Blog to Win: Jersey Tom's F1000

New Blog

2011-11-07T18:55:00.000-05:00

Hi. Long and short - I do more than enough race car shit at work to keep my mind occupied on those matters.

Next up: Food. I hold good food in as high a regard as understanding combined lateral/longitudinal slip sensitivities of quasi-radial race tires.

Name and content of new blog are a work in progress. We'll see how it shakes out.

Not about cars

2011-07-11T00:28:00.002-04:00

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

2011-07-03T14:20:00.000-04:00

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

2011-05-17T21:55:00.000-04:00

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:

"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).
"Upperclassman level" - blending in more quantitative work, putting numbers on things, elaborating on theory, etc.
"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

2011-05-17T21:12:00.001-04:00

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...

2011-02-26T18:33:00.000-05:00

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

2011-02-08T22:57:00.002-05:00

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 / ??

2011-02-07T11:17:00.000-05:00

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

2011-02-03T00:09:00.003-05:00

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...

2011-01-31T11:26:00.001-05:00

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?

2011-01-25T08:21:00.000-05:00

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

2011-01-20T23:59:00.002-05:00

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

2011-01-19T00:42:00.002-05:00

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?

2011-01-18T16:11:00.001-05:00

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

2011-01-16T14:31:00.000-05:00

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)

2011-01-16T11:30:00.000-05:00

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

2011-01-11T22:41:00.000-05:00

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 ?)

2011-01-06T13:07:00.000-05:00

"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?

2011-01-01T16:02:00.000-05:00

(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?

OK I lied - recommended reading and then I'm done for 2010

2010-12-24T17:10:00.000-05:00

Yes, it is that boring sitting around on Christmas Eve in the boondocks of Colorado. To be honest, doesn't even feel like Christmas at all! In any event I'm assuming some of you folks might be in similar situations or have some spare time to screw off over the next couple days. As such, figured I'd share some good online reading material that I've been following.

Hyperbole and a Half

One of the funniest things on the internet. Suits my sense of humor perfectly. The title really describes the content quite well, and I'm not sure what else to really say! She's cute, too! But unfortunately (for me) not single.

If you like simple funny drawings and sarcastic hilarity, scope it out.

Smart Football

Believe it or not, American football at the professional level is a very cerebral game, and takes some definite mental capacity at every position (not just the quarterback, a la Peyton Manning). Even the 300lb offensive linemen have a lot they are responsible for knowing on every play. If you don't believe me, take a look at an except from the Cardinals playbook (10 pages, from ESPN)... or you can download all 463 pages of the 2000 New York Giants offensive playbook (10MB). 463 pages just for offense, let alone defense and special teams.

In any event, Smart Football by Chris Brown is a cool inside look at football strategies... how the plays are designed to attack different defensive schemes, or how to confuse and attack the quarterback. Really interesting shit, and has made me enjoy the game a lot more since going to games smashed while in college. Even gets into some statistics of analyzing different teams or coaches tendencies in certain situations, etc.

Scarb's F1 Blog

Craig Scarborough describes himself as "a freelance journalist\illustrator who focuses solely on the technology of F1." (and in this case, the Audi R18). Pretty good technical look at a variety of technical aspects of F1 development. Fantastic illustrations.

Includes anything from aerodynamic development, recent trends in setups (including the option of no rear corner springs), sensors, ancillaries, etc.

Vintage Metalworks Blog

Dave is one of my coworkers who enjoys metalworking and restoring old cars. Personally I've always been big into machining and TIG welding since college, but Dave takes it to the next level with some really fantastic sheet metal work. Only started blogging recently, but I expect this to have a lot of good content in the next year.

Incidentally, that photo on the right is the Fadal 3-axis VMC that currently resides in his garage. Fun little side venture - he picked up the bill on the machine, and I bought most of the tooling. While mechnically it's vintage 1987, the controller has been upgraded to a 2006 model. Need something machined? We'll do it for a fair price!

Allrighty. Merry Christmas, ladies and gents. I'm gonna have a beer, watch Law & Order, and play with the dog.

Last entry of 2010

2010-12-23T22:40:00.000-05:00

I'm out in Durango, Colorado at the moment... visiting my folks for a week then spending a few days up in Boulder & Denver for shenanigans with college friends. As boring as staying with the 'rents is, I didn't bring much with me so I can't really do much racecar work. I do have a good update though!

On the simulation stuff, I made a huge step forward in the code. The previous cornering model was pretty crappy to be honest - constant velocity. I changed that up and have brake and throttle modulation working. I also changed the way it solved the straightaways. Check it, suckas-

I mean for Christ's sake, the previous version took longer to run than the lap itself! Cut it down to 5-6 seconds to solve. Also got the lap times much closer to reality... I had forgotten to make a conversion from feet per second to miles per hour so my lap times were off by 50%! Still, this isn't fully tuned... but I know the F1000 cars at Road America this year were running anywhere between 2'03"s and 2'20"s or so.. and I'm at 2'13". All is looking good.

Some interesting stats on the blog itself... with some of the stats Google started giving me:

Total views: 12,285 (don't think it started counting until middle of year)
Views in last month: 3,350
Views back in September: 1,957
Followers: 84... that I know of

I appreciate all the comments everyone has left - I try to reply to all of them. If you have a question or comment or whatever, feel free to leave it.

Despite the slow start this year, think I got a hell of a lot of momentum going here toward the end. Looking forward to 2011 - both personally and professionally. Hopefully making amends with some people (one person in particular), maybe making some decisions on what direction I want my life and career to take. Lot of things to consider.

In any event, I thank all for stopping by and hope everyone has a good holiday. I'll catch you all next year-

Jersey Tom - Giants fan, vehicle dynamics engineer, tire data guru, and all around cool guy

A thought - LoLTD vs. LaLTD

2010-12-20T18:24:00.000-05:00

Been quiet here for a couple days. Got a call from my friend on Saturday morning telling me to drive the 460 mi / 740 km out east since he had scored Giants tickets from some random dude at Starbucks.

Unbelievably embarrassing loss to watch in the last seconds of the game, but hey, what can ya do. Play the next game, keep marching toward playoff contention. Thankfully we had Sorrento's (probably some of the best cold subs you can find in the entire goddamn universe, 100x better than anything in Ohio), so that dulled the pain. Personally I recommend the #1 with onions, lettuce, tomatoes, roasted peppers, oil and vinegar, salt and oregano. As for drinking at 930am? Don't judge.

Back to the point at hand, I wanted to get a couple notes down for my own reference here. In vehicle dynamics parlance, 'LLTD' commonly refers to lateral load transfer distribution - a key number for cornering balance. An extreme example of front LLTD bias is shown below. Boogity boogity boogity.

One would think that there's an analog to this in the longitudinal direction (hence Longitudinal Load Transfer Distribution versus Lateral Load Transfer Distribution). It might be nice, on-throttle when the car pitches back, to be able to transfer more load to the inside rear tire for extra forward bite (exit speed is king) at the expense of front axle lateral capacity. Yes, you can have power-on understeer even on RWD cars.

On a road course car I can't imagine having much difference in wheel rate left-to-right on the chassis. Can we do it with some tire rate and kinematic trickery like we talked about before? I suppose if you start with negative camber all around... as you go into roll in a corner and the tires all gain inclination in one direction the insides will have a softer rate than the outsides, and your LoLTD then biases itself to dump load on the outside rear. Pretty much stuck with that with a SLA suspension. Shit. Well, at least it's something to take into consideration and highlights the importance of having good tire rate data over a range of conditions.

I crack myself up

2010-12-17T18:16:00.000-05:00

Good quote...

2010-12-16T18:58:00.000-05:00

...by the infamous Bill Cobb. Don't roll your eyes too much.

Having a Matlab wizard on a race team is as important as having a tire or engine specialist. There ought to be plenty of work to keep them busy. This is New School Racing theory. Old School is struggling...

Trail-braking: AKA, "Not driving like an idiot"

2010-12-15T23:05:00.002-05:00

Let's get ready for the meat of tonight's discussion. You'll probably need to put on some tunes, it gets lengthy. Credit to Laura for this one (an incredibly bright masters degree aerospace engineer with a passion for wedding planning and such - hence the blog).

If you've seen my earlier sim outputs, they drive the corners at constant speed (the apex speed - it's driven as a constant radius corner). In other words, all braking and accelerating is done in a straight line. Only reason for that was for simplicity, ease of coding, and getting something simple up and running. If you were to look at a plot of the driver's instantaneous inverse corner radius along the length of the track, it would look something like this:

In reality if you drive like that, you're going to be at the back of the pack. Not going to go into the details why here - feel free to read any number of racing or driving publications. In any event, given that trail-braking (and throttle modulation out of the corner) accounts for such a big improvement in lap time I was getting pretty skeptical that my sim in it's current form would give accurate direction results at all. As an aside, you can look at 'inverse corner radius' as a way to quantify the line your driver takes over the course of a lap, or a couple laps - even if speed and lateral acceleration change. If you're data logger is grabbing velocity and lateral acceleration it's a snap. Alternatively I believe it's a canned math channel in MoTeC i2. Can't say I came up with it.

Anyway, the other night while laying in bed and I got to thinking - I'm way behind on Christmas shopping, I haven't had Peking Duck in a damn long time, was completely boggled my some woman issues from this summer, and then the next logical thought in the progression was how to solve this combined acceleration problem. Might be easy.

First step - cut in the corner into two halves.

My corners already have an assigned value for apex radius and total length / duration. I'll have to set an additional variable for apex location as a percentage of the total corner duration. This way I can look at which corners benefit from early or late apex (if I'm crazy enough to do that later on). I pick some arbitrary way of defining how the radius transitions through the corner - maybe with a spline or parabola.

Second step - establish combined slip friction ellipse
I've talked about this before here. Earlier I was talking about the ellipsoid being stretched due to downforce but you'll have it from mechanical grip as well. Simple example - you have four tires to brake with, and only two (in this case anyway) to accelerate. In addition to having the ability to specify unique values for braking and acceleration I'll probably also have the ability to have unique values with left- and right-cornering. Don't think a road course car would have an asymmetric setup? Take a look at Lime Rock Park. Might as well be NASCAR in reverse. Only has one left turn, and six rights.

Third step - solve each half's forward velocity trace
Really similar to how you'd solve a straightaway... though this time my acceleration function is going to be based on the engine torque supplied and delivered at the wheels, or the combined slip ellipse (whichever is lower).

For braking, I can do the same shit in reverse for the first half of the corner. Honestly the only hard part is going to be putting in enough code to make it do something realistic when you have a corner that you don't brake for and accelerate through. I'll have to figure that one out later. Once I get this corner thing figured out though, the straights on either end should still solve themselves just the same. All this work is going to have to be put off until another night anyway. Still got other stuff to do tonight. Apparently there's a pro open-wheel team starting to look for FSAE grads with vehicle dynamics and simulation experience. Hmmmm. Tough life and career decisions, just as I thought I was ready to settle a bit and move back east or west. Then again, who would want to leave the wonderful world of working at a tire company?

As a final note, you'll see that I slightly changed the name of the blog. I got a kick out of it. If you don't "get it," you're missing some good books in your library.

Speed and accuracy improvements

2010-12-15T19:46:00.000-05:00

First off, let me tell ya... you can make just about anything into a delicious Mexican-tasting dish with liberal application of ranchera sauce. Seriously, this stuff is good. Threw some remnants of rotini, farfalle, and chicken together with some shredded rice and half a bottle of sauce. Tasty as all get out. My all time favorite dish with this type of sauce is of course 'arroz con pollo' - particularly of the style available at Tequila's. If you're passing through any of those locations in Colorado I suggest you stop in and get it. You can tell them Jersey Tom sent you if you'd like, but they'll probably reply with, "¿Que? ¿Quien es este pendejo?"

Anyway, just as I was getting to the point of saying, "Well shit... anything more to this sim thing is going to be a real pain in the ass," I had a couple pretty good ideas to improve the realism and accuracy as well as solution speed.

1. Replace integration scheme.
I considered explaining the concept of numerical integration here, but instead I'm gonna direct you to Wikipedia if you're a non-engineer and really that interested about it. As I was mentioning in the earlier post on the topic, for the moment I'm using a dumb rectangular-method integration method. Generally the least accurate of any method I know, unless you're using a random number generator. Think I'll upgrade to the trapezoidal method for now, which is plenty sufficient given that the accuracy limitation will now lay in the engine torque function which is doing linear interpolation anyway.

Another viable option is to replaced the fixed time step method with a variable step method... but I'm not too excited about that at the moment.

2. New way to solve straightaways.
Currently my sim finds the braking point on a straight by stepping the initial application point backward 1 foot at a time, starting at 0. If you have a long braking zone, that takes a long damn time. At first I had been thinking of implementing an adaptive algorithm that increments the braking length in large steps if it's way too fast for the following corner. Better method is to do a single forward integration of acceleration from Turn X, and a single "backward" integration of braking starting from Turn X+1. The brake application point is their intersection. Bam! This alone should make the damn thing run literally 100x faster.

3. Add trail-braking and throttle modulation into and out of the corners
Whoa, now. Think I'm going to have to make a separate entry about this, because it's serious stuff. So serious that it precludes the inclusion of Mexican sauces.

Weekly news - Australia beats UK!

2010-12-15T18:43:00.003-05:00

Turns out blogger.com gives me the option of looking up traffic stats for this site in a variety of ways. Giving an engineer data is always a bad decision as invariably they will waste way too much time looking at it in every way imaginable, and then ultimately present it in such a manner that suits their own ulterior motives, hidden agenda, or mood.

