Why Does a Small Wake Matter?

Wakes are easy to observe in some media. Watch a boat moving through water and the expanding wake is readily apparent; similarly, when you've been swimming and scooped your hand through the water, you have seen the trail of bubbles following the motion. Wakes are harder to see in air—nearly impossible without rain or water spray, or smoke traces in a wind tunnel—but they exist just the same. We're all intuitively familiar with wake behavior and generally know that minimizing the wake tends to correlate with decreased fluid drag (like moving your hand palm-first versus sideways through the pool water). But just what is a wake, and why does it form? Why is wake size important? Or is it?

Dragging a chopstick through a bowl of water (with food coloring added for better visibility) creates an expanding wake that looks like a "V" behind the stick. What goes on inside that wake?

Wake Formation
 
Wakes form due to the fact that real fluids are viscous; that is, there are interactions between the molecules in the fluid that make it resist shear. Some fluids, like honey or molasses, have high resistance to shear while others, like air, have low resistance, and we call this resistance viscosity. A common definition is that viscosity is resistance to flow but this is not quite accurate; viscosity measures resistance to shear stress (quantified by the fluid's strain rate in response to that shear) arising from "layers" of fluid moving at different speeds, and the inability of a substance to maintain a static resistance to shear is actually the defining characteristic of a fluid versus a solid.
 
Without a velocity gradient, there are no shear stresses in the flow and viscosity is undefined. This allows us to model a lot of flow situations in aerospace engineering as inviscid or having no viscosity. Where this assumption breaks down, however, is in the determination of fluid dynamic drag.
 
All bodies submerged in a moving fluid develop something called a boundary layer (the fluid must move relative to the body—a car is actually the opposite; the body moves through a static fluid. The important thing is that there is relative motion between body and fluid). Boundary layers form due to the no-slip condition at the body surface, which causes shear layers to develop with a velocity gradient as the flow near the body adjusts from 0 velocity at the wall to freestream velocity at the upper edge of the boundary layer. These shear layers (moving at different relative speeds) create friction which in turn dissipates energy. So, through the boundary layer there is a loss of energy and this loss of energy means, in turn, a loss of streamwise flow velocity and thus momentum.

(M. Clarke, AE416 Applied Aerodynamics Class Notes, University of Illinois, Fall 2025).

Momentum loss in the direction tangent to the body means less mass flow in that direction; that lost mass flow must appear somewhere else (since it must be conserved). Hence, fluid pushes "up" through the boundary layer and the boundary layer gets thicker the further back it is on the body. We characterize this by physical boundary layer thickness δ (lowercase "delta") and boundary layer "momentum thickness" θ (lowercase "theta"). δ is the physical distance from the body surface to the top of the boundary layer, usually defined as the point where u = 0.99u_∞ or 99% of freestream velocity. θ is a value, also measured in units of distance, that represents the loss of streamwise (i.e. in the direction of flow) momentum in the boundary layer compared to the freestream. This last is useful because it can be used to predict separation by the dimensionless "shape factor" H, which is inversely proportional to θ.

 
If airflow separates somewhere on the car and no longer follows the surface, this increases friction and dissipation in the flow—losing more momentum. The loss of momentum in the flow around the body causes a "wake" to form behind the body i.e. an area of lower momentum compared to freestream flow (momentum deficit). This momentum deficit is proportional to the drag force on the body.
 
Measuring Momentum Loss
 
So, if momentum loss is a phenomenon of all real fluid flows as they interact with submerged bodies, can we observe or measure it on a real car? Yes! By proxy, there is a simple test you can perform that will illustrate.
 
At the front of the car, there is some total pressure in the freestream (before it interacts with any of the car's surface) and, as energy is dissipated in friction in the boundary layer and areas of separated flow, there will be less total pressure and less momentum in the flow the further back it travels over the car since we aren't adding any energy to it*. Thus, characterizing total pressure along the car should give us a measure of these losses.
 
*(Be careful with this. When it comes to devices like vortex generators, you will commonly hear people talk about them "adding energy" to the flow. They do not. Quite the contrary: by inducing local separation at the device and increasing turbulence, vortex generators dissipate energy. If you don't believe me, answer this: if vortex generators "energize" the flow, where does that energy come from? What vortex generators do is convert some of the internal energy in the air into kinetic energy, but they cannot do this isentropically, resulting in an overall loss of energy).
 
To do this test, you will need to measure freestream dynamic pressure first. Do this with a total probe and static probe on a pole at the front of the car:

Then, measure pressure loss between the freestream total probe and another brass tube taped to the car body surface, facing into the flow:

If you're unsure of the flow direction at any location, use tufts to find out. Along the centerline of the car, pointing the probe opening straight forward should, due to the approximate symmetry of the body, be close enough if you wind-average (record values in opposing driving directions and average them).
 
