I don’t remember the first time airplane turbulence freaked me out, but I remember the day it turned into a nightmare, when it was no longer an unlikely event but a monster of tangible power and wickedness. The date was Oct 14, 2019, and I was on jetBlue flight B6 1715, flying from New York to San Francisco. The plane took off at 21:44 UTC-05:00 amid a heavy storm, and shortly after the city became a glistening dot in the darkness beneath us, violent blows began to thrust the plane.
I had never felt such a force from the skies. Initially, a few people—including me—were on high alert, but most passengers appeared unworried, some even amused by the rollercoaster ride. Suddenly, seemingly in a split second, our Airbus 321 aircraft was getting thrown in every direction possible. Up and down, left and right, clockwise and counterclockwise. By the tenth minute of these unrelenting blows, we were all thinking the same: we might die on this flight.
Some people prayed, some screamed, others vomited. One passenger, two rows in front of mine, spiraled into a panic attack and yelled in terror, asking what was happening, when it was going to stop. I clenched my fists, my face winced with each blow, my stomach twisted with each free fall. Like in those paralyzing dreams, I was not even able to shout.
I sent a text message to my mom on WhatsApp. I wrote that we were in very strong turbulence, that I had no idea what was going to happen, but that I loved her. I told her to tell my dad and brother the same. One checkmark appeared on the right side of my message, and then the wifi went out.
After about thirty minutes—an objectively short timeline that nonetheless felt like eternity—the turbulence subsided. Things went back to normal, and a few hours later, we landed safely in San Francisco. While we were taxiing on the tarmac, the second checkmark in WhatsApp appeared, then followed a reply from my mom, on whom the apocalyptic tone of my message was clearly lost, with a casual “honey, I was asleep. everything ok?”. There was never any explanation of what happened on that flight.
Turbulence has since become something I think about every time I have to get on an airplane. This obsessive thinking has manifested in a few ways. For instance, I always try to sit as close as possible to the aircraft’s center of gravity. Another example is that my seatbelt is always, always on, fastened almost hermetically around my waist. And if you were to judge me by the content of my carry-on backpack, you would probably think I was a survivalist.
The reactive approach has helped a bit, especially with turbulence seemingly getting worse over time once I started paying attention to it, but it’s only within the last year that I realized my self-structured exposure therapy (or at least, my self-awareness that I can’t avoid flying) would never be enough to calm my worries. I had to acquire some form of foresight, I needed to understand turbulence.
My friend, a fellow turbulence-fearer, suggested I start using turbli.com, a website that provides turbulence forecasts for any upcoming flight. The tool is neat—each trip is standardized by its duration on the x-axis, which gives a sense when in the trip one can expect turbulence, while the y-axis tells how strong the turbulence will feel when it happens. So, for instance, ahead of my flight from Taipei to San Francisco on March 9, 2024, the forecast on turbli.com looked like this (my interpretation of the chart from the website):
The app helps interpret the chart and tells how strong the turbulence might feel, but I still had no idea what any of this stuff actually meant. What was EDR, the Eddy Dissipation Rate? How did one know why some values were marked as light turbulence and others as strong? And then, obviously, what the hell even is turbulence? If I could study air turbulence, I thought—maybe, just maybe—I could conquer my newly acquired fear, by knowing the physics and math of this phenomenon, and I could approach my next flight through an investigative lens. Through a lens that would give me a sense of agency.
I became engrossed in this intricate world for months, trying to learn as much as possible before my flight from Taipei to San Francisco in early 2024, starting from turbulence as a physical concept and working my way up to the science behind the charts on turbli.com. What follows therefore is my best attempt to decode the nebulous aviation phenomenon that weighs on many travelers and, for reasons that I would learn only at the end of this endeavor, appears nebulous only because our own hubris made us believe we were entitled to any certainty in the first place.
Turbulence, as a concept, comes from fluid dynamics, a branch of physics that studies the flow of fluids. It might seem counterintuitive to be thinking of fluids in the context of airplane turbulence because air itself is a gas. Gas, however, is also a fluid because—like the other fluids that we typically think of when we say fluids, namely liquids—it can flow and take the shape of its container.