Not only do I get to see this, but also where people came from that clicked links to this blog, as well as Google search terms that brought them here as well! Some of the search strings were pretty interesting. In any event, this week saw a boost in views from Australia, mainly on account of a couple forum posts from Race Magazine. Welcome Aussies. Also had a few referrals from a 'Formula SENA' forum which I believe originates in Columbia. From what Spanish I recall, the post title was basically, "This blog has interesting pictures." ¡Bienvendio!

...e io sono un po triste che ci sono poche persone dall'Italia. Spiegate la parola, miei amici italiani!

For anyone else casually reading the blog, feel free to click the 'follow' button over on the right. It's interesting for me to see how many people check this out on a regular basis. 83 and counting!

Road America!!

2010-12-11T17:43:00.001-05:00

While the actual project lap time is way off, for the most part this matches some real F1000 data at this track - surprisingly well considering I'm taking blind guesses at most of the car parameters. There are a few reasons for the time being off, but I'm not too worried about the absolute values as much as the relative change. Still have plenty to tweak for drag, downforce, and tire grip... but this is a pretty promising result.

Even in its rough state, I played a bit with it over 3 sim runs.

Baseline
Base lateral grip + 5%, longitudinal grip -5%
Base lateral grip -5%, longitudinal grip +5%

Not going to give away which did what... but one of them results in about 1.2% better lap time compared to the base, the other is 1.3% slower. On a 2+ minute lap at Road America, I'll let you figure out what time differential that is. Of course since this model has no combined mode operation, it's tough to say if it's directionally correct.

A lap around Martinsville

2010-12-10T23:30:00.000-05:00

Ladies and gentlemen - holy fuck, we've done it. Some upbeat tunes are in order. If you're not a fan of my tunes, well, that's why this is my blog and not yours.

Allow me to show you a 30.1 second lap around Martinsville:

Right about now you may be saying to yourself, "Daaaang homie, that shit is fly." Alternatively you might be saying, "Well that looks fuckin' dumb." You'd be correct either way. It's a dinky little short track, it's not gonna look very cool. Also, admittedly, a 30 second lap at Martinsville is pretty damn slow! Cup cars (NASCAR) get around in under 20 seconds. However, my numbers for drag, downforce, tire grip level, and gearing, are all arbitrary. Also, my "driver" doesn't trail brake nor ease into the throttle, so again - absolute numbers are BS.

Believe it or not, for weighing literally over one ton more than a F1000, Cup cars also have a better power to weight ratio. A 358 ci (5.9L) V8 turning over 9000 RPM will do that!

Still got some stuff to check out to make sure everything looks legit, and then I can start breaking down a road course and seeing what it comes up with. Will have to see if I can dig up some actual F1000 DAQ at some racetrack to back-calculate appropriate numbers for drag, downforce, and mechanical grip. But for now... I'm catching up on Mad Men.

Baby steps - can put a straightaway together!

2010-12-09T00:04:00.001-05:00

Nothing too thrilling tonight. First, credit to Liz C for turning me on to People Under the Stairs.

Good tune to sit back and have a vodka on the rocks.

Anyway. Pretty much got the straightaway stuff squared away. Making the ghetto solver was definitely a blessing in disguise with being able to set a distance limit for integration, rather than time. I'm sure that excites you - in many ways.

So for example we can come out of a 30 mph corner down a 1000' straight and back the braking point up in 50' increments:

Not super thrilling to look at, but important. There is time data that goes along with the velocity and distance outputs, not shown here. All the numbers for drag, downforce, and longitudinal tire grip are just made up at the moment so don't heed too much attention to it. If I wanted to be really fancy I could probably put a segment in the acceleration solver that puts a delay between gear shifts. I'll screw around with that a bit down the road.

So next up I need to make a quick and dirty corner solver (find max speed a corner of given radius can be taken, when including both tire and aero effects) and then the actual full lap solver. To actually run my first sim I'll need to define a track. Road America, Mid Ohio, or even Nelson Ledges will take some time to break down segment by segment. Therefore, as a first pass to make sure the damn thing works at all, I'm going to start with the most simple track I can think of...

Martinsville!

View Larger Map

Should really be able to wrap most of this crap up by this weekend, which is good given that I can potentially get out and be social. You would be amazed at the look of raw animal lust in a woman's eyes when I strike up a bar conversation about racecar vehicle dynamics.

Gearbox added to engine model - more or less

2010-12-06T23:41:00.002-05:00

Positive - Added a transmission to my engine model.
Negative - Canned ODE solver no longer produces a believable result. To be honest, I'm not sure what the hell it's doing at all!

Solution: Ghetto-fy it. As in, my integration scheme is as follows:

y(i+1) = y(i) + yprime(i) * timestep;

Yeah, I know. Not exactly Runge-Kutta. But hey, whatever. Wanted something quick and dirty to make a result. It's an easy problem to solve (linear interpolation of the torque curve), and I have plenty of CPU power to just muscle it. I'm sure my other solver is failing out because of some accuracy or tolerance setting that I'm too lazy to fuck with at the moment.

To a degree this might be nice, in that instead of setting a time span for integration I can go one more step and calculate distance, and have the solver cut off after a certain amount of travel. Ultimately that's what I'm interested in for doing straightaway sims.

Here's the result though, with the following parameters. It's a little goofy under 3000 crank RPM since I have no dyno data, so I filled in some BS numbers (engine is pretty much stalled at that point!). By "Engine Thrust" it's thrust at the tires, coming from the engine. Obviously with the data below 3000 RPM being crap anyway, the 0-60 time isn't even worth looking at.

Car weight: 1000 lb
Drag model: Tuned to generate 400 lbf at 120 mph (arbitrary numbers)
Final chain sprocket reduction: 3.250
Rear tire OD: 22.6"
Shift point: 11,000 RPM

Next up.. I'll have to clean up this solver and add the distance output and solution limit, then do the same for a braking sim, then start building the actual lap solver.

More success!

2010-12-05T23:00:00.000-05:00

Giants beat the Redskins 31-7, I picked up some decent Chinese food, and I got more shit to work. Made a dinky little simulation run with a rough CBR1000 torque curve, a single gear, an arbitrary number for inertia, and a drag model tuned for a drag-limited top speed of 100 'units'.

You pumped? I'm pumped. I texted Brandon and Justin about it and they got pumped too, see below:

Next step will be to add some logic to the thrust model that flips between gears based on velocity. Shouldn't be too difficult. That will have to wait till tomorrow. I'm sure I'll be in a stellar mood tomorrow when I wake up early, see god forsaken snow outside, and then have to drag my ass outta bed to get ready for another week at work. Woo!

Piecewise ODE FTMFW

2010-12-05T12:53:00.000-05:00

Believe it or not I am pretty excited about that plot - it is the solution to a piecewise ODE function.

if y <= 10
yprime = 1
else
yprime = 2
end

Implication is that I can supply a discontinuous function for my acceleration and braking simulations - for example, an actual bike engine torque curve and gearing.

Of course in college they have you dick around finding closed-form, analytical solutions to differential equations. That's of limited or no value here! Still wish they'd have a course - "MCEN3010 - How to actually use this shit for real world problems."

Might try the torque curve bit later today depending on my mood - which will be predicated on if the Giants beat the Redskins, and how many beers I have.

Well shit, might need some new ODE's already

2010-12-05T00:02:00.000-05:00

Did a little test to see if I could get an ODE to solve at all. Simple one worked just fine. One I wrote out for my on-throttle bit? Not so much. I'm not entirely sure why it errors out, but I do have a thought.

It does shoot to infinity at v = 0. Even though the initial condition will always be greater than zero, I have a feeling this may be an issue. May be able to work around it by making a piecewise differential equation and clipping the engine thrust at a value where the tires would break free anyway. Hey, it's a numeric solution, why the fuck not?
The constant power thing isn't as straightforward as one might think. What value do you use? Obviously it isn't going to be peak power - so I have to think up some average over the power band. Interestingly, thinking about a 3200ish lb sportscar with a 0-60 time of 4.7 seconds (like the Nissan 370z), that's only an average power input of about 150hp, of the 330 rated output power. Of course, with 0-60 so dependent on starting line hook, and higher speeds introducing aero drag effects, it's not a good way to come up with an scaling value.
If I'm making a piecewise function out of the accelerating ODE anyway, I suppose I could use an actual torque curve and gearing - picking an appropriate gear based on speed (x dot), then looking up RPM and torque.

I'll have to think about this crap more tomorrow.

Lap sim - you down with O.D.E.?

2010-12-04T12:38:00.001-05:00

Yeah you know me! Actually, truth be told, by the time I took Differential Equations & Linear Algebra (APPM2360? I don't remember) I was so burned out on applied math that I retained pretty much nothing. Additionally, that was probably Fall '04 semester so it's been a while.

Before we get into specifics of writing out ODE's, let's think out loud on how the hell I'm even going to get this to work. Invariably the first thing to do is establish some assumptions. Whenever you're doing any sort of simulation or model or whatever, you are not recreating reality. Get that notion out of your head, forever. You are creating your own abstraction of reality with whatever physical laws, rules, and limitations as you see fit. These might be based on lack of necessary data (e.g. tire data), lack of the skill set to make something really fancy (e.g. me when I was in college), or constraints of time and money (e.g. running a simulation on a laptop rather than a cluster, or desk side supercomputer - badass!).

Here's what I'm thinking as far as assumptions:

Point model - no kinematics, tire data, load transfer, or anything of the sort.
Mass fixed at 1000 lb (at least initially, may evaluate being over minimum weight)
Forward thrust available from the engine at a constant power - i.e. inversely proportional to velocity.
All cornering done at constant velocity and radius - at max lateral capacity
All acceleration and braking done in a straight line
No rolling resistance effects
Downforce and aerodynamic drag proportional to the square of velocity
Mechanical grip (coefficient of friction) values in x- and y- directions held constant. Down the road, it would be interesting to do a sensitivity study and do a number of sim runs, altering the grip level of one corner at a time. Goal - determine which corner has the biggest impact on lap time, and focus steering and balance tuning toward that corner.

As far as how the thing would actually work... first step would be to run through and establish the maximum speed each corner can be taken. Pretty straight forward. The second and much more difficult step essentially comes down to finding the braking point (if there is one) on every straightaway. Haven't entirely figured out the specifics, but roughly:

Pick some arbitrary initial guess for length of braking zone on this particular straight
Use the initial velocity of the on-throttle portion from the previous corner
Run ODE solver over the length of the on-throttle portion to establish a velocity trace
Use the final velocity from on-throttle as the initial velocity of the braking portion
Run ODE solver over the length of the braking portion to establish its velocity trace
Use some sort of goal seek, objective function, or incremental loop to work the braking point backward until the final braking velocity is at or below the next max corner speed. Need to be as close to it as possible really.

For that last step, the incremental 'while' loop backing the braking point up a little bit at a time is probably the 'dumbest' approach in being computationally inefficient, but also the easiest to program.

So we come to the actual governing ODE's themselves...

On acceleration:

On the brakes:

Bam! Easy, assuming I remember anything from sophomore year. There have been many beers consumed between then and now (including a few at lunch today). I'd probably be a halfway intelligent guy if I hadn't drank like hell my last couple years in college!

Anyway. Now comes the hard part... actually making it work in code.

Getting back to top-level engineering

2010-12-02T23:20:00.001-05:00

You may be wondering why I've prominently displayed Lady Gaga here at the top center of the entry. Turns out, if you use the 'Pulse' reader app on your Smartphone (from the folks at Alphonso Labs), the preview icon for new Blogspot entries is whatever the first image is in the article. I wanted my latest preview to be something ridiculous (yes, I am easily amused). By the way, if you don't use Pulse - you should!

Much of the work I've posted up here has been "nuts and bolts" level - CAD and such. Generally this is opposite the design philosophy I preach of starting high-level and working down to specifics (up front engineering). At the same time, the CAD work has been done parametric enough so that I can go in and change my suspension points etc and have the model rebuild more or less painlessly. Anyway, it's to the point where I should back off and do some top-level design work.

I'm gonna go ahead and put on my musical selection for tonight before we get going.

Recommended reading material -this thread at FSAE.com, particularly Geoff's ('Big Bird') lengthy post November 30th, and the section 'Analysis Process.' Some really good takeaway points, namely-

If you start simple with analysis and predictive work up front, you can get some real good design insight before anything is set in stone.
Even college students can cobble together meaningful vehicle simulation programs over a couple days, in Excel, including beer breaks.
It's critically important to identify the relative importance of various performance attributes. You do not have infinite time or resources in your design cycle, ever. I've seen a number of engineers (mostly in college) get so sucked into minutiae that they completely lose sight of the big picture.

"But if we do that, we're going to be giving up some handling!"
"Yeah, and if we don't, the driver won't fit."

I've thought about it, and I might try my hand at putting together a rudimentary lap sim myself. Time investment may only be a couple nights worth of work. If it doesn't pan out from there, no big loss. If it does, I can always add in complexity. The great thing is everything builds on itself. No wasted work.

As an aside, it's amusing to me that for as aroused as FSAE students get for designing around kinematics, body motion is really a few steps up the ladder in model development. More fundamental things like tire cornering stiffness are sometimes overlooked. I wonder if I polled a number of kids the next time I'm at MIS, how many would be familiar with VSAL and how it defines camber rates, while not being totally familiar with tire properties.

