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.
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.
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.
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.
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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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
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.
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.
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.
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.
Deleted Comment
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.
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.)
They should receive an unlimited grant to produce educational content for the digital generation’s benefit.
Airfoil - https://news.ycombinator.com/item?id=39526057 - Feb 2024 (296 comments)
1. https://www.grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/a...
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
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.
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.