Sitting in the car, engine running, start my prep. White helmet is in the passenger seat, white batting gloves and sunglasses on the center console. Glance at the three rows of cars in front. Second row has gaps left by the Grid Master as he snakes through the lines right to left then left to right, releasing cars one by one to head for the start. Dave is one of those about to start. I know because I see his co-driver standing in their empty grid spot.
Plenty of time. Watch one full breath. On the inhale a feeling flows from the nose down to fill the pit of the stomach. On the exhale it flows back to the spine and then up into the neck and brain. The eyes open more. Vision gets sharper.
Slide the seat forward and reposition the seat-back. Turn up the rearview so can’t be tempted to look behind to check for cone hits. Put right foot on the brake and check clutch engagement with the left. Slide the seat one more click. Watch one breath.
A fleeting thought: yesterday’s competition left me in fifth place, one behind my co-driver who has the last of the four trophy spots, the number of trophies being based on class count. Data makes me think I was driving a couple of features incorrectly. If I fix those mistakes maybe I can move up. First and second place have checked out. Both good drivers… unlikely to massively choke on day 2. Third? Longshot. I’m probably too far back. Watch one full breath. The car directly in front is released and heads for the start line.
Reach back for the seatbelt and put it on. Adjust the CG Lock to fully cinch down the lap belt. Helmet now, then gloves, then sunglasses. An older guy in a green and yellow safety vest shuffles directly in front of the car, stands looking across the grid. He turns and gives a “five” signal with his hand. Return it with a thumbs up. Four cars, then me.
No more thinking. Expand awareness outward, into the present moment. See it. Hear it. Feel it. Breath it. Go fast.
Co-driver stands right front corner. A moment ago he came to the window and said, “Numbers are set. Pressures are set. Go get it.”
Gridmaster approaches, looking down at his clipboard, then up to see how many cars are at the start line. No thoughts. Perception expands outward. Now, now, now there is only now. Co-driver starts pulling the blankets. Gridmaster motions me out. I wait for the double-tap to tell me the blankets are clear. Pull into the lane and turn left. See everything, now. Now. At the edge of the grid turn right and proceed toward the start. Stop in front of a young woman sitting on a stool with a barcode reader. Peak around the car positioned at the start to see down the course. That’s where I’m headed. See it. Hear it. Feel it. Breath it. Go Fast. A high-pitched beep tells me the code on the helmet is read. She says, “OK.”
The car in front revs, the rear tires spin then catch and it’s gone. My turn.
Creep up until the starter makes a chop with his hand. He stares at the cars on course, looking for any trouble.
The previous car is downfield now. Now. Press the throttle pedal and raise the engine revs up, stare outward, looking beyond the first two key cones. See it. Hear it. Feel it. Breath it. Go Fast.
The starter turns to me and says, “Go when ready.”
Leave the finish chute at a slow pace and glance over at the big timing board. Wow! Pretty good time. The announcer says I’m now 2nd.
In the first post of this series I talked about transmissibility, but I never really explained it. Let’s back up and finish that thought while showing why I think double-digressive shock valving is the key to good grip. This is going to be fairly technical, but if you slog through it to the end I think you’ll feel rewarded.
In Figure 1 below I’ve reproduced the standard one degree of freedom (1-DOF) transmissibility vs. frequency ratio chart that’s in all textbooks (and many papers) about vibration isolation. A 1-DOF model means one spring and one mass. Most of you probably already know that a standard car suspension is at least 2-DOF at each corner, i.e. it has two masses (sprung and unsprung) which can both move. This was illustrated in the previous blog post. Therefore it takes two numbers to describe the state of the system, i.e. two positions, one for each mass, thus 2-DOF. So, the figure below is for a model that’s even simpler than a real suspension, but I think we can learn a basic truth or two from it nonetheless.
So, what does “frequency ratio” mean? That means the ratio of any particular input frequency to the natural frequency of the system, i.e. the Fn we talked about previously.
So, a frequency ratio of 1.0 on the horizontal axis means 1.0 x Fn which is Fn. A ratio of 2 means a frequency of 2Fn. Remember, a typical Fn for a sporty car might be 1.5Hz, so a ratio of 2 would mean 2 x 1.5 = 3Hz for that particular system. This is the ratio of the frequency (the cyclic rate) of a disturbance to the system as compared to the system natural frequency.
The transmissibility ratio, let’s call it T, are the numbers listed vertically on the left side of the chart. They mean the ratio of response to input. So if the T is 1, it means that if the tire (in our case) encounters a bump 1 inch high then the mass of the car (the sprung mass in our case) will also move up 1″. The ratio of output to input (T) is then 1.