We've established that we can simplify and build on vehicle models, but same holds true for track models - maybe even more so. Can probably simplify the hell out of a track model!

I can take some pretty damn big liberties in a track model - the lengths of straights, corner radii, etc. Why? Because I don't care what my exact lap time around Road America is going to be.

For one, you're never going to be able to predict it, within tenths anyway. Track condition, ambient conditions... enough to swing grip, downforce, engine power enough such that the time it spits out won't quite be right. Parameter identification based on previous race results is one thing - future is prediction.

Second, I'm not designing a chassis for Road America. I'm designing a car for Nelson's Ledges, Mid Ohio, and Road America and whatever else. So long as I have track models that are roughly representative of a road course, I think that's good enough for the majority or entirety of up front engineering.

Some interesting work ahead.

Revised front rocker & shock arrangement

2010-11-23T00:13:00.002-05:00

Using the two bulkhead setup allows for some extra flexibility here, including being able to package a longer damper (75mm stroke in place of 50mm). Intuitively I'm thinking that being able to use more stroke should give me some more flexibility in terms of rates and installation ratios. Not knowing entirely what kind of wheel travel to expect, I'd rather have a little much travel than too little.

Clearly I still have to flesh this out quite a bit, but you get the idea. Additional bonus is that these rockers will be stupid easy to machine, even after I add another mounting point for a F-ARB. Would be nice if I could get the force vectors of the pushrod and damper a little more in line so there isn't as much of a net force (and moment!) on the single shear rocker mount. I'll have to play around with it. At this stage of the design it's more roughing things out in terms of what space they'll have to occupy.

As an aside, you may note that when I put in blind (as opposed to 'through') weight relief pockets, I like to fillet the bottom to mitigate any stress risers. In this case I have R0.060" fillets at the bottom of the pockets on the rockers. At first, this may seem dumb from a DFM perspective - how are you going to get a DIA 0.125" ball endmill down in there without it chattering and running slow as hell?

Luckily, God gave us 'bullnose' endmills - they are clutch for this sort of application. Think of it as a flat endmill with a small radius on the end. A hybrid between a flat and ball endmill. Allows you to pocket things out with a healthy diameter cutter for efficient metal removal while leaving a nice rounded edge at the bottom. Additionally they tend to be slightly more robust. Since the cutting edges don't come to a small sharp point they are less likely to chip off. Believe they also leave a slightly better RMS surface finish. What's not to like?!

They are also known as 'corner radius' end mills. Can find them over at MSC or most places with a good selection.

Kinematic curveball - tire rates

2010-11-19T22:53:00.002-05:00

As you probably know, the balance of a car's wheel rates (front-to-rear and on diagonals in particular) play a big part in cornering feel and over/under-steer. Tire spring rate is a component of wheel rate... so any change in how tire rate is distributed has the potential to change the feel of the car.

Before I go any further, I'll share one of the tunes I'm rockin tonight as I get my vehicle dynamics on. Don't worry about the Friday night in... tomorrow night will likely have shenanigans afoot down in Columbus.

Anyway. Obviously tire rate is going to change with air inflation. Good way to make small tweaks. Tire rate also can change with camber - significantly. Typically it goes down the more you lean a tire. This in itself isn't anything earth shattering. It's public domain knowledge, and I remembering even hearing about it at a talk on tire testing & modeling at Colorado State right as I was finishing up undergrad. Never really stopped to think about the implications.

Let's assume we have some tire rate versus camber curve like below. Note: the numbers are totally arbitrary, just to serve as an example.

We'll consider some simple car with equal corner weights and identical installation rates (Ks). Kt denotes the tire rate, Kw the wheel rate.

Now we can give the car some arbitrary ride-camber rate and an arbitrary pitch input.

Fronts are going to gain negative camber, rears are going to move toward positive. Aka, fronts will soften and rears will get stiffer. How significant is a 1.4% change? That's up to you and your driver to decide. You'd be surprised what subtle changes you can notice - even playing with 0.5 - 1.0 psi increments on different corners of the car to play with tire rate.

Can also make up some arbitrary roll-camber rates and input. Let's say in this case, a car with more roll-camber change in the front than the rear (Mustang?).

In this case there's a very slight front/rear change, but a noticeable change in cross. Yeah, and you thought cross weight was only for oval racers. In this case, going up in cross during a left hand turn I believe tightens the car up mid corner - putting extra load on the RF and LR hurts front cornering capacity but helps drive-off.

Of course this is a really simple example with identical, linear tires on all corners. In reality it's a bit more involved. Opens a whole new can of worms in kinematic design - which wasn't exactly fuckin' easy to begin with! One option is to make use of rising rate motion ratios. Presumably if you knew enough about the tires you could use that to offset the change in tire rate and keep a relatively constant wheel rate.

Alternatively it may be beneficial to take advantage of some dynamic change in cross or lateral load transfer distribution - depending on how you want your balance and braking or power-on capacity to change at different parts of the corner. Trick stuff.

Of course none of this probably makes a hell of a lot of difference on FSAE teams that decide to throw heaps and heaps of spring rate in their car, in the misguided notion that it will increasingly make the thing more responsive. Brick the suspension and you don't have to worry much about kinematics, or low speed damper tuning for that matter.

Time to figure out what the hell I was working on back in March

2010-11-19T20:54:00.001-05:00

...and we're back - hopefully with some momentum. You may be wondering what I've been up to for the past 8 months. To put it mildly, 2010 hasn't been a great year. For a while I was busy with work - which isn't a bad thing, but didn't lend itself to much spare time. Late summer I had some woman issues... things inexplicably went to shit. The combination of depression and anxiety really killed any productivity at work or home. This went on for a couple months. Finally had to get a grip on things, make some changes, get back to the things I enjoy in life: Sarcasm, working out, racecar vehicle dynamics, martinis, and music. In any event, here I am. Enough of my personal life though...

Tough picking this up after so long! I barely even remember what I was working on. Apparently I got started on some exhaust routing (yes yes I know about cylinder matching, this is more just roughing out where things might go).

Some things to tackle, in no particular order:

Packaging and 'parametrization' of the front suspension with the 2 bulkhead design
...same for the rear suspension
Some legit high-level suspension engineering. I've worked hard to get things truly parametric such that I can move key points around and have the mechanical bits rebuild successfully. If you've done any amount of solid modeling, you can appreciate that it isn't a trivial undertaking! I'd like to start firming up some ideas of rates and kinematic curves though. Ultimately a big part of that is going to be picking an initial tire selection and building in enough adjustment to work with radial or bias slicks, etc. More on that in the next post.

Still gonna be slow around here...

2010-03-26T15:33:00.000-04:00

Giving a race tire data seminar in Florida tomorrow of all things.. then catching up on a million agenda items when I'm back. Sadly the racecar side project has taken a back seat to the whole day job thing...

There's a fine line between steady-state and transient vehicle dynamics

2010-03-07T23:59:00.001-05:00

Sounds silly, I know... but that's my latest theory and epiphany from this weekend. Potentially a pretty powerful concept. Everything I've gone over up until this point has been pretty basic and straightforward.. but this is actually 'good stuff.' A lot exists in the public domain already, going back to the 80's or 90's. Despite that, I'm not giving too much of this away.

A hint, is an epiphany from a couple years ago... that you really have to keep in mind the relative importance of roll response and yaw response when it comes to handling. Who gives a shit about roll response for the sake of roll response? Turn-in is about yaw. You can throw all the spring and bar, bump stop and coil bind you want at a vehicle... and at some point it doesn't do anything for you and you still have a car that's lazy. That point can come earlier than you might think.

Anyway, here's the gist of things... the more I learn about this crap, the less interested in what I used to think of in terms of transient vehicle simulation. Lap sims tell you a little bit about your car, but it's easy to completely miss a lot of the insight to why the car drives the way it does. A lot is really analogous to a spring-mass-damper system. I could have a S/M/D sitting on my desk, perfectly still. I don't need to poke it or run a simulation of it... so long as I know three basic constants (time invariant) I can completely characterize and understand the dynamic response of the thing... as it sits there in its static or quasi-static state.

I'll have to put some numbers to it... but this would make a lot of sense as to why you could have two vehicles with similar kinematics and setups... even the same instantaneous understeer gradient of neutral or even understeer... but one still feels loose and unpredictable relative to the other.

Apologies for lack of cool pictures lately...

2010-03-07T23:44:00.002-05:00

Don't worry. More stuff is coming. Been busy lately!

Anyone familiar with wind tunnel data?

2010-03-07T23:43:00.000-05:00

The whole thing of stability & control derivatives and such has made me think about this... since at 100+ mph sideforce and aerodynamic yaw moment are probably non-trivial. I don't suppose anyone out there is familiar with typical wind tunnel yaw sweep data?

What I'm wondering is this... with tire data, there is a linear range for both Fy and Mz which usually only lasts for a few degrees of yaw, before saturating, or peaking and dropping off significantly. See below (grabbed off Google but illustrates the concept)

Does aero data have a similar trend? Within a realistic range for chassis side slip angle (say 6 degrees?), are aerodynamic Fy and Mz pretty linear? Do they saturate? Peak? Do something wild?

Wheelbase, stability and control derivatives, etc

2010-02-09T22:50:00.003-05:00

There was a thread over on F1 Technical earlier discussing the merits of a short versus a long wheelbase (incidentally one of many parameters I haven't nailed down). When I was thinking of how to reply it dawned on me that I had little objective or rigorous data to back up what my initial thoughts were. As a start, some might think that long wheelbase implies stability, whereas short wheelbase implies being nimble.

As a generality, I'm not really convinced that's true, at least thinking about it to a degree in 'derivative notation.' Milliken goes over this idea around page 149 of RCVD. In a nutshell it wraps some basic tire and basic vehicle concepts together into a fairly powerful but simple way of describing vehicle dynamics.

All other things being equal, a longer wheelbase should imply higher 'static' directional stability; if you split the axles apart further it should require more torque to 'dislodge' the car from a particular attitude. It should feel planted and secure.. but that's not to mean unresponsive. At the same time as you increase the distance from the front axle to the CG you bump up the control moment derivative; the front tires have a larger moment arm with which to act about the CG, and create higher yaw moment for a given steer angle.

Given that most of my regulars here have FSAE experience, the following example may be enlightening. If there's a series that needs sharp, fast, predictable response almost all the time.. FSAE is it. If you were to test the Goodyear D2692 and D2696 back to back on identical cars, you'd find some big differences in how they drive. The '96 generally should have higher response rates (cornering stiffness) overall, while in the same construction, size, etc. As such, the static directional stability is higher. The car can feel more settled and planted. At the same time it is much more precise and responsive to steering inputs, since the front response is also up! The '92 by comparison, with lower control and stability derivatives, can feel both vague and lazy. (The '96 also has higher ultimate grip, comes in faster, and has unbelievably good wear. Pretty good improvement.)

On the other hand, while the control moment derivative increases linearly with "a" (distance from CG to front axle), if you think of that front axle as a point mass it's contribution to vehicle yaw inertia increases with a^2. In theory then you'd think a car with a short wheelbase would offer higher yaw acceleration capacity. My question is - how much yaw acceleration do you fuckin need? "More" of anything is not always better, except for beer and scallops. I may have to see if I can dig up some old DAQ to see just how much you need. If you already have 2x the acceleration potential that you could realistically need.. why add more when there may be benefit elsewhere?

I'll let you marinate on that.

New mini project

2010-02-09T22:41:00.002-05:00

This will be a good one, if / when I get it to work. One of my better ideas recently.. as usual, spurred by a couple beers. If you want a refreshing, mentally inspirational taste that's as cold as the Rockies, reach for a frost-brewed Coors Light.

Anyway, the idea is.. it will work like OptimumK in reverse... and consequently much more practical for the design engineer.

More to follow if I put something together.

Into the New Year

2010-01-03T14:33:00.003-05:00

Sittin here at DIA waiting for my flight back to Akron, Ohio... after an amazing time in Denver and Boulder.

Been busy at the end of the year, so it's been quiet around here. When I'm back, things will pick up.

Would be nice if design can get wrapped up in 2010. We shall see! Many things I'd still like to do.

In other news.. up to 47 followers now! Very cool.

Round tube vs streamline tube

2009-11-21T11:57:00.007-05:00

I'll preface this by saying I'm a big fan of "order of magnitude" approximations... i.e. spending an hour to get an answer that's 85-90% correct rather than spending a week to get an answer that's 95% correct. For any non-engineers out there.. there's really no such thing as an exact answer in a lot of this stuff. Just a question of how accurate you want to get. In my opinion some people get too caught up too early with trying to find an exact solution.

This goes along with my long-standing belief that 'perfect' is the enemy of 'good.'

It's useful to do this stuff to get an idea of where you need to focus your work. And while yes, every little bit of performance you can squeeze out of a racecar is important, you also have to keep scale in mind. Let's say for example I know I can get an order of magnitude improvement in drag... is that 100 lbf versus 10 lbf? 10 lbf to 1 lbf? Or 1 lbf to 1.6 oz? When you can easily sidetrack yourself working on a million things at once, you've got to go after the low hanging fruit first, and really ask yourself, "What is the most efficient use of my time?"

Anyway, onward. Since aerodynamics aren't my strong point, you're all welcome to check my math.

