A not-short-enough introduction to wakes and drag
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All posts in this series:
1. Aerodynamics is beautiful and strange. Wakes especially so
2. A not-short-enough introduction to wakes and drag
3. Big wakes and small wakes
4. How should we think about shear layers?
5. My mental model of wakes
My goal in this series of posts is to explain what I think is missing in our understanding of aerodynamic wakes. But to do that, we first need to get on the same page about the things everyone agrees on. So let's use this post to answer a few simple questions, like:
What are wakes?
What do they look like? (And how, generally, is the air flowing around inside them?)
Why is understanding wakes important? And specifically, what goals do car designers have when trying to understand wakes?
This post is not going to be the one where I explain where I think everyone else is wrong. This is the background knowledge (that, as far as I know, all aerodynamicists agree on) needed to get the non-experts reading these posts up to speed. So, in a sense, I expect this to be the most "boring" essay in the series—at least for someone like me who already knows aerodynamics. But it feels like I should still post it because the basic concepts here are necessary to have a more detailed discussion of wakes.
So let's try to understand the basics about wakes and drag.
What are wakes and what do they look like?
I'm in a field of aerodynamics known as "ground vehicle" aerodynamics. A 'ground vehicle' is any vehicle that travels on the ground instead of flying through the air like planes do. Cars, trucks, buses, and trains are the primary examples of ground vehicles. As a professional aerodynamicist, I've worked on projects designing cars, buses, and heavy-duty 'highway' trucks—aka 18 wheelers.
One of the main aerodynamic features that distinguishes cars and trucks from planes is the rear wake. Planes are quite streamlined—the smooth, gradual curves at the tail of the plane allows the air to merge back together relatively 'cleanly' after the plane passes by.1
Cars and trucks, on the other hand, have a relatively flat rear end. In aerodynamics jargon, we call them bluff bodies. Their shape includes sharp, distinct changes of direction, like a cliff (a bluff), instead of the smooth curves of a rolling hill. Instead of merging back together smoothly, the air behind a car swirls turbulently as it tries to fill the void where the car was until a moment ago. While a moving plane mostly slices cleanly through the air, a moving car pulls more of this air down the road in its wake—as you may have felt if you've ever been walking on the sidewalk when a big truck drove by.
The image below, showing two ways to visualize a wake, is from Aerodynamics of Road Vehicles, 5th Edition:
On the left is a picture taken in a wind tunnel. Smoke is released into the tunnel upstream of the car to show the path of the air (using a smoke wand). In this image, the wake mostly shows up as a blank space. That's because most of the air coming from upsteam flows past the car without getting trapped in the wake. Even a car like this is relatively aerodynamic, after all. Generally, only air that's close to the car's surface ends up in the wake—most of those smokelines are too far from the surface to end up in the wake.
On the right is an image generated from the results of a computer simulation2. The computer simulation results can more clearly show the path of the recirculating air in the wake, as you can simply instruct the computer to show you what the air there is doing—no smoke wands necessary. The whirlpool-like collection of lines behind the car is the wake.
Because of this difficulty in visualizing real-life wakes, it's actually pretty hard to find a video that shows you air flowing inside a wake. None of the top YouTube results for "car wake aerodynamics" actually show air flowing in a wake. For example:
How aerodynamics help make a car go faster? Doesn't show you any clear views of wakes (even though the wake is perhaps the biggest aerodynamic factor slowing a car down).
Car Aerodynamics in a Wind Tunnel? Also no wakes, but at least you can see the flow 'flapping' behind the car a bit.
Aerodynamics Explained: Inside The Secret World Of Wind Tunnel Testing? A good video in many ways but—ironically given the title—the best visualization of a wake is a picture of computer simulation results (see 10:45 for example).3
Coincidentally, one of the few videos I'm aware of that actually attempts to show you the air recirculating behind a vehicle is an advertisement for a product that I myself worked on years ago4:
But even this visualization is something of a lie, for reasons we'll discuss below.
