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Suspension Dynamics Pt. 1: Springs, Dampers, and "Jounce???"

Posted 02-09-2010 at 06:50 PM by color0
Updated 03-08-2011 at 09:31 AM by color0
So, recently there was a question posted on the forums regarding the function of springs and dampers: why do we need them, what do they do, how do we use them? I thought that this might be a good time to cover some basic theory behind car suspension dynamics, and hopefully answer these three questions using as basic language as possible.

Basic suspension tuning theory dictates that to maximize tire traction, therefore cornering speed, the fluctuations of load on the tire must be minimized. But that's too vague, so let's try to break it down using clear, precise values. We're gonna have to use math for this one.

When the car goes over a bump, or leans over while cornering, we can pick out any one wheel and, to a very rough approximation, describe its vertical motion (relative to the car body) using a mathematical equation:

Mx'' + Cx' + Kx = F(x),

where x is how far the wheel travels relative to its resting position (car standing still). Before you throw me a "WTF" look, let me explain:

M is the unsprung mass of the suspension system: wheels, tires, bearings, knuckles, etc.

C is the damping of the suspension: your disk dampers, grease dampers, oil shocks, etc.

K is the springing of your suspension: T-plates, flex plates, and -duh- springs;

Finally, F(x) is the force that pushes against the tire, i.e. the load on the tire. Recall, to make the most grip out of a particular tire, we need to minimize load changes on the tire -- in other words, we want F(x), the force pushing on the tire, to be as "smooth" as possible.

Using this information, you might deduce that suspension tuning is a process of get good numbers for M, C, and K such that F(x) can be smoothed out over the entire course of suspension action. This is key, and this is why it's necessary to adjust damping along with spring rate, or else the cars will chatter or feel sluggish, or in the worst case, even traction roll uncontrollably.

Now the funky math part. If you don't know/remember calculus, you'll have to take my word for this, but:

x'' is the acceleration of the wheel. Yes, the wheels take time to move up and down, so how fast they change direction will affect the suspension quality of the car. If you look at the first equation, you'll see that M, the unsprung mass, is the number that directly affects the acceleration of the wheel. This is one reason why we usually try to minimize unsprung mass: to allow the wheel to move more quickly as it will ever need to maintain good contact with the road surface.

x' is the speed of the wheel as it moves through the suspension stroke. C, the damping coefficient, directly regulates x'. A lower C means higher x', and vice versa; this plays a crucial part in suspension dynamics. If the wheel moves up or down too fast, the tire will likely lose contact with the road surface, leading to a loss of grip; in the worst case, if it moves too fast the wheel can enter an oscillatory (shaking) state, which is most often observed as "chatter". But if the wheel isn't allowed to move fast enough, the car will feel like it takes forever to turn, or in the worst case, could even move too slowly to follow the road imperfections, again leading to a loss of grip. That's why it's important to set the right amount of damping for any track.

Finally, x is the actual vertical position of the wheel (relative to its neutral resting position). As you probably figured, the number responsible for changing x is K, the spring coefficient. This one is probably the easiest to picture but the hardest to actually understand: the higher K is, the more force the suspension system exerts on the wheel to push or pull it back to center. Which means that if you have a stiffer spring on a particular wheel, the following things happen: 1) When the wheel is pushed upwards (relative to car), the suspension will exert more force against the tire to bring it back down, i.e. the load on the tire increases. 2) When the wheel is lifted off the ground, the suspension will exert less force in putting it back down. This implies that a higher K will cause the load on the tire to fluctuate more, hence reduce grip, which is generally true.

However, there are many subtleties in the equation that only become clear when you look at the relationship between these variable names and the physical things they actually represent.

How much the car has leaned over determines the distance, x, a particular wheel has traveled in its suspension stroke. That is to say that x is roughly proportional to the amount of weight transfer that has occured, whether in cornering or acceleration. Mini-Z racers generally race on road-like surfaces, so the general theory is that less weight transfer is better. So to minimize weight transfer, what do you do? Raise K, i.e. stiffen the springs. But no track is perfect: every kind of surface has imperfections, which means that stiffer springs will reduce the car's overall grip as it travels over bumps and tile gaps. That tells us that we can only stiffen the springs up till a point when the tires start losing grip because they never actually stay in contact with the track.

The trouble with changing K, however, is that you'll also affect x'' and x', the vertical acceleration and speed of the wheel. More experienced hobbiyists will be familiar with what happens when x'' and x' get too high: the suspension is literally moving too fast for the car, so the suspension chatters and you lose grip. The easiest fix for that is to increase C, the damping, until the wheels slow down enough to match the speed at which the car body itself changes directions. But if you have excessive damping, and you try to compensate by increasing spring rate, then you run into the problem of drastically restricting the movement of the wheel (you're reducing both x and x'), which will cause it to lose contact with the ground, once again leading to lost traction.

The implications of this observation are twofold: 1) Spring rate and damping strength must always be matched to each other, and 2) an excess or deficiency of one, either, or both will always lead to non-optimal results. Not only that, but if there's more grip on the track, then the overall balance must be set stiffer, and vice versa, since increased grip naturally leads to more weight transfer. There are a multitude of ways to change up the equation and that results in a multitude of ways to tune the car to respond to such changes. Let's leave that for next time. Moving on...

Now that we've discussed springs and dampers, where does M, the unsprung mass come in? That brings us to our final point this week. Conventional wisdom has had us trying to minimize unsprung weight for ages, mainly because parts always used to be too heavy for the suspension and we've never actually gotten to the point where we need more mass to slow down acceleration. (Perfect example: RWD Mini-Z's rear pod. There's an entire drivetrain back there that has to move with the wheels, that is a LOT of extra mass that gets moved with suspension stroke.) But there are select rare cases where the race cars have actually reached the point where tuning the effective mass of the suspension becomes useful, and one of them is Formula 1. I'm not keen on actual dates or teams, but what is important is that McLaren pioneered the use of a "jounce" damper/j-damper, that, instead of adjusting actual damping, C, adjusts M, which slows down the acceleration of the wheel when bumped, and slows down the recoil of the wheel as it comes back down. As I understand it, under specific conditions, this deliberate slowing down of the suspension does, as tuning theory requires, smooth out the loads on the tires, and thus improves overall traction. This is the newest cutting edge of suspension tuning, and the hardest one to get by feel. Adding "jounce" feels oh-so-slightly different from adding damping, and it's only the most different in the middle of travel (when the wheel is moving but not changing speeds). It's so subtle that I don't think it will be applicable in Mini-Z racing for at least some time to come (the fabrication of a j-damper is, for now, ridiculously hard to scale down), but it is good to know that it exists and that there is potential to extract more corner speed out of any 4-wheeled vehicle through this frontier of suspension tuning.




Next time: Now that the theory is down, next time we'll be applying towards explaining why accepted tuning rules work -- things like "stiffer springs for grippier tracks", etc. that most people memorize but don't always realize the reasoning behind. Cheers!
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