And it's official...

After almost 4 years of being a race tire data engineer at Goodyear, I am hanging up my hat. Next stop - Penske Racing.

Time for a change?

Some decisions in life are easy... like how to determine relative amounts of ride and roll stiffness on a race car to minimize sprung mass force transmissibility while maintaining high levels of yaw response and stability. Others decisions are much more difficult - for example whether to make chicken parmigiana for dinner, or sausage and peppers. Also, whether I want to stick around this part of the country and this place of employment... or take an offer at a very well-established race team in North Carolina.

Decisions...

New way to set target roll stiffness

How the hell are you supposed to come up with a starting point for designed roll stiffness of a racecar? There are ballpark figures given in RCVD, which I'll admit we had used before (in FSAE) and even a couple years ago (wow! Here, and here) when I did some real preliminary estimates. Ballpark values are nice for reference and a sanity check, but you should know by now - that's not how we do legit engineering.

Let me tell you - this is how we do it:

(Not really, this song is awful)

What do we (relatively young, relatively inexperienced engineers) generally associate with changing roll stiffness? I'll admit - turn in responsiveness (overall stiffness) and balance (front to rear balance). I'm not ashamed to own up to it! It works - it's the right association - but not entirely for the right or really complete reason.

If you recall my earlier thoughts on top-level engineering, in my mind there's only a one step difference between a rigid body model with instantaneous load transfer, and an elastic sprung mass model with delayed load transfer. In effect, as you put stiffer and stiffer springs (and eventually hard links) in your suspension, you're just turning your car into a rigid vehicle - like a go-kart. As such, that rigid model is the upper bound on cornering or turn-in responsiveness (fine, maybe barring some roll-steer shit and what have you). That is not to say that it's instant, because there is still only a finite amount of yaw acceleration and there's definitely yaw inertia, but it is an upper bound.

As we add a suspension and start softening the car up, it's obviously going to add a degree of laziness to the rate of load transfer. In addition to having to wait for the car to start yawing and building lateral acceleration, we also then have to wait for the sprung mass to roll, engage the springs, and transfer load across each axle. Less roll stiffness (or more roll inertia) makes the car lazier and lazier to sharp steering inputs. In one of this SAE papers, Chuck Hallum seems to mention that he thinks (thought - RIP) a conventional tire model doesn't necessarily show this, but I disagree given the rudimentary sim outputs below. I've picked a certain parameter which indicates responsiveness, and have removed the actual numbers - do your own work.

As we reach "stupidly stiff" spring rates, we get close to bumping that response limit which ultimately is a function of yaw inertia and tire properties. Want to raise it? Get new tires, or more downforce. It is absolutely eye opening when you do back-to-back tire testing (FSAE kids take note). The math behind it isn't too difficult and is both in RCVD among the concepts of stability and control derivatives. Conceptually it's really not too difficult to grasp. You can keep adding spring to car and eventually there's a limit of what it does (likewise with chassis stiffness). The trick is finding that limit.

How does this tie back into design? By doing some up-front engineering I can determine what that upper response bound is, and how quickly I approach it. From there I can say I want a responsiveness level of 'X' by a variety of ways - even if I say I want the car to be within 10% of the rigid body response. Once that target level is established, the required roll stiffness falls out, and from there the appropriate levels of spring and/or bar. QED. Science: It works, bitches.

SAE Papers - Hit or miss

Fairly on-topic.

Perhaps you're like me - in that your formal training in tire & vehicle dynamics pretty much amounts to nil. To a degree I'm almost happy that's the way things turned out. Forces you to think for yourself in a field immersed in hand-waving, subjective experiences in a narrow scope, and bullshit.

Anyway, the Society of Automotive Engineers website is a nice resource for being able to dig through their massive collection of member-submitted technical papers. Authors range from college students to industry professionals, and topics can be on aerodynamics, vehicle handling, drive train, brakes, design - you name it. Good to peruse when looking for extra bits of knowledge, experience, or information. In fact, I'm even listed as an author / contributor for an upcoming paper. Go me!

Unfortunately the content of the papers is a bit "hit or miss." Can be good, can be crap (don't worry, the paper I'm on isn't crap). Really have to exercise extreme caution in what you take out of some of these papers, given that seemingly a lot of them are based on opinion and theory without a tremendous amount of hard, factual, objective data to back it up. As such, one of my rules of thumb is to avoid papers written by FSAE students. Still worth checking out. If you're an engineering student, I'd say there's a good chance that you can get copies of the papers for free at your engineering / math library. If you're an employee of a large automotive OEM or supplier, chances are they are easily available as well.

