Also, it says "this substance", which I initially thought referred to the cube as it was just mentioned in the previous sentence. But I guess it's the "fluid".
You'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'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's Number, even if e.g. the airspeed is different.
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.
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'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's completely intuitive to understand for me. The difficulties are just in making it practical and controllable. Conversely, many people don't seem concerned at all with bird or insect flight, which I find a lot harder to understand.
Because an airplane doesn't move its wings like a bug or helicopter, and it's wings aren'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.
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.
If you watch it very slowly, the paper initially folds under the mouth and then it blows out straight.
I'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.
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' innovation was not the airfoil shape or even the lightweight motor. It was the control surfaces, to allow the operator to adjust the plane'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.
The Wrights did use a rudder and "horizontal rudder" 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't deserve too much credit on that score!
"Control surfaces" was more specific than I intended; what I meant was that their plane allowed them to control all three axes of rotation, and that was the innovation - that they could control pitch, yaw, and roll independently and that allowed them to have active stable flight.
Without those controls, flight is basically impossible, and with them, you could use nearly any airfoil shape (modulo engine power, drag, and stall speed considerations) and achieve heavier-than-air flight.
Ailerons were really only invented when they were (and named in French) because the Wrights were extremely litigious, they sued Curtiss for using ailerons and basically destroyed American aviation for a decade allowing the French a temporary lead. This had an interesting cultural effect of lots of things becoming named in French across aviation (including things like the weather code for mist being "br" for brume to this day).
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's related to shape of the airfoil.
However, it has nothing to do with magical "air has longer to travel".
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 "because if we calculate at an angle we get better values and reality is crying in the corner")
Growing up I got the "air has longer to travel on the top of the wing than the bottom" explanation, and it always smelled like BS. This is the first explanation of flight aerodynamics that really made sense to me — incredible article as always from this author.
The whole air has longer to travel thing is obviously hand waving a lot of different properties that are all combining to get better efficiencies. For example, don't forget the coanda effect and its contributions to the shape of a wing. Luckily we can always just return to the navier-stokes equations to help us out.
> It starts with how combining flows at the trailing edge of the airflow create a vortex which induces an opposite vortex around the wing,
Wait, I was under the impression this Cutta circulation was a computational simplification and the "real" reason were the pressure differences as explained in this submission. What am I missing?
Essentially the work in the article shows the harder to grok, but still half of the whole equation, with only one small mention of an effect that points to the wider environment. Essentially, this is a more close-in view of the airfoil without consideration of the wider flow around.
One comment already mentioned how position of flaps could have visible effect on pressure sensors in front of the plane, and this is slightly mentioned in how the pressure created by front of the air foil has an impact on air "at a distance" from the airfoil.
The vortices created around the airfoil result in significant change of flows, which especially at low speeds provides big chunk of the pressure changes necessary for the creation of lift, with the effect IIRC getting lower as you go faster, with transsonic regime breaking it - because that's when the resulting speeds go beyond speed of sound at given pressure in the air, which in very simplified way means that air can't move towards front of aircraft anymore in those areas, breaking all sorts of flows you depend on at lower speeds.
Without their wind tunnel optimized airfoils, the wright flyer wouldn't have flown. Without the controls, it wouldn't have flown. Without the high power to weight ratio motor, it wouldn't have flown. Which was the most critical?
Surely it'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'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'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.
It's just a matter of scale. What'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'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't, they burn tons of fossil fuels. Geese can fly over the highest mountains too and all they eat is grass.
I mean, actually, it isn't - that's the whole point about scale variance and Reynolds number and why wings that work for insects are not the wings that work for jumbo jets.
Who are these mysterious people you're interacting with who are concerned with (but don't understand) the physics of flight, but who are also not concerned with bird or insect flight?
Personally all the fluid simulation shaders I've written usually makes my fan go off, and I'm counting a few of those here so that's impressive in my eyes.
Yeah. It's impressive to my eyes as well. I was just trying to make a joke about how normal websites need 100% of your CPU to render some text and images, and here's this guy doing multiple fluid simulations on a web page written in custom WebGL and it runs on a potato.
I'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't know enough about browsers and GPUs to debug why that is, but I checked (edge|chrome)://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.
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.
