Aerodynamic Stability – Part 1: Theory

When it comes to cars, "stability" is a loaded term because it is very imprecise. Stability could mean the car's ability to track in a straight line down the highway (which is as much a function of its alignment as anything else), or its ability to maintain its direction and rotation in a constant rate turn, or ability to maintain its composure through a slalom course, or its ability to resist changes in lift, or to not be disrupted as it moves and jostles on its suspension over a washboard road, or any number of other things.

 
So, to talk about "stability" in any meaningful way, we first have to narrow it down. What sort of stability? Stability with regard to what factor or input and what measurement or output?

We'll see in just a minute why these fins might have been a bit misguided.

Aerodynamic Stability
 
Since this is a blog about aerodynamics, let's consider stability as it is influenced by the movement of air around (and through) the car. Here too we run into the same problem as above: this still isn't specific enough. What sort of aerodynamic stability? Pitch stability? Roll stability? Straight line or turning? Lift balance? Overall lift? We still have to narrow it down.
 
Let's consider the degrees of freedom of movement a vehicle experiences as it drives. Obviously, it can move forward or backward along the road surface—let's call this degree x. It can also move left or right (y). And it can move up or down (z), although too much of this is generally not a good thing when it comes to cars.
 
But the car can also rotate around each of these axes. Rotation around x is called "roll" (L); rotation around y is called "pitch" (M); and rotation around z is called "yaw" (N). Add these all together and we have six degrees of freedom. Importantly, these degrees of freedom are coupled; you can't change the vehicle's motion in one degree without affecting it in another. This happens because of the difference in the point of action in a force or torque in any of these degrees of freedom and the center of gravity of the vehicle, which is the point at which we approximate its experience of forces and torques.
 
For example, say a vehicle develops some total lift force L (don't confuse lift force and rolling moment, since we use the same letter for both!) and that L acts at point c some distance behind the front axle line. Assume the vehicle's center of gravity is situated at point d which is at a different distance behind the front axle than c. The action of L will produce a torque about the center of gravity by the moment arm c – d (moment is given by the cross product—a type of vector multiplication—of a force F and moment arm r), which means the lift force will change the pitch of the vehicle by rotation around y.

Lift and pitch are coupled, and the action of this coupled force and moment is called longitudinal stability. These two—lift and pitch—are so fundamental to good aircraft design that pitching moment is often referred to simply as "moment" (and designated M), no further specificity required.
 
Lateral Stability
 
Let's consider another form of aerodynamic stability that is quite useful in car design, this one side-to-side: lateral stability. Lateral (really, "lateral-directional") stability encompasses both side force and yaw (and, in aircraft, roll—we'll consider this coupling negligible for just a moment, since the mechanism we'll discuss is different than the primary drivers of aircraft roll stability). Yaw N is the rotation of the vehicle about z, pointing the nose toward the left or right, and side force Y is the lateral movement of the vehicle in y, pushing the entire car to the left or right. If the vehicle experiences an asymmetry in the oncoming flow—say, from a crosswind—its reaction to the resulting side force and yaw moment determines its lateral stability.
 
In aircraft design, we classify stability as static (single response to a single disturbance) or dynamic (oscillatory response to a repeated disturbance). Let's limit ourselves to static stability, or the initial behavior of the vehicle when it experiences a single perturbation like a crosswind gust. Within static stability, your car can react in one of three ways. First, it may deviate from its path, correct itself, and return to its original path and direction; this is called "statically stable." Second, it may deviate, correct itself, and return to its original direction but on a different path; this is "statically neutral." Finally, it may deviate and fail to correct at all, heading off on a new path and in a new direction; this is "statically unstable."
 
Lateral Stability Model
 
So, what makes a car statically stable when it experiences that crosswind gust? The crosswind will exert a side force on the car due to the asymmetry of the flow field and, depending on where this side force acts, a yawing moment. If the yaw moment tends to rotate the car around its vertical axis z toward the wind direction, it can steer itself back to its original path; this is called a "restoring" moment.
 
The moment coefficient derivative of a car experiencing a crosswind that produces an air velocity vector at angle β from the car’s heading (so, the change in the moment with change in this angle),

…is typically negative; that is, a crosswind from either side will tend to rotate the nose of the car away from the direction of the wind and the stronger the crosswind, the more it will turn away from it, making the car unstable (and requiring steering correction to counteract this instability). Modern cars try to minimize the size of this moment coefficient derivative by manipulating surfaces and edges, especially on the front corners, rear corners, and along the sides of the rear windscreen and trunk.

