It’s precisely eight past noon. Normally any resident of the lecture hall would be submerged in complete darkness, surrounded by rows upon rows of empty seats. Of course, as one would expect, the auditorium’s regular occupants are hard at work preparing for their upcoming mid-terms. But tonight: is a special night. For a room that is typically bathed in sunlight, has found itself illuminated by the soft glow of several banks of fluorescent lights.
As I wait patiently, my thoughts are abruptly interrupted as the auditorium’s only door swings open. I greet him: “Dr. Nio Saabish, It’s a pleasure to meet you.” He responds with a silent nod and approaches me to shake my hand. Without sparing a second, he gently places his fob on the desk and grabs a piece of half spent caulk. “The stress, which we shall denote with a sigma (σ), is equivalent to the ratio of the applied force and the cross-sectional area of deformation”. Then he quickly scribbles the equation “σ = F / A”.
He looks back at me, noting my confusion and smiles: “Believe it or not, this is the single most important equation for this evening’s lecture”. Dr. Saabish who is a little-known, yet brilliant, Physicist has taken the time to demonstrate to us the basic principle behind the front strut brace (such as the one provided by MapTun) that can be easily installed on just about any Saab. Those who have installed the front strut brace (myself included) have observed a dramatic improvement in handling and quietness within the cabin. But, what does this simple equation have to do with a bar that spans the engine compartment?
First, let us consider the scenario where the front-brace has not been installed and you drive over an uneven road. Stated in the most simplest of terms, an uneven road is that which results in one of the car’s wheels to be at a different elevation than one of the others. Obviously, for our purposes we are only focused on the front end of the car. So if the front left wheel were to encounter a small “bump” in the road. We can say that the ground is applying a force equal and opposite to that of the car’s weight.
That, ladies and gentlemen, is Newton’s third law! Dr. Saabish now sketches a (very) crude image of his prized Saab 9-3 illustrating this point. This would be the “sheer force” that we have mentioned earlier. The fact that the left side is being forced upwards as the right side is weighted down (also by the cars own weight) is the cause of “deformation” that occurs.
Believe it or not, you can actually hear this deformation, as it happens. Imagine this bump is fairly tall, yet significantly shorter of the contact area between the tire and the road. You will hear the “squeak” sounds in the dashboard and other parts directly behind it. That is because the suspension points for the left and right wheels are effectively linked through the car’s chassis and all parts attached to it.
Now let’s introduce the front-strut brace. As the front strut-brace is a rigid beam, it effectively “absorbs” the majority of the sheering force. To see exactly why this is the case, Imagine a large glass table that is supported only on the edges. Setting a heavy object could easily shatter the glass on this table, but if we reinforced the center of the table with aluminum supports, the rigidity of the glass is no longer an issue. So just as the aluminum reinforcements effectively “erase” the lack of rigidity in the table’s glass, the same is also true when a front-strut brace is added.
It turns out that there is an elegant mathematical representation of this notion. As soon as Dr. Saabish writes the calculus equation on the board, I quietly stand up and attempt to make my way towards the exit. “Hey, Sit back down! It’s not as bad as it looks!” You see, an integral can be thought of as nothing more than a short-hand for adding up quantities over infinitely small segments along a curve.
Yes, that often means “the area under a curve” but in this instance we are looking at the “bending moment” on each point (x) along the strut brace being added up from the left end of the strut brace (which we denote as “0”) and the right end of the brace (which we denote as “r”). The “Bending moment” is the tendency of a force to twist or rotate and object. Now, explaining this rigorously can get rather complicated, but intuitively: think of M(x) as a “degree” of deformation at a certain point along the strut-brace.
Since the strut-brace is a metal bar that is without a doubt: uniformly rigid. You can expect each value of M(x) to be about the same and the end-result from this equation to yield a small value. Without the front-strut brace, you are “integrating” across the entire chassis and all of the components that sit between the two suspension points (so you can expect the values for M(x) to be all over the place and a larger final value). This larger value would indicate a larger amount of “deformation”.
As Dr. Saabish has concluded his lecture, before he exits the lecture hall, I ask him: “so far we have considered how the front strut-brace improves rigidity in up-down motions. Well, how about when you are in the middle of hard cornering (side-to-side motions)?”.
“I’ll leave that as an exercise for the reader.”