The more I play with cars, the more I think the suspension is where most of the mysterious black art of the automobile lies. Sure, engines are fantastically complex, but at least they're honest about it. Valves, pistons, springs, rods, cranks, turbos, spinning things, hot things, cold things, slippery things, dirty things, clean things. There are a lot of things in an engine, so when messing around with one turns out to be complicated, you really aren't surprised.
But what about a suspension. An arm here or there, a spring, a shock, a joint or two. That's it. They're big, dirty, and can be taken apart by guys named Bubba down at the local Grease-and-go. Seems almost too simple, doesn't it?
Suppose you want to improve your car's performance either by fiddling with the engine or messing around with the suspension. The engine is, once again, the more honest piece. If you did a good job, your engine will make more power. You'll know this because it will accelerate harder when you mash the gas. Pretty simple, no? If you did a good job on your suspension it will handle better. You'll know this... how? Because you can go faster around your favorite entrance ramp? What about that other entrance ramp, the one with the broken pavement, ruts, and bumps? Is it better there too? What about those railroad tracks? Suspension development is so much harder because you never know when you're done.
I'm not going to solve that problem right now. Sorry. I'm just going to drag out a few examples of little corners of the suspension design world that are not quite what they seem. Then I might toss around some equations and dace around a bit. It'll be fun, trust me.
First let's look at something that is easier than you might think: Anti-roll bars. These suckers are really pretty simple. You take a big bar, bend it into something vaguely U-shaped, and bolt the ends to the suspension arms so that in a corner, when one arm goes up and one arm goes down, the bar has to twist. It's a simple torsion bar spring. Most anti-roll bars are bent into horribly complex shapes simply because they are the last part to be designed, and they therefore have to snake their way around everything that has already been put under the car. If you imagine a nice, simple bar like the one pictured here, it is actually quite easy to figure out how stiff that bar is going to be. All you need to know is the diameter of the bar, the length of the part that gets twisted, and the length of the arms that attach to the suspension. (Actually, if they are not perpendicular to the bar, you need to know the distance from centerline of the bar's pivot point.) Plug those lengths (in inches) into this formula:
and voila! You have a totally meaningless number!
Not only is this meaningless because you don't know what you would want to do with, say 754 lb/in. of roll stiffness, but also because there are very few cars with anti-roll bars simple enough for this formula to really work.
This formula is still helpful, though, for comparing two bars of similar shape, but different diameter--exactly what you have when you are planning to change bars on your car. Let's say you have an Integra GS-R, which has a 13-mm (0.512-in.) rear anti-roll bar, and you want to replace it with a 22-mm (0.866-in.) anti-roll bar from a Type R. How much stiffer will it be? You don't need to bother measuring the length and lever arm, since they are the same on both cars. Just take the "Length x (Lever arm2)" factor from the equation and re-name it Bob. A 13-mm (there are 22.5 mm in an inch, so use 0.512-inches in the formula!) bar has a spring rate of 80,951/Bob, while the 22-mm bar has a spring rate of 662,547/Bob. That's 818-percent stiffer!
While changing bar diameter can make huge differences, changing the lever arm length with an adjustable anti-roll bar can still be worthwhile. The NuTech adjustable anti-roll bar we just tested on our Project Sentra SE-R (July '00) for example, had a lever arm of 6.125, 7.125, or 8.125 inches, depending on which hole you used for the end link.
Now, take the Diameter4/Length part of the equation and name it Frank, and you have 31,400*Frank on the stiffest setting, 23,204*Frank for the middle setting, and 17,844*Frank on the softest setting. Moving from the softest to the stiffest setting increases the bar's stiffness by 175 percent. Compared to the gain from increasing bar diameter a few millimeters, 175 percent is fine tuning, but it is still a very noticable difference from behind the wheel.
Now let's look at something that makes a lot less sense: Springs. Springs are just a simple coiled-up torsion bar, and just like the anti-roll bar, they work by twisting a steel bar. If you zoom in on a small section of spring--maybe an inch-long piece of the wire--you will notice that compressing the spring is really just twisting that section of wire just a little bit. (And every other section of wire.) If a spring of the same length has fewer coils, every inch of wire has to twist more when the spring is compressed. OK, so far things are simple. More coils softer, fewer coils stiffer. Good.
Now what about the tender springs you see stacked in a series with the main suspension springs on race cars and over-the-top street cars (like so many of our projects). Let's say you have a 300 lb/in. main spring, and a 200 lb/in. tender spring. Intuitively, you might expect the combination to act like a 200 lb/in. spring until the tender spring fully collapsed, and then act like a 300 lb/in. spring. Intuitively, you would be wrong.
Actually it would behave like a 120 lb/in. spring until the tender spring stacked up, and then move on to 300. How's that? By stacking the two springs, you end up with more coils, and therefore less twisting in each inch of wire. A series of mathematical gyrations unsuitable for well-adjusted adults will result in a simple formula that will tell you what the initial rate is. That formula goes something like this:
Play around with this formula a little bit, and you can really start to smoke your brain. For example, you can take a 300-lb/in. spring and make it softer by stacking a much stiffer, 550 lb/in. spring on top of it. Do the math--you end up with 194 lb/in. That's so counterintuitive, it hurts.
Still, once you get your grey matter over that little hurdle, this is still a relatively simple concept--certainly no harder to comprehend than the math around anti-roll bars--and, so far at least, I haven't encouraged you to come up with pet names for any mathematical formulas.
The problem here lies not in figuring out what spring rate you will have, but deciding what to do with these rates. You could set up the springs so that they start soft and transition to stiff after an inch or so of compression--this might work well on a rally car in the snow, for example. Or you could set them up to start stiff and only go soft when the suspension is in droop.
Without a spring factory, this discussion might seem completely academic, but Eibach has seen to it that such confusion is totally accessible. Its line of race springs come in such a dazzling array of sizes and rates as to make it possible to waste away a lifetime shooting in the dark for the perfect setup.
The most impressive example of dual-rate suspension magic that I have ever seen was hidden away in the front wheelwell of a BTCC Volvo S40. Built and campaigned by TWR until this year, the front suspension on the car I saw used a spring rate that actually got softer as the suspension was compressed. How? The tender spring was pre-compressed; held in partial compression with a simple tethered spring perch. Let's say that the front spring would see a maximum of 1000 lbs during normal competition driving. With the tender spring pre-compressed to 1000 lbs, it didn't move at all in normal driving. But hit a curb, as BTCC cars do when their drivers get aggressive, and the force would be enough to get both springs involved. Suddenly, with two stacked springs working together, the suspension would go soft and suck up the impact of the curb. With cars often going three wide, fender to fender for several laps at a time, being able to hop curbs at will could be a serious advantage.
That may seem easy enough, but you try being the one to figure out just the right pre-load for the tender spring so the suspension never goes soft in a normal corner. Even with more conventional uses, deciding when it should go from soft to hard, trying to optimize damping for two different spring rates, and making sure the whole mess still fits in the wheel well can be a real challenge. I've been trying to do just that on one of our project cars and frankly, my brain hurts.