If you move the surface probe progressively further backward on the car, you should find increasing total pressure loss. Use your measured values to find total pressure coefficient C_P,tot by

You can do this at one speed or varying speeds to check for Reynolds (Re) sensitivity. Plotting total pressure coefficient as a function of displacement at one speed (55 mph) on my car shows:

The negative gradient of C_P,tot shows increasing total pressure loss in the direction of flow—and corroborates what we ascertained above. Notice that this trend holds generally but there is some discrepancy on a finer level. This is due to the turbulence in the boundary layer. Cheap, digital manometers (as I used for this test) have a fairly low sampling rate and so there is some margin of error in their ability to capture fluctuations in the turbulent boundary layer, so some locations show an apparent slight increase in total pressure. If you have access to a pressure scanner with a high sampling rate, it should handle these measurements better. But even a low-cost manometer captures the trend with enough accuracy for our purposes, showing increasing total pressure loss in the boundary layer as the flow moves along the car body, and generally higher total pressure along the smooth upper body than the rough lower body (which loses a significant amount of energy even near the very front of the engine undertray—an indication that flow separates there).
 
Characterizing the Wake
 
Wakes can be measured by total pressure loss or velocity loss behind the car, with velocity inferred from dynamic pressure or measured directly by a hotwire probe (similar to what your car uses in its MAF sensor). Since velocity and momentum are directly proportional, loss of velocity is the same as loss of momentum with constant mass flow. Less momentum loss in the flow means less drag on the body, while more momentum loss means more drag.

The sectional drag coefficient of this cylinder, C_d (lowercase subscript means a sectional coefficient, or "drag coefficient per unit span"), was calculated from the difference in average velocity between upstream and downstream flow, measured by a hotwire probe.

Plotting the average velocity shows the shape of the wake at two streamwise locations, 67 mm and 238 mm behind the cylinder (freestream velocity during this trace was approximately 20 m/s). The wake expands downstream of the cylinder.

You should see now why most bodies achieve their lowest drag when lift is minimized. In order to have lift, the body shape and interaction with the ground must result in an increase of the fluid's momentum in the vertical direction (up or down, depending whether you want it to make negative or positive lift respectively). Since the airflow upstream of the car only has horizontal momentum and we can't create or destroy momentum spontaneously, this means some of that horizontal momentum must be lost in order to increase vertical momentum. That momentum loss in the horizontal results in an increase in drag on the car.
 
You should also guess that just making the wake as small as possible isn't a guaranteed drag reduction. If we made all our cars 50 feet long and tapering to a point, there might be no separation and smaller wake thickness but there would also be significantly more momentum loss in the boundary layer along that extra length. This brings up the important point that all bodies, even fully streamlined ones, develop wakes. Thus, the name of the game is not minimizing wake "size" but minimizing momentum loss in the flow behind the vehicle and, especially for systems like cooling and interior ventilation, momentum loss through internal ducts. This is done by balancing small wake size with minimum to no separation over the body (shaping it with gradual and smooth changes in cross section area, using smooth surfaces such as flush windows as much as possible, minimizing the number and size of protuberances like mirror housings and antennae, avoiding steps and corners, etc.). Additionally, to minimize unavoidable momentum loss due to the boundary layer and resulting friction drag, we want the car body to be as short and small as possible with minimum wetted surface area and to maintain laminar flow as far back on the body as possible. Finally, we also have to consider momentum loss in asymmetric flow e.g. crosswinds, designing a car not just for lowest drag in all expected flow conditions but good stability as well.
 
Estimating Friction Drag
 
Without viscosity, aerodynamic bodies such as cars would not develop boundary layers and would not feel any aerodynamic drag force. This inviscid model is the basis of potential flow theory—something that was recognized early on (in the 1700s) to be incomplete. Potential flow does not model dissipation and friction, so it predicts zero drag and no wake for a body of any shape.

For example, this cylinder in crossflow (of the same dimensions and freestream velocity as the wind tunnel experiment) has two stagnation points in potential flow—one at the front and one at the back (in other words, there is no loss in total pressure), where a real flow would form a wake like the cylinder in the wind tunnel above.

Mathematical derivation from fundamental equations gives basic relationships for aerodynamic coefficients associated with friction. First, friction coefficient is a function of Re and can be estimated by:

However, since these equations are derived from analysis of a flat plate, they are frequently adjusted to better predict friction drag. For example, Raymer (2018) gives an equivalent friction coefficient for various classes of aircraft that can be used to give an initial estimate of friction drag.
 
