It’s not obvious how a wind tunnel helps engineers obtain a car’s drag coefficient. It blows high-velocity wind up against a car, but then what? What exactly is being measured and how do you get a drag coefficient from it? How do you make sure the wind speed is exactly what you need it to be? And how do you factor in things like air temperature? Join me, an aerospace engineer, as we answer these questions.

If I say “aerodynamics,” I’m willing to bet that the first thing that springs to your mind is a car surrounded by neat trails of smoke in a wind tunnel. While we spend a fair amount of time talking about the car here at the Autopian, no one ever mentions the tunnel. “It’s just a big tube with a fan in it!” you might think. And you’d be right. But also, wrong. So, buckle up, because I’m gonna blow your mind! Here’s how a wind tunnel actually works, and how it actually calculates drag coefficient, the parameter that describes a car’s “slipperiness” (EX: The Tesla Model S’s drag coefficient is 0.22, the Jeep Wrangler JL’s is 0.45).

Airminology

Before getting into the meat of the subject, I’d like to give you some aerodynamics vocabulary, so I don’t sound like a foreigner beyond my thick French accent:

• Test model or test subject; it’s the thing we want to analyze in the wind tunnel
• Test section: it’s the area of the tunnel where we position said thing for measurements
• CFD: Computational Fluid Dynamics (or Colors For Directors as we funny bunch say) is a computer program able to simulate fluid behavior on a virtual 3D mock up. It’s the thing that produces those fun colorful images of streamlines flowing over cars and through their cooling openings
• Fan: it’s the same thing that you’ve been using  during the ’23 summer from hell, except it’s enormous

Sizing The Test Section and The ‘Vein’ Of A Wind Tunnel

To learn about these awe-inspiring marvels of technology, we’ll pretend like we’re engineering interns. We’re tasked with designing a wind tunnel for a car: the Verissimobile, we’ll call it. The car looks like crap because the eccentric CEO only cares about drag reduction, but he pays our engineering company handsomely to design the best test facility ever, so let’s indulge him.

The first order of the day is designing the test section around the test subject we want to analyze. We know how big the car is: two meters wide and one meter high. As clueless interns we are tempted to make the smallest section possible, let’s say 2.2m x 1.1m, so as to need as little air flow as possible. That’d be our first mistake of the day!

If the walls of the tunnel are too close to the model being tested, they will impact the flow around the test subject by reducing the available area in the car’s vicinity, accelerating the flow thanks to the good old Venturi effect that I wrote about before. That isn’t something that’d happen in the real world driving down a highway unless you’re speeding in one of Musk’s “Boring” tunnels, so we’ll scrap our design and get back to the drawing board.

Let’s make the section just large enough to be outside of the Venturi effect. Did we account for the boundary layer (which I’ve mentioned in a previous piece) on the tunnel walls (this is the tendency of air to “stick” to surfaces)? No? The flow isn’t uniform around the model then! Back to the drawing board again!

Make it way huge so we’re sure to be uniform? Bravo, our tunnel now needs a nuclear power plant next to it to keep it powered.

After some more unpaid design/CFD iterations (remember, we’re interns), we finally Goldylock our section! Not too big, nor too small. Perfect! Now we just put a big fan ahead of the car, draw a straight section behind the car to act as an exhaust, and…right away our colleagues start mocking us. “An exhaust on a wind tunnel? Do you also open the windows when you turn on the heat?” they joke.

The condescending enfoirés have a point. That’s a lot of wasted kinetic energy; we’re trying to avoid needing that power plant, remember. How about a loop? This way we only need to fight off the internal losses of the flow in the tunnel. We’ll throw some guiding vanes at the corners of our 90° angled loop, because we don’t feel like buying more land to make a nice big circle, and our vein is done! Let’s get the air moving now!

Sizing The Fan

Picking a fan requires knowing two important parameters: its mass flow and its pressure drop. To (over)simplify things, the air speed that the fan produces will be dictated by the pressure drop and the air’s mass flow by the fan’s diameter.

[Editor’s Note: If you’re averse to nerdy equations, you can skip down to the black and white photo of the giant fan and start reading from there. -DT]. 

With the flow path finished (see above NASA design for reference), we can now estimate pressure losses in the tunnel. We can use CFD (computational fluid design) computations that make awesome colors and badass animations which are basically the reason we chose fluid dynamics as a specialty. Or, we can save ourselves a few weeks of work and open up the Idel’Cik reference book to get our pressure loss coefficient. Yeah, let’s do that.

We’ve got our pressure loss coefficient for the entire installation, but that’s not enough to choose a fan. We need to determine what kind of mass flow we need. For that we must know our test section (that’s the area of the part of the tunnel where we’ll test our car, which we chose earlier), our target speed (call it 200mph for a car), pressure (1 atm) and temperature (15°C is standard). We plug all these numbers in the following formula and we get our mass flow:

For pressure =1 atm, T=15°C, we know ρ=1.225 kg/m3. I could show you the math but there’s no time! The customer awaits!

