**Smooth Ride or Best Grip?**

Your car’s suspension is classified by ~~engineers and dynamacists~~ nerdy types to be a spring-mass-damper vibration isolation system. Most of the automotive world looks at this system and wants to know how to best provide a smooth ride for the occupants. They typically use a thing called the transmissibility factor to evaluate how good the system isolates the passengers from the not perfectly smooth roads which impress forces onto the tires. The basic question is, given a bad bump or pot hole, how much of the force (or displacement or acceleration or jerk) at the tire gets transmitted to the passenger? That’s given by the transmissibility factor and (and this is key) the value of the transmissibility factor varies with the frequency of the input disturbance.

It’s really kind of sad. The engineers long ago figured out how to provide an excellent ride. It turns out that 90% of the answer is the shocks. Unfortunately, by and large, the car companies have not wanted to spend the money to provide better shocks, so lots of cars, even luxury cars, give a pretty poor ride compared to what it could be. (Edit: Of course, good shocks can be very expensive. Examples for my Corvette with approximate retails costs are 1) OEM C6Z06- $600, 2) Koni 3013- $1400, 3) Penske/Ohlins/JRZ, etc- $4,000. How many people want to spend 10% of a car’s cost on just the shocks? Answer: Only us idiot autocrossers.)

Of course, passenger comfort is not worth much if the driver can’t control the car. So a subset of these investigations aims at what it takes to assure controllability. A subset of **those** investigations is concerned with how to maintain best grip from the tires in the guise of least force variation at the tire’s contact patch, which is what we autocrossers are mostly interested in. Well, it turns out that maintaining best grip by minimizing contact patch force variation is not totally different from providing best comfort. In fact, they tend to go hand in hand to a significant extent. This is good for racers. Otherwise the racing world would have had to invent all the math themselves!

**Transmissibility and Tire Force Variation**

A mathematical factor called *transmissibility* is a key component in these ride quality, car control and grip maintenance investigations. Transmissibility is how much of the force input from a bump gets through the suspension and into the body of the car. We will discuss transmissibility in-depth in Part 3 of this series, but for now we just need to know that low transmissibility equates to a good ride and basically assures low tire force variation.

Transmissibility is highly dependent upon the relationship between input force frequency and the natural frequency (Fn) of the spring-mass-damper system. What that means is that how much force gets into the body will be different for different input frequencies. For instance, a series of small bumps, say one every half-second, might not be felt much at all. The transmissibility of that input would then be near zero. But, if those bumps were slowed down to hit the tire every 1 second, we might feel a very annoying vibration. The transmissibility of that bump frequency is then quite high. The Fn for each corner of the car is easily calculated if you know the masses, the spring rates and the damping rates. (The damping rates are how fast you take energy out of the system after you start it moving with an input. In a basic sense, that’s what shocks do.) Generally the front corners of the car are basically identical as are the rear corners, but the front and rear Fn values may be slightly different from each other.

Engineers design most mechanical systems to operate far away from the system Fn if at all possible. With cars and their suspension systems it is not possible. As we drive the car we are guaranteed to have inputs below, at, and above the system Fn, either from what the driver does or the world does. This is because we start from zero, i.e. one large-amplitude strike from a big pothole, all the way up to the short but sharp high-frequency input from a cobblestone street. To handle the whole range the Fn will necessarily be somewhere in the middle Let’s explore the input from driving a slalom, that signature autocross maneuver.

**Slalom Input Frequency**

A slalom is driven at about 1.1s per cone in my Street class Corvette as detailed in a previous post here. An interesting fact is that the distance between the slalom cones doesn’t matter much. It always takes about 1.1s. (This is a feature of the fact that the longer the distance between cones the faster we can travel, so the time between cones stays almost constant.) A complete cycle from left to right cornering is accomplished in this 1.1s. Therefore, the average excitation frequency input to the suspension by a slalom maneuver is the inverse, or 1/1.1s = 0.9Hz.

In a stiffer (non-Street) car the slalom time could be (will be) less, maybe about 0.9s, also shown in the post linked above. Then the frequency is 1/.9 = 1.1Hz. A little faster.

I have no idea what the slalom time is for something like an FSAE car, but it might be even lower, which means again a slightly higher input frequency.

OK, so what? The what is that we really don’t want the input forcing frequency to be near the natural frequency, Fn, of the suspension. There’s a feature of spring/mass/damper systems called resonance where the system motion can actually increase and go out of control. We control resonance with damping. If the damping at the associated shaft velocity of the shock absorber is very low, as it typically is with OEM or cheapish after-market shocks, or even zero, like with a blown shock, then wacky things can occur. The least of the bad things that can occur is a loss of grip. The worst is total loss of control of the car.

Any guesses as to what the natural frequency is at each corner of a typical passenger car on the road today? 1.0Hz to 1.5Hz.

Houston, we have a problem.

Example: Once I had one blown front strut on my SUV and didn’t know it. I pulled out from the Tee at the end of my street, turning and accelerating quickly onto the busy road, as you must do since the sight lines are really bad and the cars come fast up the hill even though they can’t see over the top. I nearly lost control of the car and thought for a moment I was going over the curb. I went back to the garage and found a puddle of fluid on the floor. I had trouble controlling the car on a city street just from accelerating and turning through a single corner with impaired damping on one strut. So, having a sufficient amount of damping at the Fn of the suspension is critical for maintaining control of the sprung mass of the car as well as maintaining grip at the tire patch.