And just like most substances around us, air is made up of various molecules—primarily oxygen and nitrogen—with a few particles making guest appearances, such as water vapor and carbon dioxide. We can’t see air with the naked eye because there is a vast separation between its molecules, which leads us to think of air as nothing, perhaps an empty space, perhaps something that needs to be filled.
And yet, air is very much something. It is a fluid and it flows in all directions, and as a fluid, it can be deformed. When you wave your hand in the air, you deform it, causing the various molecules in air to disperse and change the direction of their flow. Like every fluid, air has an inherent resistance to this deformation, a fluid’s property known in physics as viscosity, better understood as the fluid’s “stickiness.”
As you have probably guessed by now, air is not sticky. The vast separation of molecules in the air means that air doesn’t have a lot of inherent resistance to deformation. When you wave your hand, you don’t feel anything preventing you from doing that, which is a sign of the air’s low viscosity.
The flip side of a fluid with low viscosity is that, once deformed by an external force, it doesn’t have enough “strength” to bounce back smoothly from this deformation and the fluid’s flow therefore becomes turbulent. Conversely, if a fluid has high viscosity—honey is a great example of such a fluid—it will be very resistant to deformation. Just imagine being inside a jar of honey and trying to wave your hand through the thick plasma. It would be near impossible.
What does all this have to do with planes? Let me try a visual, theoretical example. Imagine the air, a smooth jet stream, flowing west to east, without any interruptions on its way. Just the plain skies above and the plain fields below. This is what you see as the horizontal red lines in the image, on the left.
Physicists would call this laminar, sheet-like flow because the layers of the fluid are moving smoothly past each other. Then, a plot twist: the air’s flow encounters a nature’s massive obstacle on the way, like the Rocky Mountains in the United States or the Alps in Europe. This encounter will deform the air, and because the air is not viscous, it won’t be able to easily dampen the effect of this deformation. Enter turbulent flow, which are the red swirls seen around the mountain tops on the right.
The swirls are called eddies and they are the central characters in the agonizing story of turbulence. All sorts of causes—obstacles (like the mountain shown in the image), wind shear, temperature differences, and so on—create these eddies by applying stress to the fluid. In a way, eddies can be thought of as the unfortunate aftermath, an incurred cost perhaps, of the fluid’s low viscosity. When stress is applied to a low-viscosity fluid, that energy is injected into the fluid’s flow and, because the low-viscosity fluid is not great at resisting this process, its only way to respond to this chaos is to have swirling motions, eddies, to dissipate the energy. Hence the Eddy Dissipation Rate (EDR).
Planes get affected by eddies because an airplane is a three-dimensional object moving through a medium (air), and that means one cannot talk about flying in the skies without talking about the axes of an aircraft1, the imaginary lines that pass through the aircraft’s center of gravity at 90° angles of one another.
It’s normal for any three-dimensional object to move around these axes, in movements called yawing, pitching, and rolling. Pilots maneuver aircraft across the three axes to ascend, fly, and descend, which is all swell, but the air’s turbulent flow, with its swirling eddies, can also move the aircraft along these axes.2 So, to feel turbulence as a passenger on a plane is to feel the (sometimes violent) movements of the aircraft along these imaginary lines, caused by the air’s eddies.
Hopefully apparent by now is the inherent pecking order between air turbulence and an airplane caught in air turbulence. Turbulence happens, and it happens regardless of whether the airplane is flying through the region of air that has become turbulent, so it is not surprising that the formula used to calculate the Eddy Dissipation Rate—the turbulence metric supreme—has nothing to do with the aircraft itself.
In a 2012 research paper3, NASA researchers have outlined the following formula for calculating the Eddy Dissipation Rate (ϵ):
where e is the turbulence kinetic energy (TKE) and Le the integral length scale of turbulence; the former measures fluctuations of the (turbulent) three-dimensional velocity components from an average velocity, the latter measures the average size of the most energetic eddies within the turbulent flow.4
Rather unintuitive at first glance. To make it more palatable, it’s crucial to understand what this turbulence kinetic energy in the numerator really is. In classical mechanics, kinetic energy is usually expressed as the product of mass and velocity squared, denoting the importance of the singular object that possesses this energy due to its motion. In fluid mechanics, however, one studies the continuum of fluid particles, so to have valid comparisons and calculations of the phenomena within the fluid, it becomes necessary to standardize the kinetic energy by mass. In other words, to divide the unit of energy (Joule) by the unit of mass (kilogram).