The plane is just up in the air moving relative to the air around it, it doesn't care how the air it'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't give a shit about that.
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.
If you took a plane flying in still air and magically, instantaneously replaced all the air around it with a tail wind equal to its velocity then yes the plane would stall and fall out of the sky.
Fortunately that kind of instantaneous change doesn't happen in real life.
Do you mean landing with a tailwind? A headwind should allow the plane to create the same amount of lift it needs to avoid stalling at lower ground speeds.
Yes, that’s correct, but the headwind stops being so headwind-y near the ground, so your plane needs to go a bit faster to compensate for the loss of headwind-ness in the seconds before touchdown.
On the flip side you also get ground-effect when you are low to the ground where the high-pressure underneath the wing gets trapped against the ground creating a cushion of pressure increasing lift.
Yes, the wings are useless once the air is moving close to the speed of the plane. Thankfully, we have jet engines that help planes move a lot faster than the 100-200 knots that jet streams can reach. They'll still affect the flight but only temporarily.
These sudden changes do indeed happen in stormy weather, as adjacent layers of air can move with different velocities relative to the ground (the technical term is “wind shear”). If an airplane climbs or descends through those it will look like your speed (relative to air) is suddenly increased or decreased by some amount and you would have to compensate. It’s also a bigger problem for large, heavy airplanes as you have more work to do to accelerate for a given amount of speed loss.
Jet stream boundary is usually not this sharp, and the airplane would fly much faster than the difference anyway.
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/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/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'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.
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.
Airplanes are always traveling forward relative to the wind, at some angle of attack. Tailwinds don't work by blowing against the airplane'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'll be doing N+10 kt over the ground, if they are inside a 50 kt tailwind, they'll be doing N+50 kt over the ground. If they are inside a 25 kt headwind, the'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.
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 :)
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'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're all just standing on the bottom of a roiling ocean floor that is very sensitive to heat changes from the sun.
> 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
This stops being true for quick changes - because there's still the inertia of the aircraft. So if the wind speed changes quickly, the aircraft can'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.
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 "backward" ground track.
Same thing as if you were trying to swim upstream in a fast river. How fast you move through the water doesn't have anything to do with how fast the water is moving across the land.
It'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'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's stall speed, you can hover in place by flying straight into the wind! (example here: https://www.youtube.com/watch?v=n_e6ijREScE)
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.
It's pretty interesting that many airfoils used in aircraft design were derived by NACA in the 1920s and 1930s [1]. You'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.
Eh, it'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).
>You'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'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.
"better" airfoils are used in experimental craft design. for example mark drela wrote and used xfoil to design wings for mit'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's a delightfully oldschol fortran program.
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 "industry" standard). I just asked him about xfoil and he observed that there are more modern programs for (as he put it) more "realistic/complex" designs, but said it was a good starting place.
oh i'm sure state of the art has advanced since then. i have the necessary physics background, but it's not otherwise my domain: i once used xfoil to design an airfoil for an autonomous model glider as a hackerspace project back when i had free time for things like that many years ago. the glider was also loaded into x-plane to develop and test the autonomous part. so whenever various experimental aircraft projects popup, i'm likely to look into them, and then also notice the peculiar foils they use.
Because Fortran was the industry standard for any heavy scientific calculation (like aerodynamics or nuclear bombs), the Fortran compiler has been optimised to death... And thus Fortran is still the industry standard.
It really depends. Up until the 90s Fortran was completely dominant. These days a lot of people have moved to C++. Important open source codes such as OpenFOAM and SU2 are in c++.
NACA and the other published airfoils[1] are generally a good starting point for hobbyist/RC folks. However if you want to eke out that last 5% bit of performance (ie. you are a company/institution), you would start with one of the above airfoils and optimize them to fit your flight envelope & mission profile. Here's a neat video of optimizing a round profile into an airfoil optimized for supersonic speeds [2].
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.
Case in point would be modern gliders (sailplanes). One simple parameter that describes their aerodynamic performance is the maximum achievable Lift/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/energy, go over 2 times further horizontally. The L/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/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/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 (>24h) unmanned drone, but I bet it's rather high as well.