Also note that whatever damping is provided by the shocks tends to change (decrease) the dynamic Fn. It’s not much for small amounts of damping, but significant for large amounts. As much as 40% according to one paper I read at 80% of critical damping. (We’ll get into critical damping at some point later on.) So, large amounts of damping can do two things simultaneously, 1) make the problem worse by lowering the dynamic Fn closer to the input frequency, and 2) make the problem better by damping any bad effects. What happened when I added lots of damping to my Corvette’s 1.5Hz Fn by installing those high-dollar revalved pimp shocks? Perhaps it went from 1.5Hz down 30% to 1.0Hz, right at the slalom input frequency. Sheesh! Ah, but what’s a lot of damping doing to the grip? Turns out that depends on a lot of things I’m not ready to go into here but I will say this: for frequencies below Fn x the square root of 2 (1.414 for the non-nerdy types), which would be 1.5 x 1.414 = 2.1Hz on my Corvette more damping generally decreases tire force variation and thus increases grip at the same time it increases control. Finally, something working in our favor! (And a justification for those pimp shocks.)

Guess what happens if you add damping above Fn x the square root of 2? Hint: grip doesn’t improve with more damping for inputs above that limit, which contains basically all bumps and even some of the driver induced effects for a Street-class car. You have to have some, but really not very much at those higher frequencies.

Increasing Fn numbers from the factory (i.e. stiffer suspensions) may be one reason why modern sports cars with Fns of ~1.5Hz (or higher) are so much better at autocross as compared to standard cars or older sports cars that were significantly softer. (The ride, however, is generally worse, because stiffer springs are cheap but better shocks are not.) This also goes some way to partially explain why the addition of a much stiffer FSB (Front Sway Bar) for a softly sprung car in Street-class autocross is so necessary. The stiff FSB increases the effective roll stiffness during transient events, moving the dynamic Fn higher and a safe distance away from the input frequency. So, the car with the stiff FSB gives us faster response and more control. (We won’t mention understeer here, but you can think it.)

In classes where you can change the springs and get Fn anywhere you want then a super-stiff FSB is no longer necessary to avoid inputs near the suspension resonance nor to provide acceptable front-end response. Nor is it required to contribute as much to roll control.

Even if Fn is well above the input frequency, the analytical studies say we still need good damping at the input frequency to limit force variation at the tire patch and thus maintain good grip. That’s why significant damping forces at 1Hz, for instance, are necessary. We only get that in good shocks properly valved, i.e. I can almost guarantee that your car didn’t come from the factory that way. But, we don’t see frequency on our shock F-V plots do we? We see shaft velocity. So, what’s the shaft velocity that corresponds to our 1Hz input in a slalom? It’s not difficult to estimate.

**Maneuvering Shock Shaft Velocities**

If the shock shaft travels a total of 3″ in a 1s slalom then the average velocity is 3/1 = 3in/s. This assumes that the shock shaft moves 1.5” on either side of the static position, which seems reasonable to me for a stockish car. (Note: this is in roll, not heave.)

If the shock shaft travels only a total of 2″ in 0.9s, which might represent a non-Street autocross car that’s low and stiff then the average velocity is 2/0.9 = 2.2in/s.

The peak velocities will be higher, of course, since at each end of the stroke the velocity is zero, but the peaks are limited if the shock provides significant damping. Shocks slow down the shaft velocity by providing an opposing force while increasing the rate of weight transfer. If that’s not clear to you, go read this old post.

This is good support for Dennis Grant’s claim in Autocross To Win that driver-induced frequencies are mostly up to 3in/s so you need to valve the shocks with this in mind. DG provided shock shaft velocity data from three autocrosses in his Street Modified car to support his point.

On the other hand this is poor support for Ross Bentley’s claim (in *Shocks For Drivers*, pg.12) that driver-induced shock shaft speeds only range up to 1 in/s. Bentley provided no shock shaft velocity data to support his point. I think he might have misunderstood the data he was looking at. For instance, it may very well be that the majority of the time, when looking at a shock velocity histogram, the shocks operate below 1in/s. Especially for a race car on a smooth track. That this is true is easy enough to verify on the internet and I have done so. However, this would say nothing about what velocities are the most important during specific maneuvers, such as corner entry and exit or, God forbid, an autocross slalom.

One last thought. Even if we are convinced that we need significant damping at low shaft velocities to maintain good grip when maneuvering we are still faced with another choice: do we provide the damping equally split between bump and rebound, or do we weight it one way or the other? Traditionally almost every analytical study you can find assumes equal damping in both directions. (Makes the math so much easier!) Just as traditionally almost every shock you can find that’s ever been fitted to an automobile since it’s invention provides more rebound than bump, sometimes many times more. Why? In the *Shock Absorber Handbook*, 2nd Edition, 2006, the author John Dixon states, “[I have] questioned various vehicle dynamicists informally on this point, and received less-than-convincing replies. Generally, there is a belief that there is a simple explanation, but this was not actually forthcoming.” But 2006 was back in the dark ages, man! I’ve found some more current data of interest. We’ll be delving into this question in the next installment of this series.

For your reading pleasure.

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