The key features of wakes
So, what do you need to know about what wakes look like? Here are a few key features:
The general shape of a wake is a 3-D 'vortex' of air flowing around in a circular pattern behind the vehicle.
The "shear layer" is our name for the thin region where the slow-moving air in the wake gets close to the fast-moving air coming from upstream. Interesting things are happening here, including more mini vortexes.
The flow in a wake is ever-changing and turbulent. A snapshot of the airflow at one moment won't match what's happening at other moments. One way engineers deal with this is by creating images of the "average" flow. These images are useful in some ways, but are also a lie in some ways.
Here's a diagram I created for a work project a while back (the annotations were added for this article). In this case, the wake 'splits' into an upper vortex and a lower vortex of relatively equal size. This is common on certain vehicles (The right side of Figure 1 above also has an 'upper' and 'lower' portion, but the lower portion is much smaller):
When we're looking at these side views, we're looking at a 2-D slice of a 3-D phenomenon. The wake doesn't really have a "lower vortex" and an "upper vortex". Instead, these are two parts of one 3-D ring vortex—imagine a tornado whose "top end" circled around to connect to its "bottom end".
The images above all show "streamlines"—lines that show the path of the air. But software used to visualize the results of aerodynamics simulations can be used in many other ways, too. The image below shows the "eye" of this "tornado"—air is curling in towards the vehicle in the space in the middle of the ring, and moving back downstream—away from the car—on the outside of the ring, on all sides.
So, while we'll often look at just a 2-D slice of a wake, since it's both easier to comprehend and easier to visualize, this "connected tornado" or "donut vortex" is the 3D truth—air curling in towards the car in the space enclosed by the vortex ring, and curling away downstream in the space outside the vortex ring. In other words: if we were to look at a top down view of the wake, we'd see a "left vortex" and a "right vortex". But all four of these—left, right, upper, and lower vortex—are all just slices we're seeing from the same 3D donut. I'm sadly struggling to find a paper that actually shows a top-down view.
Side note: A quick word on how aerodynamics engineers talk about cars and the air around them:
When a car is driving down the road, the wake contains air that's being pulled down the road by the car.
But in wind tunnels, which work by blowing air past a stationary car, the wake consists of air that's stationary (relatively speaking)—it's trapped behind the car and not flowing downstream with the rest of the air. Aerodynamicists usually prefer to use this "stationary car" reference frame, and I'll mostly use it here, as well.
From a physical perspective, these two options are equivalent5, since the relative speeds of the car and air are the same.
For example, in Figure 2 above, I write that "high speed air above the car will often 'miss' the wake entirely". That's true in the car-centric, wind tunnel perspective, where the air flows by the car and then keeps flowing through the tunnel. However, in the real world, it's the car —and the air in the wake behind it—that are moving at high speeds. The air up above the car is, of course, not moving at all (assuming it's not a windy day).
Hopefully this isn't too confusing. From here on, I'll generally use the stationary car frame—i.e. I'll continue to refer to unmoving cars and the moving air flowing past them—even though actual cars are obviously moving when driving down a road.
It's also typical to show a car "moving" from right to left in images—or put differently, air flowing from left to right. I believe that'll be true in all the images I show in these posts.
Shear layers
The next feature of wakes worth mentioning is shear layers. The wake itself consists of air swirling relatively slowly. Outside of the wake, air is moving past the car at high speeds. The border region where this high and low speed air meet is known as the shear layer.
The 'shear' in shear layer comes from the concept of shear stress. I think of shear stress as being basically like friction. Take one hand and rub it back and forth across your other forearm. Because of friction, your hand will pull the skin of your forearm slightly in the direction your hand is moving. The skin on your forearm, likewise, is pulling your hand against the direction it wants to move, making it slightly harder to move your hand.
Something similar happens to fluids like air. When a high speed flow interacts with a nearby low speed flow, the high speed air will "pull on" the low speed air, causing it to speed up a bit. The low speed air, likewise, will equally "pull against" the high speed air, slowing it down slightly. Here's an image with annotations highlighting the shear layer:
We'll talk a lot more about shear layers later, so I'll keep it brief here. There's two basic things to know about them. First, as described above, there's a lot of frictional "pulling" back and forth between the low-speed and high-speed air.
