Not about cars

Few things on the agenda here.

First - I'm putting on some tunes. A pretty decent cover of one of my favorites from The Meters

Second - It would indeed appear that I've managed to inadvertently delete all the graphic content off the blog. Managed to do that while exploring all my automatically linked accounts on my Google+ page. Eek. My apologies! I do still have the raw images, suppose at some point I could go back through and reconnect all the graphics. May take time.

Third - Special congrats to Rachel, about to ship out and get her MSc in the UK and then on to F1.

Fourth - Recently I got to follower #100 here. That is pretty damn awesome. That one hundred people, internationally, have had some level of entertainment or interest out of this astounds me. I sincerely appreciate all the comments and questions along the way.

This made me think a bit about living in a crucial part of the explosion of the Information Age, which Wikipedia (good enough) describes as:

...an idea that the current age will be characterized by the ability of individuals to transfer information freely, and to have instant access to knowledge that would have been difficult or impossible to find previously.

"Freely" and "instant" are a bit relative - I can't purchase and download an album quite in the snap of my fingers, but relative to a 28.8kbps line I had in high school it's pretty damn fast. The theme is there - characterizing an age by the rapid breakdown of agents limiting free communication and information exchange. It does amaze me that on a given night I could be blogging about mechanical design, reading what's on Mike Tyson's mind (which I honestly follow frequently - some of it is quite good), or not long ago hearing and reading messages left by protesters in Egypt.

Taking a step back, have we not been pushing for free and rapid communication for thousands of years? Written and verbal communication, couriers, general telegraphy, radio and television, the internet, and now the explosion of mobile communication via wireless broadband and smart phones. Seemingly then this has been a social "stress" (impetus and catalyst of change) for some time.

Furthermore, generally when I think of an environmental stress I'd imagine it as some exponential decay curve, tapering off to reach the desired equilibrium condition. In our case we seem to be in an increasing growth! Fifteen years ago it was a big deal if I called someone outside of my area code or had more than a few floppy disks worth of stuff worth having in digital format. Now, I think nothing of having a high resolution video chat across and ocean, carrying 16 GB of information in my hand, or 1TB in my pocket. As much as we expand our capabilities, we immediately fill them and push out further.

By the way, think about it - going from 1MB to 1TB is an outrageous jump in scale! In any other measure of a thing, that growth rate of 1,000,000x is almost impossible to fathom. We take for granted this growth of many orders of magnitude, when as followers of this blog likely know, a gain of a few tenths of a second (say on the order of one percent) in racing is enormous.

As an aside, if you want to find some interesting images, do a Google search for 'internet map' or something similar. Some of the results look almost cosmic. Interesting to think about what lives on each individual dendrite - be it a vehicle dynamics blog, a Nigerian bank scheme, a love letter, or a video of a crackhead chasing a laser like a cat.

In any event, thank you for following along over the past several years!

Oops

While screwing around on Google+, which apparently ties all your Google-related things together... I may have accidentally deleted all the pictures from this blog.

Shit!

Will see if that can be resolved...

Some decent reading material

A while back, Neil Roberts (of Swift Engineering) was nice enough to send a copy of Think Fast over here. I told Neil I'd give him a more in depth review once I got a good chunk of spare time - but that hasn't quite happened yet!

From what I did have the chance to read, I'd recommend it. Similar in some regards to what you'd find in the Carroll Smith series - maybe has a bit more "why" than just "what," but still reads well without getting bogged down. Has a lot of stuff I agree with, and a few subtle points I'm not entirely on board with (a couple tire specifics). Definitely some good driver points that I'm becoming more a fan of now that I'm working directly with a team. I also particularly liked some points on tire side-slip drag, as well as the entire section on cheating.

As far as target audience goes, is it probably a good pick up for the FSAE, SCCA, or semi-professional racer? Absolutely. Is it going to bring about some tremendous "ah-ha!" moments for well-established pro stock car or pro open wheel engineer? Probably not. But hey, Neil's still working professionally on this stuff, guy can't give away too much.

I should write a book one of these days - after we've won at least one pro level championship, and after I'm retired from competitive racing. If/when I do, it will probably be as thick as RCVD - or much more so. I want to have something for everyone:

1. "Underclassman level" - the basics .Qualitative over quantitative. An important thing IMO is establishing how to approach problems of this nature (as I've said many times - top down rather than bottom up). 
2. "Upperclassman level" - blending in more quantitative work, putting numbers on things, elaborating on theory, etc.
3. "Graduate level" - Would assume there's already a firm understanding of concepts and focuses on novel applications, methods work, etc. Math heavy.