This is exactly the case at zero frequency ratio (the left, vertical axis) and it might represent, for instance, going over bumps very slowly. Imagine slowly creeping over a series of 4″ high speed bumps. How much does the car lift over each one? Right. 4 inches. If you go slow enough the spring won’t compress at all and the sprung mass won’t bounce upward.
Now please notice the five curves that are labeled with the values 0, 0.1, 0.2, 0.5 and 1. These numbers indicate percent of critical damping or damping ratio in the system associated with each curve. 0.1 means 10% of critical damping, 0.5 means 50% of critical damping, etc.
Critical damping is the exact amount of damping that will make the disturbed mass return to it’s original position in the least amount of time and not overshoot. Anything less and there will be some overshoot, i.e. some amount of bouncing around the zero point. Any more damping and it will take longer for the mass, once disturbed, to get back to the zero point. It might take 0.5 seconds, or 5 seconds, to get back to zero, depending on the damping level. If we have excess rebound damping in our shock absorbers as compared to bump damping the system responds too slowly after a compressive impact and doesn’t have time to get back to zero (the static ride height) before the next input, i.e. the spring can’t force the shock to extend fast enough so gravity drops that corner of the car a little bit. After a series of inputs near Fn the entire car may “jack down” onto the bump stops. On the other hand, if we provide more bump damping than rebound the car will tend to jack itself upward, increasing the ride height until the bumps (or driver inputs) cease. Fine tuning the shocks with shaft velocity histograms, something most professional race teams do, is at least partially based on the idea of equalizing the damping (energy dissipation) between bump and rebound, in which case the car will not tend to jack in either direction. Most academic papers do not make the distinction between bump and rebound, only referring to total damping. This makes the math manageable, but leaves real racers in the lurch.
An aside: Do you think you could fine tune a shock that has, say, four times as much rebound as bump, as many linear-valved shocks do have, to produce equal energy dissipation over a complete lap or run between bump and rebound? Not bloody likely. All that goes up must come down. When equalizing energy dissipation between bump and rebound I don’t think you can ever end up with anything except roughly equal shock forces for the same shaft velocity in both directions. Certainly not on a smooth race track where almost all the input energy comes from what the driver does to the car. The bumpier the surface, the more they might depart from equal, depending upon the geometry of the bumps.
If there’s no damping at all in the system, then theoretically, if the disturbance is at Fn = 1, the system will resonate out of control. This is why the upper portion of the damping ratio = 0 line can’t be seen. It’s off the top of the chart. It goes upward to infinity.
Please note that as the damping is increased the resonant peak we see at a frequency ratio near 1 becomes less pronounced. When the damping is critical (1.0) then T is just slightly more than 1.0 at a frequency ratio of 1 (Fn). Even though there’s no line on the chart for more than 100% critical damping, nothing physically prevents us from using more, but the T-curve will never drop below 1.0. The higher above critical we go the more the shock tends to act like a solid strut in a dynamic situation. Remember, however, that the shock shaft has to move to produce force, so it can never really act like a solid strut.
One more key thing about this chart: notice that all the lines converge back to exactly T = 1 at a certain point, about Fn = 1.4, and then to the right of this point they all descend below 1, but they are not all equal after Fn = 1.4. The 100% critically damped line transmits about 60% of a disturbance at a frequency ratio of 3. At the same frequency ratio the 10% damped line transmits only about 15% of the disturbance. This is a huge difference, a factor of 4. That would be the difference (400%) in the vertical movement of the sprung mass of a car in our case.
Again, I need to remind you that this is a very simple system model, but this chart says that no matter how much damping you add, T equals 1 at Fn x the square root of 2. No matter how much damping we add it won’t ever go below 1 from zero to 1.414Fn frequency ratio, though at least we’ve obtained control over the resonance. That means that for any spring-mass system there’s a range of input frequencies that will always significantly affect the mass. This is a basic limitation of this type of passive vibration isolation. (Only an active system can get around this limitation.)
Alternatively, to the right of 1.414Fn damping hurts transmissibility. The more damping we have the higher the T at all frequencies above 1.414Fn. If we don’t have any damping out there then T can get very small. This basic relationship has been shown to mostly carry through to 2-DOF systems (what we have at each corner of our cars) as well. (See part 2 of this series where a 2-DOF model showed this result.)
Why do we care? Basic Truth #1: It turns out that we can basically equate low Transmissibility to both good ride quality and low tire force variation. We then equate low tire force variation to high cornering grip.