When fabricating control arms and pushrods you've basically got two choices for tube profile. Round (as I've shown so far in CAD for simplicity's sake) and streamline. This particular streamline tube profile is available at Chassis Shop (they have some damn good pricing on CrMo tube!). While it's cool looking and tempting to use on everything there are also some definite constraints. It's generally 3-4x more expensive than round tube, it's more difficult to fit to itself for welding, and you have to make special end adapters for your rod-end and spherical bearings. This particular one I found on the Baumgartner Race Car page.

In order to justify the added expense, we should have a pretty damn good reason for using it.

Aerodynamic drag is generally given by the following equation:
Where F_d is the drag force, rho is fluid density, v is relative air speed, A is exposed frontal area, and C_d is the dimensionless drag coefficient. You had damn well better get your units straight for this one. Using Imperial units, density should be in slugs per unit volume.

C_d itself varies significantly with shape and with Reynolds number. For this particular analysis I'm assuming relatively high Reynolds number flow, where the drag on an infinitely long cylinder is around 0.5, and drag on a streamlined object is around 0.05.

I'm making a gross simplification and calling each control arm and pushrod a single tube exposed to the oncoming air. I'm also going to say they're all 0.625" diameter tubing, and all roughly 18" long. That gives me a grand total of 135 sq. in. frontal area. For velocity we'll use 100 mph (1760 in/s). For density we'll use 1.2 kg per cubic meter, which works out to 1.347e-6 slugs per cubic inch.

Turn the crank and I come up with 140.8 lbf drag. Given that it takes about 0.00267 horsepower to push 1 lbf at 1 mph (power = force * velocity)... at 100 mph that comes to 37.6 hp. That's quite a bit for a ~180 hp engine!

If I use streamline tube of the same height, since C_d goes down by a factor of 10, so does drag and power. 14.1 lbf drag, and 3.8 hp. Or in other words, going to streamline tube frees up 30+ hp at high speed. Looks like I'll be taking that approach. Realistically that might not mean an awful lot in terms of increasing drag-limited top speed since the tires and chassis have massive frontal area, but a couple extra mph makes a difference on a long straight.

Just for some perspective, if you were to do the same thing on a FSAE car... let's say at the top end of an acceleration run you're at around 60 mph. Let's assume we're using the same tube shapes and lengths. That's a reduction from 50.7 lbf to 5.1 lbf, and 8.1 hp to 0.8 hp. On a FSAE car then you'd expect to "free up" an extra 7 hp at high speed. On a restricted engine that's only making probably 75-80 hp to begin with, that's a non-trivial amount. To prove it to design judges of course you'd probably want to find a long stretch of asphalt and do acceleration, top speed and coast down runs with both styles of control arm. That'd be an interesting experiment and a good junior project.

Steering and alignment settings (part 1 of ?)

2009-11-21T00:11:00.004-05:00

Getting late and this may get involved... but we'll put on some Wes Montgomery and start at taking a crack at it. Steering (Ackermann) and alignment (toe) settings are an important design and tuning point, but for us at least seemed to be last on the list of things to adjust. More often than not I think we never really did much of it!

Even if you wanted to tune it on the skidpad or a simple 'squared off' course you've got plenty of combinations to run through if you take the brute force approach:

Front axle: Toe in? Parallel? Toe out?
Rear axle: Toe in? Parallel? Toe out?
'Static' Ackermann: Generally positive? Parallel? negative?
Ackermann 'progression': No change? Transition toward more negative at high steer angle? Transition to more positive at high steer angle?

Bearing in mind that in theory, those above parameters can change based on changing static camber settings or bolting on a different set of tires, or even just by adding or removing roll stiffness (changing dynamic camber).

That's a bitch. Good luck track testing all of that and getting any sort of consistent read on subtle changes.. when the track is evolving (rubbering in, changing temp).. while ambient air temp is changing (slightly changing downforce, drag, and engine power).. and as you're wearing down tire sets. Really I think the only good way to do it is by using tire data, which hopefully (but not always) is sufficiently accurate.

Even then, you have to know what you're designing for. In my opinion a good part of it is getting the left and right slip angles "matched" so the tires saturate at the same time. Wish I had a good graphic to describe this. Maybe tomorrow. But let's say at a given limit cornering loading your outside tire peaks at 6° slip angle and your inside tire peaks at 8° slip angle. The left and right wheels really aren't that independent, so the only way you're going to get the tires to both peak at the same time is to run some pro-Ackermann steering and/or toe out. Otherwise if you had been completely parallel and steering both tires to 7° you'd be overdriving and abusing the outside tire while underutilizing the inside tire. I'm not sure of a great way to determine this using telemetry without using wheel force transducers.

That's my limit steering strategy. On-center (near 0°) is a bit more difficult for me to grasp. Intuitively I'd think you wouldn't want to run dramatic amounts of toe in any event as it will slow you down on the straights (tire is generating lateral force but starting to point backwards).

The thing that I'm not convinced of are the "conventional wisdom" that toe-out on the front "helps turn-in," toe-in on the rear "helps rear stability," and that any amount of toe-out rear is going to make the car a bitch to drive. The reasons why are not obvious to me at the moment. I'll have to think about that. With the rear tires anyway, if they don't peak at the same point (and chances are with your luck they won't) you're invariably leaving grip on the table unless you can split the slip angles a bit!

Long story short: "Limit" steer settings are a hell of a lot more obvious to me than on-center ones.

The Following

2009-11-20T23:59:00.002-05:00

24 people 'officially' follow this blog. That is cool! I recognize a couple FSAE names outside of CU. Even cooler. Hope this is at least interesting to read.

If you do check up on this regularly, don't be shy. Click that follow thing over on the right. I think so long as you've got a Google / Gmail account (why the hell don't you??) you don't have to sign up for anything. Lets me know people are enjoying it.

Cool feature on the Ferrari F60 brake system

2009-11-20T23:37:00.002-05:00

Little did I know Rob Smedley speaks pretty decent Italian. Better than mine. Then again when you're 'Phil' Massa's race engineer at Scuderia Ferrari I suppose it makes sense. Some Italian reporter caught up with him and asked some questions about the '09 car.

For those of you who understand even less Italian than I do, here's what I interpret as roughly what he's saying:

For a while he's going on about the seat, how they mold each one to each driver, et cetera. Then he gets into the steering wheel and describes some functions, but those are generally well-known. At 2:40 he gets to the cool part about in-cockpit brake adjustment.

The lever and the knob both make brake balance changes. The settings are something to the effect of baseline, and +/- 1% front balance. So for example if you have a really high speed braking zone with heaps of downforce and forward load transfer, you'd flick the lever forward to add some front balance. A couple corners later if you've got a low speed braking zone without as much load transfer, you can flick the lever back to get a little more bite on the rears. The nice aspect is you can quickly, easily, and repeatedly get to the same bias settings without having to constantly screw around with a knob. I'd suspect as little as 0.5-1% balance change is noticeable.. so being able to make repeatably adjustments is key.

The knob acts like you'd be used to in a racecar and makes a 'global' balance change, for example as fuel burns off or as the front or rear tires go away. So, let's say your lever positions are 54%, 53%, 52% to begin with, a twist of the knob might make them 55%, 54%, 53%... and another twist 56%, 55%, 54%.

How applicable is this in a F1000 chassis? Good question. May have to think about that, though initially I'd suspect it's probably not worth it. The top speeds and downforce are just not going to be the same. Doubt many F1000 drivers are braking at 5G.

Cool feature though.

Another note on force-based centers

2009-11-15T13:08:00.004-05:00

Got to thinking about this some more, and how you'd determine your centers in advance of K&C testing. Really just comes down to a somewhat involved statics problem. If I remember right, Racecar Engineering had an article at some point in the last year that showed how to go about solving it, but they did leave out one big item in their simplification. I'd actually suspect it's one of the bigger points for why the true centers digress from the kinematic centers.

I've kind of gone over this point before, but I've made more sense of it to myself now.

Under high lateral load, the tire - being the non-rigid structure that it is - deflects in a couple different directions and moves laterally under the wheel. If you have your own racecar and put a camera watching the tire footprints you can see it pretty clearly, even on a FSAE car.

This gives rise to a non-zero overturning moment at the contact patch (not to be confused with the total overturning moment at the hub, which also comes from lateral force and puts substantial radial load into wheel bearings). Alternatively you could think of this as the vertical reaction force vector moving laterally with the tire. I believe in the RCE article they just assumed a purely lateral and vertical force, at a fixed position.

In any event, you'd think that adding that moment would change how the forces are resolved through the suspension links, and thus how those lines of action act about the CG. The greater the deflection of the tire, the greater this effect. While I had realized that tire Mx played into total load transfer, I didn't know how it was distributed.. be it as a geometric or elastic effect. I'd think it would be purely geometric, at this point in my understanding.

As an interesting consequence, bolting on two different tire sets, even of the same size, could result in different true roll centers (force application points, whatever you'd like to call them) when out on the track.

Really, Bridgestone?

2009-11-15T12:49:00.003-05:00

In an online article in Racecar Engineering, they made a note of the new "slim" front tires Bridgestone will be running in their final year in Formula 1.

Interestingly enough, they included a drawing of the inflated profile of the provisional 2010 tire compared to the 2009 front, including a labeled scale!

Big differences between the two profiles. That will be a substantially different tire. Also hadn't realized that they were using 12.75" wide rims. While I understand the teams would be very interested in getting that for doing aero simulation, I'm surprised they made it totally public. Then again I'm sure no one at a rival tire company would digitize it and put it in CAD or anything.

Side project to the side project

2009-11-14T13:24:00.007-05:00

Ohh y'know.. just a cool toy to have around and play with (a 1990 Penske Indy Car)

All in a (couple) day's work. Went together very smoothly with help from the lead engineer at the Vintage Metal Works.

Not the best design, if you ask me. Few interesting points. All the dampers are a pain in the ass to get in and out, given that they're all vertically oriented, rather than horizontally (which has become the more popular trend these days). You can adjust the front dampers from the cockpit however, along with front and rear bars, and brake bias.

A total of 4 (!) bolts hold the monocoque to the engine. That's it. Not very large ones either, all less than 1/2" diameter if I remember right.

Also, for those curious... yes, it is this yellow car... which finished 4th at this particular race.

I really like the eye-level onboards better than the roll bar stuff. Much better feel for what the driver is seeing and doing. Feel free to watch the commercials from 1990 at the end, haha.

Torque and power

2009-11-14T01:28:00.004-05:00

Not even sure how I got to this thought, but I can't sleep anyway.

The "which is more important.. torque or power" debate is popular in shop talk, and if you ask me, pretty dumb. I believe there's even the saying, maybe even from Carroll Smith himself, "horsepower sells cars, torque wins races" or something to that effect. The two are so closely related with speed it makes absolutely no sense to compare the two as separate entities. Let's go over some simple concepts though.

With a large enough gearing, I could turn a crank with my feet and make more output torque than a Formula 1 engine. That doesn't do me any good however, as I'd never be able to turn the crank at that load, at a high enough speed to make anything of it.

To accelerate an object (read: car) to a given speed requires an energy input. Pure and simple. To get a car up to 100 mph requires a fixed quantity of energy transfer, I don't care how you do it. You want to get this done in the shortest time possible. Work over time is power. The quicker you want to get to 100 mph, the more power you need.

There is however also an acceleration requirement to get to a given speed in a given amount of time. That requires a fixed value of average thrust at the tires, and thus torque. If I had a really high power engine with extremely long gears, it would do me no good as I'd never produce the required thrust to do anything useful.

To achieve maximum acceleration, there is an engine power and WHEEL torque requirement, and the two are related by gearing. That's all there is to it. Keep in mind of course, if you have a high power motor and you're not developing enough thrust, you can always gear it down to bump the torque up. You can't however pull power out of your ass.

Another way to think of it is as such. To keep a car going 100mph you have to overcome some amount of drag. Drag force itself lends itself to a torque requirement... but force times velocity is a power requirement.

Or, think of what the race engine is basically required to do. You want to burn the most fuel as quickly as possible, and efficiently as possible (without blowing up). You want to be able to release as much as that chemical energy in the fuel as possible in the shortest amount of time (again, maximizing how much mechanical power is made). To that point, to burn more fuel, you generally need more air. As a corollary, for a given mass flow rate of air there's only so much fuel you can burn, and so much power you can extract. For you FSAE folks, as a fun challenge, find the maximum mass flow rate of air you could possibly hope for, through a 20mm restriction. Find how much power can generally be extracted per unit mass flow of air, and then find out the most power you could hope to get out of it.

It's fun comparing the maximum theoretical power output of one of those restricted motors with how much some teams claim to make, ie the guys who say they can make more. It is good to know though, what max RPM your engine should be choking the restriction at. I really wish we'd had the time to get some cams made up designed around that. Oh well.

In any event, going by peak values, as is typical, is as meaningless in my opinion as calling a car "tight" or "loose." Really doesn't tell you anything. Area under the curve seems like it would be the more important parameter.

Edit - Was originally gonna include some thoughts on the claims of some engines to "give tires time to rest between cylinder pulses and regain grip" but I'm saving that for another day.

Rear damper packaging

2009-11-08T19:39:00.002-05:00

I'm thinkin'... somethin like this:
Though I will probably move the rear chassis-side point of the upper a-arm rearward. This should allow me to use a damper with more travel (3" in place of 2"), and will also look cooler!

Still need to come up with a good way to mount it to the frame...

And where I'll put the R-ARB..

Regarding Titanium...

