Measuring Spoiler Performance

In my previous spoiler testing, which was extensive, I made a lot of mistakes due to the fact that I only had a little education in engineering. Specifically, there were two major issues that I now want to correct: I did not normalize pressures (that is, turn them into dimensionless values for easier comparison), and I tested at only one Reynolds number. Because of these issues, the results aren’t really generalizable and are not easy to interpret. Let's fix that.

Production spoilers are often art as much as—or more than, given how much styling sometimes dictates their shape—functional devices. This Toyota 86 has a very aggressive spoiler design for a production car.

Recap
 
One of my most-read posts here has proven to be an article on spoilers I wrote early on, back when I didn't really know anything yet since I hadn't formally studied aerodynamics. I got the criticism of online theory right (yes, that weird theory that spoilers create "ideal" streamlines—whatever that means—and reduce pressure on upstream surfaces is a load of crock) but not the fundamental explanation of how spoilers work. That comes down to a momentum balance, using the fact that momentum cannot be spontaneously created or destroyed within any arbitrary control volume. At steady state, all the momentum that comes into the volume must be accounted for on its way out—convected out of the volume or transferred to a surface through pressure and shear stresses—and any change in the momentum inside of the volume must be accompanied by a force acting on the fluid. If one surface of the control volume is a physical surface that does not allow flow to cross (such as a window or panel on a car), the momentum changes and reaction force will show up as changes in panel pressure.
 
I wrote about this more recently in my post on how to think about aerodynamics, with this example test you can do at home: measure pressures on a board taped to your car, bending it down, flat, and then upward. What happens to the pressure along it?

That's what spoilers do: by increasing upward momentum they must rob it from longitudinal momentum, and this momentum change shows up as an increase in pressure.
 
History
 
Spoilers were an invention of aviation before they migrated to cars, and their original purpose was and is twofold. When you've flown before, you might have noticed the spoilers on the wing upper surface deploying during landing. They aren't fully deployed in any other flight segment (they may be partially deployed on one wing during flight to counteract unwanted roll) because their primary purposes are 1) to "spoil" lift by stalling the wing (separating airflow over the wing upper surface while the wing is at a high angle of attack, a "positive incidence stall"), and 2) to increase drag so the friction brakes have to do less work slowing the aircraft down.
 
You might have also noticed that wing spoilers on commercial aircraft are not placed at the trailing edge but somewhere in the middle of the wing surface, ahead of the flaps and just behind the location of maximum wing thickness:

(Image credit: Reddit).

Because they disrupt fast-moving flow over the wing, spoilers increase pressure both ahead of and behind the device; placing them at the wing trailing edge would make them less effective.
 
It's a different story in cars, where we typically want a spoiler to decrease lift (the same as in aircraft) but to do this with minimal drag increase or even drag reduction (very different from aircraft, where a drag increase is desired upon spoiler deployment). For this reason, spoilers on cars are typically placed at trailing edges where they can be very effective at reducing lift while adding minimal drag or sometimes even decreasing it.
 
Nondimensional Pressure C_P
 
Nondimensional coefficients are useful because they normalize absolute values. This normalization means we can better or more easily compare the behavior of airflow parameters with some built-in agnosticism to ambient conditions such as temperature and density, and changes in the parameter with variables such as vehicle speed can be more easily discerned. In the case of body surface pressures, our nondimensional static pressure coefficient is defined as

where p_∞ is freestream static pressure, q_∞ is freestream dynamic pressure, and p_s is local static pressure. If you're measuring differential (gauge) pressure of a body surface tap/disk referenced to a static probe at the front of the car, then you already have the term in the numerator. The denominator can be found by measuring the difference between the same freestream static probe and a total probe (a tube facing forward into the flow).

C_P can also be defined by the ratio of local and freestream dynamic pressure (you can derive this yourself from the equation above):

From this you can see that the maximum possible C_P is 1, and that C_P is negative if local flow velocity is higher than freestream and positive if local flow velocity is less than freestream. A common point of confusion: this local velocity is the speed of the inviscid flow outside the boundary layer. At the surface of the car, flow velocity is always 0.
 
