I thought this was going to be about pipeline workflows... but then I saw it was Bartosz!I know what I&#x27;ll be spending a stupid amount of time reading today :)

LOL! Yeah, so the next should be at least in 2025-Q1.

Wake up babe, new Bartosz Ciechanowski just dropped

You can also see all-time top posts: <a href="https:&#x2F;&#x2F;hn.algolia.com&#x2F;?dateRange=all&amp;page=0&amp;prefix=true&amp;query=&amp;sort=byPopularity&amp;type=story" rel="nofollow">https:&#x2F;&#x2F;hn.algolia.com&#x2F;?dateRange=all&amp;page=0&amp;prefix=true&amp;que...</a>The mechanical watch post is 6th on the list

If you&#x27;d like to see more of their work, ranked by what HN thought was most interesting: <a href="https:&#x2F;&#x2F;hn.algolia.com&#x2F;?dateRange=all&amp;page=0&amp;prefix=true&amp;query=%22https%3A%2F%2Fciechanow.ski%2F%22%20-ask&amp;sort=byPopularity&amp;type=story" rel="nofollow">https:&#x2F;&#x2F;hn.algolia.com&#x2F;?dateRange=all&amp;page=0&amp;prefix=true&amp;que...</a>

If you like his work, here&#x27;s his patreon: <a href="https:&#x2F;&#x2F;www.patreon.com&#x2F;ciechanowski&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.patreon.com&#x2F;ciechanowski&#x2F;</a>

Wow, I never realized this detail. What a wonderful thing.

It&#x27;s a bit sad this isn&#x27;t the norn for education articles (and mostly everything else too).Bartosz&#x27;s dedication and craftsmanship is really inspiring.

It&#x27;s right there. unminified and unobfuscated. just click save

IIRC you can view the source and it&#x27;s all custom WebGL available for viewing.

Absolutely beautiful article and presentation

From the HTML:<pre><code> &lt;div class=&quot;slider_viscosity&quot; id=&quot;fdm_hero_sl0&quot;&gt;(...)</code></pre>

Also, it says &quot;this substance&quot;, which I initially thought referred to the cube as it was just mentioned in the previous sentence. But I guess it&#x27;s the &quot;fluid&quot;.

You&#x27;re kind of correct on both guesses. You can get that change by changing the viscosity OR the airspeed.He elaborates later on, but you&#x27;re changing the Reynolds Number - a calculated value from the velocity, fluid density, viscosity and length. The cool thing about a Reynolds Number is that you get identical (in theory) airflow characteristics for two setups with the same Reynold&#x27;s Number, even if e.g. the airspeed is different.

I think it would benefit by being broken up into modules and a little less simplified, at least naming the things.

I think this is entirely intentional. All articles by Bartosz build up from simple basic principles and avoiding specific technical terms is a good way to onboard viewers of mixed backgrounds without scaring anyone off. Viscosity is actually mentioned for the first time only roughly three quarters into the whole thing.

Why does the first slider with the cube not say what the “one property” the slider controls is? Viscosity? Airspeed?

It is currently the 6th most popular post on HN:<a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=31261533">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=31261533</a>

His mechanical watch internals page is also equally amazing.

Of course it moves its wings. That&#x27;s what the runway is for.

Rectilinear fan blades are shaped very similarly to aircraft wings. And it does only move laterally until the ailerons are moved away from being parallel with the ground.

Because an airplane doesn&#x27;t move its wings like a bug or helicopter, and it&#x27;s wings aren&#x27;t shaped like fan blades. One might look at a plane and conclude that since the wings and engines are parallel to the ground, it must only move laterally.

If you watch it very slowly, the paper initially folds under the mouth and then it blows out straight.I&#x27;m guessing the initial puff creates a high pressure area on top of the paper, rolling it downward and back. Them after the puff has pushed the air away, there is now a low pressure zone on top of the paper which lifts it up as the air below is rushing upwards around the sides of the paper.

That seems like the Coanda effect more than anything.

I guess this is somewhat counter intuitive:<a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=NBsvzMi9-f8" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=NBsvzMi9-f8</a>So yeah, fans are puzzling too.

The Wrights did use a rudder and &quot;horizontal rudder&quot; on the 1903 Flyer, but they were for some time determined to achieve roll control by warping the wings rather than using control surfaces, and were only forced to adopt ailerons as other pioneers began demonstrating how superior a paradigm that was. So they don&#x27;t deserve too much credit on that score!

Because the explanation in school misses something like 90% of the detail replacing it with zero-explanation magical thinking.For example, yes, the air above the wing moves faster than the air below the wing, and it&#x27;s related to shape of the airfoil.However, it has nothing to do with magical &quot;air has longer to travel&quot;.It starts with how combining flows at the trailing edge of the airflow create a vortex which induces an opposite vortex around the wing, which is a bit counter-intuitive (but it has nothing on why swept wings work, which can be summarised for practical aircraft design purposes of &quot;because if we calculate at an angle we get better values and reality is crying in the corner&quot;)

Without their wind tunnel optimized airfoils, the wright flyer wouldn&#x27;t have flown. Without the controls, it wouldn&#x27;t have flown. Without the high power to weight ratio motor, it wouldn&#x27;t have flown. Which was the most critical?

I think many of us were taught in school that airfoil shape was somehow magical -- that the fact that it was bowed more on the top was responsible for the fact that it worked.This is only partially true, though; a totally flat wing can also support flight. The shaped nature of the wing contributes to its efficiency (and other factors) but do not make other wing shapes incapable of supporting flight.The reality is that the Wright brothers&#x27; innovation was not the airfoil shape or even the lightweight motor. It was the control surfaces, to allow the operator to adjust the plane&#x27;s attitude on the three axes of rotation, allowing actively stabilized flight.Paper airplanes and kites demonstrate all the same principles of heavier-than-air flight (the Wright brothers even had a kite version of their airframe they used for testing), despite the fact that they generally do not exhibit shaped airfoils.

I think you mean incredible oversimplification

This is an incredible (over)simplification of flying.We still don&#x27;t have a very good understanding of turbulence.Navier Stokes equations still make Aerospace engineers drink.Yes its stupid simple if you care about the simplest of analogies, but if you try to understand it, there are reasons why 80% of people drop out.