I know, that’s a lot of equating, but each has been shown to be basically true by many different people.
What’s the real-world effect? Here’s an example. I used to work at a high-tech place where I traveled over a very poorly paved country road on my way home each day. It was not a series of isolated bumps, but a consistently bad, quite rough surface. At the speed limit the ride was really bad. But, if I slowed down (reduced the bump input frequency) the ride got even worse. About 20% below the speed limit was the worst… in fact, it could get downright dangerous. The car would begin to bound and yaw even though the road was straight. On the other hand, once I sped up to 20% over the speed limit the ride began to smooth out. At 200% of the speed limit it became smooth, though it had become dangerous for other reasons. (Many coworkers were ticketed for speeding on this stretch of road.) Near the speed limit the bump frequency was probably exciting either the Fn of the unsprung or sprung masses of the car, perhaps sending the wheels off the pavement and causing the corners of the car to pitch and jump.
The classic example of an input with a consistent frequency is a road paved with cobblestones. At the perfect speed, which is actually quite slow, driving over cobblestones can produce an input of around 10Hz. Guess what has an Fn of 10Hz? The unsprung mass at each corner of many cars. From the outside the tires can be seen lifting off the surface of cars with “normal” amounts of damping in their shocks. The tires move vertically up and down more than the vertical gap between the stones, i.e. T is greater than 1.0. The unsprung mass is resonating at it’s natural frequency, the tires are spending a lot of time in the air instead of in contact with the stones and it can feel like you’re driving on ice.
Remember, this is a theoretical result for a simple system. There is no system in nature that actually has zero damping, but there are plenty of systems that have so little damping that resonance is a real problem. Resonance can destroy crankshafts, for instance, if they are run at the natural rotational frequency and the harmonic “balancer” (damper) is incorrect, non-functional or has been removed. This is also why the Porsche flat-12 engine developed in the 1960’s for the 917 has the power take-off from a gear in the middle of the engine block. This divides the crankshaft into two shorter, stiffer halves, each half having an Fn above the maximum engine speed just like the flat-six of the 911. No harmonic damper was necessary and the crankshafts didn’t break (too often.) Most V8 motors have crankshafts that are not stiff enough to push the Fn above the RPM limit, so they must have harmonic dampers to prevent failure due to resonance.
Now we have arrived at Basic Truth #2 that I think we can take from this standard Transmissibility chart: Since, to produce the least T and therefore produce the best grip (if you accept all the “equates”) we want lots of damping to the left of 1.414Fn and little to no damping to the right, that means we want digressive (or even regressive) shock valving.
If you don’t quite see how I got to this point it may be because on a shock dyno chart we don’t see a frequency ratio, we see shock shaft velocity. So, there’s one more “equate” I must bring in, namely:
High shaft velocity equates to high input frequency and vice-versus.
When it comes to actual roads this relationship has been shown to be basically true. High shaft velocities are typically caused by short, steep bumps where the peaks are close together, producing a high frequency input. Low shaft velocities are caused by longer, smoother bumps where the peaks are farther apart, producing a lower frequency input. This is simply a fact given the nature of paved roads. and, presumably, parking lots. We know from data gathering in cars that driver inputs, like corner turn-in, produce a low-frequency, low shaft speed input as well.
Where is the dividing line between high and low frequency input? It’s at Fn of the sprung mass times the square root of two: 1.414 x Fn as stated previously. In the automobiles we drive Fn ranges from about 1.0Hz for a softly sprung passenger car up to 3Hz for a very stiff, non-aero race car, which gives us dividing lines that range from about 1.5Hz to 4Hz. (The Fn of the unsprung mass is, in all cases, quite a bit higher than 4Hz, which is an interesting twist and will probably be discussed in the future.)
Ah, but what shock shaft velocities are associated with this range of frequencies? That’s not so clear. The general relationship of higher equals higher and lower equals lower holds, but there is no hard and fast precise relationship, I don’t think. (That would make this too easy!) Dennis Grant decided to use 3in/s as the dividing line for a car set up with 2.2/2.5Hz front to back Fn numbers as discussed back in the original post of this series on shock tuning. I’ve seen everything from this number down to 0.5in/s on actual shocks. The ones I’ve been running have knees at about 1in/s when set stiff, though this was done by a shock rebuilder long before I knew what to ask for and they are, in general, too stiff, i.e. they have too much total damping due, I think, to the linear rebound curve and the aggressive (but digressive) bump curve. (I think I told them “somewhere to the left of 3in/s” and I have to run them at full soft in compression to get best grip, which is not optimal for shock performance.)