2009-11-06T00:23:00.002-05:00

Holy shit. I take back what I said.

Initially, to do the crazy (and probably dumb) idea of making those tripod housings out of billet 6-4 Ti, would have been about $467 / part in raw material cost. Found another place that can supply it for $182 / part. $182 for a 3" diameter x 3" long bar of certified Grade 5 Ti. That's pretty reasonable, even though 416 or 4130 would be ~$30 / part.

Handful of Ti parts on the car would pull 10 pounds out. May be worth keeping in mind.

Drivetrain solutions

2009-11-02T00:42:00.006-05:00

A couple ideas anyway.

First up is the driveshaft itself. The general Taylor Race arrangement is as follows...

Splined halfshaft into a tripod CV joint. That joint sits in a roughly inch thick housing, open on both ends. Torque is then transferred from the halfshaft, into the tripod by a spline, into the housing by direct contact, and then into the hub flange by the 6-bolt pattern. I don't like having 6 wired fasteners to take apart, and I don't like the open end on the tripod housing. As soon as you take it off, grease goes everywehre and you have to make sure other crap doesn't get in there.

I like the idea of sealing off one end of the housing, as shown above. It becomes a bit thicker, but by going to aluminum the total weight is considerably down. While bare aluminum likely wouldn't hold up to the Hertzian stress imposed by the tripod rollers... a thick, hard anodize or hardened steel sleeves might be up to the task.

Still haven't figured out a good solution to using less fasteners, and getting rid of safety wire while still having an easy positive stop on. I'll have to think about that.

I'll add, I'd like to avoid cutting splines where possible. Expensive, and not always necessary.

I am thinking about something similar to the above for a diff housing carrier. I'd like to have an assembled, billet "diff box" that holds the suspension and differential. Placement of everything will require some creative packaging. This way however, the diff can pivot and rock back and forth on the bottom mount, allowing chain tension adjustment. By undoing the two long bolts, the whole diff can be rotated 90 degrees and then slid out from the left side. That large opening in the plates is longer than it is tall.

Drivetrain challenges

2009-11-01T12:00:00.002-05:00

Jumping around a bit here from suspension to drivetrain, but I don't want to get too locked into the component level (actual control arm geometry) until I do some more parametric design (getting a good read on what camber curves, etc I want).

On our FSAE cars, while the drivetrain layouts we used were generally functional, serviceability was lacking. I wish I had some pictures to illustrate, but for now it appears the remote CU Durning Lab login is down. Anyway, items requiring service:

Adjusting chain tension. Invariably we had to do this as chains wore in, when going with a different sprocket arrangement, or when replacing a chain. We generally used a two turnbuckle arrangement holding the diff carrier to the frame, so alignment and position could be adjusted. It wasn't ideal, and certainly wasn't fast.
Replacing driveshafts. While we never broke a shaft, these had to come on and off for a variety of reasons. Snapping a shaft definitely is a possibility with a higher power car. In any event, our setup was a splined shaft, with a tripod and housing on both ends. Total of 12 socket head cap screws (SHCS), in 6 pairs of safety wire, had to come out to get the thing off.

Not to mention, the process was a mess and you'd wind up putting bags around everything to keep from losing all the grease and what have you.
Swapping sprockets. You'd have to take tension off the chain, undo another 6, safety-wired fasteners, and get the thing off. Time consuming.
Removing the diff. Similar story, time consuming. Remove tensioners, cut safety wire, undo 12 bolts, take it out, do whatever, replace it, 12 bolts in, safety wire them all.

Time to think up some solutions that make all those quick and easy. Maybe I'll have some CAD this afternoon between games. Giants @ Eagles, Vikings @ Packers, Yankees @ Phillies.

I'd be happy if both teams from Philly lose, and if it's a good matchup at Lambeau.

Another damper mount option

2009-10-25T01:38:00.002-04:00

Credit to Dave F for pointing this out.

I may be able to get some better packaging options by using a second billet bulkhead to mount the damper to.

That may give me some much improved options for load paths, both through the bellcranks and into the bulkheads themselves. As an added bonus I might be able to shoe-horn in a damper with 3" of travel. At the moment I am using one with 2" of travel.

Why one damper length over another? There are some pros and cons related to overall motion ratio (inches of wheel travel to inches of damper travel). I'll get into that later if I haven't already. I have to sit down and think about that, figure out if a MR > 1 or < 1 is better in terms of minimizing the effect of damper friction.

In any event, there are some issues associated with putting a 2nd bulkhead back there. Namely, it might not be great for bringing in that front roll hoop bracing. May also make getting fasteners in there a bitch. We'll see.

Front rocker assembly

2009-10-19T00:32:00.005-04:00

For those of you who have not had the joy of doing suspension design, particular on a tube-frame car, this crap is a mental challenge. Either that, or I'm mentally challenged, or both. The challenge is that ideally, everything needs to be co-planar so that the bell crank is loaded in 2-d shear. Once there is misalignment among the components you get ugly bending moments which dramatically reduces the stress limit factor of safety on the bell crank.

The following points need to all be (roughly) in the same plane:

Rocker pivot
Rocker - damper connection
Rocker - pushrod connection
Rocker - antiroll link connection
Damper mount / pivot
Pushrod / lower control arm connection
Antiroll link / antiroll bar connection

Given that 3 points define a plane, you're trying to design a really over-constrained system. Replacing one of the frame elements with that big billet aluminum piece should help a good deal with making sure everything's aligned. The '68 Lola T150 features something similar on the rear of the car, but not quite for the same purpose. The damper and rocker mounts are in single shear which isn't ideal, but you can live with it. The mounts are fairly stout, but still not heavy.

At the same time you're getting everything in plane, you have to attempt to..

Have good load paths
Meet your targeted installation ratio and progression
Make sure none of your components intersect the frame, control arms, driver, or other such things.

I haven't even taken a look at installation ratios yet. I'll have to see how terribly hosed those are and make adjustments. For now I wanted to have something where I knew I could physically locate the damn thing. All of this helps to locate the front anti-roll bar (FARB) assembly, among other things. In this case there will be another pickup point on the front end of the rocker, which will shoot a link forward to the FARB assembly. My intent is to have both the FARB and RARB adjustable from the cockpit.

Oh I hate this part of suspension design

2009-10-17T21:07:00.001-04:00

Moreso than anything else, getting the push/pullrod, rocker, and damper oriented in a good way on a steel spaceframe is a total bitch.

Caster change a la Lola

2009-10-17T15:50:00.004-04:00

Been quiet around here. Work has been intense lately! Also, I'm working on some 'big stuff' for this car which is kinda long term.

Anyway. Wound up taking apart, moving, and re-assembling a 1968 Lola Indy car with a couple guys. Pretty slick little car. Fit and finish wasn't all that great in some places, but it had some cool design features (including an aluminum monocoque and all wheel drive!) and modularity.

Hadn't thought of changing caster this way...

So I borrowed the idea...

There were a few other crafty design features I may borrow. Most of all I'm very keen on having everything from the main roll hoop back be modular and easy to service. One of the biggest pains in the ass of all of our FSAE cars was getting the engine and assorted drivetrain components in and out.

The challenge will be getting the rear end of the car to be modular and serviceable, while maintaining high axle-to-axle stiffness and keeping the engine semi-stressed.

Mo' Simulation

2009-07-27T18:46:00.003-04:00

Last night I posted up some of the sim outputs, and I've been working on packaging it up in a GUI. Still not quite finished, but this is turning out pretty nice.

Now, usually, I don't do this but uh, go head' on and break 'em off wit a lil' preview of the remix....

Get to click through at any point, from straight-ahead to limit cornering and take a look at individual tire states, how saturated they are, and tweak the design from there. Pretty legit.

Some basic simulation outputs

2009-07-27T00:25:00.008-04:00

Reworked how I want to do my suspension simulation and engineering. Have two separate programs now, one which generates the virtual suspension (almost identical to what I posted earlier) and one which post-processes the results. Right now it only works on one setup at a time, eventually I'll get a batch process working so it can crank on say 1,000 suspension iterations while I'm at work or out drinking or what have you.

1,000 iterations is surprisingly not much. And at 5-10 seconds an iteration that's about 1.5-3 hrs. I could easily come up with a test plan for 10,000 iterations.

I'll post up prettier picture when I have the post-processing GUI better set up. For now, just some examples of the outputs.

What's interesting to note, is even though the suspension setup is 100% symmetric, there is a noticeable amount of asymmetry in the results. I chalk this up to plysteer in the tires. I'll have to mitigate that with some alignment settings.

The understeer (balance) plot is a little funky as it is a function of the sign of trimmed lateral acceleration, and the results are off-centered. I'll come up with a better way to account for that.

Narrow nose

2009-07-07T00:27:00.003-04:00

Oh yea. That's where it's at.

Not much activity lately... just got back from a week in Jersey and Brooklyn. Good stuff. Bartenders that give out free Guinness and Ketel One? So much win.

Thoughts on roll centers & geometric load transfer

2009-06-18T13:01:00.009-04:00

Some discussion at F1 Technical got me thinking about this some more. Depending on who you talk to, there are a variety of opinions on how best to determine geometric weight transfer and jacking forces. Unfortunately none that I've seen back anything up with hard data.

How accurate are kinematic roll centers for use in WT calculation? Are individual instant centers better? How do these deviate from force-based approaches? How important is it to use a tire model to get lateral force split between the tires?

What I do know is the following: On an SPMM I can measure the effects of geometric load transfer.

The SPMM (Suspension Parameter Measuring Machine) is a kinematics & compliance rig. It is not very dynamic, like a 7-post shaker rig is. You can measure any number of things... your true, as-built kinematics... compliance rates... roll rates... damper friction... mechanical hysteresis in your suspension joints, etc. The machine clamps onto the sprung mass, and the tires sit on force pads. You can either move the sprung mass and measure corner forces (ride, roll, and pitch rates), or keep the sprung mass in place and apply tire forces and measure compliances.

In a compliance test where the sprung mass is fixed, if a lateral force is applied at the tire... the Fz changes without the suspension moving! I couldn't derive how this happens in a SLA suspension, much less something like a NASCAR rear suspension, but it happens nevertheless. If I do a lateral force compliance test with the forces in opposite directions, those force vectors intersect at the force-based roll center, which I'm thinking should be close to the kinematic roll center. I don't have data on that.

Anyway, we can use that knowledge to then figure out geometric force effects. Below is how I think it all shakes out.

The interesting items to note are that using RC's and IC's give the same result for non-rolling overturning moment, as do symmetric forces versus asymmetric (at least in the case of a symmetric suspension). What does change is the amount of jacking on the sprung mass, which admittedly will slightly change total lateral load transfer in general. In this example though, even if my axle rate is as low as 200 lbf/in, that +6 lbf jacking force amounts to... jack.

And even with regard to jacking or anti-jacking forces, who is to say they're bad! On a FSAE car, you're not very ride height sensitive. It may not be a big deal to have some jacking force. On a full aero car on a fairly open track (Lime Rock? Watkins?), maybe you want lots of anti-jacking mid corner to really squeeze the ride height down and get maximum downforce out of the underbody? Plus at a track like that, corner entry isn't very abrupt, so a more sluggish roll response may not matter.

Looks good with the (first pass at a) new aero package

2009-06-10T22:10:00.003-04:00

Holler.

I'll probably narrow up the front of the nose a bit to get the front wing assembly to do some more work. Do work.

Interaction between the main roll hoop and the rear wing assembly will be a challenge. In any event that kinda CFD is well down the road yet.

Dihedral wings are sweet

2009-06-10T00:20:00.005-04:00

Or at least they look cool -

Whether or not I'd use one or keep the whole front wing in ground effect is yet to be determined. I'll have the option. Currently this is a specialized high-lift airfoil profile which I happen to like. As I mentioned before, the original "wing" layout was entirely placeholder based on the original 312B-x cars. Changing that a bit.

Modifying the front end of the body with a lateral cut out, effectively raising (and closing) the nose giving some room for a full front wing, and also creating a dam. Keeps the same lines as the original car though. That, the new front wing assembly, and a new rear wing assembly are on the to-do list for tomorrow.

Well this is a bitch

2009-05-24T23:25:00.002-04:00

Seems at some point I saved my CAD model and now it's too big to open!

In other news, on deck for tonight are the following:

Grilled shrimp and gnocchi in some rockin lemon garlic butter sauce
Coors Light
Reviewing some track data in Pi Toolbox (i2, in my opinion, is vastly superior)
Maybe some Men of War?

But since I wouldn't want to leave my fans without something visual, we'll give you this -

Jackie Ickx gets it done.

Amazing what you can do with tire data

2009-04-26T23:36:00.004-04:00

I mentioned earlier that some race tire manufacturers do have empirical tire data available if you ask nicely. Unfortunately it also tends to be confidential so I can't really show much detail, but you'll get the idea.

Believe it or not this is fairly rudimentary and only took about a full day to throw together, in between getting assorted other crap done. It does allow you to do a lot, though.

The most important thing is that I can do engineering as opposed to tinkering (see aside*) and do high-level design work rapidly. I don't want to spend weeks bullshitting around with suspension points to see what they do. I can pick my kinematic curves, roll stiffness, lateral load transfer distribution and all those basic macro parameters... and once a lot of these are defined they really lock in where your points have to be to achieve them. There's fine tuning to be done with the realities of what rates are possible given constraints of chassis and wheel dimensions, etc... but this gets you pretty close, pretty quickly.