It&#x27;s just a matter of scale. What&#x27;s impressive to me with the big aircraft is that we can organise thousands(?) of people to build something that big. But when it comes to the principle of flying it&#x27;s just a bigger version of the fan. If you were to say they used the same amount of energy as a fan then that would be impressive. But they don&#x27;t, they burn tons of fossil fuels. Geese can fly over the highest mountains too and all they eat is grass.

Surely it&#x27;s a less impressive result that something powered by mains electricity can move the air in a draft than that a multi-hundred-ton aircraft can fly over the highest mountains.It&#x27;s the size of the aerodynamic forces and the complexity of the physical mechanisms that create them that many people have trouble with. In particular: intuitions can be pretty wrong, most simplified explanations are wrong under simple experiments, and the problems exhibit scale variance that is unfamiliar (e.g. Reynolds number).One time I was working on air data computer for a transonic aircraft that could fly up to about M0.95 - during flight test, an air data probe mounted on a nose boom was used to supply impact and static pressures, angle of attack and sideslip etc. for various air data calculations like airspeed and altitude.I was fascinated that there was a term in the calculation that related to the aircraft flap position - what&#x27;s happening way out on the trailing edge of the wing actually has a meaningful effect of pressures measured on a boom out the front of the nose during certain regimes of flight.

Who are these mysterious people you&#x27;re interacting with who are concerned with (but don&#x27;t understand) the physics of flight, but who are also not concerned with bird or insect flight?

This looks incredible as usual. What puzzles me, though, is why some people find flying puzzling. At least the kind that we do, ie. helicopters and fixed-wing aircraft. It&#x27;s easy to accept a fan works: just put your hand there and feel the draft. A wing is just like a linear fan pushing air down. It&#x27;s completely  intuitive to understand for me. The difficulties are just in making it practical and controllable. Conversely, many people don&#x27;t seem concerned at all with bird or insect flight, which I find a lot harder to understand.

Yeah, I mean come on, we&#x27;re not rendering something hard and expensive to compute, like a React website that has to list items in a shopping cart.

They’re simple shaders and it’s amazing what a computer can do billions of times per second.

I think they pause when they scroll out of view?

I&#x27;m on Ubuntu and Edge (v122.0.2365.59) could barely render the page. Chrome (v122.0.6261.94) worked just fine, though. I don&#x27;t know enough about browsers and GPUs to debug why that is, but I checked (edge|chrome):&#x2F;&#x2F;gpu and nothing stood out as appreciably different.Edit: interestingly, it seems to only be the first animation. If I scroll it out of view the others all seem to render fine.

Blows my mind that my computer isn&#x27;t even turning on its fans considering how many shaders are running in this thing.

It is too late for us to be saved, my friend, way too late...

What? A ciechanow.ski airfoil explainer? But I have things to do today!

It&#x27;s truly impressive. the amount of time and dedication its uncanny.

This man to me is a modern day Da Vinci of the Web

His work is always a good reminder the open web is still an amazing place!

Yes that makes sense at a high level, but there must be a point of transition between calm air and a jet stream that makes the wings useless to the airplane for at least a few seconds.

It also changes a lot for sailboats, and even more for faster sailing craft (windsurfers, etc.).You can feel a much stronger pressure in the sail when moving towards the wind on a fast windsurfer&#x2F;windfoil as you can do 15-20kts 45deg towards the wind, giving you an apparent wind that is 10-14kts stronger than the true wind.On the same craft, going away&#x2F;downwind, you will feel the apparent wind at a similar angle 10-14kts less. In fact, because of the change in drag and forces, you&#x27;ll probably be going faster and feel even less wind on the downwind leg.When you turn, this can be a big benefit for going downwind (jibing) as at some point the sail feels zero apparent wind (your motion cancelling out the true wind), feels very light in your hand, and easy to rotate to face the other way. Even knowing the physics of it, the timing and execution is still something that takes a lot of practice...especially on big race gear with a 9.0m2 sail.

The plane is just up in the air moving relative to the air around it, it doesn&#x27;t care how the air it&#x27;s in is moving relative to the ground.A tail wind is just saying that the air is moving in a certain direction with respect to the ground (the same direction the plane is flying). The plane doesn&#x27;t give a shit about that.

Yes airplanes have to travel faster (in terms of ground speed) to not stall. This is why head winds are preferred for landings and take offs as it allows ground speed to be lower. But during cruise you want a tailwind to reduce the amount of drag for a given ground speed.

Planes move through the air, and relative to the air mass.

Airplanes are always traveling forward relative to the wind, at some angle of attack. Tailwinds don&#x27;t work by blowing against the airplane&#x27;s surface and pushing it forward. Since the airplanes are themselves traveling at, say, N kt forward relative to the wind, then if they are inside a 10 kt tailwind, they&#x27;ll be doing N+10 kt over the ground, if they are inside a 50 kt tailwind, they&#x27;ll be doing N+50 kt over the ground. If they are inside a 25 kt headwind, the&#x27;ll be doing N-25 kt over the ground.

The bottleneck when it comes to a plane going faster is drag which increases with the square of velocity relative to the air. More drag means the plane has to consume more fuel to stay at its current velocity. So if a plane normally goes 600 mph with no wind then a 100 mph tailwind will allow that plane to go 700 mph relative to the ground to experience the same amount of drag as if it were flying at 600 mph on a day with no wind.

It works by reducing the amount of CSS the plane needs to carry.

I’ve noticed this effect while diving. When you’re in a current, you’re basically the same density so you’re moving with the water. In mid-water with poor visibility, this is really freaky, because you have no way of telling in what direction you’re moving, and how fast. If you “forget” your orientation, you can’t really recover it. Thankfully, you always have highly accurate depth gauge, but as for lateral movement, it’s an eerie feeling. You could just pop up anywhere.

Yeah, I wish meteorologists explained this concept better to the general public, since they&#x27;re basically poised for it. One day I was just wondering where wind _started_ from, and started digging deep into the topic, but essentially we&#x27;re all just standing on the bottom of a roiling ocean floor that is very sensitive to heat changes from the sun.

&gt; So with that in mind, once the airplane is in the air, it doesn’t “know” if there’s a headwind or a tailwind at allThis stops being true for quick changes - because there&#x27;s still the inertia of the aircraft. So if the wind speed changes quickly, the aircraft can&#x27;t immediately move along with it.This is why gusts are so dangerous to landing aircraft. A strong gust from behind can cost you all your lift, and a strong gust from the front can temporarily stall your wing.

