Testing and Improving Stability: Part 1

Driving back and forth to a city about an hour and a half from here for rehearsals and a concert recently, I wondered if I could measurably improve the stability of my Prius.

I was transporting and playing this, a 2008 Zuckerman Flemish double harpsichord. You can buy kits to put an instrument like this together yourself.

As it usually is here in the Midwest, it was windy all three days I had to make that drive and I found myself paying attention to how much I had to turn the steering wheel to keep the car going straight down the freeway. I wondered, is it possible to give my car better directional stability? And could I measure anything that would tell me, objectively, if a change I make has an effect?
 
Defining “Stability”
 
Stability, in aerodynamics, is a complicated subject. It depends not just on the aerodynamic characteristics of a car but also how these interact with the car’s suspension, tires, weight distribution, and handling tendencies. It also depends on how the driver interacts with the car. Further, we have to distinguish between static and dynamic stability; steady-state driving conditions (say, a car driving along in still air or a constant crosswind) is a different situation than transient (a car that encounters a sudden gusty crosswind, for example, or a car turning in a constant wind).
 
I’ve already made a modification that (unintentionally) resulted in better dynamic stability. The current version of air curtain ducts I’ve fitted to my front bumper cover seem to improve the Prius’ response to sudden gusts of crosswind from passing trucks, although this is a subjective assessment. After I noticed this, I measured the pressure difference between each side of the car in a strong crosswind. With the ducts in place, that difference was reduced from 180 Pa to 160 Pa—so I knew the ducts do something measurable.


That pressure difference should improve my car’s stability in “steady” conditions too, as it means less sideforce acts on the car.
 
Sideforce
 
Sideforce, as implied by the name, is the component of aerodynamic force that tends to push a car to one side or the other as it drives. In order to continue on a straight path, this force must be countered by steering in the opposite direction—and this steering is measurable! Specifically, we can measure the steering wheel’s angle as the car drives along a straight road in a constant wind and infer the magnitude of sideforce acting on the car: the greater the sideforce, the larger the steering angle required to counteract it.
 
My first attempt at measuring this was low-tech; I opened the Bubble Level app on my phone (which displays the phone’s angle as it rotates) and taped it to my steering wheel. Then I drove out to the countryside on a day with 20 mph winds out of the west and found a section of open N-S road. I measured the steering angle without and then with the cardboard fins I’ve been testing, over a long section of exposed road and then just after a windbreak (farmhouse with lots of trees). I found the following:
 

 

No Fins

Fins

Open Section

8.x°-9.x°

10.x°-11.x°

After Windbreak

10.x°

12.x°

 
As we would expect, the increase in area results in a greater sideforce acting on the car in a crosswind, which means I have to turn the wheel slightly more to keep the car going down the straight road. This has been found in wind tunnel tests of simplified car models with and without fins as well:


But look at that second graph—that’s a plot of yawing moment, or the car’s rotation about its center of gravity (or another vertical reference axis; some aerodynamicists use the center of the wheelbase). Fins increase sideforce but reduce the yawing moment, and reducing the yawing moment and/or the yaw derivative (that is, the change in yawing moment per change in yaw angle) can help make a car feel more stable.
 
Rotation
 
Whenever a force (or resultant of a distributed force) acts at a distance from an axis about which it can rotate, it creates what is called a moment. Think of tightening the lug nuts on your car’s wheel: pushing down on the end of a wrench some distance from the nut itself causes it to rotate. The moment can be calculated by taking the cross product of the distance/radius and force, r x F = M (bold type here indicates vectors). Increasing either the force or radius will increase the moment, which is why slipping a long pipe over your wrench’s handle can help you free nuts that are otherwise stuck with the same effort on a shorter wrench. You can think of the moment as a vector sticking out perpendicular to the force and radius (that’s what a cross product is); to figure out which direction that is, use the right-hand rule. Align your right hand (not your left; this only works with the right) with the direction of the radius as seen from the point of rotation, then curl your fingers in the direction the force acts. With your hand in this position, stick your thumb out; that’s the direction of the moment vector.* If that vector points “up” along whatever you’ve defined as a positive axis, the moment is positive, and if it points down, it’s negative. Conventionally, rotation counterclockwise as you look at something rotating is considered positive.
 
After using my phone to measure steering angle, I checked back through some of my materials and found that I could pull up an X-gauge on the Scangauge computer to display steering angle. This should be easier to use than the phone in future, although it turns out it only displays in intervals of 1.6°. Look at the bottom right part of the display (the numbers in front of "STA") and you can see that the computer reports counterclockwise rotation of the wheel as positive, and clockwise negative:

From left to right: +17.6°, 0.0°, -17.6°.


I’ll use this display next time I get a windy day to test and see if the resolution is small enough to be useful at all.
 
Unfortunately, I can’t really measure the yawing moment or yaw derivative on the road right now (although I have some ideas I might try to see if I can). For now, my goal will be to reduce the crosswind sensitivity of the car in steady winds, since these are the conditions I most often encounter on long highway drives, and I’ll use steering angle to measure that. I don’t know if it will be possible to make huge changes, but we’ll see.
 
[*This is useful for any cross product, not just moments. For example, crossing a charge passing through a magnetic field, q x B, gives the direction of the resulting magnetic force. Pretty cool!].

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