This post has presented the core analytical support for having the damping force vs. shaft speed curve rise quickly to a “knee” and then change to a lesser slope after that. This is the real reason for double-digressive shock curves. This is also why linear shock curves, either on bump or rebound, are generally not the best for grip. They tend to be incapable of producing enough damping below the dividing frequency (1.414Fn) without producing too much damping above it, especially if you must run on a poor surface. Given this limitation, and the fact that too much bump damping throws a car off-line when hitting a sharp bump, the builder (or revalver) of cheap shocks has little choice but to crank in a lot of rebound, often the 4 to 1 ratio mentioned earlier, to get the total damping up high enough for good body control and sufficiently fast transient response. This is clearly not optimum and why expensive shocks are required to get both good handling and good bump absorption.
June 2021 Update: My friend’s B-Street Prepared Turbo Miata engine is finally running. As I was the planned co-driver, I got the privilege of specifying the spring rates and how the shocks would be valved… over a year ago.
I did the calculations for sprung and unsprung weights, calculated the front and rear unsprung weight natural frequencies and put together a set of specifications to go to the shock rebuilder. I asked the owner to increase the rear spring rate by 100lb/in (the fronts were perfect) to get the car to 2.3Hz in the front and 2.5Hz in the rear. Using Dennis Grant’s on-line calculator we specified shock damping forces equivalent to 65% of critical at 3in/s (or less) double-digressive, with twice as much rebound as bump. Robbie at RPI Racing Suspension was able to get the Penske double-adjustables to hit the targets perfectly. This past Sunday we got to autocross it for the first time.
First of all, what a rocket! 2300lbs and well over 200hp and 200lb-ft of torque to the rear wheels, thanks to tuning by Brett at Fusionworks Fabrication. Secondly, the grip was fantastic, even on the old Hoosiers we were using. Thirdly, the handling was spot-on. The car did everything we asked of it with no complaint. No more hobby-horsing like it used to do. Not one bad habit. The suspension absorbed the significant bumps in that lot like they weren’t even there. It never occurred to either of us to even think about making a shock adjustment. The car was fastest-fendered vehicle on raw-time that day. Only a shifter kart was faster.
July 2021 Update: We took the BSP Miata to the Bristol Championship Tour where I was able to trophy in 2nd place. The car owner had the fastest time in class on day 2. Handling and grip were fantastic. We never had any reason to touch the shock adjustments.
From time to time people ask me things like: “Why do you give away all this stuff you figure out to the competition? Maybe you should keep it within our autocross group.”
First of all, half of this stuff is probably rubbish, in which case I’m not doing my competition any favors, assuming they read these blog posts. Secondly, my writing isn’t always perfectly clear. Sometimes I mislead people even when I’m not trying to, so that could be a competitive advantage! Thirdly, I admire the people who make the effort to figure things out and I feel good if I can help them. Sometimes they return the favor. Fourthly, I have to write it all down anyway. It’s part of the process.
After writing it then I’d have to make the decision to just sit on it. Maybe if I was younger I’d do that. But, I’m not and I don’t. I think I need to know that other people are going to read it and think either “What a fool!” or “Maybe he’s got something there.” That peer pressure is good for the quality of my thinking and the quality of the product.
OK. For a long time I’ve been trying to figure out the answers to some questions that relate to shock absorbers. (I’m not going to call them dampers.) Questions like these:
Can we figure out how stiff they should be for a given car?
Should the characteristic damping curves be linear, single-digressive, or double-digressive? (And now we can have regressive curves too!) If you don’t know what those terms mean, better google them.
Should the damping be symmetric or asymmetric, i.e. equal rebound and compression forces or skewed one way or the other?
Now I have a confession to make: I don’t have all the answers. I’m writing this after several years of off-and-on research into these questions. I think I have a few answers or at least it seems like I’m getting close. The fact that I’m helping set-up a Street Prepared-class car that I plan to be driving next year has spurred me into a renewed emphasis on finding firm answers to these questions. Another confession: the rear springs were changed and the shocks have already been revalved per my suggestions on the car I’ll be driving. If, by the end of this series of blog posts, I figure out that I was wrong then I may have to pay to have the shocks revalved again!
Why Have Shocks?
It occurs to me that maybe I need to answer the question above. The quick (and true) answer is we have shocks because we have springs.
Actually, we have two major types of springs within the suspension system. The first type are those coiled pieces of metal. (Or flat fiberglass beams if you drive a Corvette.) The second type are what used to be called “balloon” tires to differentiate them from the hard rubber that preceded the modern tire.