Our intuitive experience with wind on the ground is wrong. Next time it’s windy outside imagine the entire volume of air stretching out for miles and miles moving across with the wind speed, we’re just standing at the bottom of this vast air ocean. It will blow your mind and you’ll think about wind differently from then on. So with that in mind, once the airplane is in the air, it doesn’t “know” if there’s a headwind or a tailwind at all, unless you have a way to reference the ground somehow (for example, with a GPS) - just like a boat doesn’t “know” it’s carried by a current downstream. If you are still on the ground, it is very possible that the tailwind is strong enough for you to not be able to takeoff in the available runway - but then you would go in the opposite direction or more likely sit the storm out :)

This is a kind of relativity thing.The only connection a plane has to the universe is the air around it. It simply does not know or care what the ground is doing until the ground is quite close.A small plane in a very high wind is perfectly happy having a &quot;backward&quot; ground track.Same thing as if you were trying to swim upstream in a fast river. How fast you move through the water doesn&#x27;t have anything to do with how fast the water is moving across the land.

It&#x27;s like swimming in a stream. Even if you did nothing you would move basically at the rate that the water is moving.Lift only comes from the interaction of the air and the wing, so if there&#x27;s zero relative motion then you will fall out of the sky, regardless of if you have a 200 knot groundspeed.This also means that, if the wind at altitude is above your plane&#x27;s stall speed, you can hover in place by flying straight into the wind! (example here: <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=n_e6ijREScE" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=n_e6ijREScE</a>)Similarly, if you are in a packet of air that is moving at 200 knots, the fact that you are moving at 500 knots indicated airspeed does not mean you are flying supersonic from an aerodynamic perspective, despite having a groundspeed of 700 knots.

Both drag and lift depend on the speed of the airplane relative to the wind, not relative to the ground. So, if the maximum efficiency dictates that the airplane should travel at speed X relative to the wind, and the wind is flowing at speed Y in the same direction as the airplane needs to travel, then the airplane, flying at maximum efficiency, will be travelling at speed X+Y relative to the ground.

Something that was never clear to me at this level of detail is how a tailwind enables an airplane to move faster. In other words, if the airflow is coming from behind, the lift equation should fall apart and the airplane should fall out of the sky.<a href="https:&#x2F;&#x2F;www.skytough.com&#x2F;post&#x2F;tailwinds-make-plane-faster" rel="nofollow">https:&#x2F;&#x2F;www.skytough.com&#x2F;post&#x2F;tailwinds-make-plane-faster</a>

Eh, it&#x27;s more like you can get to 90% of where you want to be with the 100 year old airfoils (though several of the other series are quite a bit newer).<a href="https:&#x2F;&#x2F;aviation.stackexchange.com&#x2F;questions&#x2F;20798&#x2F;are-naca-airfoils-used-in-modern-aircraft-design" rel="nofollow">https:&#x2F;&#x2F;aviation.stackexchange.com&#x2F;questions&#x2F;20798&#x2F;are-naca-...</a>&gt;You&#x27;d think that with modern computer software it would be possible to design better airfoils, but apparently, those shapes have already been mathematically perfected by hand and by experiment.No, modern computer software indeed does better, but there&#x27;s not a whole lot of room to do better, small changes to bump performance a percentage point or two. These are optimizations which can be (and are sometimes) skipped for many commercial projects.

I have a friend whose PhD is in computational flow dynamics, as applied to airfoil design. He works almost exclusively in fortran (which is wild to me, for someone under 35, but I guess its the &quot;industry&quot; standard). I just asked him about xfoil and he observed that there are more modern programs for (as he put it) more &quot;realistic&#x2F;complex&quot; designs, but said it was a good starting place.

&quot;better&quot; airfoils are used in experimental craft design. for example mark drela wrote and used xfoil to design wings for mit&#x27;s project daedalus, a human powered long distance flight aircraft. this is the case where, like sibling commenter stated, you need that extra % to get better performance characteristics. you can still run xfoil, it&#x27;s a delightfully oldschol fortran program.

Not really, they&#x27;re a nice first step though, or if you require something &quot;good enough&quot;.

NACA and the other published airfoils[1] are generally a good starting point for hobbyist&#x2F;RC folks. However if you want to eke out that last 5% bit of performance (ie. you are a company&#x2F;institution), you would start with one of the above airfoils and optimize them to fit your flight envelope &amp; mission profile. Here&#x27;s a neat video of optimizing a round profile into an airfoil optimized for supersonic speeds [2].[1] <a href="http:&#x2F;&#x2F;airfoiltools.com" rel="nofollow">http:&#x2F;&#x2F;airfoiltools.com</a>
[2] <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=FHYTBguMfWc" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=FHYTBguMfWc</a>

Case in point would be modern gliders (sailplanes). One simple parameter that describes their aerodynamic performance is the maximum achievable Lift&#x2F;Drag ratio, and that dimension-less ratio has climbed from ~30 in the 1960s to as high as 75 today. That means modern gliders can, using the same altitude&#x2F;energy, go over 2 times further horizontally. The L&#x2F;D is not the ultimate decider of performance but it is quite representative of the aerodynamic performance improvements.BTW, all lift based flying objects have an L&#x2F;D ratio (which depends mainly on the airspeed), this includes birds, fighter jets, commercial airliners; and the discrepancies can be pretty interesting. For example if one looks at the L&#x2F;D of the Concorde vs a subsonic jet it becomes clear why it was so damn expensive to operate. Or why the U-2 looks like a glider :). I cannot find any aerodynamic performance data on any famous long endurance (&gt;24h) unmanned drone, but I bet it&#x27;s rather high as well.

Not quite true! Modern airplanes are way more complex. First of all, all modern airplanes have supercritical airfoils which go back to the 60s and 70s. Secondly, the airfoil of the wing root is typically different than the wing tip. Finally, new composite wings are adaptive during flight. They change their shape slightly to maximize efficiency.

Different airfoil shapes for the root and tip were common already in WWII era planes.

The big variation now though is that the airfoil shape varies quite a bit from one end of the wing to the other.

my recollection was that the P51 wing used a NACA airfoil and it had low drag properties not commonplace at the time

NACA airfoils aren’t so much a numbered set of standard, tested designs as a useful set of mathematical curve formulae for making airfoil-like shapes, and describing them using parameters.NACA published empirically determined wind tunnel performance numbers for selected parameters, which was useful research but not a declaration of ‘these are the good values, you should only use these’.It’s a bit like saying all satellites follow TLE orbits derived by NASA&#x2F;NORAD in the 1950s - they do, but only because that’s just a standard way of writing down the orbital elements that describe a particular ellipse, not a catalog of ‘known good’ orbits.