Another good example is the space shuttle. It does actually glide back down. But it glides like a brick at first (1:1 during its initial braking into the atmosphere), and then like a less dense brick (2:1 while it's still supersonic), and then like a brick with shitty wings (a whopping 4:1 or whatever on final approach). Which is about what the Concorde is during landing, 4:1, yea.
Pretty crazy stuff
(Obviously the space shuttle was a tradeoff for, you know, getting it into orbit via rocket)
Your numbers are right but your analogies are misleading. I get “glides like a brick” is hyperbole, but you’ve added enough detail I can see people taking it seriously.
A brick’s L/D is much worse than 1:1. I’m seeing people say 1:10 online, but I can’t find a source and I think that’s incredibly high. A real brick is going to tumble and essentially not make any lift.
A less dense brick will have the same L/D. L/D is about the shape, not the mass.
I’m trying to get my head around the L/D being independent of mass. Does lift scale with airspeed at the same rate as drag? Or is L/D only considering lift-induced drag (whatever the term is) and not total drag including parasitic drag?
Roughly speaking, both lift and drag are proportional to v^2 for a given geometry.
Neither lift nor drag has anything to do with mass. They are entirely determined by the surface of the object, and are not affected at all by the interior properties, including density.
L/D changes with angle of attack. You can have a different airspeed at the same angle of attack and the ratio does stay the same. I think the Wikipedia page gives good descriptions.
Something a bit misleading done generally is aircraft don’t have one L/D, they have many, depending on angle of attack. When you see one number, it’s usually the best one.
The way I've had it described is that when two objects of the same shape pitch for optimal glide (i.e. highest L/D) then the heavier one will reach the ground sooner (go faster), but both will take the exact same path and land the same distance away. In other words, same L/D.
This is not the explanation you are looking for, but "aha the heavier object takes the same path but drops faster" was what made me okay with L/D not depending on weight.
Space Shuttle pilots themselves referred to it as “The Flying Brick,” I think that is mostly what they were referencing. It was a term of endearment :)
If you want a real "orientable brick in atmospheric reentry regime", check out how they steered the Apollo capsules back down. Kinda bonkers, but worked - they made it asymmetric and then rotated it depending on if they wanted to go down faster, slower, left, or right. Obviously it can't fly, and its glide ratio is actually brick-like unlike my facetious description of the shuttle. But it worked enough.
Kinda like a single control plane missile that spins (rolling airframe?), except... without the control plane lol.
I guess you get maximum L/D out of a brick by giving it some serious backspin (which is a stable configuration so it might be able to maintain it on the way down) to set up the lifting circulation around it. But would this count?
Tumbling itself can produce lift. The difference in drag between one side and the other can result in net pressure differences for a moving object. This is the basis of many baseball pitches. Spin a brick fast enough and it might just be able to climb if thrown horizontally.
If static airfoils are complicated, try looking into airfoils that rotate or otherwise move in relation to airflows. A Russian engineer once said that all problems in aerospace are placed on the tip of every helicopter blade.
The Magnus effect is super confusing to think about. Basically, to provide lift, the brick or ball or whatever would need to be "rolling" backards, like a wheel. In baseball, e.g. fastballs are usually thrown in such a way as to "roll" backwards, which causes them to climb. Curveballs are accomplished via topspin. Sinkers roll forward. You can even tune this behavior by making the surface of inconsistently "sticky" to the air, so flow of air is more or less affected by the objects rotation. This is why licking the baseball is against the rules.
Curiously, the rotation can also lend the ball's path greater stability against changing air currents/densities and crosswinds. Knuckleballs are famously hard to throw because they have very little spin, but they are also notoriously hard to hit because the trajectory is so subject to the vagaries of airflow between pitcher and batter.
This is to say nothing about when the axis of rotation is predominantly parallel to the direction of travel (e.g. rifle bullets and American footballs), where the Magnus effect effects the rotating objects ability to continue to rotate parallel to the direction of travel. Get it right and the spin makes the path more stable, but get it wrong, it becomes less stable. The hows and whys of that are beyond my understanding of fluid dynamics, but its fun to think about how complicated it can get.
I saw the space shuttle land once. From my perspective, it seemed to drop like a rock (fast!) and then as it got closer to the ground, it started "flying". I'd never seen anything like it.