Some examples:

• 901734 - Four Parameter Evaluation Method of Lateral Transient Response. I would seduce this paper with sushi and martinis if I could (and if I wasn't already engaged to MATLAB - see below). For a 20+ year old paper, I think it's gold. Domo arigato, Tetsushi sama.
  
• 2002-01-3302 - Dynamic Traction Characteristics of Tires. I have a lot of beef with some of the content of this paper, and I feel that it is generally poorly written without much of an "objective engineering" tone.
  
  In particular, I don't agree with Chuck's assessment of heat generation in tires, and that "improved turn-in" response by adding (front) roll stiffness is contradictory to "classic" (Pacejka) tire force curves. Seems to be ignoring the effect of chassis roll and time-delayed lateral load transfer on yaw response and how quickly the system settles. This is something I'll probably cover with my own thoughts on a later date. Suffice to say, my opinion is that adding roll stiffness (front or overall) moves you toward approximating a rigid body and tire-limited yaw response.
  
• 1999-01-0046 - Roll Centres and Jacking Forces in Independent Suspensions - A First Principles Explanation and a Designer's Toolkit. Pretty good, found this today. Well-written and I think describes lateral load transfer and roll centers well. Also seems to agree with my thoughts here, particularly that jacking forces only arise in a geometrically symmetric suspension when lateral tire forces are asymmetric. Pretty good feeling, makes me feel less like an idiot alone in the world!

There are several dozen other papers of varying degrees of value that I have squirreled away. If you're willing to do some data mining and look for buried gems, go to the website and start looking.

Off topic - how are you people being notified that I post?

Any time I put up a good entry or two I get a pretty big spike in traffic - as one would expect. However, of all the blogs I "follow," I don't get any email notification or anything if there's new content. Just have to check it at random intervals or if I see something new on Pulse. Is there some trick setting I'm missing to be notified?

Tight, loose, understeer, oversteer, other malarkey

On Matt's start up blog, he has a few comments on under/over-steer and what he's been looking at in DAQ to sort it out. Talks more about analysis than how balance is actually defined. For as much as "we" (engineers, drivers, fans) talk about balance... and if a car is tight or loose, understeer or oversteer... I think it's pretty damn difficult to define, and a lot of the "textbook" definitions are very incomplete.

Part of it, as Matt mentions, is limit trim - which axle's force capacity saturates first, and is the result a car that "plows" (sideslip angle and yaw rate saturate reach and asymptote) or "spins" (yaw rate increases and sideslip angle takes off to some undesired value.. on the order of 180 degrees!). Even then, you could break that up into limit trim of pure cornering... brake-in-turn... on-throttle... high- and low-speed, etc. Furthermore, racecars are not at the grip limit all the way around a racetrack. Ultimately as a setup engineer (or driver) your goal is to minimize time spent over the entire lap. What about the large radius corners and bends where you're not grip limited? Esses? Corners you barely have to brake for? The part of corner exit where the throttle is at 100%?

I'd say most drivers would attest you do not need to get to 100% of the lateral limit to feel something about balance. What's the sensation, and what's good or bad?

Is it yaw (sideslip) angle? I think a lot of people, myself included, immediately associate oversteer with huge body angles and drifting (such as with the Apikol car pictured to the right). If for some given speed and corner radius tire set A requires front slip angle = 2° and rear slip angle = 2°... but tire set B requires front slip angle = 3° and rear slip angle = 3° ... the difference front to rear in both cases is 0. The steering angle in both cases will be the same. There will be a 1° difference in sideslip angle between them, but is that something we notice? Besides, think of the times you've done some power-on oversteer on fresh snow. You can get the car to big body angles, but is the car loose? With "loose" I think of a car that's very hard to control, twitchy, and easily gets away from you. I can drift around on a snowy parking lot for a long with nice easy-to-control, predictable motion. Sideslip angle gradient by itself... insufficient.

A textbook (RCVD) definition of understeer might include difference in front and rear slip angles, the rate they build up, and deviation of actual steering angle from the Ackermann steering angle (not to be confused with Ackermann steering geometry). That might work if you have the same tire on all 4 corners of the car. What if I have really stiff, low-grip tires on the rear... and really soft, high-grip tires on the front? Initially it will take a lot more slip on the fronts than the rears ("textbook understeer") but eventually the car will spin out. Slip angle difference by itself... insufficient.

Claude, from what I recall, isn't as interested in angles as much as reserve yaw moment capacity of the car (really a measure of if the front or rear axle has more grip left - more "headroom"). While that does give more insight to limit trim, I can think of examples of different cars that have identical reserve yaw moment capacity but drive completely differently in terms of stability and response because of tire curve differences. Reserve yaw moment capacity by itself... insufficient.