For gliders the naca airfoils have been abandoned around 1970, when the first glasfiber composite gliders were made. We mostly use airfoils from German professor Wortmann (FX) , Quabeck (HQ) or Boermans (DU). 
The naca airfoils are still used in wind turbines though.

It&#x27;s pretty interesting that many airfoils used in aircraft design were derived by NACA in the 1920s and 1930s [1]. You&#x27;d think that with modern computer software it would be possible to design better airfoils, but apparently, those shapes have already been mathematically perfected by hand and by experiment. So nowadays if you want to design a plane you can just look up the desired NACA airfoil from a table based on the speed, air pressure, etc that you require.[1] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;NACA_airfoil" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;NACA_airfoil</a>

I swear Bartosz’ posts deserve to be pinned to the top of hacker news on release day at this point.

That’s my mental model as well. The incompressible fluid-based explanations never made much sense to me

Actually, it is quite true. Gravity is exercising on the airplane a force F equal to the weight of the plane, towards the ground. For the airplane to stay at the same height, air needs to exercise a force that is equal and opposite to that of gravity. For an airplane buoyancy is negligible, so the force comes from accelerating enough air towards the ground so that F = M*A when M is the mass of air being accelerated, and A the (average) acceleration.Notice that this isn&#x27;t a separate effect from the effect of pressure - it&#x27;s just a different way of seeing the same effect. The wing is accelerating the air both upwards and downwards, but because the pressure is higher below the wing than it is above it, more air is accelerated down than it is accelerated up - which lifts the airplane, but makes the air go down.

Except that negative pressure is not a thing. Air molecules are not grabbing the wings and pulling them up - they are just not pushing down on the top as much as the ones underneath are pushing upwards.

Although it is a nice mental model, that&#x27;s not quite true.&gt; The wings act like a scoop forcing air downward behind the wingOnly bottom side of the wing acts as a scoop, creating positive pressure. Upper side, in opposite, creates negative pressure which &quot;sucks&quot; the plane into it, creating additional lift.It surprised me how much lift is coming from the negative pressure - about a half: <a href="https:&#x2F;&#x2F;aviation.stackexchange.com&#x2F;a&#x2F;16202" rel="nofollow">https:&#x2F;&#x2F;aviation.stackexchange.com&#x2F;a&#x2F;16202</a>

The airfoil shape causes formation of vortex around the wing, which ridiculously changes the relative speeds and pressures involved. At low pressure you compensate with speed, which is squared in lift equation.

The pressure differential is what causes the direction change of the flow, pushing the air down. The shape of the wing and the angle of attack cause the pressure differential.

Ya, I was hoping for more nuance related to this. I&#x27;m sure the air foils generate lift, but atmospheric pressure at cruising altitude is ~4psi, and the pressure differential across the foil must be only a tiny fraction of that. According to my understanding of Bernoulli&#x27;s principle, you&#x27;d have to quadruple the speed to cut the pressure in half, and I can&#x27;t imagine the top air traveling that much faster than the bottom air.Yet a 747 can produce 850000 pounds of lift with only 729000 square inches of wing? Feels like a very incomplete description at best

... I&#x27;m honestly surprised it&#x27;s possible to get PPL(A) without learning about wing vortices responsible for lift generation.In order to use &quot;scoop&quot; approach for lift, you need to have either very low wing loading (think paper airplanes) or very high speeds (above transsonic range).

I think what they were saying is that from a pure &quot;Newton&#x27;s 3rd law&quot; standpoint, if the plane has an upwards force, then the air has a corresponding downward force, which must go somewhere. Yes, it is spread out and complicated and turbulent, etc, but ultimately must balance out.If we could somehow &quot;draw a box around&quot; the entire plane+air system, then the plane&#x27;s upward lift will create a corresponding downward force on the box, one way or another.So, in the broad sense that you push the earth away from you when you jump, the plane also pushes the earth away from it when it flies (mediated by a bunch of fluid dynamics).Or, classic example: if a (sealed) truck full of birds is jostled so that they start flying, does the truck weigh less? [1][1] <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=lVeP6oqH-Qo&amp;t=35s" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=lVeP6oqH-Qo&amp;t=35s</a>

The simple newtonian deflection model is correct however, As you engineer your deflector to have the least possible drag the airfoil shape naturally falls out.Actually that is a bit of a lie, the airfoil shape only falls out due to a third implied force that needs to be accounted for. the wing needs to be strong enough to hold itself up. if you had infinitely strong materials the deflector shape that would fall out would be like a slightly bent piece of paper.A clarification note on fluids: you are deflecting fluids, and everything this implies. just because I say newtonian deflection don&#x27;t think I mean billiards balls, or if it has to be billiard balls think trillions of them simultaneously

&gt; If one were to build a large scale on the ground, as an airplane flies over it, the scale would register the weight of the airplaneNo, it wouldn&#x27;t.I think the article does a pretty good job building a more complete understanding than the simplistic &quot;deflection&quot; mental model.

The wings of an airplane in level flight direct air downward with a force equal to the airplane&#x27;s weight. If one were to build a large scale on the ground, as an airplane flies over it, the scale would register the weight of the airplane.
The wings act like a scoop forcing air downward behind the wing. At least that&#x27;s the way I think about it when I&#x27;m out flying around in my Cessna.

The future of education is as an entertainment. There will be no need to educate oneself in the AI future (except for merely egotistical reasons?).

This is the future of education. Very approachable and seems to target the most common denominator of knowledgeable people that out there.I wonder will there be articles in the future with more math and code snippets?

Yes, that. Call it enhanced learning?
For instance, add Dan Carlin - Hardcore History podcasts for your history lectures.
If everyone listened to those podcasts, then all you would need is a good teacher&#x2F;professor to discuss what you learned - and there is &#x27;so much&#x27; learned from any one of his episodes.

What&#x27;s missing for it to be real education? Genuine question :)

While this is good quality, this is not replacement for real education. Real education involves sweat and hard work, not just consumption. This is somewhere between education and entertainment.

Imagine a world in which all education was this level of quality.Imagine how much more you&#x27;d know, be able to do and understand.I really wish good education was valued more highly in society.