We can’t do much about the tires and usually don’t need to. The tires are so stiff that their natural frequency is too high to affect the other two masses, the sprung and unsprung ones, and too high to be damped by the shocks in any case. Tire vibrations go straight through the shocks and coil spring to the chassis. It only takes a bit of elastomer in the mounts to block them, however.
Only when the natural frequency of the sprung mass, via super-stiff springs, become similar to the tire’s own natural frequency does the spring rate of the tires become a significant problem. Think Formula 1 and inerters. (If you don’t know what an inerter is, you can google that as well. As my wife constantly reminds me, google is your friend.)
The existence of the coil springs divides the car’s mass into two parts, the unsprung and the sprung, and each have their own natural frequencies which are relatively low (1.5Hz and 8Hz, perhaps, for a sporty car) and are definite problems. Each mass will vibrate and, left unchecked, resonate (amplify) at its own natural frequency, if excited at that natural frequency by either the surface or the driver’s actions. Resonance can cause loss of grip and/or loss of control. (We won’t mention ride quality. We don’t care about that.) A single strike at the tire that causes the correct velocity in either the sprung or unsprung masses can start a resonance… it doesn’t require repeated inputs like ripples in the pavement. But there are differences in results. Single sharp inputs are handled by a different department in the world of Shock and Vibration, the Transient Response department. In any case, whether caused by a repeating (harmonic) input or a single whack, the primary job of the shock absorbers is to stop any resonances in their tracks.
Understanding the surface on which we race
As autocrossers, I think we are uniquely interested in grip on less than perfect surfaces, i.e. surfaces that are generally worse than typical race tracks. These consist of moderately bumpy asphalt surfaces and less bumpy concrete surfaces that are typically criss-crossed by expansion and water runoff joints. These joints can be quite sharp though the elevation changes are relatively small. In addition, either of these surface types can sometimes contain a significant solitary bump or dip right on the driving line. Sometimes these bumps are located where the car is driving on the cornering limit with the suspension on one side significantly compressed. It’s also possible that these significant imperfections in the surface occur just as the car is in the middle of a transient maneuver, such as in the middle of a chicane. (Our courses are chock-full of chicanes, some that we create ourselves, on purpose, and don’t appear on the course map.) Occasionally we compete on more perfect asphalt or concrete surfaces, but we can’t count on it.
I think we need to carefully consider the differences between these surfaces we compete on and 1) race tracks, which are generally quite a bit smoother (yes, I know there are exceptions) and 2) the much wider variety of surfaces and conditions for which the typical passenger car must be designed.
Though the stock passenger car design has to negotiate a wider range of conditions than the same cars when autocrossing, including bigger bumps and potholes, they are not expected to be cornering or transitioning at the limit at the time. By and large the driver of a passenger car is expected by law and insurance companies to reduce speed as necessary to maintain an appropriate safety margin at all times. Anything less is considered reckless driving. Autocrossers don’t operate in this manner. We take essentially those same cars and drive them, shall we say, inappropriately. We even race them in the rain, sometimes through deep standing water!
Speaking of transitions, that’s another key differentiator. We have these things called slaloms. And Chicago boxes. And thread-the-needle features. No other form of automotive sport places such high emphasis on transitional capability.
Because of these surface and usage differences I think there are some things we need to be careful about as we proceed:
We need to be wary of slavishly copying the set up strategies of road-racers, even if your car really is a road-race car. Lots to learn there, but…
We need to be very careful of our own tribal knowledge, given the vast ability of humans to quickly adapt to situations, to not know what they are actually doing, or to not be able to accurately describe what they’re doing or who have completely nutty ideas about why they are successful. Then there are the vagaries of luck and skill that can see someone win a championship in spite of a poorly setup car, or win because a particular course design suited a particular car or driver by accident.
When considering the conclusions of academics who study things like shock damping on cars or trucks we need to remember that 1) probably no single group on the face of the planet has a more difficult time seeing the forest for the trees, and 2) academics tend to look for their house-key under the streetlamp even though they dropped it on the dark porch, i.e. they use the tools available even if such tools are not up to the task. Sometimes this is called the when you’re wielding a hammer everything looks like a nail syndrome.
Now that I’ve pissed off academics everywhere let’s start with one who wrote a paper I admire. His name is Venu Muluka and his thesis at Concordia University in Montreal was entitled Optimal Suspension Damping and Axle Vibration Absorber For Reduction Of Dynamic Tire Loads way back in 1998.