Friction coefficient or equivalent friction coefficient can then be used to predict friction drag coefficient by,

If you’re trying to estimate friction drag on your car, it's a close enough approximation to assume that the entirety of the flow over it is turbulent (which we want, mostly, since turbulent boundary layers will follow aggressive surface curvatures that laminar boundary layers won't). Estimating the wetted surface area of my car from its dimensions, at a speed of 65 mph its friction drag coefficient is in the ballpark of ~17.9% of its overall drag, a reasonable estimate that is close to the "rule of thumb" of 15-20% friction drag/80-85% pressure drag for typical cars. This friction drag is a small fraction of overall drag, of course. Pressure drag accounts for the majority of aerodynamic drag on cars and, importantly, even on a fully streamlined body there will still be pressure drag due to the presence of the boundary layer, which changes the pressure distribution. Importantly, both of these are captured in momentum loss and wake characteristics, as in the cylinder experiment above; pressure drag likely accounted for most of the force on the cylinder as it does on cars.

Pressure

Wait a minute, you might be saying, I've always heard that there's a low pressure wake behind cars? Isn't it the low pressure that causes drag?

Pressure, friction, and momentum are all related in the Navier-Stokes equations. These equations are derived from a control volume drawn arbitrarily around a volume in space through which fluid passes. The walls of that volume can be placed anywhere we want; if we draw a volume starting well upstream and extending downstream of the car where static pressure is approximately equal in both locations, then all pressure forces exerted by the fluid are internal, as are viscous forces. These two—pressure and shear—are, as I've written before, the sole mechanisms by which the fluid exerts force on the car body. These internal forces (with respect to the flow volume) are equal to the momentum change in the fluid. Hence, the wake is the area of momentum deficit behind the car. There is low pressure in the wake that acts on the rear surface or base of the vehicle (but not as low as a lot of people seem to think) which accounts for part of its pressure drag, but this pressure drag is reflected in the momentum loss in the flow further downstream of the car.

Two more comments on wake behavior. First, vortices are shed by the body, and the frequency of the vortices changes with Re. In the same cylinder experiment above, we also measured these vortex shedding frequencies at multiple wind tunnel speeds, and the fluctuation in velocity showed:

Because of these fluctuations, base pressure is not constant but fluctuates as well (something I noticed the very first time I ever tried measuring static pressure on my car: taping a tube to the rear license plate and connecting it to the test port, the needle on the Dwyer Magnehelic I was using bounced around at a regular frequency that increased with the speed of the car). Second, as Re increases, the "shape" of the wake changes; it is not constant with speed but can change dramatically. Schematically, variation in the flow over the cylinder with Re results in a wake that looks like:

(AE460 Lab Manual: Hotwire Anemometer and Cylinder Wake, University of Illinois, Fall 2025).

The same is true of the wake behind your car. It is not a constant shape but varies with how fast you drive, and the frequency of vortex shedding and base pressure also varies.
 
Important Lessons
 
The key takeaways here are:
 
1) All bodies develop wakes, even fully streamlined ones.
2) Wakes form due to momentum loss in the flow past the body, and this momentum loss is proportional to the drag force on the body.
3) Because even streamlined bodies have wakes, they still develop pressure drag because the presence of the boundary layer changes the pressure distribution over the body.
4) When you see someone claim that adding a long tail to your car guarantees "no pressure drag," "no wake," and lowest drag overall, now you know they're lying or misinformed and you know why they are wrong. Reality is much more complicated, and low drag is not necessarily about minimizing wake "size." Rather, it's a result of minimizing momentum loss in the flow behind the vehicle.

Addendum

I mentioned earlier in this post that many useful situations in aerospace engineering can be modeled with inviscid flow. Why is this?

The cylinder solution will illustrate. Previously, we saw the symmetric flow field around this body. If we add circulation by superposing a point vortex of some strength Γ (uppercase "gamma"), the streamlines change and the two stagnation points move downward:

Now, there is lower static pressure above the cylinder (where the velocity along streamlines is faster) and higher static pressure below it, producing a lift force. In a real cylinder, circulation could be produced by spinning it; you've seen this in videos of people putting "spin" on balls to increase the distance they travel when thrown by producing lift or sideways force (depending which direction they spin e.g. curveballs) and the cylindrical rotating "sails" on some cargo ships.

If we model the surface of an airfoil as a series of small vortices, we can actually find its total lift force; this is called the "vortex panel method" and it underpins many, many flow simulation programs for both airfoil and full wing modeling. Potential flow solutions work well for predicting lift forces even if they can't predict drag!