I&#x27;m taking a sailing class, and learned sails in addition to keels utilize this concept.

For anyone really interested, this is the authoritative reference for NACA, etc. airfoils.Theory of Wing Sections by Abbott and von Doenhoff (1959)<a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Theory-Wing-Sections-Aeronautical-Engineering&#x2F;dp&#x2F;0486605868" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Theory-Wing-Sections-Aeronautical-Eng...</a>

Speed. Drawing thousands of objects (such as the blades of grass or air molecules) with 2D canvas will be very slow. WebGL allows all drawing to be offloaded to the GPU, which can draw thousands of objects in parallel given a single CPU command. 2D canvas also doesn&#x27;t provide any 3D primitives (as the name would suggest), while WebGL natively supports rasterizing 3D triangles with perspective correct texture mapping and z-buffering.The downside of WebGL is its complexity, but there are many libraries to help with that.

I&#x27;ve never used webgl -- what&#x27;s its advantage over normal 2d canvas drawing for a project like this?

The javascript code is not minified and is easy to follow. Beautifully done.<a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;js&#x2F;base.js" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;js&#x2F;base.js</a><a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;js&#x2F;airfoil.js" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;js&#x2F;airfoil.js</a>

As part of building my own truck-top camper, I got into researching aerodynamics of vehicles in order to try to reduce loss of fuel efficiency. The most interesting ideas I found were that aerodynamics don&#x27;t matter much on most vehicles until they pick up significant speed.Most automobiles are pretty heavy, so the engine has to do significant work just to get it to move. At a certain point, the vehicle can change gears to get the engine to do less work and use less fuel. But around the same time, the force of the air is increasing. By the time an automobile goes over about 50mph, the air forces are getting increasingly strong, and the engine has to work harder to keep the vehicle moving. At this point, beginning to lower the air&#x27;s coefficient of drag on the vehicle will lessen the work the engine needs to do to keep the car moving at speed. So you can optimize the design of the vehicle&#x27;s exterior to reduce the drag coefficient, which will reduce things like flow separation and turbulence, creating fewer rear pressure zones and causing less drag.So you might wonder, why aren&#x27;t more cars teardrop-shaped like the airfoil? The answer is, it depends. Most people want something that looks good more than they want efficient operation at speed. But sometimes having more drag actually helps. For example, the Lotus Elise: while it is smaller and looks more sleek than a Tesla Model 3, it actually has a much worse drag coefficient than a Tesla Model 3. The Lotus has way more force acting against it at speed than the Tesla. But the Lotus is a sports car, and sports cars benefit greatly from increased traction, and you can get more of that traction by increasing the downforce on the car. So the Lotus&#x27;s design sacrifices top-speed drag coefficiency in order to gain some downforce which helps traction when cornering at speed.What about pickup trucks? Even though modern pickups actually have lots of subtle design changes to improve drag coefficient, they all tend to have open beds, which is terrible for drag. It creates this giant messy turbulent pressure area in the bed which drags on the tailgate and the rest of the car. By adding a truck topper, the drag is significantly reduced, but you don&#x27;t see most trucks driving around with a topper on. But trucks naturally have worse gas mileage, so nobody really thinks twice about the aerodynamics.(To be fair, the air&#x27;s impact on gas mileage is minimal unless you&#x27;re going quite fast. But for trucks with extremely bad gas mileage, like 18-wheelers, it makes much more difference. That&#x27;s why they often have airfoils on the front of the truck, gaps between cab and container closed, and skirts to reduce drag from the undercarriage. Strangely though, the biggest improvement to reduce drag coefficient actually comes from modern European big-rigs whose containers are actually tapered like a teardrop. The rear of the vehicle&#x27;s shape makes the most difference to how severe flow separation is, and thus how big of a pressure area develops, pulling on the rear of the vehicle. If we wanted to make trucking more fuel efficient globally we&#x27;d change the shape of the containers to be more like teardrops, but that would make handling and shipping them much more awkward)You&#x27;ll usually only see these effects on automobiles at higher speeds, due to the vehicle needing to overcome gravity before the air forces build up. Lighter vehicles (say, bicycles) with less impact on them from gravity will be impacted earlier (at lower speeds) by the force of the air, so optimizing drag coefficient is much more important, which is why bicycle racers have to put so much into aerodynamics at significantly lower speeds than an automobile. Interestingly, the drag coefficient on a bicycle and rider is actually equivalent to that of a small car.

Well in defense of the GP, the &quot;planes can observably fly upside down&quot; point (and its close cousin the &quot;flat wing cross sections can fly too&quot; point) is a good one, this pokes holes in the usual two-dimensional &quot;the air goes faster on top&quot; themed explanation that omits any discussion of vortex shedding&#x2F;third-dimensional effects.

Unfortunately, your explanation is entirely wrong... and you&#x27;re attacking a &quot;lies to children&quot; simplification with your mention of &quot;needs to run longer way around&quot; bit.

And it&#x27;s an &quot;even more wrong&quot; explanation than the &quot;lies for children&quot; diagram used in school physics class.For reference, actual &quot;proper&quot; discussion of lift in textbooks on aerodynamics have tendency to start with a sphere&#x2F;cylinder.

Yea, I agree and try to explain it this way to friends. Airfoils help, but it&#x27;s ultimately just the wing pushing air down and why planes can fly upside down.FWIW, aerospace engineering degree, used xFoil, did tons of fluid sims, etc.

&gt; Yes, the air above the wing needs to travel a longer distance with the typical section used in wings, which means that it goes faster than the air below the wing.Both of these sub-clauses are true, but the &quot;which means&quot; connecting them aren&#x27;t. There&#x27;s no law of physics saying a fluid that has a longer path ahead of it speeds up in anticipation.

I once found an explanation that finally made it clear to me why the shape of the airfoil can create lift. Yes, the air above the wing needs to travel a longer distance with the typical section used in wings, which means that it goes faster than the air below the wing. It also leaves the wing moving downwards - and when this downward-moving, faster flux of air meets the slower one from below, the result is that a mass of air is pushed downwards - exactly as needed to lift the plane, as you correctly said.As the article says, you can have lift by just changing the inclination of a symmetrical airfoil, but an asymmetrical one can generate lift even without inclination (and with lower drag). The article also explains that acrobatic airplanes have symmetrical wing sections exactly because they need to be able to fly just as easily inverted.