I feel as though there's a lot of material that blends #1 and #2. I might even break #3 into Masters and PhD. Masters level material would probably be along the lines of RCVD, and Tire and Vehicle Dynamics. If you have a pretty firm understanding of things at that level, you're probably doing alright for yourself. PhD level probably doesn't see the light of day, as it's the good shit that wins championships, and is what keeps me employed while trying to develop it!

Bit of a conundrum

Been a while. Turns out this NASCAR engineering thing keeps me busy all day, and some nights and weekends. However, I still enjoy it. Love it. Learning an absolutely immense amount of stuff seeing the other side of my previous employment.

Hopefully settling in a bit, at which point I can get back to this stuff. Here's the catch: at this point it would be tough not to use all my new knowledge in designing this thing, and blogging about all that shit has the potential to give away some competitive advantage. Hell, Ed Lover knows better than to do that.

"Givin away all the tricks? Get the fuck outta here widdat bullshit"

And speakin' of bullshit, y'all - we haven't won a race yet this season. Going to have to work on that. In any way, you see the source of my motherfuckin quandary .May have to limit future stuff here to just pictures of CAD, mechanical design, or other bits and pieces. Maybe even take a whole new direction on things? I'm open to suggestions. Comment away.

After 2 weeks at a pro race team...

I tell ya what, it's been busy! Figure I'll give an update while I'm not doing design work in this transition period.

Par for the course is about a 7:00-6:00 or 6:30-6:30 (that's 0700-1800 or 0630-1830 for you military and central European types). I've also been doing a 7 hour drive between Charlotte and Akron every weekend to clean and pack stuff at my old apartment, since I had all of two days between ending my first job and starting my second.

It's fun though. Challenging, with an immense backlog of work to do. Pace is wild. Finally starting to do some work with an impact. Gave my report in advance of this weekend's race at Phoenix, where the #22 just qualified 2nd. Really had the pace to be a pole lap by a wide margin. Had the fastest car in first practice by half a second, so the up-front work by the race engineers can't be too far off.

Hopefully on Monday morning the feedback will be, "Tire info looked good," rather than, "Yeah that data was way off, we had to work with something completely different."

In any event, as I said, still in the process of moving shit down there. Hopefully I'll pick things up in another couple weeks.

Some of the best words in motorsport engineering

I started getting into suspension design and vehicle dynamics in late 2005 during an independent study (upright redesign). Going on early 2011, I'm just now getting comfortable with how to understand things at a total vehicle, "systems" level of engineering.

That's not to say I understand all the causes, effects, and relationships in tire / vehicle dynamics. That is far from the case. Read it again: it has taken me 5-6 years to figure out how to think about and understand things. How fucked up is that? 5+ years to learn how to learn. Admittedly this is on top of some specifics, and what I'm free to share in this blog probably amounts to 5-10% at best, and all public domain information.

As I had been alluding to in a previous post, to stay afloat in this business I think you need to be damn good at figuring shit out yourself - or at least having the balls to try. Anyway, the obvious question is - "What the hell takes so damn long?" For me - and I'm sure I've mentioned this before - it's been the lack of a teacher or an "all-knowing source" that has all the answers. Yes, even Google falls short sometimes. Unfortunately some engineers take what they hear for gospel (to a degree I suppose this is classroom mentality). As such, we come to some of the best words in motorsport engineering, and ultimately what has kinda become my MO. Stumbled across it when I opened up an old copy of Tune to Win, in the Preface of all damn things - which I probably never even read in college:

I am fully aware that much of what I have to say in this book is subjective. I wish that my knowledge and wisdom were such that this were not so. Many readers are going to disagree with my interpretations, conclusions, and recommendations. I offer no apology. In each case I will put forth my personal best shot on the subject at the time of writing. I reserve my right to change my thinking at any time.

Our knowledge of any field whose title includes the word dynamics should be constantly expanding. This is because, particularly in motor racing, we approach a complex subject from a base of abysmal ignorance and also because, in a field defined by compromises, knowledge gained in one area can and does modify our thinking in related areas.

IMO, that mentality is as important and relevant now in 2011 as it was in 1978.

It does make me think that it's a bit of a shame there's no definitive - or close to definitive - guide for all this stuff. Hell I don't think there's any publication that comes remotely close to touching tire data engineering well. This is good for my job security!! As much as I like the works of Smith, Milliken, and Rouelle... I feel as if each has their own strengths and weaknesses, but even in conjunction don't quite grasp it all. This is particularly true as I learn well with many examples anchored in hard data. I have yet to read over Neil Roberts' book.