Also makes it much easier to anticipate things like, "If I buy a couple sets of tires to test, when I take off Set A and bolt on Set B, what if anything do I need to change?"

As an *aside... and I'm not sure if I mentioned this earlier... when it comes to design like this there are two ways you can go about it. The way we did at CU for many years was not suspension engineering. It was tinkering. You play with suspension points, move one up, another one over, and see what it does. Maybe you have an idea of where you're trying to go with the design, maybe not. This is a ground-up design approach. Can take days or weeks to get where you want to be.

The other method is to engineer a solution from the top down. You pick the performance parameters you want. Start at a high level. Once you start defining what you need to get the car to handle how you want, the small stuff falls into place. If I want a caster angle of 'X' and a mechanical trail of 'Y' there's one unique solution for how that works in the side view. It does the work for you!

Revised brake duct and inner wheel fairing

2009-04-19T18:49:00.003-04:00

Hadn't really been a fan of that previous brake duct inlet. Looked like a leaf blower. Revised that, and added the start of a simple inner wheel fairing. Easy drag reduction, why not.

At the moment the materials are defined as CRFP just for looks, but there are some rules I'll have to revisit on what can be carbon fiber as opposed to glass. S-glass still gives a fairly rigid structure between typical E-glass and carbon. It looks complex but if I use one-off molds with dissolvable foam, it shouldn't be too bad.

Alternatively what might be the best bet would be to direct rapid prototype those complex curvature duct pieces. SLA gets a bit expensive, but 3d-printing out of black ABS is relatively cheap. The machine we had at school was something like $5 per cubic inch of material, and there's not an awful lot of material there.

CFD - Revisited

2009-04-17T23:53:00.007-04:00

Keeping boundary conditions and air properties the same, but this time going with a much less aggressive airfoil pattern. NACA3409.

Pressure field looks a lot better...

As does velocity. Flow does start to separate toward the end there, which we can fix... by adding a Gurney flap. If you're not familiar, Google it.

Does pretty much exactly what you'd expect. Extra low pressure zone directly aft of the flap helps suck the air flow back to the foil and moves the separation point further back.

Also, as one would suppose, builds up some stagnation pressure ahead of the flap on the top side of the foil. All in all you still have drag, but should be more downforce.

Pretty bad ass.

Next up will be to try to do some validation work on something simple like a NACA0009 profile to see if it at least captures trends for cD and cL at varying AoA. From there I can look through some airfoil catalogs, pick a handful that look promising and start playing around with increasing their operating envelope and performance level through slats, flaps, and all that good stuff.

CFD - What in the hell...

2009-04-17T22:54:00.011-04:00

I forgot to mention the last time, another integral part of making good use of FEA/CFD is being able to interpret the results properly. Easier said than done for someone whose background is in big billet aluminum pieces, tires, and suspension.

So I figured I'd play with some CFD with a stock airfoil profile. Not knowing what kind of camber, thickness, and AoA is appropriate, I took a random guess. Used an inverted NACA7412, a crapload of AoA, and a 25 m/s (~55mph) inlet velocity boundary condition. Boundary conditions for the top and bottom of the mesh are dU/dn = 0, and V = 0, with outlet being some extrapolated pressure.

Kinematic viscosity 2.59e-5 (a bit high for air I later remembered)

Since I'm ultimately interested in downforce and drag, I decided to look at pressure after my model ran for a bit.

Results sucked!

What in the hell is that shit? Pressure balls floating off my airfoil? Is that real? Wtf? Even as a tire engineer I have some sense to know that's probably not good.

Upon closer examination of the velocity field...

Kinda looks like flow separation. Or at least that's my guess. Major league flow separation. Like whoa. Edit - That looks like a typical von Karman vortex sheet now that I think about it... at least in the velocity view. Had never looked at pressure before!

I'm just playin' around for now, have to figure out how to grab cL and cD from these, but after some experimentation maybe this airfoil is a bit aggressive for the application (at least unmodified with no slats, flaps, Gurneys, etc)! I think this one below I even ran at at more proper viscosity of 1.59e-5

To be continued... later tonight.

CFD - General

2009-04-17T08:13:00.002-04:00

I'll write this up while I wait for the drier to finish.

I'm sure as soon as I get into the meat of any CFD or FEA I'll get comments of criticism. Some out of genuine concern and interest (cool), others just so they sound like experts while really just being a dick (not cool).

The accuracy of such analysis always comes into question, and rightfully so. In my limited experience doing designer-level structural FEA in college, and just from watching some stuff at work, good results inevitably come down to the following:

Assumptions made. Could be assuming your upright material is isotropic and homogenous (more or less true on billet, not at all on a weldment!) or that flow around an airfoil is incompressible.
Boundary conditions / loads / constraints. Maybe it was just CU, but FSAE students seemed notoriously off in this regard, just from inexperience.
Refinement of mesh. Pretty self explanitory. Capturing fine details (be it a Gurney flap or a non-radiused corner for a stress riser) requires localized mesh refinement.
What you expect to get out of it.

As an example of 2 & 3, on one of our FSAE cars we had a highly-loaded structural part (wheel hub). Billet aluminum, with material properties well-defined. Design criteria was based on von Mises stress, with FOS=2. The part had a thin tube section of about 0.06" wall thickness. I believe the mesh used globally in the model was 0.10 - 0.12". Additionally when I looked at it years after, the constraints were off. As a result, the first time driving the car this part sheared as soon as the driver got on the brakes. FOS=2, not so much.

On the other hand, we designed the same part years later with a different method. Billet steel. I think it actually wound up being lighter than the aluminum one (steel rocks). Design criteria again based on von Mises stress, with FOS=1.2. May sound low, but 20% is a lot of overshoot! Very carefully looked at the constraints and conditions with a highly refined mesh. Part never failed.

Good examples of how changing a few small things has a big impact on results. For this 2-d CFD work I'm not looking for absolute numbers. I'm interested in directionality in how to increase negative lift, reduce drag, look at effects of Gurney's, etc. Hopefully I won't get in too much trouble.

Unsteady 2-d flow simulation

2009-04-14T20:21:00.003-04:00

A preview of things to come in the blog?

Very possible.

Darren Engwirda put together Matlab code for a 2-d mesh generator, and 2-d Navier-Stokes solver. Pretty slick and easy to use. We shall see how well it works.

Static cross-weight

2009-03-15T13:47:00.005-04:00

While I'm at it I might as well get into cross-weight. You might be thinking...

Well who cares on a road racer? Besides I can just corner weight the cross load out.

Just you hold on a minute. Two things to think about...

First, what is it and what does it do? Percentage of load taken up on a diagonal. I do it as the percentage of load taken up by the RF and LR, but either works. On an oval setup it's a good trick to get power down better out of a corner. With a cross-weight > 50%, you are "preloading" load transfer to the outside on the front axle, and the trade is you can "preload" load transfer to the inside on the rear axle. Having extra load on the LR tire in that case will let you get on the throttle earlier and more confidence. Obviously the trade off is the car will understeer more since you're overloading the RF more.

On a road course car, cross-weight > 50% will give you asymmetric balance, particularly on-center. Car will understeer left and oversteer right. Not what you want when trying to tune the car. Having looked at some of the telemetry from my guys' FSAE car last year they had that issue, and I'm kinda curious now if they had a cross-weight problem.

When doing corner weights, you can get rid of static cross-load by lengthening or shortening pushrods and such. Now that I think about it though, I suspect you could be fooling yourself by doing this, particularly if you have asymmetric wheel rates. Asymmetric wheel rates are surprisingly easy to get if your manufacturing isn't perfect or if your spring rates aren't all the same. Having measured springs on the FSAE car, there's a damn lot of variation. Four springs all stamped "300 lb/in" could easily range from 290 to 340.

An interesting way to check would be to take corner weights with and without the driver.

The above example are some representative FSAE numbers. It shouldn't be too hard to position the seat on centerline. While I'd expect the F/R load split to change a bit when the driver gets in, the cross sure shouldn't! Cross changing with vertical load, or acceleration, could lead to some weird stuff... if you put a different driver in, as fuel burns off, or even if you just get onto a section of track with some banking.

In the above example, if everything had been manufactured perfectly and air pressures were set, I'd suspect maybe the RF and LR springrates are a bit higher than the LF and RR. A swap of the LR and LF springs might fix it.

Food for thought.

Hopefully I'll get back to more design-related stuff soon. Been busy with other crap, and gotta drive up to Buffalo at 430am tomorrow morning...

Preload and bump stops

2009-03-15T11:52:00.006-04:00

It appeared there was some speculation or confusion elsewhere as to the impact of spring preload on handling. Bump-stops are related. Both are important parameters. Unfortunately I don't think we really appreciated what they all did when I was on FSAE.

Balance is essential to good race handling. Balance inevitably comes down to managing dynamic tire conditions. Load is one aspect.

I think most people get the basics. More front bar (or spring, or damper [momentarily]) = more lateral load transfer relative to the rear = more understeer. The opposite is true for adding rear stiffness.

If you were to put your race car on an SPMM, you could generate a plot similar to what's below... looking at lateral load transfer as a function of chassis roll angle. Rough indicator of cornering balance. Ideally you'd want load transfer as a function of lateral acceleration (Ay)... the two plots are related but not the same.

Anyway. This might be a typical baseline setup with no preload, not hitting bump stops, and linear installation ratios. The slopes, and difference in magnitude between front and rear load transfer are what's important. In this example it's pretty straight-forward. The front has a higher roll stiffness, takes a higher percentage of the load transfer, and all other things being equal (50/50 corner weights, same tires all around) the car would probably understeer slightly. The feel should be very progressive and predictable.

If you were to add a hell of a lot of front preload, it may look something more like this.

If your tires and suspension were infinitely rigid, that initial slope would likewise be almost vertical. The front suspension is locked. Since the tires have a spring rate and inevitably there's compliance in your suspension, the rate is just very high.

There was an article in Racecar Engineering that (I believe) claimed lots of front preload would help a car "cut in" on entry from extra heat into the outside front tire. I find that hard to believe. It's no different than having a stiff anti-roll bar that "switches off" after a given amount of displacement. There are other reasons I won't get into, and I can also vouch for SPMM plots.

Until I see instrumented track data that proves otherwise, to me, I'd think front preload will "numb" the handling on-center.

Bump stops I am damn sure of, and the way they behave backs up my thought on pre-load.

If you roll onto a bump stop in the rear, your rear roll rate is going to increase substantially, very quickly, and rapidly shift the balance to oversteer.

The point of all this being, unless you manage it all carefully, going overboard with preload and bump stops and what have you can make for really non-linear or bizzarre handling. If you don't need it, or can't justify the reasoning for it... why bother?

Further clarification on Mz and Mx

2009-03-05T12:37:00.003-05:00

Thought about this some more, given that a few people asked about it. Best way I can think of each of them is a dynamic measure of where the force center of the footprint is.

When making a simple vehicle model you might assume tire lateral force acts right under the centerline of the spindle. This isn't the case. Due to the black magic of tires, the lateral force trails the centerline, which is what gives rise to pneumatic trail and aligning torque. Mz is really a measure of how the pneumatic trail is changing, and where that "Fy action point" is moving around. Since yaw moment is dependent on Fy cross-multiplied by the distance from the "action point" to the CG, the fore-aft movement measured by Mz does affect your vehicle balance.

Likewise with Mx, in a simple model you might assume your track width to be constant or just a function of how much lateral scrub your suspension generates. In reality as the tire deflects under lateral load, the center of pressure ("Fz action point") deflects as well and your track width changes length or shifts over (deflects toward inside of turn). That in turn will definitely modify your lateral load transfer!

Bottom line, they're both important and non-trivial.

If I were running a MechEng department... [Some of this stuff is really practical!]

2009-02-18T23:34:00.008-05:00

...I'd want a class for "Practical Application of Engineering Tools." 3000 or 4000 level, based heavily in Matlab. Probably 4000 level, since MCEN3030 - Computational Methods, is a junior class and pretty much murders you. Back then I eventually got decent at Matlab from having it thrown at me mercilessly, but when I got to work I couldn't do anything PRACTICAL with it. Like.. how to load a damn Excel file. Matlab has so much built in stuff it's unbelievable and I didn't know about any of it.

On the other hand, a bunch of crap that was just theory without application, as far as I was concerned, is really practical! Bode plots for example, who knew!! I sure didn't. I think I either skipped that lecture to work on the racecar, or it was when I had sliced my finger open on a lathe. (Freak accident, but don't EVER think you're the master of the machine. It can, and will get you).

Anyway. Don't let anyone try to fool you into thinking ride quality isn't important on a racecar. It's critical. There's a reason why professional race teams put a lot of time in 7-post ("shaker") testing.

What is a 7-post test? You put your vehicle on a special contraption, and shake the hell out of it. More precisely you recreate the disturbances and undulations the car is going to experience on a racetrack.

Why? We know that tire load variation is bad for grip. If you didn't know that, it's easy to conceptualize. If your suspension is stiff as a brick, if you had rigid links instead of springs, the car would chatter, skip and bounce over the race track. The whole reason for having a suspension is so it can be compliant and ride easily over bumps without upsetting the tires and chassis. The ratio of input from the ground, to force passed up into the vehicle, is transmissibility.

Where do Bode plots come in? It's a way of plotting signal amplification (transmissibility) and phase lag versus input frequency.