Reynolds Number
 
Reynolds number is an important value in fluid dynamics since it gives us a lot of information about how a flow will behave. In fact, Reynolds number and Mach number are dimensionless values called "similarity parameters" because, in order for a flow to behave the same way over a scale model as it does over a full-size vehicle, these are the two parameters that must be matched within some reasonable range. Reynolds number, abbreviated Re, is the ratio of inertial force to viscous force in a flow:

where u is flow velocity, L is characteristic length, μ is dynamic viscosity, and ν is kinematic viscosity (dynamic viscosity divided by ρ, fluid density. That's the Greek letter "nu," not Roman "v").
 
As Re increases, small disturbances and instabilities in a flow that would naturally be damped at low velocities have more tendency to be amplified instead. The fluctuations that result from these amplified frequencies are called "turbulence." The onset and development of turbulence in the flow affects everything from separation points and how strong an adverse pressure gradient the flow will tolerate before detachment to the amount of friction drag the vehicle experiences. Further, as vehicle speed increases, the local Reynolds number Re_x (Re at a given point on the vehicle body) will increase proportionally, as will total Reynolds number Re (based on the full characteristic length of the vehicle; in cars, this is approximated as the straight-line distance from front bumper to rear. In aircraft, this is typically the "mean aerodynamic chord" [MAC] of the wing). This variation can affect things like the performance of spoilers, especially when placed at the back of the car where the change in Re_x with vehicle speed is highest.
 
Testing
 
So, let's see how C_P on the rear window and body varies with Re, first with no spoiler. Then, let's observe variation in C_P with two different cheap, commercially available spoilers. I'll measure pressure in the middle of the rear windscreen ahead of the spoiler, and in the center of the lower window below the spoiler.

I installed this strip after the comprehensive test (I'll label this one "short" in the plots below). Unfortunately, it has shrunk over time, leaving one end exposed that was originally fitted into the fairing cap; its imminent replacement is what prompted this test.

The alternative is another cheap tape-type spoiler with more aggressive height ("tall"), and this one extends slightly from the trailing edge of the stock flat spoiler.

What I'm going for here is highest C_P on both the rear windscreen and lower window. Higher pressure on the windscreen reduces both drag and lift; higher pressure on the vertical window reduces drag. I'm especially interested in the behavior of C_P at 50 mph and above, as these are the speeds where aerodynamic drag predominates my car's total resistance.
 
Results
 
On the lower window, C_P for each configuration varies with Re as,

Highest pressure coefficient is achieved in the stock configuration, which does not vary with Re. The "tall" spoiler performs almost the same, improving as Re increases and matching the stock spoiler at higher speeds. The "short" spoiler, however, does the opposite: C_P is more strongly negative with higher Re, potentially increasing drag as vehicle speed goes up. This variation of C_P with speed is called "Re sensitivity."

 
On the windscreen, each configuration shows,

Now there is a marked difference between the performance of each spoiler, with Re sensitivity in all three (C_P varying with Re) and the "tall" spoiler showing the largest increase. This last is clearly the winner here, with highest C_P at all speeds tested and consequently the greatest reduction in sectional lift—and this improves as Re increases. Since it appears that it does not decrease C_P on the lower window, I'll probably install this spoiler permanently to replace the old one.
 
The realities of testing meant I did not have sufficient time to measure pressure variation laterally (side-to-side) across either window, or at other locations on the hatch. This is just a fact of life: we have to make decisions based on limited data. In this case, the tall spoiler is almost definitely reducing rear lift and doing this better at higher speed, and it may do this with less drag than the short spoiler I've got on the car now. Since I like the style of the tall spoiler and the old spoiler needs replacing anyway, that's enough reason to go ahead and tape this one on permanently.
 
As always, go try this yourself on your own car!