The flare-out is really difficult to get right, from what I’ve read. As soon as you start leveling off, air speed is going to drop really fast, and you have very little time to get that bugger on the ground before you get in a stall. They used to practice using a modified jet, flying from high altitude to a landing with thrust reversers engaged all the way!
I personally give the space shuttle a little slack on the aerodynamics department when I remember that it enters the atmosphere at nearly Mach 25, and is big enough to produce two separate sonic booms. It was probably a very wasteful design (burdened by the military requirements), but it's like nothing else we've ever built!
The case with gliders and U2 and the max L/D is due to the wing aspect ratio (look up the formula for drag polar). Modern aircraft have much higher L/D because they have long skinny wings and these wings are possible because we moved from aluminum to carbon reinforced composites.
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/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.
To be nitpicky: I wasn't irked by the article's title, but by the framing in the lede.
To be constructively nitpicky: a box used as a wing is absolutely an "airfoil" inasmuch as the term has any meaning. It's not the shape being "special" that makes a wing work, it's the shape that the airflow around it takes, which is to first approximation just a function of its "tilt" along its major axis relative to the flow direction. The business about shape is all just optimization, not what you want to describe if you want to know how an airplane flies.
It goes into great lengths to show how lift is generated with symmetric airfoils or even flat planes and that the asymmetric airfoil is for efficiency and conditions.
It does not invoke any kind of magic. Even the part you quoted doesn't. Indeed they even animate a flat plane at different angles of attack showing lift.
I don't read that sentence to mean what you do. The article is indeed "looking at the forces generated by the flow of air around the aircraft's wings" and it's definitely focusing "on the cross section of those wings" which is a shape known as an "airfoil."
Later on TFA says "the shape and the orientation of the airfoil helps airplanes remain airborne" which is closer to your criticism, but still true; a shape that generates more drag or less lift in the equivalent airflow would not help airplanes remain airborne.
Maybe if TFA included a simulation of a rectilinear wing and showed how it stalled at very low angles of attack, that would improve things, but I find it to be "just fine" as an introduction to lift.
Indeed, with sufficient thrust your wings can just be flat plates with a small angle between the plane of the plates and the direction of travel. Airfoils are first about reducing drag, second about stall speed and angles.
But airplanes are quite constrained things, if you have a bad attitude and refuse to use airfoils many planes wouldn't even get off the ground and all the rest would have abysmal performance. Sort of like how with imagination everything is a hammer, but this being technically true doesn't mean that you shouldn't really use a hammer when one is called for.
The wings of an airplane in level flight direct air downward with a force equal to the airplane'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's the way I think about it when I'm out flying around in my Cessna.
Although it is a nice mental model, that's not quite true.
> The wings act like a scoop forcing air downward behind the wing
Only bottom side of the wing acts as a scoop, creating positive pressure. Upper side, in opposite, creates negative pressure which "sucks" the plane into it, creating additional lift.
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't a separate effect from the effect of pressure - it'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.
GP was not disputing the redirection of flow or the magnitude of force/air momentum change. They were just saying that not all of this is because of the "scoop" effect from the bottom of the wing: a significant part of the redirection also comes from the low pressure above the wing (at least in practical cases).
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.
That’s just a pressure differential, and not what the OP meant by ‘negative pressure’. 100% of the lift force on a wing is attributable to the pressure differential across it, after all.
They (or their stackexchange source at least) are - like the referenced article and as is commonly done in aero engineering - subtracting out ambient pressure as a reference pressure, and then viewing pressure above the wing as ‘negative’ and pressure below as ‘positive’. It’s a convenient choice to make, for various reasons, but it is essentially an arbitrary one.
The problem comes when you then go on, like OP did, to come across statements like “how much lift is coming from the negative pressure - about a half”
Now, since in analyzing the pressure we have subtracted the reference pressure and made a zero point in between the low pressure value above the wing and the high pressure value below it, it actually shouldn’t surprise us at all that ‘about half’ of the lift seems to be attributed to the positive pressure below the wing, and half to the negative pressure above the wing.
This is just saying that half the lift on the wing is attributable to the first half of the pressure differential across the wing, and about half the lift attributable to the other half.