Et paf! Mass flow! As a bonus, we can use the speed in the duct in conjunction with the pressure loss coefficient to determine how much pressure our fan is going to face:

Et voilà! Now we can pick a fan! 

We could go into more detail about how fans and even compressors work, but as always, it’d take a full article. Maybe some day we will! I have to work through the trauma of 2 years designing APU compressors first though.

The fan we’ve picked won’t be running its entire life at full chat. It’s important to be able to measure the wind speed encountered in the test section in order to correct the fan’s speed. The most common tool used to do that is the pitot probe — you know, those little pointy tubes found on airplanes

By measuring the difference between the total and static pressures, we can deduce the wind’s speed. A single probe is fine if the flow is perfect but it’s usually a good idea to have an array of probes to account for turbulence, boundary layers and overall unexpected air behavior. 

Controlling Air Density

As a gas, air has a density that changes with its pressure, but also its temperature, as stated by the ideal gases law (that’s the one I used to compute air density before without showing my math).

You now know that density is everywhere in our equations, so it’s important to control it. That means we need to keep pressure and temperature in check. Controlling the pressure in an automotive-focused wind tunnel would be an expensive and overall pointless endeavor, as a car is destined to remain at ground level, so that parameter is only monitored using static pressure probes. 

However, since the fan will gradually heat up the air in the tunnel, we need an actual temperature control system in the form of heat exchangers (or radiators if you insist on using wrong terminology) — you can see one in the McLaren F1 wind tunnel in the video above. A single radiator is fine if you only care about temperature, but since it would be too easy, we also have to control humidity, as it can impact the air density too! That’s why we need a heating radiator just after the one for cooling in the tunnel. 

The principle is simple. If you cool down the air, it can’t hold as much humidity and condensation appears (just like on your cool soda on a hot summer day). That allows you to trap some water in liquid form, and then if you reheat the air, you can control the amount of vapor in it. 

The tunnel features temperature and humidity probes in the vein. Monitoring those values allows setting the heat exchangers parameters (flow and temperature) to make sure the conditions in the tunnel are exactly the ones required for the test.

Controlling Turbulence And Boundary Layers

I’ll be straight with you: You won’t walk out of this article knowing what turbulence precisely is, nor what it means for aerodynamics — that’d require its own article(s). Just know that it’s a bunch of vortices that make the math we deal with a saloperie. A putain de saloperie even. These aren’t good things.

One way to control turbulence is to limit the vortices’ size. We can do that with a pattern of surfaces that are going to break up those structures. It’s basically a cheese grater that will give us fine little bits of turbulence instead of a big block of it, reducing their energy and therefore impact on aero. We can put a mesh screen and/or honeycomb structure ahead or our test subject to achieve a laminar(ish) flow, which is what you are most likely to encounter on the road, unless you’re a storm chaser.

Even though we made our test section wide enough so that the boundary layer on the walls won’t impact our car’s aero, we still have to deal with the boundary layer on the ground (the BL on the DL if you will). The simplest solution? A raised platform so our test vehicle sits outside of it! I wish it were that simple, but the issue is that automobiles are… mobile.

Indeed, when you drive, the road and the car’s underside have a relative motion which creates shear. This can have a dramatic effect on aero, so it’s got to be simulated in the tunnel, too. To do so, there are “rolling roads” on which you can set up the car (Mercedes is explaining that to Lewis Hamilton in the video above). It’s like a dyno, but instead of rolls for each wheel you use, essentially tank track(s) for the whole car. 

As you can see on that schematic, those rolling roads include a “boundary layer removing system.” There are several techniques to have a nice and constant velocity profile, but in our case I believe the best way to do it is either by sucking the boundary layer (case 3.c in the illustration below) or blowing air near the ground (case 4.c).

How Do You Measure The Drag Coefficient? You Don’t — You Calculate It

Despite how nice trails of smoke look on a PR brochure, it’s not the main focus of aerodynamics engineers. Just like any engineer, an aero one is a numbers person. A spreadsheet fetishist even. If something isn’t quantifiable, it can’t be optimized, and optimizing stuff is what we engineers are paid for. That’s why we need to be able to know the forces acting upon the car to derive the lift and drag coefficients of the car.

To do so, the car is maintained on the rolling road with what’s called a “balance.” It’s a support that holds the model in place, either using one big arm connected to the body of the car, several rotating arms connected to the wheels, or both. These balances feature calibrated strain gauges on certain sections. The deformation of those sections will impact the electrical resistance of the gauge which allows measuring the force acting upon them. By having six gauges in strategic locations on the balance, we can deduce the forces and moments acting on the three axes of the balance, and therefore on the model.