Muluka was primarily interested in how to save highways from being destroyed by heavy trucks. He focused on the loads the tires impart to the pavement, both the peak magnitudes and the fatigue loads and how those loads can be lessened by better shock absorber damping. Even though he wasn’t writing a thesis on race-car grip, he developed information that’s relevant to us, I believe. If you can learn how to use the shocks to reduce tire load variation then you’ve learned a way to increase average grip as well. At least, that’s a theory to which many who study race-car dynamics subscribe.
Muluka based his study on big trucks, but the ones with standard suspensions are similar to most cars in that they have similarly low natural frequencies in bounce, pitch and roll of the sprung mass and somewhat higher natural frequencies for the unsprung mass. Muluka also studied other types of suspensions that are found on trucks such as walking beam, hysteretic leaf springs (when leafs are designed to rub against each other with high friction to produce damping) and air springs, but we won’t be worrying about those.
First Muluka uses a typical quarter-car model. His full model is shown in Figure 1, below, (his figure 2.3) but for this first part he uses only one side, which, when using the appropriate values for mass, etc. is called a quarter-car model. (I love that he hand-drew his figures! So 1998!)
Starting from the top, the big rectangle represents the sprung mass of the vehicle and how it can translate vertically and rotate in pitch. Ksf is the main suspension coil spring (either just one or both fronts together) where K stands for the spring rate. Csf is the shock absorber parallel with the coil spring where C stands for the damping rate. The Mf is the unsprung mass of the front tires, wheels, axles, etc. Ktf and Ctf are the spring rate and damping rate of the front tires. Ctf is very small and is almost universally ignored, but not by Muluka. This guy kept it in his math, at least as far as I can tell by inspection of the equations he develops that represent the model. The Z’s at the bottom are the input displacements from the roads, i.e. bumps and holes. He uses mathematical forcing functions for the Zs that represent smooth, moderate and rough roads, specifically the roads in his area of Canada which data someone else had collected.
Muluka then creates shock absorber models that are more sophisticated than most studies I’ve read. When he looked at typical truck shocks he found that they were 1) asymmetric, i.e. had different values for compression and rebound, and 2) had blowoff valves on the rebound side. Such shocks have characteristic curves as shown below in Figure 2 (his Figure 2.13).
In Figure 2 note that the rebound is shown as positive, the opposite of what we normally see in shock dyno charts. (This is typical of many analytic treatments… the sign convention is opposite.) Also, we usually see the negative side of the graph folded over in an over/under manner, but academic papers rarely do that.
This figure throws us right into several of our questions. It has linear compression and digressive rebound with asymmetry. Cool!
Muluka begins with symmetric linear damping in his quarter-car model, i.e. equal compression and rebound with no knees in the curves, and then later gets more complicated. With symmetric and linear damping he found that a damping ratio of only 10% had a huge effect on the Dynamic Load Coefficient (DLC) as compared to none. DLC is a measure of load variation at the tire. Muluka was interested in saving the pavement while we are interested in maximizing grip, but all the studies show that they tend to go hand in hand so we’re going to assume that DLC is a proxy for grip.
Muluka found that 25% to 30% of critical damping produced the best (minimum) DLC as shown in Figure 3 below, which is his Figure 4.2.
Increasing the damping above 25% doesn’t improve things though the DLC doesn’t get much worse either. Remember, this is symmetric and linear damping. No digression, regression, progression and no blowoff. He only goes up to 50%, but the trend indicates to me that even at much higher values, 60%, 70%, 80%, which we may want to use for transient response reasons, the theoretical loss of grip is minor.
Then comes one of the most interesting charts in his entire study from our standpoint. In his Figure 4.3 which I have reproduced below as my Figure 4, Muluka varied the ratio of rebound to compression damping from 1:1 to 9:1, that is up to 9 times more rebound than compression.
He found that the best (lowest) DLC values came for a ratio of 4:1, i.e. four times as much rebound as compression. The best ride, as represented by Rms Acceleration, was at 5:1. (RMS stands for Root Mean Square…sort of an average value.)
AFAIK, this is the earliest published analytical result supporting the widely used practice of weighting towards high rebound and low compression which was the nearly universal damping characteristic used since the dawn of the automobile. This provides a rational answer to Dixon’s question about asymmetric damping in the automotive industry I talked about in part 1. Apparently Dixon, even in his 2006 2nd edition of The Shock Absorber Handbook, didn’t know about this result in Muluka’s thesis from eight years before. Since then there have been numerous studies which confirm Muluka’s results, i.e. more rebound than compression produces a better ride and better grip.
