www.grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/a...
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.