One of the problems of using a relative pressure and thinking about negative air pressure is that it gives the impression that negative air pressure, like positive air pressure, can grow arbitrarily large. It can’t. You can’t have a negative air pressure lower than negative ambient air pressure, because the absolute air pressure cannot go below zero.
But what you’re talking about is a relative pressure differential. We can have an arbitrarily large negative pressure differential because we can have an arbitrarily high pressure on one side of it.
It's not arbitrary: negative gauge pressure above the wing means that (by definition) there is a pressure gradient increasing away from the wing (because the absolute pressure far from the wing is ambient pressure), so the net force on the air there is downward.
> made a zero point between ... shouldn't surprise us
Whether or not you are surprised is immaterial, but it is not guaranteed a priori -- you could get a net upward force with ambient pressure above the wing and positive pressure below or with ambient pressure below the wing and negative pressure above (meaning gauge pressure, relative to the ambient pressure distant from the wing, to be clear). The person who started this thread seemed to be implying that the former was a good mental model, and the person you replied to was just saying that in fact for practical wing designs it is somewhere in between.
FWIW it is very common to talk about positive and negative gauge pressure. Some people may say that without understanding what is going on, but it is a mistake to assume that they don't understand just because they use that language.
Ya, I was hoping for more nuance related to this. I'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's principle, you'd have to quadruple the speed to cut the pressure in half, and I can'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
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.
... I'm honestly surprised it's possible to get PPL(A) without learning about wing vortices responsible for lift generation.
In order to use "scoop" 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 "Newton's 3rd law" 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 "draw a box around" the entire plane+air system, then the plane'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]
It's wrong though. A large, hypothetical scale under the plane would not register the weight of the plane as it flies over. And not just because diffusion but that being one of many reasons.
Certainly if we flew the plane very low over the ground, the air pretty directly pushes down on it, and the hypothetical scale would register something. Just look at the grass when a helicopter hovers over it.
As the aircraft flies further up, we'd need a bigger scale to capture the full area affected, and if it's moving there would be increasing lag between the location of the plane and the (large) area where the downward force hits the ground.
Or do you disagree with that? At what point does the scale stop working?
Obviously there would be practical limitations — that force is so spread out that it would be hard to measure. But let's not have practice get in the way of theory (:
Planes fly through gas, not solid particulate. Gas has intrinsic kinetic energy when energized. Diffusion plays a huge role in all this of course.
The airflow is split at the leading edge. The area of positive pressure is not entirely below or focused under the wing. The top and bottom of the airfoil are both involved in turning the air flow.
The pressure under the airfoil increases a bit, but the pressure above decreases by as much to much more depending(2-3x or more). This hypothetical scale is under the aircraft but much of the lift occurs by decreasing forces on the top surface.
Scales measure weight/mass. Barometers measure changes in atmospheric pressure. So it's not even the tool for the job even if the stone skip theory of lift was accurate.
Perhaps my mention of Newton's third law gave you the impression that I was advocating for that "stone skip" theory — I assure you I wasn't! Especially as presented on that page, it is obviously junk (:
But surely you agree, broadly, that if birds are flying inside a sealed box, the box still weighs the same amount as if they were standing, right? (modulo some fluctuations)
All of the pressure differentials and whatnot have the net effect that an upward force on the wing results in a downward force elsewhere. The purpose of the scale is to measure that force — like measuring the weight of the box with birds in it.
In the hovering helicopter example, wouldn't you agree that a (large) scale directly under the helicopter will measure a weight corresponding to the helicopter's lift force? Like if I blow directly onto a kitchen scale — it will measure some grams.
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't think I mean billiards balls, or if it has to be billiard balls think trillions of them simultaneously
I did not say reflector as implied by that link but deflector, a thing put in the fluidstream to move it somewhere else. airplanes lift because you are moving air down. People get hung up about the convex side of the airfoil but what else is the fluid going to do, stay a vacuum? it is going to move in the way the deflector shaped, adding to(actually providing most of) the downward flow. There is a lot of engineering that goes into it but at the end of the day an airfoil is the shape that moves enough enough air downward with the least drag. The only reason it is a thick teardrop shape is it has to be strong enough to support itself and the airplane. otherwise the ideal shape would be super thin shaped like the upper surface of the wing bending slightly from the cord(aspect directly into the stream) to the trailing edge(a few degrees of slope).