To me the most intuitive and practical mental image is imagining two large bubbles of lower pressure above the wing that hold the wing up by suction (you can see those literally as condensation under certain conditions). As you increase the angle of attack the bubbles get larger and stronger, until the angle is so large that they “break off” and the wing stalls.

IIRC that is due to other issues, not aerodynamics.For instance, the engine no longer receiving oil at negative 1 g, or fuel, as the system is designed for gravity flow.Stunt planes and airplanes capable of long inverted flight need special oiling and fuel systems to keep the engine from starving from either.

&gt; planes can obviously fly invertedMany (most?) planes cannot sustain inverted flight.

You mean it is more akin to those grills you position to control your AC pushing the air in a certain direction. But with just one surface you get the AoA too high problem. Hell I am gonna stick my hand out next time in a car (being safe about it!) and see the stall angle of my hand.

I wish every presentation on how planes fly started with an actual flat plane. A wing that has a flat crossection. I think the shape of the airfoil of the wing is absolutely distracting and prevents people from understanding what is really happening.Every person who ever stuck a flat object outside the window of a moving car knows that you do not need a fancy shape to have lift.And so many people are stuck thinking that the shape of the airfoil is responsible for the plane to be able to fly, supposedly because the air needs to run a longer way around the foil above the wing than below the wing. And this somehow causes pressure difference due to Bernoulli law and this is what keeps the plane up. Which is almost total BS because planes can obviously fly inverted.Now I admit I only skimmed the article, and although the animations are beautiful, I am missing what really is key to understanding of what is happening.I am looking for a bigger, far away view of the wing and showing what happens to the air BEHIND the wing.Because how the plane really works is as it flies forward, it diverts large masses of air downwards. It pushes off of air.Part of the air is diverted by the lower portion of the wing, but the much larger portion of lift is generated by larger masses of air above and behind the wing. Those can be thought as being sucked down behind the wing (if you look at it from the point of view of a stationary air mass, not from the point of view of the wing).And the main role of the airfoil is to keep that mass of air behind the wing stuck to the airfoil at wide range of angles and speeds as possible, because a flat sheet is very poor at doing this.

Obligatory XKCD comic (also with the name &quot;Airfoil&quot;):<a href="https:&#x2F;&#x2F;xkcd.com&#x2F;803&#x2F;" rel="nofollow">https:&#x2F;&#x2F;xkcd.com&#x2F;803&#x2F;</a>

Or if your Cessna isn’t equipped with a flapping system.

Fixed airfoil physics become really important at very high speeds.

Give it a strong selective pressure towards speed and a few million years and you will have your supersonic duck.

Hummingbirds go to mexico to vacation a lot more than I do. Imagine if humans had a manadatory 2000 mile trip and 6 month layover twice a year to survive.Once you have technology that enables flapping type motion, it&#x27;s opening up the applicable physics to like 6 degrees of freedom versus zero in current wing technology (fixed = 0 degree of freedom); much more complex and interesting to study.How else will we move toward ornithopter style wings, or vehicles that can hover via wing movement.

The arctic tern flies from the north pole to the south pole.

But when that fancy duck wants to get to Paris in a hurry, it still has to hop on a fixed-wing Concorde like everyone else.

&gt; this duck is literally just paddling air with his wingsGrossly speaking, sure. But I feel like this simplifies away a lot of the interesting bits. It&#x27;s not as simple as, say, someone on a canoe paddling. Why is the duck&#x27;s wing shaped just so, and not another way? Why does it move its wings just so instead of another way?I&#x27;m reminded of an analysis of fruit fly wings, showing how they re-capture energy from the air when flapping[1]. Maybe the duck is doing similar; I don&#x27;t know.Of course, these animals make it look easy, thanks to millions of years of evolution (:<a href="https:&#x2F;&#x2F;www.nature.com&#x2F;articles&#x2F;s41598-021-86359-z" rel="nofollow">https:&#x2F;&#x2F;www.nature.com&#x2F;articles&#x2F;s41598-021-86359-z</a>

I think you might be experiencing a bit of a dunning-kruger effectAlso, in my experience there’s a huge difference between having an intuition for something and having an understanding of something to the point where you could model it.

I grew up duck hunting and learned intimately how ducks use their wings and the variations of shapes at different velocities as they slow down to land on the water. I also grew up boating and swimming and have a likewise similar understanding of paddling, tracking a canoe straight, and using boat motor trim to &quot;get on the plane&quot;.I guess I struggle with articles like this because it&#x27;s already so intuitive as a mix of air and fluid dynamics. In fact, fixed airfoils are so boring when you see what a duck can do.<a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=-3CVZYY8xS4" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=-3CVZYY8xS4</a>So for all the fancy physics talk, this duck is literally just paddling air with his wings. The same physiology I use to stay afloat when treading water while swimming.

Attachment isn&#x27;t as much of an issue with paper planes since the small size and low speed give much more favorable Reynolds numbers.

Huh, odd. I was under the impression that for swept&#x2F;delta winged paper airplanes one wants a smooth top surface to encourage attachment and any steps on the bottom to provide decalage. (I.e. the area ahead of the step acts as a canard-like surface.)Is this an airfoil that works for tailed aircraft but not tailless ones, perhaps?Edit: I just skimmed the book on paper planes by KF and indeed they are using the variation with the step on the bottom for their paper planes.I&#x27;m actually even more surprised now. How on Earth did they manage to patent the idea of reflex on a delta wing to give a tailless plane stability? This seems like the thing that (a) was known since early human-carrying gliders, and (b) implicitly discovered by anyone that folds a lot of paper airplanes. I will definitely read their book in more detail.

For an example of a flat-ish airfoil that performs well enough for model airplanes (and is easier to build than a NACA &amp; co airfoil), see the KFm airfoil family:<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Kline%E2%80%93Fogleman_airfoil" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Kline%E2%80%93Fogleman_airfoil</a>Very useful when making model airplanes out of foamboard.

I think many of these kinds of comments are driven by a form of insecurity. They subconsciously wish they had written the article and are envious of the attention the author is receiving… so they find whatever small nitpick they can in order to tear it down.