Second, as a result of all this pulling, the shear layer is full of smaller mini-vortexes. I won't bother trying to expain to you here exactly why that happens, though I do think it's sort of beautiful. The patterns of mini vortexes in the shear layer generally look something like this:
If you're following closely, you might have a question at this point: well, why weren't those little vortexes present in the previous images we've seen of wakes? And that brings us to our next topic.
Turbulence and transience
There's one other important feature of wakes that all the images we've seen so far don't highlight well: wakes are turbulent and chaotic. Chaos is a fitting word here (as discussed in the last post): like the person who makes a small decision that takes their life in a totally new direction, two air particles that start out close together may end up nowhere near each other after entering a wake. Or to put it another way, the wake at one moment never looks quite the same way it looked a moment ago, or a moment from now. The smooth lines we see in the images above show us what the air is generally doing—but any particular air particle is taking a much less smooth path through the wake.
The above diagrams—which are pretty typical in aerodynamics—are a simplification: they show the airflow 'averaged' over a long period of time. That average smooths away the swirling chaos in the wake. At times, it can be useful to think in terms of this type of average. At other times, it will be useful for us to talk more about what's happening in that unaveraged, chaotic flow field. (The term transient—"changing with time"—is often used to described this unaveraged airflow.)
The image below, also from Aerodynamics of Road Vehicles, attempts to highlight the difference between the real-time, chaotic flow (the top two images—each uses a slightly different technique to display the data) and the averaged flow pattern (the bottom image, looks much more like the other examples I've shown so far):
In short, we've now covered the basic features you should know about the wake behind a car or truck:
The overall structure is something like a 3D whirlpool, with air circling around (like a whirlpool, tornado, or hurricane). The relatively calm "eye of the vortex" is in the shape of a 3D donut, with air generally moving back towards the car in the 'hole' of the donut, and curling away from the car on all sides (top, bottom, driver side, passenger side) outside of the donut
The shear layer is the area on the edge of the wake where the high-speed upstream airflow meets the slow-moving air of the wake. This meeting leads to many smaller vortexes being spawned, which then travel along the edge of the wake.
Wake flow is turbulent and chaotic, with mini-vortexes of air swirling all around in an ever-changing way. Engineers often use images of the "average" wake, which highlights some features of the wake while "smoothing away" other features.
Drag—why and how wakes matter
Now we know what wakes look like, but why do they matter? Why should we care about shear layers, etc, other than out of pure curiosity? In short, what we "actually care about" is drag. Aero engineers endeavor to design a car that's more aerodynamic—that cuts through the air more smoothly.
Drag is the word we use for the force of the air that's resisting the car's forward motion. There are other forces a car feels, too, pushing in other directions: side force is the force pushing your car to the left or right—a crosswind hitting your driver's side window will create side force. Lift is the force pulling the car up (into the air) or down (towards the ground). F1 cars have wings angled to catch the air in a way that the air pushes the car into the ground, which helps the car's traction.
The forces a car feels from the air come mostly from the air pressure6. In general, the force on a surface is the area of that surface multiplied by the pressure acting on it. And pressure always acts perpendicular to the direction a surface is "facing", so to speak. Pressure on the front license plate will only push a car backwards, not to the side, while pressure on the driver's side window will push a car to the side, but not backwards. If you add up the [pressure times area] of every surface on a car, while accounting for the direction that surface is "facing", you'll calculate the drag of the car.
Some surfaces, of course, will be angled in a way that they contribute to multiple forces. Air in contact with the front windshield will contribute to both drag and lift, as in Figure 8 below:
The funny thing about wakes is that they're at the back of the car. If air pushes on the rear windshield...it pushes the car forwards! But what happens in real life is that the wake is a slight vacuum—because it's "hard" for air to get in there, the pressures are slightly negative—and that negative pressure pulls the car back towards it, adding to the drag.7
So when a car has a "worse" wake (drag-wise), it's because the pressures in the wake are lower—there's a stronger vacuum pulling the car backwards.