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/professor to discuss what you learned - and there is 'so much' learned from any one of his episodes.
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.
332 comments
[ 4.0 ms ] story [ 381 ms ] threadI know what I'll be spending a stupid amount of time reading today :)
The mechanical watch post is 6th on the list
Bartosz's dedication and craftsmanship is really inspiring.
He elaborates later on, but you'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's Number, even if e.g. the airspeed is different.
https://news.ycombinator.com/item?id=31261533
https://www.youtube.com/watch?v=NBsvzMi9-f8
So yeah, fans are puzzling too.
I'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.
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' innovation was not the airfoil shape or even the lightweight motor. It was the control surfaces, to allow the operator to adjust the plane'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.
Without those controls, flight is basically impossible, and with them, you could use nearly any airfoil shape (modulo engine power, drag, and stall speed considerations) and achieve heavier-than-air flight.
For example, yes, the air above the wing moves faster than the air below the wing, and it's related to shape of the airfoil.
However, it has nothing to do with magical "air has longer to travel".
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 "because if we calculate at an angle we get better values and reality is crying in the corner")
Wait, I was under the impression this Cutta circulation was a computational simplification and the "real" reason were the pressure differences as explained in this submission. What am I missing?
One comment already mentioned how position of flaps could have visible effect on pressure sensors in front of the plane, and this is slightly mentioned in how the pressure created by front of the air foil has an impact on air "at a distance" from the airfoil.
The vortices created around the airfoil result in significant change of flows, which especially at low speeds provides big chunk of the pressure changes necessary for the creation of lift, with the effect IIRC getting lower as you go faster, with transsonic regime breaking it - because that's when the resulting speeds go beyond speed of sound at given pressure in the air, which in very simplified way means that air can't move towards front of aircraft anymore in those areas, breaking all sorts of flows you depend on at lower speeds.
We still don'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'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'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.
I mean, actually, it isn't - that's the whole point about scale variance and Reynolds number and why wings that work for insects are not the wings that work for jumbo jets.
Edit: interestingly, it seems to only be the first animation. If I scroll it out of view the others all seem to render fine.
https://www.skytough.com/post/tailwinds-make-plane-faster
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't give a shit about that.
Fortunately that kind of instantaneous change doesn't happen in real life.
Jet stream boundary is usually not this sharp, and the airplane would fly much faster than the difference anyway.
You can feel a much stronger pressure in the sail when moving towards the wind on a fast windsurfer/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/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'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.
This stops being true for quick changes - because there's still the inertia of the aircraft. So if the wind speed changes quickly, the aircraft can'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.
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 "backward" ground track.
Same thing as if you were trying to swim upstream in a fast river. How fast you move through the water doesn't have anything to do with how fast the water is moving across the land.
Lift only comes from the interaction of the air and the wing, so if there'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's stall speed, you can hover in place by flying straight into the wind! (example here: https://www.youtube.com/watch?v=n_e6ijREScE)
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.
[1] https://en.wikipedia.org/wiki/NACA_airfoil
https://aviation.stackexchange.com/questions/20798/are-naca-...
>You'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'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.
[1] http://airfoiltools.com [2] https://www.youtube.com/watch?v=FHYTBguMfWc
BTW, all lift based flying objects have an L/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/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 (>24h) unmanned drone, but I bet it's rather high as well.
Another good example is the space shuttle. It does actually glide back down. But it glides like a brick at first (1:1 during its initial braking into the atmosphere), and then like a less dense brick (2:1 while it's still supersonic), and then like a brick with shitty wings (a whopping 4:1 or whatever on final approach). Which is about what the Concorde is during landing, 4:1, yea.
Pretty crazy stuff
(Obviously the space shuttle was a tradeoff for, you know, getting it into orbit via rocket)
A brick’s L/D is much worse than 1:1. I’m seeing people say 1:10 online, but I can’t find a source and I think that’s incredibly high. A real brick is going to tumble and essentially not make any lift.
A less dense brick will have the same L/D. L/D is about the shape, not the mass.
Neither lift nor drag has anything to do with mass. They are entirely determined by the surface of the object, and are not affected at all by the interior properties, including density.