To be clear, the article was amazing. That has already been said multiple times by others so if I left a comment saing just that I would contribute nothing. Besides, the size of the criticism (in this case small, as you point out) is an even better measure of quality than number of fawning comments.I also publish articles (though nowhere near as good or ambitious as this one) online and the comments I look forward to most are the constructively critical ones. They are the reason I publish in the first place.My only goal of giving and receiving constructive criticism is to improve our collective understanding of the world. There&#x27;s nothing sinister or ill-natured about it as another commenter suggested.(This extends to comments as well. I really appreciate you prompting me to check my tone.)

It&#x27;s amazing how the article did such an incredible job building a deep understanding of how the airfoil works, yet you managed to completely miss that and find something to so small to critique.

I thought they made it very clear and talked at length that the shape isn&#x27;t the key important factor. They do also then go on to talk about the benefits of different shapes and why they are chosen.

An odd thing to say for a SWE. There&#x27;s huge differences in the quality of apps, both from a user perspective and an internal&#x2F;dev perspective.

Don&#x27;t get me wrong -- for practical flight it is really important to expand the reasonable range of angles of attack because angle of attack is one of very few ways one has of controlling the aircraft.But for explaining how lift appears, it is an irrelevant detail.The purpose of modeling is not to mimick reality at high fidelity but to focus attention on the o
parameters that matter for a specific situation. When you change the situation (going from explaining how lift happens to trying to fly) it is not surprising to have to switch to a different model.

You gotta wonder why the Wrights spent so much time optimizing an airfoil. You could have been there to tell them to use a barn door wing and flat plate prop to save them a lot of time.I have noticed this &quot;it works or it doesn&#x27;t work. Everything else is nuances.&quot; binary thinking among SWEs. It&#x27;s odd.

This article shows how a flat plane can create lift. It doesn&#x27;t start with that, it starts with a familiar airfoil, deconstructs it until it reaches the flat plane making lift, and then builds back to showing why airfoil shapes are used when simpler flat planes still make lift.

I agree with the other commenter that the specific shape of the cross section of the wing is overemphasised in almost all material including this one. Any shape longer than it&#x27;s thick will, at a reasonable angle of attack, provide lift.This article did provide a barn door model also, but it was quite far down.The shape is mainly about efficiency and increasing the range of reasonable angles of attack, and then further nuances.

Ah, I wasn&#x27;t clear. There&#x27;s a bunch of both in the same giant file.

Just a small note, that code looks like Context2d rather than WebGL unless you were looking at something else in the code

Yeah, the &quot;draw_car&quot; snippet quoted by parent is from the JS file that you linked.It looks like maybe an SVG file converted into JS? Do you know if there is some standard tooling that generates this?

Yeah, that&#x27;s the file I was looking at. I was wondering how that file got created. By hand, or generated somehow?

Not sure what you are looking at but <a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;js&#x2F;airfoil.js" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;js&#x2F;airfoil.js</a> is the JS that contains the code for the graphics&#x2F;visuals. And it is completely readable.The 2d part though is probably generated.

It doesn&#x27;t look like it&#x27;s publicly viewable but he has a writeup of his process for patrons at <a href="https:&#x2F;&#x2F;www.patreon.com&#x2F;posts&#x2F;on-airfoil-99289324" rel="nofollow">https:&#x2F;&#x2F;www.patreon.com&#x2F;posts&#x2F;on-airfoil-99289324</a>

Pretty impressive. I was curious how they made the whole thing so I went to look at the source for the images. It&#x27;s mostly in one 10000 line JS file which draws all the graphics onto &lt;canvas&gt; in JS, plus a bunch of WebGL that goes over my head. The code looks like<pre><code> function draw_car(ctx, rot) {
 ctx.save();
 let sc = 0.04;
 ctx.scale(sc, -sc);
 ctx.lineWidth \*= 1 &#x2F; sc;
 ctx.translate(-286, -51);
 ctx.beginPath();
 ctx.moveTo(463.93652, 9.89137);
 ctx.bezierCurveTo(462.12793, 6.72347, 461.22363, 3.5344, 461.22363, 0.32417);
 ctx.bezierCurveTo(447.58911, -1.16177, 434.20691, 2.81333, 434.85754, 5.10777);
 ...
</code></pre>
I wonder what their workflow was. Surely all those curves weren&#x27;t programmed by hand?

I&#x27;m surprised hang gliding doesn&#x27;t get more attention. It&#x27;s the closest human activity to flying like a bird

You can&#x27;t say that without mentioning <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;British_Airways_Flight_009" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;British_Airways_Flight_009</a>Where the pilot said what is probably the most British thing ever said in history:&gt; Ladies and gentlemen, this is your captain speaking. We have a small problem.&gt; All four engines have stopped. We are doing our damnedest to get them going&gt; again. I trust you are not in too much distress.

This is a very important point.The key difference is that a rock (like any ballistic projectile) accelerates until terminal velocity. In contrast, a 747 (like any airplane) descends with a constant vertical velocity when they lose power.

A 747 won’t fall like a rock. It will glide.

not to mention authors of rfc-1925 as well :o)

The engineers at Boeing are going to be really embarrassed once someone tells them they don&#x27;t actually need to put wings on their aircraft...

Things fly because of thrust, not wings. Rockets, missiles, don&#x27;t have wings and yet they still fly even longer distances. Shut the engines of a 747 and it will fall like a rock, no matter how perfect the airfoils.Bernoulli and Coanda are important but without thrust&#x2F;velocity there is no lift

I expected to see a mention of the Joukowski airfoil (<a href="https:&#x2F;&#x2F;complex-analysis.com&#x2F;content&#x2F;joukowsky_airfoil.html" rel="nofollow">https:&#x2F;&#x2F;complex-analysis.com&#x2F;content&#x2F;joukowsky_airfoil.html</a>). I guess there was plenty of other content to cover though.

Thank you, this feels helpful.Though I don&#x27;t think I missed a part of the article, I feel more like the author did ;)What I still don&#x27;t get is what the difference between high and low viscosity looks like on a particle level. I don&#x27;t understand why he introduced the collision between two molecules and then never explained that.. :)

Not really a full answer for you, but one thing that this page clarified for me:I had generally previously thought of viscosity as &quot;how slow&quot; a fluid is. High viscosity means high &quot;thickness,&quot; which means it flows slowly (like molasses vs. water).But as presented on this page, viscosity is actually a measure of &quot;how fast&quot; — how fast the effects on one molecule can spread out from there to neighboring molecules. Perhaps you could think of sounds waves moving through a substance — a &quot;thick&quot; substance like solid metal propagates those waves quickly (on a molecular level), while with a &quot;thin&quot; substance like air it&#x27;s much slower. In the more precise language from the article: &quot;viscosity controls the diffusion of momentum...&quot;So, because this diffusion happens quickly in a high-viscosity situation, little whorls of turbulence are inhibited, because the forces governing those whorls get spread out&#x2F;diffused quickly.Perhaps you missed the part of the article talking about diffusion, or did not see the connection? The link between that and viscosity was not immediately apparent to me, either.