Insetting the rear window below the quarter panel bodywork leaves a sharp edge, where airflow can separate in a crosswind.

Many cars and trucks today use a sharp edge on the front bumper cover corners, sometimes in conjunction with an air curtain duct, as on this Volkswagen ID.4.

If we want, we can also add a vertical stabilizer (fin) to the car, and this fin will also develop some side force and exert a moment, changing the car's overall yaw moment coefficient derivative by the sum of the two,

In this way, the overall moment can be altered by changing the size and location of the fin so that the car has less instability or, perhaps, is stable and rotates toward the wind rather than away from it. The moment coefficient derivative of the fin is proportional to its area in the x-z plane (S_f), its distance behind the car's center of gravity (l_f), and the dynamic pressure ratio the fin "sees" (q_f/q_∞); as any or all of these are made larger, the restoring moment the fin produces increases since the "lift" on the fin is larger or its moment arm longer. We can make these bigger by:
 
1) placing the fin up and away from the body (increases q_f/q_∞)
2) making the fin as large as possible (increases S_f)
3) placing the fin as far behind the center of gravity as possible (increases l_f)

Commercial and military aircraft, such as this F-16 in Thunderbird livery, use large, tall vertical stabilizers placed well behind the aircraft's center of gravity for these reasons.

So, it would seem the thing to do is put a big fin on the upper body at the back of the car, as tall and large as we can make it. This won't work, however, and you can probably guess why: putting that big fin out there in the crosswind will increase the side force acting on the car, pushing it away from the wind and requiring more moment correction to steer back to its original path (aircraft use rudder trim to counteract this). Further, putting the fin up high will cause the car to roll away from the wind, decreasing its roll stability (aircraft use wing dihedral and sweep to counteract this. Notice that none of these—rudder, dihedral, or sweep—are available to us in car design). Work through the math again, and we find that the side force coefficient derivative is proportional to fin area S_f and dynamic pressure ratio but, crucially, not to l_f. This tells us something important.
 
Fin Design
 
Unlike aircraft, to add a fin to your car that has the best chance of providing a restoring moment while minimizing undesirable side force and rolling moment, we should:
 
1) balance the size of the fin S_f—smaller rather than bigger
2) balance the dynamic pressure ratio q_f/q_∞ the fin experiences by placing it closer to the body where flow speed may be lower
3) maximize l_f by placing the fin as far back on the car as possible
 
Additionally, if we put the fin under the car instead of on top of it (below the center of gravity rather than above it), the rolling moment induced may counteract the car's natural tendency to roll away from the wind direction. Look under production cars and you may see these results in action:

Fins can be flat plates or airfoils with changing thickness along the chord (introducing thickness variation/surface curvature typically increases stall angle of attack). This Sienna, along with a number of older Toyotas, places curved symmetric (zero camber) fins in the middle of the diffuser panel where l_f is smaller but the dynamic pressure ratio may be higher than at the very back of the car.

My Prius uses similar fins: curved airfoil profile (these are a fairly thick, low-speed profile at t/c = 0.15) and no camber, so that zero-lift angle of attack is at α = 0°.

More typical of stabilizing vanes on newer street cars are these, on the 2026 Subaru Solterra; placed in the middle of the diffuser panel, they have a simply curved root and flat tip profile.

Or on motorsport cars:

Upper body fins tend to be used on low cars, like this Nissan LMP car, where there isn't as much distance between the center of pressure of the fin and the center of gravity of the car. This minimizes the detrimental effect on roll stability.

Or on concept cars:

The Ford Probe V concept car is a particularly good example of an upper body fin; notice its small size, position down low and close to the body surface, and placement almost at the very back of the car. (Image credit: Classic & Sports Car).

You should see now why the big plywood fins I tested on my car were misguided: they were large surfaces, placed up high. Unfortunately, the testing I used to try and measure their effect (steering angle) gave only vague results with no way to decompose the test data into side force and yaw moment contributions. So next time, I'll see if I can develop some simple testing you can do to start measuring lateral-directional stability on your own car (I don't know yet if this will work, so stay tuned!).