Does this mean we want 4X as much rebound damping as compression damping on our autocross car? No it does not. We must be careful not to jump to conclusions. I have a friend who received a set of expensive shocks that had 4X the rebound as compression. They were absolutely horrible, probably because the gross amount of damping was too high. The car may also have been jacking down terribly onto the bumpstops.
Can we ask why this result is what it is? You can ask, but that’s outside the scope of Muluka’s thesis. When you simulate with a model you get certain results. The question of why is separate. Not unimportant, but a separate consideration. It’s left to us to figure out the why, where the results might apply and whether the model is actually good enough to pay attention to in the first place. None of these questions have easy answers.
Next Muluka investigates optimizing asymmetric and non-linear shock damping. The result is very interesting.
He reverts to his more complicated full model shown in Figure 1. He uses the full shock characteristic curve as shown in Figure 2 where the rebound blows off at a certain shaft velocity. He investigates compression damping values that range from 5% to 20% of critical, which is low by our autocross standards, unfortunately. He looks at results at 80kph (49.7mph), 100kph (62.1mph) and 120kph (74.6mph) on a smooth road and a rough road. I will focus on the lower speed of about 50mph and the smooth road results. He finds the optimum rebound damping and blow-off velocity for each compression level.
The results were that as compression damping rises rebound damping needs to drop or the DLC gets worse. When compression was only 5% the best value for rebound was a whopping 82% and no blowoff helped. After that the best rebound value moved linearly down as compression went up and you needed to blow off the rebound at a certain velocity. With 20% compression damping, rebound damping was best at only 60%. (The mean damping was about 45% of critical for best results.) These results are shown in Figure 5, which is reproduced from a portion of his Figure 4.1.
This inverse relationship between compression and rebound values may explain why very different shock valving strategies can produce similar results. In this study 10%/80% asymmetry produced the same results as a 20%/60% asymmetry. I can only expect that raising the compression damping further, as we do in autocross, would require additional decreases in rebound to prevent hurting DLC and thus grip. For instance, we may want much higher compression damping than would ever be considered on a passenger car or big truck for other reasons, such as in the pursuit of better transient response. I think what this does tell us is that as we increase compression damping ratios above 20% then we’ll probably find that we must decrease the ratio between rebound to compression even further than the 3:1 ratio Muluka ends at or we are likely to start losing grip. I note that Dennis Grant recommends a 2:1 ratio at recommended total damping levels of 65% of critical (bump and rebound combined) and that for FSAE cars KAZ Technologies recommends shocks with 50% more compression than rebound, flipping traditional damping asymmetry on it’s head. KAZ Tech also recommends a damping ratio of as much as 400% of critical, but only at extremely low shaft velocities. (They are double-digressive.) At higher velocities they reduce to less than critical. However, those shock characteristics appear to be intended for an FSAE car that also has a very different, non-traditional setup.
So, be careful and don’t take the numbers literally. This is not a model of your autocross car. What I’m attempting to take away from this are trends and basic truths, not specific values.
Finally, Muluka investigates a comparison of linear but still asymmetric shocks, i.e. shocks with no rebound blowoff, vs. his optimal damper with rebound blowoff as shown above in Figure 2. He shows that the optimal damper with rebound blowoff, at 50mph on a smooth road, reduces the DLC at the front by 30% and 21% at the rear compared to a linear damper. The effect is not quite so large on a rough road at low speed, but reverses at high speed. At high speed blowing off the rebound provided best results on a rough road and wasn’t quite so important on a smooth road.
My takeaway is that this last investigation indicates that no matter the level of bumpiness it is best to blow-off (digress) rebound damping at some particular shaft speed for best grip. If we assume that we’re going to digress the compression as well (not studied by Mukula but common in autocross) then this argues for a double-digressive shock characteristic.
This makes me feel good about convincing the owner of the car I’ll be driving next year to invest in double-digressive pistons!
Someone on the internet asked someone else for an easier to understand explanation or translation of my most recent blog post about shock tuning. I feel for that person, but there’s an issue. I want to illustrate the problem with the following quote from Understanding your Dampers: A Guide from Jim Kasprzak, available at kaztechnologies.com:
“In fact in the U.S. they are often called shock absorbers, even though they really don’t absorb shock!”
I’ve heard this a lot. I may have even said exactly the same thing. As an engineer I think, Okay, this is technically correct, but is actually sort of an arrogant way to talk to college kids in an FSAE program, which is the intended audience. (I do understand that starting to teach by challenging assumptions is a valid technique. It tends to wake people up and prepare them for consuming a new idea. I do it all the time, so I don’t want to be too hard on ol’ Kaz. I hope he’ll forgive me.)