There's one thing that I think is pretty indicative of both limit and sub-limit balance, at least in a steady state case. Not going to give it away, but it's related to curvature rather than slope.

In any event, all of these are basically related to constant speed, neutral throttle, quasi-steady state cornering. Not to mention combined slip or transient behavior which adds significantly more complexity. Just more evidence that this shit isn't as straight forward as it might seem when you start to wrap your head around it... and there can be a lot that's really based on opinion and personal experience.

Back to mechanical design - parameterizing the rear suspension (part 1)

Enough of the code crap for now. Ultimately the intent of doing simulation and up-front, top-level engineering work is to set objectives which then feed into flexible, parametric design. The front suspension is fairly well designed to that degree - by altering bulkhead coordinates I can pretty easily change the parallelism and relative lengths of the control arms. Ultimately those two things really define your kinematic curve. The rear suspension, as I have it set up at the moment, is not as easy.

The lower points don't need to be quite as flexible. The upper pickups do, and I drew out roughly what kind of design space I have to be able to flesh out. Now don't get it twisted - I don't need to have that much adjustment range in the car when it's built. As I iterate in the design phase though, I would like to have a relatively painless way of adjusting the mechanical end of things to meet whatever rear a-arm geometry I feel is best.

It would be nice if I could also do this in a manufacturing-friendly design to keep end cost down. One option does exist in machining those side plates out of monolithic plate stock. OnlineMetals offers 6061 in up to 4" thick stock, and I'm pretty sure I've seen thicker material available at places like ALRECO (talk to Bob if he's still there). Admittedly while it would be a blast, and a challenge, to machine down stock that size to something reasonable - it's also expensive as hell.

Making simple, long mounting brackets that stand off from the base plate is another potential option I guess - but not great. When you get to something like I've illustrated... either the manufacturing becomes a bitch to keep the thing in-line with the control arms, or I'd get some really high bending moments on the thing and it would lose all rigidity.

I'll have to think this one through. Maybe a combination of monolithic block and mounts.

Some places I've been

Nothing racecar related today. Been sick for about a week, and busy. Currently procrastinating from doing more work for a variety of meetings tomorrow.

Anyway. Put together an interesting graphic of some of the driving I've done over the past 6-7 years. You'd be surprised, after a few long trips being in the car for 7-9 hours on a stretch really isn't bad.

Steering and alignment settings (part 2 of ?)

"Of course... a child could do it."

It's amazing how things that were as alien to me as brain surgery a year ago, now seem like child's play in comparison. Such is how it goes when there's no one around to teach you this crap and you have to stumble through it yourself.

A while ago I was having a hell of a time sorting out what various alignment settings (namely toe) really do for turn-in response, stability, etc. Limit steering settings made a hell of a lot more sense to me in terms of getting the inside and outside tires working the way you want them to.

As usual in motorsport "engineering" there is a lot of hand waving and not a lot of example data, nor explanations of how to come to these conclusions. Even with as much as I like Carroll Smith's books - including 'Engineer in Your Pocket,' they do a lot to lay out the "what" and not so much the "why." In my opinion, if you're an engineer and someone is laying out a lot of "what" and not a lot of "why" then there should be red flags going up in your head, and the needle on the 'BS meter' should be steadily rising.

How then do we put some real numbers to everything? Simulate the damn thing! It's almost too easy. The equations of motion (sideslip rate, yaw rate, etc) are no big mystery. Figuring out what exactly you want to look at to quantify transient response does require a bit more thought, unless someone has already thought of it for you. Hint: there are a variety of papers in the public domain on this topic. Bottom line, it's super simple to run some combinations of front and rear toe and see precisely what they all do to vehicle response. Very enlightening. Can also probably see the effect of roll stiffness, and how it approaches a rigid body model as the spring rates approach absurd (read: FSAE) levels.

I may or may not post those results up. If I do they will be completely un labeled and with no legend... but if you want to research it on your own it's pretty straight forward.

Need MATLAB? No money? Don't want cracked software?

(Recovering from a hangover in a hotel room in Colorado... Had this written up a while ago, figure I might as well put it up.)

Try Octave. Wiki article describing it is here. You can get get a Windows-compiled version here.

Basically it's a freely-distributed program that's eerily similar to MATLAB. It's driven off *.m files and uses much of the same syntax. In fact, I was able to take a MATLAB script I had put together and run it in Octave with the only change being in the plot command. Does seem to run slower, at least with for-loops... probably on account of MATLAB's just-in-time compiler.

MATLAB is more polished, has a broad range of toolboxes, and is more user-friendly (believe it or not!), but if you need something in a pinch, Octave works well.

Lacking anything particularly cool and racecar-related to show off, I put in a Lorenz attractor. Fuck it, why not?