Notice the lack of dependency on mass in the terminal expression once the units of mass are canceled out. In a way, the turbulence kinetic energy (e) is like an average, a statistical summary. But, a summary of what exactly?
A summary of its raw data points, which are the three-dimensional velocity fluctuations mentioned earlier. Turbulence is, for all intents and purposes, chaos, which means there are numerous particles with localized velocity fluctuations from the average velocity of the fluid, and it’s these fluctuations that carry the kinetic energy. Expressing each fluctuation on its own is not helpful, so one takes an average of fluctuations in each of the components, and then also squares them to ensure bidirectional motions (which could cancel each other out) do not obscure the average magnitude of those fluctuations.
Once we account for the unit of the fluctuating velocity components, which is the same as the unit of velocity itself because we are simply measuring the difference of two velocity values, we get the same unit of turbulence kinetic energy.
Put simply, the turbulence kinetic energy (e) in the numerator is about the kinetic energy contained in the velocity fluctuations of the turbulent flow, which themselves are part of the turbulent swirls—the eddies. And, what about the denominator? The Le?
Here, it’s perhaps easier to think about the turbulence kinetic energy again. In the same way the kinetic energy of a singular object is not very helpful to the field of fluid dynamics, which is why we standardize it by mass to extract a new measure, that same turbulence kinetic energy on its own is not very useful to a pilot who has to fly through an apparently turbulent region of air. That’s because the turbulence kinetic energy doesn’t say anything about how that energy is distributed spatially. It’s not the same if the same amount of energy (standardized for mass) is spread over a tiny region versus a large one.
Intuitively, this is why the turbulence kinetic energy gets divided by the integral length scale, the average size (length) of the most energetic eddies in the Eddy Dissipation Rate formula. Revisiting the formula,
it’s obvious, albeit surprising maybe, that the Eddy Dissipation Rate and the integral length scale of turbulence are inversely proportional. Holding the numerator (the turbulence kinetic energy) constant, the smaller the integral length scale of turbulence, the larger the Eddy Dissipation Rate. Conversely, the larger the integral length scale of turbulence, the smaller the Eddy Dissipation Rate. So, if the most energetic eddies are really large, the Eddy Dissipation Rate will be really small. Uh, what?
Turns out, despite all the chaos inherent in a turbulent flow, the system—the fluid, and all the dynamic processes in it—works to keep things in an equilibrium. It’s the core principle of thermodynamics, that nature ultimately seeks to reduce instability. Larger eddies, by the nature of their size, allow “more room” for gradients of velocity and pressure across the fluid, which means the magnitude of forces acting at the interfaces between eddies and the surrounding (laminar) layers of fluid are smaller. In other words, smoother dissipation of energy, smoother transition. Smaller eddies, on the other hand, are the opposite of this: quick dissipation of energy, sharp gradients at the interfaces, more instability. It’s worth noting again: the energy in a turbulent flow does not come from the size of the eddies, but from the magnitude of the fluctuations, the magnitude of the gradients.
Knowing the unit of the integral length scale of turbulence, which is the unit of distance (meters),
we at last can derive the unit of the metric on the y-axis of turbli.com charts, the unit of the Eddy Dissipation Rate (EDR):
By doing this derivation, I realized that the EDR does not measure the probability of turbulence happening. The unit of meter squared per second cubed tells the pilots how turbulent—how chaotic—the atmosphere is, but, as is now evident from the derivations, that in itself is not a probability of turbulence happening, and, perhaps more interestingly, without any reference to the aircraft’s mass, it is not a direct indication of how the aircraft will experience the turbulence if it does happen. The latter confused me. I knew from my own experience as a passenger that bigger planes handled turbulence better.