Of course shock absorbers do absorb shock in every sense except a narrow technical one. In fact, they turn kinetic energy into heat! Energy gets put into them and it (almost) magically disappears. You don’t have to deal with that energy any more. The spring, which is what Kaz and others want to call the “real” shock absorber, can’t do that. They give back (almost) all the energy they “absorb” and you still have to deal with it, just on a different time scale. Springs are time shifters! There, I created a more accurate description of what springs do. (Didn’t I?)
Anyway, when someone like me assails you with the quote above they’re falling back on a technical idea of “shock” of which the regular person is unaware. That idea is the rate of change of acceleration, technically called jerk.
When you get hit by a truck as you cross the street you get “jerked”. You go from no acceleration to mucho acceleration very quickly. The rate of change of acceleration (the definition of jerk) is very high and that hurts. If you were dressed in a suit of springs the acceleration wouldn’t be so bad. As the springs compress they deliver all that energy of impact to you over a longer period of time. They time shift the energy. You might even survive, at least until those springs give back all that energy and launch you into the next county because only the “shock” was absorbed. You still must deal with all the energy of that impact, one way or another. Unless you have shock absorbers.
When your tire moves up and down for any reason, bumps, potholes, little ripples in the pavement or, God forbid, you turn the steering wheel, all the energy contained, released or transformed by the event goes into the mass of the car despite the springs and make it move.
Unless you have shock absorbers.
The next statement that follows the warning that shock absorbers don’t really absorb shock is usually something like “What shock aborbers really do is damp mechanical motion.” So, we special ones (technologists of whatever sort) have our special, correct word for them. We call them dampers!
When someone says this to the non-technologist has it delivered any useful information to them? I don’t think so. Not much, anyway.
But, wait just a second, you say, filled to the brim as you are with common sense. Don’t springs do that too? When the tire hits a bump doesn’t it get 1) jerked (see, I learned to use that word in a new way, you jerk) and 2) accelerated upward into the car? Doesn’t it start moving very fast and then it slows down and stops? Isn’t it the spring that stops it? Doesn’t the spring provide a force opposing that upward velocity and reduce the velocity and extent of that motion? Didn’t the mechanical motion get damped? So, isn’t the spring a damper too?
Of course it is. Except… oh, never mind!
If you want to understand this stuff then you will have to get beyond the words and develop new, deeper and more accurate ideas. Specifically, you will need to gain some understanding of the theory of mechanical vibration of spring-mass-damper systems, which will be the subject of my next blog post. (I think.) It will take some work. It can’t be “translated” into easier to understand terms because common terms and ideas just don’t contain the necessary concepts and functions. Just like you can’t fully render Shakespearian ideas into the language of a 3rd grade nap-time story. The 3rd graders don’t have the necessary vocab, concepts or life experience. The have to grow up and learn a lot before they can comprehend, much less appreciate, the content of old Bill’s “stories.”
So, buckle up. Springs do more than one thing on a car and so do the shocks/dampers. And to give Kaz his due, he goes on to tell us what those things are. So, maybe you want to go read what he has to say.
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 contact patch force variation 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, which is good for us racers or the racing world would have had to invent all the math themselves!
This transmissibility I mentioned is a key component in these ride quality, car control and grip maintenance investigations and is highly dependent upon the relationship between input force frequency and the natural frequency of the spring-mass-damper system, denoted herein as Fn. The Fn 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. That’s what the shocks are for.)
Engineers design most mechanical systems to operate far away from the system Fn. With cars and their suspension systems this is not possible. As we drive the car we are going to have inputs at, above and below the system Fn guaranteed, either from what the driver does or the world does. Let’s explore the input from driving a slalom, that signature autocross maneuver.
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. 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 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 forcing frequency input to the suspension to be near its natural frequency, Fn. Bad things tend to occur if we excite resonance around Fn, especially if the damping at the associated shaft velocity is very low, as it typically is with OEM or cheapish after-market shocks. 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 of a typical passenger car is on the road today? 1.0Hz to 1.5Hz.
Houston, we have a problem.
Example: Once I had one blown shock on my Corvette 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 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 shock fluid on the floor. I had nearly lost control of the car on a city street just from accelerating and turning through a single corner with no damping on one shock and lots of damping on the other three. (Though to be fair, they were all probably adjusted full soft at the time.)
Also note that whatever damping is provided by the shocks tends to decrease the dynamic Fn. Not much for small amounts of damping, but significantly 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 very far 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.
Increasing Fn numbers from the factory as delivered (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.
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 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 3in 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 2in 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. Of course, 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 who claims (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 says 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 and will be delving into this question.