Airfoil (2024)

Airfoil - https://news.ycombinator.com/item?id=39526057 - Feb 2024 (296 comments)

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.

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"

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/

And going kinda meta, learning about the principles:

https://worrydream.com/LadderOfAbstraction/

https://vimeo.com/906418692

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.

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.

https://estsauver.com/blog/scaling-visualizations

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.