This was the final piece of the puzzle. While the EDR is indeed not dependent on the aircraft’s mass, aircraft’s mass affects its own weight, because the force exerted on the aircraft by gravity is directly proportional to the aircraft’s mass.
The aircraft’s weight, in turn, is a critical component of the stall speed5, an aviation measure that signifies the minimum speed at which the aircraft must fly to stay aloft, and this part is a bit more intuitive—heavier aircraft has to fly faster than a lighter one to stay in the air. A higher stall speed ultimately means higher turbulence penetration speed, which is the greatest safe speed at which the aircraft can operate in moderately rough air6, and above which structural damage might occur in choppy skies.
Notice the implication here (albeit a bit simplified because many other factors are at play as well): the same turbulent atmosphere, in the same spot, at the same altitude, will appear “weaker” to a heavier aircraft because it will need more “strength” to counteract the plane’s high momentum, caused by its large mass and velocity.
turbli.com says that the EDR values (once multiplied by 100 for easier interpretation) translate to the following categorical turbulence classifications: light (0 — 20 m2/s3), moderate (20 — 40 m2/s3), severe (40—80 m2/s3), extreme (80—100 m2/s3). This means the app does not adjust turbulence classification according to the aircraft weight.
Other sources7 point out that these particular ranges are appropriate for medium-sized aircraft, like Boeing 737 and Airbus 320, whose maximum takeoff mass is between 15,000 lbs and 300,000 lbs. But for heavier aircraft, like Boeing 777 and Airbus 330, different ranges apply: light (0 — 24 m2/s3), moderate (24 — 54 m2/s3), severe (54 – 96 m2/s3), extreme (96 — 100 m2/s3). This would be of interest to me on my upcoming trip.
When the time came for my flight from Taipei to San Francisco on March 9, 2024, I opened turbli.com the day before, and saw the following chart:
Using turbli.com’s classification, without taking into account the model and the weight of the aircraft (Boeing 777-200ER), I overlaid the chart with the following ranges:
It seemed the flight was going to be slightly bumpy at the beginning, moderately-to-very and consistently bumpy in the middle, starting 5.5 hours into the trip and lasting for about an hour, and then very bumpy, though briefly, at landing. But I was curious how the weight-adjusted version of the chart would look if I took into account the maximum takeoff mass of Boeing 777-200 ER, classified as a heavy aircraft at approximately 600,000 lbs of maximum takeoff mass.
Adjusted for weight, the EDR chart for this flight would have the following overlay:
In this version, the trip should never be in the strong (severe) turbulence category, and even the biggest peak in the middle should feel mostly like light-to-moderate turbulence. The bump at landing should still feel notable, though not as severe as it would in a medium-weight aircraft.
On March 9, 2024, a rainy and foggy Saturday in Taiwan, UA852 took off at 13:19 UTC+08:00 from Taipei to San Francisco, and I, sitting in 35C, diligently documented how each hour of the flight felt, knowing that things would likely get scary five hours into the trip.
Flight Log: UA852
From: Taipei, Taiwan
To: San Francisco, CA, USA
Original Duration: 11h 14min
Actual Duration: 10h 25m
Departed at: 13:19 (UTC+08:00) / 21:19 (UTC-08:00) [9 min late]
Arrived at: 23:45 (UTC+08:00) / 07:45 (UTC-08:00) [40 min early]
- Hour 1: Slightly bumpy takeoff.
- Hours 2—5: Smooth cruising.
- Hour 5—6: It’s showtime.
- 02:30 UTC-08:00: Cabin lights on; flight attendants very quickly distribute snacks, clearly in a rush.
- 02:38 UTC-08:00: Pilot announces turbulence; jump seats secured.
- 02:49 UTC-08:00: Moderate turbulence begins, feels mostly okay.
- 03:15 UTC-08:00: Loud thump and strong shaking for 5 minutes. Feels rough.
- 03:25 UTC-08:00: Stabilization; turbulence eases.
- Hour 6.5: Cooldown.
- 03:55 UTC-08:00: Seatbelt sign off; smooth cruise.