Changing masses, spring rates, and damping rates will change the shape of your curves. If I know what the major frequency content is of my suspension in a critical part of the track (big braking zone, corner exit, whatever) I can adjust my suspension rates to deaden that vibration out and increase my mechanical grip.

Wheel rate, tire rate, and damper rate are easy enough to get, as are the sprung and unsprung mass at a corner. If you knew the tire damping rate (hint hint) you could in theory fire up Matlab, play with some of your rates, and do a form of virtual 7-post testing. The Bode plot is a good way of seeing at a glance if your suspension is doing what you want or if you're moving in the right direction. Up until now I just thought it was some silly thing without a practical use.

As an aside, since at each corner of the car you have a sprung and unsprung mass, you'd think one would be acting as a mass damper relative to the other. For a long time there's been the phrase that you want to "always reduce unsprung mass." Generally I think this is true. There may be the case though that you could tune your unsprung mass to go along with everything else and really zero in on the frequency response you want.

Aw snap.

Ohhh... yea...

2009-02-09T23:48:00.005-05:00

I gotta give it up to the folks at the F1-Info site, wow. Some amazing photos and drawings.

This... is a beast. 1972 flavor of the 312B-2. I do kinda like that extra fairing that blends the roll hoop into the rear wing, and the NACA ducts which feed the oil coolers.

Also the '70-'71 312B-1...

And the '69-'70 312B

FVSAL Decisions

2009-02-08T12:18:00.007-05:00

Allright enough screwin around. Time to decide on a few things, namely baseline FVSAL and how it progresses through heave and roll. In case it has been a while since the last time you designed an independent suspension, we'll go through a refresher. Take a look at the following graphic I stole off a Google image search:

You can see the a-arms, and if you virtually extend them out they intersect at a point, A. The distance from A to the center of the spindle (NOT to C) is your "swing arm length." Basically when the wheel moves it's going to act like it's just on a beam that pivots around A. This length defines your camber gain in ride and in roll simultaneously. You cannot change one without changing the others.

Really long FVSAL: Very small camber gain in heave. At FVSAL = +inf, bump-camber = 0 degrees per inch, and roll-camber = 1 degree (wheel) per degree (chassis).

Conversely, short FVSAL (near half your track width): Small or zero camber change in roll, and high camber change in ride.

You can also have a negative FVSAL... it's all summarized here:

The equations to generate the above are very simple, and can be found in RCVD around page 625 (plus or minus).

Essentially how parallel or non-parallel your a-arms are, defines your FVSAL. To make things more difficult though, your FVSAL changes as your suspension goes through travel.

Equal-length a-arms: no change.

Top a-arm shorter than bottom: outside FVSAL shortens in roll, inside FVSAL extends (and can go negative). FVSAL also extends in heave, shortens in squat.

Top a-arm longer than bottom: outside FVSAL extends in roll (and can go negative), inside FVSAL shortens. FVSAL also shortens in heave, extends in squat.

By the way I figure

I want the integral of the roll-camber curve to be relatively small. I don't necessarily care what it is on-center, so long as when the car takes a set in a corner I haven't lost too much camber.
Going down a straight, when not grip limited, I can probably stand to have some bump-camber (while still having little bump-steer). The benefit is I pick up some roll-camber control.
When mid-corner I want to take care of the outside tire more than the inside tire, as it is going to be most heavily loaded and dominating grip level.

As such I believe I want a positive, non-infinite FVSAL on center, with the top control arm longer than the bottom so as I go into a corner my outside tire bump-camber control gets progressively better. Additionally, under braking when the fronts are highly loaded my FVSAL will extend for progressively better camber control over bumps... and if I do the same in the rear, under acceleration I will have the same effect for when the rear tires are heavily loaded!

Bits of drivetrain

2009-02-07T13:01:00.005-05:00

Got to working a bit more on the rear wheel assembly and drivetrain layout. I'm still on the fence for differentials, though I'm leaning toward the chain-drive Salisbury offered by Williams Racing Development. The other option is the chain-drive Quaife ATB from Taylor Race Engineering. In any event I'll be using tripod joints on both ends of the axle.

Craig Taylor's FSAE and DSR tripod housing is billet steel. Bullet proof in that application, but also weighs in at about 1 pound. There are some alternatives for Formula Fords that are billet aluminum with steel sleeves to take up the load from the tripod rollers. We played around with this on the '07 FSAE car, but the trick is getting the sleeves to stay in place. I suppose I could bond them in there. In any event, if I remember right it saves about 1/4 lb per unit.

In other news... got camber? I do. Got all the wheel mates set up properly so I can adjust track width and maximum static camber fairly easily. I'm assuming I won't throw more than -4 degrees of camber at the tires. Certainly won't on belted bias slicks, but I'm keeping the option open to run radials as well.

Tire data!

2009-02-05T18:19:00.004-05:00

Amazing what you can get when you just ask for it. Managed to get free-rolling cornering, and spring-rate data on both a 20 x 7 front and a 22 x 8 rear, as well as some relevant compound information from one of the manufacturers I've been looking at. Excellent!

Unfortunately... the quality of data is not that good. It's a belted bias construction and has some of the same somewhat questionable things I've seen in similar tires (from FSAE). Even contains Pac '96 coefficients, which I may be able to tweak to get to more reasonable values.

Not the best, but it may give some insight for initial mass distribution, alignment, spring and bar rates.

Revised kinematic... ideas

2009-02-03T23:50:00.005-05:00

Did some thinking. The scallops were bangin, by the way. I'm tempted to make some ravioli now. (Edit - I'm doin it!)

Anyway. Was thinking, and rambling to Grant about how the hell I'm gonna do this analysis. You can look at any variable vs any variable with a suspension. It's an overload of information. It's ridiculous. It's overwhelming.

There's a school of thought that you can't really do suspension design without tire data. I used to even agree with this myself, but realize now it's at least half bullshit. True, without tire data I'm not gonna know what camber and inflation to keep a tire at mid-corner, for a given load, to generate the most cornering force. But some shit is pretty clear.

Roll-steer, probably particularly front to rear balance of roll-steer, is always going to do the same thing to a car on entry. Over- or under-yaw (though I can think of situations that might be beneficial). Diabolical amounts of bump-camber or bump-steer while at the limit of traction, is going to upset the balance of the car. As such, those two items I can probably work to minimize and then leave static alignment settings for when (if) I do get tire data.

The plan is now as follows. Evaluate a set of metrics at each of the following "snapshots" in time This allows for a few quasi-steady state pictures of what the car is going to do through a corner. It's not the full "movie," it's not just a "picture," but it's at least a couple slices that you can hopefully interpolate between:

Static (baseline)
Straight-line braking
Trail-brake entry
Pure cornering
On-throttle exit
Straight-line acceleration

These are the metrics, to be evaluated at each corner:

Load
Inclination angle
Steer angle
Bump-steer (linear fit for +/- 0.5" wheel movement.. or some arbitrary amount)
Bump-camber (linear fit for +/- 0.5" wheel movement.. etc)

At this point you might think that I don't give a damn about roll centers. And you're right! At least in and of themselves. Their effect is wrapped up into "load." Ultimately it all comes down to the tires, and the tires react to loads and angles imposed on them. They don't care about imaginary points and lines in space. If when its all said and done it looks like the setup favors something where the kinematic roll center (KRC) moves around a whole inch or two or three, so be it! I don't care what it does so long as it makes my tires happy. Designing around low KRC migration because some old men said so, is silly. Doing anything just because some old men said so (even Carroll Smith or Claude Rouelle), is silly. Prove it to yourself, and screw anything else. I bet the late Mr. Smith would even support that.

Not to mention supposed KRC's are kind of a load of crap anyway, particularly at high loads, deflections, and compliances. Roll Center Myths and Reality (W.C. Mitchell) is a good read for those interested.

The advantages of small tires

2009-02-02T20:33:00.005-05:00

Got some time to kill while my scallops dethaw. Drove all the way up to Cleveland to go the damn Whole Foods hoping they'd have dry scallops. Fresh out, did get a bag of frozen ones. They may turn out to be legit, we shall see.

Anyway. Seems these days that everyone and their brother is all about megawide tires.

Yea brah, think I'm gonna put some 325's on my Z28 Camaro. Gonna be wicked fast and everyone knows it. That'll get me some respect. That and the T-tops.

A lot of the time wider is better, but there's a limit.. particularly on light, low-power cars. At some point you can have too much tire and not enough load and speed to get it working right. There are definite advantages to using small tires in open wheel, since uncovered tires generate lift and drag. Yea, lift.

Tommy Sizzle... that's crazy, brah! So like, how significant are we talkin' bout with the lift and drag?

Glad you asked. I was thinking about that earlier today! I don't personally have test data, so I'll reference some values from Race Car Vehicle Dynamics, and we'll pick 120 mph as our test speed. Pretty sure these numbers only hold true for being in relatively clean air, but since I don't have any sort of reduction for the rears I got nothing better than to use the same assumption all around. It is what it is.

20.0 x 7.0F, 20.0 x 7.0R (FSAE): 26 lbf lift, 83 lbf drag (27 hp @ 120 mph)
21.5 x 8.0F, 22.5 x 11.0R (Star Mazda): 39 lbf lift, 124 lbf drag (40 hp @ 120 mph)
22.0 x 9.0F, 26.0 x 12.5R ('70 Ferrari 312 B): 48 lbf lift, 155 lbf drag (50 hp @ 120 mph)
FSAE with flat wheel caps: 25 lbf lift, 70 lbf drag (22 hp @ 120 mph)

That's a significant quantity I'd say. Non-trivial at least. Essentially an extra 23 hp @ 120 mph by going from original spec wheels to FSAE size, and an additional 5 hp on top of that with caps.

There are a couple 13" radials I'll be looking at which might be good for this application. Light construction, and relatively soft compound that I can probably get away with. The thought is that with increased footprint efficiency I can get equivalent or better grip than a big bias slick, with a little better wear rate, and smaller profile. Win win win.

I love it when a plan comes together

2009-01-31T22:51:00.006-05:00

To be perfectly honest I'm amazed this worked. I'll likely be using the upper control arm mount bracket to adjust static camber by means of shims. As such, no shims will be the most camber you can throw at the thing, and I have to design accordingly. Previously I had been doing all my design at 0 inclination. Went in, changed my mates around to set the RF wheel and tire at -4 camber, and bam! All the a-arms automatically regenerated and no mates fell apart. No parts flew off into infinity! Now I can go change my track width, max static camber, upright geometry, or chassis geometry, and everything should automatically regenerate to fit. Beaut!

And yes, I realize that wheel-side upper control arm pickup is going to bind in full droop. It's all placeholder.

What's next? Tried getting some of the rudimentary geometry into the OptimumK demo, but had some issues. Cool software but to be honest it doesn't seem very robust. Don't think I'll be shelling out $1700 for it just yet! I'll have to think of a better way. Now that I think of it, for simple stuff where I don't have any anti-___ geometry I could probably make a simple front-view sketch in CAD and do some simple analysis that way. That might be perfect! Nice!

Beginnings of the RF suspension linkage

2009-01-31T01:41:00.005-05:00

Booya! Got some of the RF a-arms set up this evening.

It pays off big time, to set this shit up right in advance. The tube end inserts are free to float around the wheel-side and chassis-side ball joints, and then are mated so they are coaxial. The actual individual tubes that comprise each a-arm are made to automatically generate at the right length between the chassis-side and wheel-side insert. That way you can change static camber, ride height, track width, whatever... and all the a-arms regenerate to the exact appropriate size. In theory anyway, assuming the heap of mates that comprise the thing don't all explode, as they have a tendency of doing.

The tube inserts are my own design, rather than the stuff you'd buy at Chassis Shop. The latter are decent, but don't have flats machined on them for a wrench to tighten up the jam nuts, and are kind of a loose fit in the actual tubes. Mine also have a nice 0.050" chamfer on them for a J-bevel weld, or full bevel if I chamfer the end of the tube as well.

Yes, that does put the IC (instant center) at an interesting location. But that may be exactly what I want. If not, it's easy enough to change. Again, in theory if I change the chassis points everything should auto update. For now, I'm gonna pass the hell out.

Kinematic objectives

2009-01-29T23:12:00.005-05:00

Allright. Let's go back, take a look at our general suspension objectives and come up with a strategy for achieving said goals by use of kinematics.

Just so we're clear on terminology here...

kin⋅e⋅mat⋅ics
–noun (used with a singular verb) Physics.
1. the branch of mechanics that deals with pure motion, without reference to the masses or forces involved in it.

As opposed to...

ki⋅net⋅ics
–noun (used with a singular verb) Physics.
the branch of mechanics that deals with the actions of forces in producing or changing the motion of masses.

Kinematics I focus on inclination and steer angles of the tire relative to the ground (for obvious reasons) as well as the pitch and roll attitude of the chassis which drives it, and has a big effect on aero.

Kinetics I focus on distribution of steady state tire loads, and controlling load variation on the sprung and unsprung masses.

Anyway. Suspension objectives were:

High grip levels in cornering, trail-brake entry, and on-throttle exit
Predictable, smooth transitions between corner phases
Predictable, smooth reaction to bumps and load transfer
Appropriate range of adjustment
Quick method of changing chassis parameters

So how the fuck are we going to attack that? Before I go further, with all this text I can see I've lost your attention. Enjoy this fresh, hip new musical interlude...

First item, the grip levels... I haven't picked a tire yet so I can't go after static and dynamic camber, dynamic change in VSAL, etc.