Something a bit misleading done generally is aircraft don’t have one L/D, they have many, depending on angle of attack. When you see one number, it’s usually the best one.
I thought the point was that aerodynamics change from one domain to the next as shockwaves cause flow separation or eddies on or behind surfaces.
This is not the explanation you are looking for, but "aha the heavier object takes the same path but drops faster" was what made me okay with L/D not depending on weight.
I mean it looks like a brick and it flies
“Steerable brick in an atmosphere”… or the slightly more accurate “orientable brick in an atmospheric reentry regime”…
Kinda like a single control plane missile that spins (rolling airframe?), except... without the control plane lol.
https://www.youtube.com/watch?v=XqUgUgiToNs
Tumbling itself can produce lift. The difference in drag between one side and the other can result in net pressure differences for a moving object. This is the basis of many baseball pitches. Spin a brick fast enough and it might just be able to climb if thrown horizontally.
If static airfoils are complicated, try looking into airfoils that rotate or otherwise move in relation to airflows. A Russian engineer once said that all problems in aerospace are placed on the tip of every helicopter blade.
Curiously, the rotation can also lend the ball's path greater stability against changing air currents/densities and crosswinds. Knuckleballs are famously hard to throw because they have very little spin, but they are also notoriously hard to hit because the trajectory is so subject to the vagaries of airflow between pitcher and batter.
This is to say nothing about when the axis of rotation is predominantly parallel to the direction of travel (e.g. rifle bullets and American footballs), where the Magnus effect effects the rotating objects ability to continue to rotate parallel to the direction of travel. Get it right and the spin makes the path more stable, but get it wrong, it becomes less stable. The hows and whys of that are beyond my understanding of fluid dynamics, but its fun to think about how complicated it can get.
edit: got my spin directions confused
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/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.
To be constructively nitpicky: a box used as a wing is absolutely an "airfoil" inasmuch as the term has any meaning. It's not the shape being "special" that makes a wing work, it's the shape that the airflow around it takes, which is to first approximation just a function of its "tilt" along its major axis relative to the flow direction. The business about shape is all just optimization, not what you want to describe if you want to know how an airplane flies.
It goes into great lengths to show how lift is generated with symmetric airfoils or even flat planes and that the asymmetric airfoil is for efficiency and conditions.
It does not invoke any kind of magic. Even the part you quoted doesn't. Indeed they even animate a flat plane at different angles of attack showing lift.
Later on TFA says "the shape and the orientation of the airfoil helps airplanes remain airborne" which is closer to your criticism, but still true; a shape that generates more drag or less lift in the equivalent airflow would not help airplanes remain airborne.
Maybe if TFA included a simulation of a rectilinear wing and showed how it stalled at very low angles of attack, that would improve things, but I find it to be "just fine" as an introduction to lift.
But airplanes are quite constrained things, if you have a bad attitude and refuse to use airfoils many planes wouldn't even get off the ground and all the rest would have abysmal performance. Sort of like how with imagination everything is a hammer, but this being technically true doesn't mean that you shouldn't really use a hammer when one is called for.
> The wings act like a scoop forcing air downward behind the wing
Only bottom side of the wing acts as a scoop, creating positive pressure. Upper side, in opposite, creates negative pressure which "sucks" the plane into it, creating additional lift.
It surprised me how much lift is coming from the negative pressure - about a half: https://aviation.stackexchange.com/a/16202
Notice that this isn't a separate effect from the effect of pressure - it'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.
If you take the difference between the pressures above the wing and below the wing, you get a negative number.
A thing not existing absolutely can still exist relatively.
They (or their stackexchange source at least) are - like the referenced article and as is commonly done in aero engineering - subtracting out ambient pressure as a reference pressure, and then viewing pressure above the wing as ‘negative’ and pressure below as ‘positive’. It’s a convenient choice to make, for various reasons, but it is essentially an arbitrary one.
The problem comes when you then go on, like OP did, to come across statements like “how much lift is coming from the negative pressure - about a half”
Now, since in analyzing the pressure we have subtracted the reference pressure and made a zero point in between the low pressure value above the wing and the high pressure value below it, it actually shouldn’t surprise us at all that ‘about half’ of the lift seems to be attributed to the positive pressure below the wing, and half to the negative pressure above the wing.