This all brings us to one final point about the relationship between drag and wakes: as I said above, drag is calculated purely using the pressures on the surface of the car. The flipside is that any air that isn't in contact with the car's surface is not directly relevant to the car's drag. Of course, the overall features of the flow field will determine what the pressure is right next to the car's surface. But only pressure on the surface matters for calculating drag.
Why does this matter? Well, we aerodynamics engineers will often talk about features of the airflow that are not directly in contact with the car—the length of the wake, the angle of the shear layer, the location of the "vortex core", etc.
But an aero engineer ultimately cares most about drag, and thus ultimately cares about air pressures immediately on the car's surface. To understand wakes, we need to understand how their features help determine the pressure felt on the surface of the car, and that's where things often get complicated. We like to think we know how a change in the wake shape influences drag, but in my experience, when we take a closer look those explanations are more hand-wavy than they are science.
In summary—drag and wakes
Aerodynamics engineers care about wakes because we care about reducing drag—reducing the force of the air pushing on the car that makes it hard to drive forwards.
Because the wake is behind the car, the way wakes increase drag is by pulling the car backwards. They are, relatively speaking, a vacuum.
In order to say we understand wakes, we need to have a clear understanding of how certain features of the wake relate to the thing we ultimately care about—the drag force experienced by the car. To fully understand wakes, it's not enough to talk about the shape of the wake itself, we also need a reliable understanding of how that shape ultimately affects the air pressure on the car's surface.
With that extended introduction out the way, in the next post we'll finally start exploring aerodynamicists' convoluted attempts to understand wakes.
References
Duell, Edward G., and A. R. George. "Experimental study of a ground vehicle body unsteady near wake." SAE transactions (1999): 1589-1602.
Schuetz, Thomas Christian. Aerodynamics of road vehicles. Sae International, 2015.
Tadatsu, Masaya, et al. "A Study on Aerodynamic Drag Reduction for Two-Box Car." Transactions of Society of Automotive Engineers of Japan 44.5 (2013). (Japanese: "2Box 車の空気抵抗低減に関する研究")
Zhang, Yang, et al. "Vehicle aerodynamic optimization: on a combination of adjoint method and efficient global optimization algorithm." SAE International Journal of Passenger Cars-Mechanical Systems 12.06-12-02-0011 (2019): 139-153.
This is simplifying things, of course, but it's true enough for our purposes. It's not that "planes have no wakes", but rather just "ground vehicles have much larger/bulkier wakes, relatively speaking".
As we’ll discuss more later, this simulation result is showing the average path of the air. The path of any particular 'particle' of air is more chaotic, and generally won't follow the path of the average flow, especially in the wake.
If you know of any better videos, let me know
Again here, we’re looking at the path of a hypothetical "average" air particle
At least as far as car/air are concerned. However, the road should be moving at the same speed the air is (i.e. both are unmoving if you're outside on a non-windy day). Wind tunnel companies go to extraordinary lengths to make this realistic as well, using what are essentially treadmills to move the ground past the car at the same speed as the air.
There is also drag due to friction of the air traveling past the car's surface. Friction drag isn't super important to our discussion here, so I'll ignore it from here on. It plays a larger role in airplane aerodynamics, since (1) airplanes have a much larger surface area, and (2) airplanes have (in general) much lower "pressure drag".
This is another simplification. All pressure is positive pressure—at a basic level, it is the macroscopic result of air particles bouncing off a surface. But most aero engineers tend to think of the pressure in a wake as a vacuum, as the pressure is lower than that of the surrounding air. So it's not that the wake is actually pulling the car backwards, but rather, it's just not pushing the car forwards very much. That said, I may default to talking about it like a vacuum in the future.
Did you have any posts regarding science and flying disc like lift, stall, drag, gyroscope, staring velocity stuff? pretty curious about it