Imagine having a front-row seat at a debate on some hot-button political issue. Words are flowing and emotions are getting heated. Interruptions abound and tempers flare. You are trying to keep up with the conversation but it's all just happening too fast! What can you do to get a grasp of the crux of the argument? Unfortunately, my brain just isn't quick enough to keep up with this kind of discussion. I like to go back and rewatch the debate several times if I can.
Take for example a debate on kitchen cleanliness. The first time I go back to watch it, I might focus on one person and ask, ”What is the pro-dish-soap advocate thinking and saying?” Then I go examine what the anti-dish-soap advocate is thinking and saying. Finally, I see how these two are interacting with each other.
This is what we have done so far in examining our airplane in-flight. We first looked only at how the airplane bent and groaned when forces acted on it. We then looked at how air and airplanes interact with each other through Angle of Attack. Today, let's just look at how air responds to the airplane acting on it.
You might be surprised to know that as far back as Archimedes in 250 BC, we have known that fluids are made up of individual particles. The size and interaction of these particles, however, remained a mystery until much more recent times. Today we know that fluids are made up of an ever changing conglomeration of either atoms, molecules, or a mixture of the two. These particles are in constant motion relative to each other and are not stuck together like solids are. In fact, they spend their days playing a constant game of bumper cars.
Let’s follow along with Ollie the Oxygen Atom as he carries out his normal existence up at eight-thousand feet. The clock strikes midnight and Ollie is currently zooming straight up at 1000 mph. In only 50 nanometers he collides head-on with another oxygen atom travelling straight down at 500 mph. Now Ollie starts travelling straight down at 500 mph and his collision buddie is travelling straight up at 1000 mph. What just happened is known as an Elastic Collision and since it was head-on and both colliders weighed the same, they exactly traded speeds with each other. This is, however, relatively rare. As Ollie starts travelling straight down at 500 mph he makes it about 60 nanometers before a nitrogen atom only going 50 mph collides with him at an angle. They both glance off at angles and at speeds only a nerdy physics student could calculate.
All of this collision business has been going on for as long as Ollie has existed. He has been over the north pole at 60,000 feet, bounced off the wings of butterflies deep within the Amazon rainforest, and even had a fly-on-the-wall spot for the signing of the Magna Carta. Millions of creatures have breathed him in and exhaled him out. He has collided off of his fellow oxygen and nitrogen atoms more times than you could tally using all the pieces of paper on earth. At Ollie’s scale though, temperature, sound, and friction don't really exist, among many other properties we are familiar with at our scale of observation. In fact, between Ollie and his nearest neighbors vast areas of empty space exist relative to their size. In fact, Ollie is only 346 trillionths of a meter in diameter. To put that in perspective, you would need almost 500 million oxygen atoms lined up side by side to make it across the dot of an i on this page. All Ollie has ever known is this constant game of collisions. At this scale, what seems to only be chaos rules.
Today Ollie is in for a treat. He has stood nearly still for some moments and has also gone well over 1500 mph during others. As the dawn breaks, Ollie notes a slight increase in the umph of the collisions he's experienced. He still slows down some, but on average he noted he's been moving faster. To us humans, we would sense this increase in atomic motion to be temperature; the air hitting our skin would be moving faster and we would recognize it as heat.
At 7:00 am, Ollie starts to sense something strange is happening--he's still getting hit from all sides but he has noticed he's had fewer neighbors and fewer collisions off his right side. He notices he is starting to drift ever so slowly to the right since he is getting the normal punches on his left but fewer off his right. At about 7:04 he notices this drift is starting to get stronger. He has moved an extra inch or so to the right. At 7:06 things get really crazy as this slow crawl to the right rapidly turns into a crowded stampede. Three seconds later things have gotten really violent and Ollie gets a front-row seat to the madness as all of a sudden a blade swings violently toward him. A hard aluminum molecule makes contact and yet another collision is added to Ollie’s list. He surges even harder to the right as the aluminum molecule gets a shove to the left thanks to the swinging follow-through of the prop. They part ways never to encounter each other again.
Through many more random collisions with other oxygen and nitrogen atoms in the ensuing milliseconds, Ollie quickly shares his experience of the blade by giving away some of the energy he received. He still bounces up and down, left and right, and side to side, but overall, he's moving to the right.
Despite having had a one-in-a-billion chance among his neighbors for a direct collision with what was the propeller of our airplane, only a split-second later Ollie is directed through the never-ending motion of his friends towards the bottom of the wing. He strikes a paint molecule just below the leading edge and gets a kick downward and forward, yet the billions of molecules near Ollie drag him along under the wing like an unwilling country music hater in a Willie Nelson flash mob. Ollie's downward collision from the wing is definitely not unique. In fact, a billion of his closest neighbors also struck the wing, crowding them all closer together to allow a path for the wing to pass through. Being closer together caused even more collisions among themselves. We would recognize this at our scale as a slightly higher pressure. This experience with the wing has forever changed Ollie’s path in life. In fact, he will pass along the presence of the wing in every collision he ever makes after this event. He will band along with trillions of other oxygen and nitrogen atoms that have also encountered the wing and will pass along this information far upstream for other atoms to prepare a path that will allow the wing to pass. This communication is the essence of what allows fluids to create beautiful streamline paths around wings.
To sit back and examine such a scenario seems mind bogglingly complex. Through the chaotic motions and collisions of seemingly innumerable atoms and molecules, a beautiful and consistent flow pattern is created. We have reached the heart of aerodynamics, an incredibly complex study of how airflow can be harnessed to create useful forces like thrust and lift. No human or computer has ever been, or will likely ever be, able to fully predict exactly how these rambunctious particles will behave around a certain shape like a fuselage or a wing. That is what is so incredible about aerodynamics; no full understanding has ever been found and if I can wager a guess I highly doubt one ever will be.
We must, however, ask ourselves what we have learned from this example.
1. Motion of air is incredibly complex and chaotic on small scales, yet it can be incredibly uniform and orderly on large scales.
2. By means of roundabout communication through elastic collisions, individual atoms share their local understanding of other particles and objects like wings and propellers with other fluid particles at a distance.
3. Fluid particles always order themselves in a way that is in complete harmony with the laws of nature.
4. Fluid particles and the greater flow of fluids are never aware of the simplifications humans use to understand or explain aerodynamics.
If all of these observations are correct, we have to wonder what all of the fuss is about in aerodynamics textbooks. There certainly are some fundamental facts of nature that we use to understand aerodynamics but they aren't the answers to our problems themselves. Historic figures like Bernoulli and Newton gave us some amazing insights, but each of them is just a dim glance at something that is so incredibly beautiful and complex that humans just aren't capable of fully grasping it. So, the next time you hear terms like "Bernoulli's Equation", vorticity, circulation, and Navier-Stokes, know that these are only approximations or parts of something so incredibly complex and amazing that lets us fly and see the world in a way few in all of history have ever been able to witness.
If you haven't been bored to tears yet about fluid motion, take a look at this cool gas simulator by Paul Falstad.
Clear skies and tailwinds,
David
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