This is just saying that half the lift on the wing is attributable to the first half of the pressure differential across the wing, and about half the lift attributable to the other half.
One of the problems of using a relative pressure and thinking about negative air pressure is that it gives the impression that negative air pressure, like positive air pressure, can grow arbitrarily large. It can’t. You can’t have a negative air pressure lower than negative ambient air pressure, because the absolute air pressure cannot go below zero.
But what you’re talking about is a relative pressure differential. We can have an arbitrarily large negative pressure differential because we can have an arbitrarily high pressure on one side of it.
> made a zero point between ... shouldn't surprise us
Whether or not you are surprised is immaterial, but it is not guaranteed a priori -- you could get a net upward force with ambient pressure above the wing and positive pressure below or with ambient pressure below the wing and negative pressure above (meaning gauge pressure, relative to the ambient pressure distant from the wing, to be clear). The person who started this thread seemed to be implying that the former was a good mental model, and the person you replied to was just saying that in fact for practical wing designs it is somewhere in between.
FWIW it is very common to talk about positive and negative gauge pressure. Some people may say that without understanding what is going on, but it is a mistake to assume that they don't understand just because they use that language.
Yet a 747 can produce 850000 pounds of lift with only 729000 square inches of wing? Feels like a very incomplete description at best
In order to use "scoop" approach for lift, you need to have either very low wing loading (think paper airplanes) or very high speeds (above transsonic range).
No, it wouldn't.
I think the article does a pretty good job building a more complete understanding than the simplistic "deflection" mental model.
If we could somehow "draw a box around" the entire plane+air system, then the plane'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] https://www.youtube.com/watch?v=lVeP6oqH-Qo&t=35s
Certainly if we flew the plane very low over the ground, the air pretty directly pushes down on it, and the hypothetical scale would register something. Just look at the grass when a helicopter hovers over it.
As the aircraft flies further up, we'd need a bigger scale to capture the full area affected, and if it's moving there would be increasing lag between the location of the plane and the (large) area where the downward force hits the ground.
Or do you disagree with that? At what point does the scale stop working?
Obviously there would be practical limitations — that force is so spread out that it would be hard to measure. But let's not have practice get in the way of theory (:
Planes fly through gas, not solid particulate. Gas has intrinsic kinetic energy when energized. Diffusion plays a huge role in all this of course.
The airflow is split at the leading edge. The area of positive pressure is not entirely below or focused under the wing. The top and bottom of the airfoil are both involved in turning the air flow.
The pressure under the airfoil increases a bit, but the pressure above decreases by as much to much more depending(2-3x or more). This hypothetical scale is under the aircraft but much of the lift occurs by decreasing forces on the top surface.
Scales measure weight/mass. Barometers measure changes in atmospheric pressure. So it's not even the tool for the job even if the stone skip theory of lift was accurate.
Perhaps my mention of Newton's third law gave you the impression that I was advocating for that "stone skip" theory — I assure you I wasn't! Especially as presented on that page, it is obviously junk (:
But surely you agree, broadly, that if birds are flying inside a sealed box, the box still weighs the same amount as if they were standing, right? (modulo some fluctuations)
All of the pressure differentials and whatnot have the net effect that an upward force on the wing results in a downward force elsewhere. The purpose of the scale is to measure that force — like measuring the weight of the box with birds in it.
In the hovering helicopter example, wouldn't you agree that a (large) scale directly under the helicopter will measure a weight corresponding to the helicopter's lift force? Like if I blow directly onto a kitchen scale — it will measure some grams.
Edit: I feel we are kinda re-hashing the Bernoulli/Newton discussion also addressed at the nasa site: https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/a... — 'So both "Bernoulli" and "Newton" are correct ...'
For reference, the correct Newtonian explanation (flow turning) is also covered: https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/a...
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't think I mean billiards balls, or if it has to be billiard balls think trillions of them simultaneously
I wonder will there be articles in the future with more math and code snippets?
Imagine how much more you'd know, be able to do and understand.
I really wish good education was valued more highly in society.
Anything that fits the above as was stated :)
Theory of Wing Sections by Abbott and von Doenhoff (1959)
https://www.amazon.com/Theory-Wing-Sections-Aeronautical-Eng...