As far as the rest go though, I'm thinking minimizing ___-steer (bump-steer, roll-steer) is going to be F essential. Bump steer in particular, as I'm thinking "bump" inputs from road undulations and rapid application of the brakes would be the most abrupt wheel transition, with roll inputs being a bit smoother. Even with that, I know the ___-steer curves will be different at static ride, at full roll, full pitch, etc.

This is gonna be a pain in the ass.

General design drivers

2009-01-29T21:39:00.006-05:00

I suppose this should have come earlier, and I don't think I have mentioned it before.

It is a key consideration though to realize what exactly is driving the design of your vehicle. Which are the independent variables, which are the dependent?

It's my feeling that there are three systems on the car that are independent and drive everything else. From a performance standpoint, everything else on the car has to exist to maximize the potential of these three things. They are:

The driver

Sufficient visibility to be aware of surroundings and pick the racing line
Control ergonomics
Linear, predictable feel to the vehicle's handling
Etc...

The engine

Come to temperature quickly
Stay in a sustainable range of operating temperature
Supply air and evacuate exhaust gas at maximum rate
Maximize area under the torque curve
Etc...

The tires

Come to temperature quickly
Keep footprint planted and oriented as optimally as possible through all handling
Minimize over-stressing carcass to provide adequate durability
Minimize over-stressing tread to prevent graining, feather, blading, etc
Minimize load variation
Etc...

If you're making a performance or critical design decision on the car, it should probably serve to benefit as many of the above as possible. If not, why are you doing it? And no hand waving.

The above is why I fundamentally disagree with the notion of setting a car up to have the absolute maximum theoretical grip level. If you throw an insane amount of camber at a tire just because that's where maximum grip is, you ride that line too long and you blow a tire and end you race. Likewise, you make the car handle like shit and you're taxing the driver's time with reacting to everything the car does, rather than freeing him up to drive it.

General suspension goals

2009-01-29T18:22:00.008-05:00

Gettin' to be about that time to outline objectives for suspension design, so I have a roadmap of what to target. Figured I'd write this up while my shrimp dethaw (for a delicious stir fry in a bit!).

I had a discussion with a coworker the other day, as we were discussing racecar stability issues. Among other things, I believe his comment was to the effect that the race engineers were going to set up the car for maximum possible grip, and then let the (very well paid) driver deal with it and get the car around the track, even if the car drives poorly.

I respectfully disagree (SB!), or at least that will not be my MO. Maybe that would work for a qualifying setup, but the race is what matters and it's not like you're going to be changing your kinematic package between Saturday and Sunday.

Drivers are human. I don't care if it's Kyle Busch or Felipe Massa or Joe Blow. Eventually they deviate from perfection, and when grip limited if it's bad enough that means you're ending the race one way or another, flying into the wall, another car, a gravel trap, or what have you. Chance of screwing up royally will generally increase with:

Long duration races (a matter of probability)
Pushing your or the machine's limit closer to 10-tenths (decreases margin for error or deviation)
Having someone fighting you for position (have to mentally process more things)
Having an unpredictable, twitchy, inconsistent race car (increases inherent deviation and variation from the perfect lap)

Realistically you're not going to be putting down 10-tenths all-out qualifying laps every minute of the race. Too great a chance of wadding the car up, as you would be constantly at the absolute limit with zero margin for error. Realistically, a driver is going to want to drive around the edge of his comfort level and be able to "dig deep" when required to make a pass for position or the lead, when strategy dictates. That's why there is a "race pace" and "qualifying pace." Obviously more talented and experienced drivers have a broader comfort zone than rookies, but there's still a limit!

Edit - Now that I think of it, Dale Jr. may have proven this point a few times in the 2008 NSCS season. I seem to remember a few times he drove the hell out of the car, right up near the wall, at the limit... moved forward in position... but inevitably something went awry from pushing too hard and it cost him. The other HMS drivers seem to be able to back off ultimate pace a bit and conserve their equipment until the end and/or when they really need it.

If your car isn't predictable and drives like absolute shit, there's no way you're going to feel comfortable driving as hard as if it were smooth. Your race pace might only be 8-tenths instead of 9. Plus, every fraction of a second you're spending correcting a poorly handling car, is time off your perfect lap.

The point being, it makes sense to me that you want to make the car as pleasant and easy to drive as possible. Even if it isn't the absolute maximum theoretically possible level of grip, and might have a longer "perfect" lap time, over the course of a race the lower probability of the driver blowing a braking zone or corner... and the smaller sum of small errors over a long race, would probably make up for it.

As such, suspension goals (kinematic and kinetic) will include:

High grip levels in cornering, trail-brake entry, and on-throttle exit
Predictable, smooth transitions between corner phases
Predictable, smooth reaction to bumps and load transfer
Appropriate range of adjustment
Quick method of changing chassis parameters

Worthy of note, generally I think maximum cornering grip is what most people focus in on, or at least look at first. It is hard however to make a pass mid-corner. You're already near the limit of adhesion with the cornering power of the tires saturating, and don't really have that much maneuvering potential. It is much easier to out-brake someone or pass them on the next straight by getting the power down early. I will probably be willing to sacrifice some cornering grip for being able to brake deeper and get the power down sooner.

How to achieve those goals with kinematics (linkage movement) and kinetics (springs, bars, dampers)... will come up next. Now it's time to prepare my shrimp.

#@*& Calipers!!

2009-01-28T21:41:00.002-05:00

Decided to go back and make a little more accurate version of my DynaPro CAD model. Good thing I did! As it turns out I had gotten a dimension wrong. I knew that caliper clearance to the wheel looked too good.

With the revision, my minimum clearance from the caliper to the interior of the wheel shrunk down to about 0.125" This had been a recurring theme on our FSAE cars, though I believe there were instances of clearance between caliper, upright and wheel being less than that. Even negative!

That's a bit close for comfort, not knowing how much wheel and bearing deflection to expect! That was using the DynaPro caliper spec'd for a 0.81" wide ULHP-30 rotor at 10.75" OD... made some changes and went with a 0.75" wide UL-30 rotor at 10.50" OD and I get up to 0.25" clearance, which I'm more comfortable with.

The caliper is spec'd for a 0.81" wide rotor, but I can't see this being much of an issue. Pads and disc wear down anyway!

On the plus side, the caliper looks damn good now. Even cut some threads on the hub (to be suppressed for any real work) to illustrate...

Rear wheel assembly preview

2009-01-28T00:44:00.008-05:00

Now, usually, I don't do this but uh... go 'head on and break 'em off with a lil' preview of the remix...

Bam!

Got to keep the same upright. At the moment I can use the same design on the RF, RR, LR, and LF. Of course this is before even playing with suspension geometry at all so things can change. But at least I haven't had to completely redo things. If I can use the same upright and same hub that saves at least a few hours (3-5?) of programming, setup, and tool changeover time. With CNC time at $65-120 / hr, that adds up quickly!

A small (currently aluminum) adapter piece fits the radial caliper mounts on the upright, and meets up with the DynaPro Single. Yes, it's single shear. I'm generally not proud of such things. I'll evaluate how much that twists later in FEA but given that everything is packaged pretty tightly it might not be bad. The adapter piece is also pretty simple and machineable. Three setups tops, all use a standard vice and quick stop. The upright for that matter shouldn't take more than 5, again with a standard vice setup. No special fixtures! Nice large corner radii in the pockets, with short length-to-tool-diameter ratios should mean high metal removal rates.

Right now I have the hub drive flange set up to accept a standard tripod housing, in this case from Taylor Race. They make good stuff! Craig and Scott are also very helpful.

The brake disc is a bit bigger than I thought. F'in heavy. They have a drilled one but I am wary of those. Still lighter than the vented front rotor, but not by much! I'll have to think of a good way to direct some cooling to it... as well as maybe evaluate something smaller. That's for tomorrow night.

Rear brakes

2009-01-27T20:19:00.004-05:00

Jumping back and forth between front suspension and rear wheel assembly...

According to my quick and dirty brake calculations, outboard 2-piston calipers should be adequate for the rear. To keep things consistent on the car that means Wilwood, which pretty much means Billet DynaPro Single.

Not a bad CAD model if I say so myself, especially for an hour and a half and only two drawings to go from on the Wilwood site!

The DynaPro Single is the successor to the Dynalite Single, which we had used for many years on our FSAE cars (2 outboard on the front, 1 inboard on the rear on the differential). The Dynalite definitely had some rigidity issues and when pressurized and putting force on the rotor you could watch it flex significantly! May have been part of the reason we had trouble getting really good solid brake feel. Wilwood claims to have addressed the flex issue in the DynaPro Single. I hope so!

Likely will be using solid, relatively thin discs at the rear.

Ideally I'd be able to use the same L/R upright on the rear as the front, though the mounting style of the DPS may render that impossible. We shall see, may tinker around with that in CAD later tonight.

Doing this the legit way is both a pain in the ass, and requires much RAM

2009-01-26T22:46:00.005-05:00

...the legit way being detailing down to the nut-and-bolt level. I give a lot of credit to the '04 team for having been as detailed as they were. A tradition which never caught on!

Speaking of which, at the moment I'm leaning toward rod-end bearings chassis-side. I had thought about using sphericals all around - they're cheaper - but they're definitely more difficult to set up and replace. I will be using sphericals at the wheel side, since we all know putting rod-ends in bending is the work of Satan and will condemn you to an eternity in Hell. Or at least that's what the FSAE judges would lead you to believe!

Bolts are a less obvious choice than one might think. It's tempting to just use AN hardware all around. But I'm sure we've all been in a situation where you go to put your AN suspension hardware into your closely toleranced bearings and spacers only to find they're all undersized! Generic socket head cap screws tend to be the same way. Then you get slop in your suspension, the bolt bangs around in there, and if you're using aluminum spacers it will inevitably lose its shape and gall or seize up. Seriously, who hasn't had that happen to them at least once?

There are NAS series fasteners which are close tolerance for such precision shear applications, and at the moment I will be using those. Likewise I will be using stainless top hat spacers all around. No rust, and no fumbling around like you would with normal barrel spacers. I'll take the small weight penalty over aluminum for the added hardness!

Full brake ducting

2009-01-26T19:38:00.003-05:00

Tenative layout for full brake ducting. The carbon work makes up a 3-piece assembly, consisting of a velocity stack at the inlet, a center piece, and the piece that brings the air to the center of the upright. These would be fabricated separately and then bonded together.

Kind of looks like a leaf blower.

At a minimum, it's manufacturable.

Glamor shots

2009-01-25T23:54:00.003-05:00

Daaaaaanng. Not sure why on earth Photoworks calls this motif "dusty antique" but it looks wicked.

Even more progress!

2009-01-25T22:31:00.003-05:00

Added the beginnings of some brake ducting, though I have to figure out yet how to get from this simple shroud to a location in the airstream with a bit larger diameter inlet. Shouldn't be too bad. I'm also tempted to route some cooling to blast directly on the pads.

Also added a sheet metal.. contraption.. to the spare brake caliper mounts on the front face of the upright. I can use this to mount my wheel speed sensor (shown) as well as an IR sensor for the rotors (not shown).

This assumes I can get my suspension geometry right so I can use one bracket at the top of the upright for both the steering pickup and the upper control arm pickup. Again, shouldn't be too bad.

Considerable progress on spindle assembly...

2009-01-25T18:39:00.004-05:00

Bam!

Had to rework a good bit of the upright so I could make modifications without a million constraints and sketch values erroring out.

Spread the bearings a bit wider, and redid everything for the Wilwood DynaPro caliper. 1.5" pistons up front with a 0.81" x 10.75" dia straight vane, vented disc. Top hat will be as simple as I can make it, likely a plate of AL2024 for retained strength at high temperature.

Added a wheel for a Hall effect wheel speed sensor. I may make it a simpler flat plate version, depending on how exactly I want to mount the damn thing. At this point I need to figure out how I'm going to mount and package (a) the wheel speed sensor, (b) the brake ducting, and (c) ideally an IR sensor for the rotors.

Mx - Also not a joke

2009-01-20T23:38:00.005-05:00

On the note of overlooked forces and moments: overturning moment (Mx). Previously we saw how Mz was important as the tire moments can be translated to an understeer moment on the car, which effectively "robs" the front axle of lateral force.

What is overturning moment? Moment about the SAE x-axis (forward/back) produced by the tire. This is NOT just the moment created by the Fy vector crossed with the loaded radius. Explanation later...

Generally though, it would appear that if you assume your track widths are fixed, or only dependent on lateral "scrub" of the suspension... your predicted lateral load transfer will be low. Mx is the culprit. Check it.

We start on the left, in a cornering scenario. There's the normal load transfer we're familiar with, but then there's also a non-zero overturning moment at each tire. Since everything's all connected anyway, we could also sum all the Mx acting on the chassis and dump it in with the rolling and non-rolling moments we're already familiar with, generated by inertial chassis forces. Since things are in equilibrium, that moment has to be reacted by a change in Fz at the four wheels. In this example, it increases load on the outside tires. What I'm not sure of, and I'm open to comments, is how the tire Mx and that increase in LLT is distributed among the axles... ie if its a function of roll center height relative to the CG or what.

The other way of thinking about this is as follows: Your track width isn't constant! Certainly not if defining track width to be the distance between the effective center of each tire footprint. As the tire deflects from camber and lateral force the footprint does move around relative to the chassis, and it can shorten up or shift the track at an axle and destabilize the car a bit.

Think about that for aggressive camber curves and compliant tires...