Testing and Improving Stability: Part 3

In my first two posts on testing directional stability, I used first a cellphone with angle measure and then a Scangauge reporting steering angle from my car’s OBD system to try and measure changes in its stability. That worked okay but I had no way of logging data to verify that what I thought I saw on the gauge reflected a real change.
 
Not anymore. I bought an OBD Bluetooth scanner that connects to an app that can log hundreds of different parameters through the car’s computers. In this first test, I’ll see if I can use it to record steering angle in a crosswind as I’ve been doing. To see just what it can show, I’ll first move my car’s center of gravity around and record the differences.
 
How to Calculate the Position of Your Car’s Center of Gravity
 
Figuring out where your car’s center of gravity sits longitudinally (that is, its location between the front and rear axles) is quite simple. All you need are front and rear axle weights, something you can get at any truck scale for around $15 USD. CAT scales are located across the US; download the “Weigh My Truck” app, make an account, and you can weigh your car just about anywhere without even getting out of it.
 
Before I stopped at the scale, I loaded up two big plastic bins with books and bought some bags of top soil at the hardware store (I’ll use the top soil later this spring in my garden). This gave me 320 lbf of ballast that I could position at the very rear of my Prius, behind the rear axle, or just behind the front seats near the center of the wheelbase. I weighed the car first with the load at the rear and again with it at the center:
 

	Front Axle Weight (lbf)	Rear Axle Weight (lbf)
Rear Load	1900	1680
Center Load	2000	1580

 
Then, I went online and looked up the wheelbase of my car. You can usually find this on the manufacturer’s website if your car is newer; otherwise, check car magazines or consumer review websites, anywhere that has specifications or dimensions listed. The Prius’ wheelbase is 106.3 in, a dimension it shares with many Japanese cars because of domestic regulations.
 
Next, I’ll draw a free body diagram (FBD) to illustrate the external forces acting on the car as it sits on the scale. Note that the axle weights the scale measures are actually the normal forces, the forces exerted by the scale pushing up on the car, and its weight can be represented as front and rear components at each axle or as total weight acting at the center of gravity (aha!):

Unlike the process we used for coastdown testing (where the free body diagram was set equivalent to a kinetic diagram representing accelerations and masses), here there are no accelerations acting on my car—so that side of the equation is 0. We can use this to figure x_CG by setting the forces equal to zero (since the car is not accelerating in any linear direction) and moments equal to zero (since the car is not being rotated in any direction):
 
{∑F_Y = 0 = N_R + N_F – W
{∑M_O = 0 = N_R(0) + N_F(x_W) – W(x_CG)
 
I’ve placed the reference here, O, at the rear axle, which gets rid of the moment produced by N_R, but you can place it anywhere you want and the result will be the same. Be consistent with the directions of your moments (here, I’ve used the standard positive = counterclockwise).
 
From there, simple algebra will give you the distance of x_CG from your reference. On my car, the rear load puts the center of gravity 56.4 in ahead of the rear axle (49.9 in behind the front axle), and the center load moves it forward 3 inches (59.4 in ahead/46.9 in behind).
 
Crosswind Stability
 
Now, the question is: does moving the center of gravity three inches and loading or unloading the front and rear axles with 100 lbf measurably affect the stability of the car in a crosswind? To find out, I drove it on a 1-km section of E-W road on a day with 20 mph winds out of the SSW. Since I can now log data from the OBD system, I exported it to my computer and graphed steering angle as a function of time to compare the center load (heavier front axle, center of gravity further forward) and rear load (lighter front axle, center of gravity further backward) with no other changes to the car:

In both directions, the steering wheel is closer to center (marked with a line at 1.5 degrees, not 0, as I found driving around and watching the steering angle gauge) with the load in the center of the car. We can see this better by using a box plot to show the center and spread of the data. I recorded at 0.05 s intervals, or 20 measurements per second—which means these 35-second runs generated several hundred data. The box plot shows a rectangle that contains 50% of the data, with the median marked as a line and mean as an x. The spread of that data in the box is called the interquartile range, and the bars extending out from the box reach to the furthest datum within 1.5 IQR from the median. Anything outside of that range is considered an outlier. Box plots are an easy way to compare the centers and spreads of datasets at a glance.

In both directions, the rear load negatively affects directional stability, with greater steering angle required to keep the car going straight down the road.
 
Center of Pressure
 
Next, I’ll see if changing the aerodynamic characteristics of the car will have a measurable effect on its stability. Just as the center of gravity is a theoretical point at which the force of gravity acts on a car, the center of pressure is a theoretical point at which the aerodynamic force acts.

A.J. Scibor-Rylski, Road Vehicle Aerodynamics 10. The center of pressure is marked "C.P." here. C.P. location can be found by integrating surface pressures over the whole car and calculating the resultant force's location of action using a force balance, just like we did with the center of gravity.

We saw above that I was able to move the center of gravity backward by placing mass at the rear of the car. I can do the same with the center of pressure by adding surface area on which air pressure can act at the back of the car. The easiest way to do this is with plywood fins or some other stiff structure hanging off the rear:

The lead image shows these fins before cutting with the pictured crosscut saw. To round the corners like I did, take your jigsaw and make a small cut into the board perpendicular to its edge, then reset the saw in the direction of the curve. Your blade will be able to "bite" into the wood without slipping.

Here are the plots of steering angle over time and center/spread comparisons for each direction and each load placement:

The fins measurably improve stability in most cases, especially with the front axle unloaded and center of gravity shifted rearward. The exception is with the center load eastbound, where the airflow the car “saw” had a larger yaw angle than in the other direction and the car was naturally more stable with the load centered. For whatever reason, in this case the fins didn’t help. But overall they seem to be an improvement, especially with lots of weight in the back of the car—similar to how the car is loaded when I take it on road trips. That’s reason enough to continue investigating this fin type, perhaps even extended downward and across the width of the bumper as a box cavity.
 
After testing the fins by themselves, I added the splitter I used in my last round of stability tests. Now, the improvement was even more marked, with the same behavior varying with load and yaw angle:

Equipment
 
I gathered this data using an OBDLink LX tool connected to the free OBDLink app on my Android phone. The Toyota-specific PIDs cost $14.99, so all-in this equipment cost just over $100 USD—similar to the equipment sets I’ve used for other testing. It’s not that expensive, and after the initial investment you can use it as much as you like without ongoing costs. Try it yourself!