Alternatively, you can even have strain gauges on the entire platform to achieve the same result! You just need to have a little bit of space available below your wind tunnel test section.

Knowing those loads allows you to determine how much the wind pushes the car back, which is the very definition of the drag force, as I showed in a previous article.

That force Fd pushing the vehicle back is the only thing one needs to measure in the wind tunnel in order to derive the drag coefficient of a car. Indeed, the air speed is controlled in the tunnel, so we already know what the “v” parameter value is. Same thing for the air density ρ thanks to the pressure and temperature probes. 

The frontal area could be derived from the CAD file, or you could do it the DIY way, with a camera, a scale and mad Photoshop skills, as shown below:

Or you could use an expensive sciency system that does it all on its own like this one from German company S.E.A. GmbH:

Once you’ve got that frontal area measurement and the drag force from the load cells under the platform that the car sits on — and since you know things like the air speed and density — the drag coefficient can easily be computed by rearranging the drag equation:

And there you have it! You can now compute your car’s drag coefficient!* 

*provided you have access to a multi-million dollar facility, crew, electricity budget and logistics

Beyond Air: Precipitation And Radiation

You were probably wondering why I mentioned humidity. Well, some wind tunnels can do more than drag testing; they also allow to test your car in simulated climates. They’re called climatic wind tunnels (duh!), and they are AWESOME! 

Your mom’n’pop wind tunnel can already control temperature in the vein, but if you add heating elements, you can simulate the sun’s radiation on your cooling system. A set of spray bars can give you rain, fog, snow or even frost! 

These tunnels are incredible! You can test during the same day how snow is going to stick on your windows in Norwegian weather to make sure visibility isn’t impeded, and then measure your engine bay temperature during a drag race in Dubai!

The only downside is that you’ll spend your entire day alternating between 20°C in the control room and -40°C in the tunnel. You WILL get sick as a dog. Ask me how I know!

Beyond Cars: Altitude Simulation and Supersonic Flow

I’ve never heard of altitude simulation for cars, and I doubt it’d be useful but since I’m in charge here, I’m gonna tell you about it anyway! Wind tunnels are useful for cars, but they’re even more important for aircrafts, which fly at altitudes where the pressure car be very very low (down to a fifth of the ground pressure for planes) and that matters a lot for a wing or a turbine.

So, in order to account for this one last parameter, all you’ve got to do is vacuum air out of your airtight tunnel! That’s simple enough, but what if you want to do that with supersonic speeds? Well, first you need more airflow and pressure in your fan. You need so much more of these that you’ll have to use a compressor instead. It’s basically a fan on steroids, so it doesn’t change much regarding the design of your tunnel. 

Then, you’ll need to change your test section, which may require a throat to allow a subsonic to supersonic transition. That’s what we see on the red nozzle in the diagram. Supersonic flow is another thing we could dive into, but again, it’d deserve its own article, fuzzy math, confusing graphs et tout, et tout.

[Editor’s Note: I’d like to just add this info from NASA, as it really breaks things down the idea of how strain gauges are getting all the forces through the platform:

From NASA on a wind-tunnel test for a jet:

During a test, the model is placed in the test section of the tunnel and air is made to flow past the model….The most basic type of instrument used in this type of testing is the force balance. We must measure six components, three forces (lift, drag, and side) and three moments (pitch, roll, and yaw), to completely describe the conditions on the model. For some tests, only three components (lift, drag, and pitch) are measured.

[…]

As shown in the figure, an idealized fighter plane model is attached to a platform located beneath the test section by a two strut mount. There are six strain gages, labeled A through F, that are connected to the platform. Each gage measures a force by the stretching of an electrical element in the gage. The stretching changes the resistance of the element which changes the measured current through the element according to Ohm’s law. The model can be rotated in pitch and roll by its connections to the struts, and rotated in yaw by the circular section in the floor of the test section.

A test is conducted in the following manner. With the tunnel turned off and no air passing through the test section, the weight (W) of the model and mounting system is determined as the sum of the forces from gages A, B, and C. The tunnel is then turned on and air flows over the model. The model generates aerodynamic forces and moments that changes the readings on the strain gages.

The lift (L) is given by:

L = A + B + C – WThe drag (Dr) is given by:
Dr = E + DThe side force Y is:
Y = F

I didn’t include the moment calculations, but you get the idea. You have gauges measuring the forces that are being imparted from the jet to the platform. And all those forces get used to calculate the performance values you’re looking for. -DT]

If you made it this far, I’m giving you a good grade for your internship! I tried easing up on the equations as we’ve cemented some important theoretical concepts in the previous torture sessions articles, hopefully that format is to your liking! If you have questions, I’ll be lurking in the comments despite the time difference because I care about my interns! You deserve the whole confusing theory behind these cool schematics.