Thank you. I seem to have trouble using rate as a concept, especially dividing by it :)
But I think I get it when I add a virtual distance into what you are saying.You are saying (force &#x2F; area) &#x2F; (1 &#x2F; time). I add two distances that cancel out: (distance * force &#x2F; area) &#x2F; (distance * 1 &#x2F; time) and get (energy &#x2F; area) &#x2F; speed, which is energy used per area and speed. I can feel that, and it seems to be what you are saying, right?

viscosity has very interesting units - stress (force &#x2F; area) divided by rate (1 &#x2F; time). viscosity is measured (a field known as rheology) by, in some way, moving a thing through a fluid at increasingly fast accelerations, or equivalently, at increasingly high frequencies. that is, imagine moving your hand back and forth in a fluid - the faster you do so (the number of back and forth motions per second), the more resistance you will feel from the fluid. for newtonian fluids, the resistance you feel (measured in force &#x2F; area, ie the area of your hand), is proportional to the frequency of your hand moving back and forth in the liquid, so, the graph is a line. non newtonion fluids do not have a linear relationship between shear stress and shear rate. air is also a fluid - all gasses are, and thus possess rheological properties. air, however, at stp, is essentially an ideal gas, that is, it is non-interactive, and thus, has 0 viscosity. the point here, is that viscosity is a consequence of the interactions of particles. as gases become denser, their viscosity increases. liquids, for comparison, is ~1000x as dense as air. the details of how molecular interactions lead to viscosity is actually quite complicated.

I really enjoyed reading this, and felt excited when the author promised to explain viscosity at a particle level. But there was just a short presentation about two colliding molecules and I didn&#x27;t understand the connection to viscosity. It&#x27;s like a section is missing or something..?How does viscosity work?

If you find this interesting, I would also recommend <a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;bicycle&#x2F;" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;bicycle&#x2F;</a>. It is by the same author.

I&#x27;d love to know how long it takes him to make each one of these &quot;interactive essays&quot;

His mechanical watch piece is really something to behold.

You probably want to check out the rest of his site, which is pretty much on par with this: <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;from?site=ciechanow.ski">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;from?site=ciechanow.ski</a>

Also check out <a href="https:&#x2F;&#x2F;pudding.cool" rel="nofollow">https:&#x2F;&#x2F;pudding.cool</a> if you’re unfamiliar and enjoy extremely high effort visualizations alongside editorial and educational text content.

This is one of the best thought out UX I&#x27;ve ever seen. It&#x27;s extremely well laid out and simple to navigate through, all the design choices are very meaningful, UI elements (like the unit conversion) are available inline when you need them...Not to mention the content itself is great.I&#x27;m taking notes.

I agree! His articles always have fantastic content!

Regardless of all the exacting comments, this is one of the most astonishing accounts and content on a topic I&#x27;ve seen for years; beautifully delivered and interactive to boot.

In what ways do so many people who try to teach approach it like it’s 1878?

Without doubt. Question is why so many people who try to teach approach it like it’s 1878.

Ciechanowski is likely the best content producer we know, absolutely fascinating reads. Imagine having such a person as a teacher - he could probably excite students about any scientific topic.I&#x27;d love to spend my time working on such articles when I&#x27;m retired :)

As an aerospace major in college, this has content from several semesters combined into a really well structured, clear and visual explanation of various aspects of flight dynamics. Thank you.

Oh, thanks todsacerdoti. I really need such thing. Actually, I love reading contents which related to Planes, Wings and the base reasons of their flying. It shows that you and your posts are going to be the best items for my hobbies in the future. Thank you.

Thanks. Yes, it&#x27;s Firefox, but apparently it supports WebGL 1 &amp; 2.

You&#x27;re probably lacking webgl HW accleration.<a href="https:&#x2F;&#x2F;webglreport.com&#x2F;" rel="nofollow">https:&#x2F;&#x2F;webglreport.com&#x2F;</a> , or check about:support if you&#x27;re on firefox.

That page made my laptop fan start roaring.

What an astounding amount of work must have gone into that post...

Amazing work as always.Is it just me who sees diagonal lines on the first interactive graphic? Are they a bug? They appear after a little while, fade out, then reappear<a href="https:&#x2F;&#x2F;gist.github.com&#x2F;RobinL&#x2F;aa4a5e14d35e61e46c1e99c8198d0b9b" rel="nofollow">https:&#x2F;&#x2F;gist.github.com&#x2F;RobinL&#x2F;aa4a5e14d35e61e46c1e99c8198d0...</a>

The same author has a great similar piece on mechanical watches. Love the format!<a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;mechanical-watch&#x2F;" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;mechanical-watch&#x2F;</a>

Not a single mention of Bernoulli. Bravo!

For anyone interested in bio-inspired aerodynamics, there&#x27;s a fascinating study published in Scientific Reports exploring the aerodynamic efficiency of dragonfly and NACA4412 airfoils in ground effect. This research uses URANS simulations to offer insights into optimizing MAVs&#x27; (Micro Air Vehicles) performance close to the ground.
<a href="https:&#x2F;&#x2F;www.nature.com&#x2F;articles&#x2F;s41598-022-23590-2" rel="nofollow">https:&#x2F;&#x2F;www.nature.com&#x2F;articles&#x2F;s41598-022-23590-2</a>

This guy&#x27;s whole corpus reminds me of Nevil Shute&#x27;s _Trustee from the Toolroom_: quiet, fastidious, and expert work appreciated worldwide.

<a href="https:&#x2F;&#x2F;ciechanow.ski&#x2F;mechanical-watch&#x2F;" rel="nofollow">https:&#x2F;&#x2F;ciechanow.ski&#x2F;mechanical-watch&#x2F;</a>

Oh no. A while ago I stumbled on this guy&#x27;s page about mechanical clocks - a subject I was never interested in - and was forced to spend the rest of the day studying clocks.

An important question before I read something that long (or anything, really): Who is Bartosz Ciechanowski?