At this point I am going on 4 years into a career in motorsport engineering, presumably with another 5+ ahead of me. Maybe one day I'll write a book - I'd enjoy it.

Until then, I should probably get back to designing this fucking F1000 / Formula B car, yeah?

Slow here the next days / weeks / ??

Let's talk about the future, shall we? Oh and pardon if I'm a little out of it today, drinking over the duration of the Super Bowl last night usually makes me a little foggy.

Anyway, got my move to North Carolina coming up, starting the new job, probably working a shit ton of hours (though thankfully not traveling too much - at least initially). May not have much activity here.

Additionally, given the nature of what I'll be working on, may have to cut out any of the vehicle dynamics / sim stuff and keep it a little more strictly to CAD. We'll see.

What you're taught in college vs. what you're going to work on

I have to admit, I enjoy perusing the interwebs. Sometimes you come across some really great gems of information (case in point). Other times, shit is just disappointing. Can't even make this stuff up, here is a recent post from FSAE.com

i am new member of fsae. i wud like to know what be the optimum values of
1.toe angle (rear and front for a rear wheel drive car)
2.caster angle
3.camber angle and shud all the wheels have same camber??
4.kpi
5.caster trail
6.scrub radius
plz reply soon
its urgent

There was also a thread on F1 Technical asking about benefits of a pull-rod suspension in comparison to a push-rod setup as well... not nearly as bad but generally oversimplified. Point of both of these is that there generally aren't all-encompassing answers to problems, even if problems in undergrad engineering tend to lead you to one precise solution, arrived at by some fixed process. I think most people grasp that things will be more difficult in industry, but perhaps the true scope of which isn't put in the right magnitude.

Allow me to illustrate!

Classroom Engineering Problem

"Find the minimum of this function."

Not too difficult! Illustrates a concept (minimization / optimization) in a pretty straight-forward manner. The problem is well-defined, and even if you're not 100% sure of the best way to solve it, you can fake it. Alternatively, you can just copy the solution off someone, or consult The All-Knowing Oracle.

FSAE-Level Engineering Problem

"Find the minimum of the function with respect to x- and y-. No worries, you have a few months to work on it."

Shit's starting to get real. Not quite as simple and straightforward if you're used to looking things in a purely one dimension manner of y = f(x). You'll get a different answer looking at it along one slice of x as another. Furthermore, if you ask different people how to go about analyzing it, you might start getting different answers. Lay a few line plots on top of each other at discrete input values? Plot a surface?

Harder to "brute force" these problems too. Takes some time to run through thousands, or tens of thousands of combinations of toe, camber, spring rate, ride height, etc. Overall it's manageable, and ultimately you're competing to be less of an idiot and have your shit held together by fewer zip ties than the competitor in the paddock stall next to you - who is asking for 1" chro-moly tube and a welder, after the first round of tech inspection.

Real World / Pro Motorsport Engineering

"Here's a rough idea of what you're looking at. Try and figure out what the problem is, because it's not really even defined. The number of variables you have to worry about is somewhere between 1 and infinity - depending on who you talk to - and the people who claim they have all the answers are usually full of shit. You have 5 minutes to find the global minimum, and at some point between 2 and 4 minutes in, the problem is going to change. Also, you will lose partial credit for every minute you take to solve the problem, even if you get it entirely correct at the end of your allotted time. Try to score the most points."

Ouch. The problems really are that challenging, open-ended, and undefined. There are generally dozens of theories and opinions on how to solve the damn thing, and the people who are probably the best source of an answer are the ones you're in competition with.

It's really challenging to prepare for this sort of work. Can attack the problem a number of ways and get different answers every time, depending on where you start and what you feel is important. Then there's always the feeling that's similar to what inevitably goes through your head during at least one exam you've taken...

Oh hell... I don't know any of this shit! Any confidence I had just flew out the window. Fuck. I wonder if anyone else is as clueless, let me take a look around... OK good we have some other blank stares... who are these people who are already furiously writing answers?! Oh well, guess I'll write something down and hope for the best. So long as everyone else fails out I will look brilliant by comparison!

The point of all this is what I feel is important to teach in engineering. Equations for principle stresses? Guess they're good to know, but you can look those up in a book at some point in the future. More so, how to approach problem solving when you don't know the answers, the process, or even the problem. That's what engineers and scientists get paid to do - pull answers out of chaos, and/or data that's typically shitty, insufficient, and can be interpreted in many ways. Some institutions, and seemingly even areas of the world, emphasize this more than others.

It's another reason why FSAE teaches you really good life skills - beyond just cooking with a blowtorch or heat treating oven (done them both!).

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?