- Hour 8:
- 05:12 UTC-08:00: Brief and light bumpiness; seatbelt sign back on.
- Hour 9:
- 06:02 UTC-08:00: Some shakiness, but not like the big thump earlier.
- Hour 10:
- Smooth final hour.
- Hour 10.5:
- 07:45 UTC-08:00: Strong but short burst of turbulence upon landing in SF.
The forecast was mostly accurate; everything just happened a tad earlier than expected, probably because the plane took a slightly different route once we got delayed or because the jet streams gave us an extra speed boost. It’s hard to say, however, which version of the categorical turbulence classification was better suited for my qualitative evaluation of the experience. The weight-adjusted chart, in which only the one-hour timeframe in the middle is classified as moderate turbulence seems more appropriate, though I probably would have answered differently in the moment.
I wish I could say this scholarly ordeal made things easier when the first frightening thump struck at 03:15 UTC-08:00. Sure, I felt somewhat comforted by the chart, knowing the turbulent episode wouldn’t last too long, but those five minutes still felt like an agonizing eternity. My stomach was still up in knots, my right hand still pressed tightly against the seat in front of me. I was still afraid.
When the turbulence settled and the flight attendants turned off the lights, I kept thinking, at the edge of sleep, about this predicament of mine. It occurred to me that I was not afraid of death from extreme turbulence, that’s not what made me feel so uneasy. Make no mistake, I never felt indifferent about it. I am always deeply vested—I might say even passionate—in making it to my destination in one piece and continuing on with the minutiae of my daily life on planet Earth. But, you know, if it’s meant to be my time, then it’s meant to be my time.
The discomfort, that dreadful feeling of doom in my gut that creeps in each time turbulence strikes, comes from the liminal time period between the onset of turbulence and its end, which seems to continuously slip away, trapping me in a quantum superposition—like Schrödinger’s cat—both alive and dead, awaiting the outcome dictated by forces beyond my control.
It comes, perhaps, from the the sobering reality of my—and our—poetically fragile existence, a stark reminder that, despite the technological advancements we make, despite the reassuring air travel statistics we cite, despite the scientific frameworks we impose on the world around us, when we confront nature’s fury and greatness, we also confront our defenselessness and insignificance.
Never clearer is this universal truth than at the precipice of moderate to strong turbulence, like in that split second on my jetBlue flight in 2019, when even the most phlegmatic of us all, previously unfazed by the atmosphere’s violence, shriek in terror. It’s at this moment that we confront our lack of agency in the grand scheme of things.
As nihilistic as this all sounds, that day, in that moment, on my way from Taipei to San Francisco, in the suspended state of sleep, between lucidity and delirium, it somehow made the monster feel less scary, as if I realized that it had always been there—I just never acknowledged it.
Factual references
- U.S. Department of Transportation, Federal Aviation Administration, Airplane Flying Handbook (2021), FAA-H-8083-3c, Glossary G-2. ↩︎
- National Weather Service, ZHU Training Page — Turbulence. ↩︎
- Ahmad, N. & Proctor, F. (2012). Estimation of Eddy Dissipation Rates from Mesoscale Model Simulations, NASA Langley Research Center, pages 2-3. ↩︎
- Jafari A., Ghanadi, F., Arjomandi, M., Emes, M. & Cazzolato, B. (2019). Correlating turbulence intensity and length scale with the unsteady lift force on flat plates in an atmospheric boundary layer flow, Journal of Wind Engineering and Industrial Aerodynamics, Volume 189, pages 218-230. ↩︎
- Szirtes, T. & Rózsa, P., (2007). Applied Dimensional Analysis and Modeling, 2nd edition, Chapter 18 – Fifty Two Additional Applications, pages 527-657. ↩︎
- U.S. Department of Transportation, Federal Aviation Administration, Turner, T. Flying Lessons for May 6, 2010, (copyright of Mastery Flight Training), pages 1-2. ↩︎
- Aviation Weather Training (AvWxTraining), EZWxBrief Pilots Guide. (No color version, updated 5/28/2024), Version 2.0.0, pages 47-48. ↩︎