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Thread: Autocross Setup - using math to get me in the right neighborhood

  1. #1
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    Autocross Setup - using math to get me in the right neighborhood

    Here's the thing: I can't really make any sense of most of the forum-standard recommendations for Z3 M Coupe setup.

    From a popular reference (http://farnorthracing.com/autocross_secrets5.html), here are some basic steps:
    Code:
    Summing Up Suspension
    
    So then, here's the sequence:
    
    
    1. Replace all the rubber suspension bushings with spherical bearings;
    2. Measure and model the suspension to get:
      1. Motion ratios (and directly measure these to confirm the model);
      2. Unsprung weights;
      3. Sprung weights;
      4. Natural Frequencies;
      5. CG Height;
      6. Camber curves in roll and bump; and
      7. Bump Steer in roll and bump;
    3. Pick springs to set the natural frequencies where you want them;
    4. Set ride height as low as possible given camber curves and tire clearance;
    5. Fix bump steer;
    6. Go testing;
    7. Input your test results back into the model; and
    8. Tweak suspension settings to get your tires happy and the car balanced.
    Step 1 is a no-go for SCCA STR class. But I'll replace bushings with class legal items so that I have a solid base to tune from.

    Step 2 and 3 have been discussed in numerous threads on here over the years but here's where I'm lost. Everyone recommends setups for coilovers like 450#front/550#rear. But based on the model of the suspension, the motion ratios for this car are 0.94 front/0.67 rear. Assuming a 50/50 weight distribution and a weight of 3055 lb. (half a tank of gas, 170lb driver, lightweight seats/exhaust/battery/wheels as allowed by STR).
    Let's put it this way...it appears to me that TC Kline only sells one combo of springs that makes any sense within these parameters: 300#front (the softest he has) and 700#rear (the stiffest he carries). When you calculate your ride frequency within these assumptions, you get 1.96Hz front / 2.13Hz rear (8.7% difference between front and rear) which is really only a medium-aggressive setup. For more aggressive frequencies of 2.25Hz front/2.55Hz rear, you'd need 400#front/1000#rear. And for something more streetable, people should be running more like 200#front/500#rear for ride frequencies of 1.6Hz front/1.8Hz rear, which is still reasonably snappy.

    Let's pause here...what am I missing? Why does no one recommend or run setups like this?

  2. #2
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    Not enough people running that competitive in the Z3 to get the testing done. The shock also has to be able to cope with the spring rate as well. I would love to find the answer to my main handling issue. The rear end will "bounce" under high lateral load. I run F400# R600#, I went stiffer in the rear, maybe softer in the front would balance it out more. Or up to #700

  3. #3
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    Quote Originally Posted by SunzOut View Post
    Not enough people running that competitive in the Z3 to get the testing done.
    This thread definitely won't solve that problem. But I feel like people are testing around some different local maximum because their starting points are so different than what I've suggested above. So that's why I wanted to look at the math and try to at least get in the right neighborhood to start, so that we can maybe improve on that once we're in the right neighborhood.

    Robin, I pulled the trigger on 17x9s this year and plan to make it to >6 Chicago SCCA events this year. The CCSCC Test'n'Tune is already scheduled, but it may end up as the first weekend of Chicago Region SCCA...

    Quote Originally Posted by SunzOut View Post
    The shock also has to be able to cope with the spring rate as well.
    TC Kline seems to have said some goofy stuff with the spring rates I mentioned in the first post, but they've also said multiple times that DAs are valved to handle 700# easily.

    Quote Originally Posted by SunzOut View Post
    I would love to find the answer to my main handling issue. The rear end will "bounce" under high lateral load. I run F400# R600#, I went stiffer in the rear, maybe softer in the front would balance it out more. Or up to #700
    I'm not an expert on this topic, which is why I started this thread. But back to the math, 400/600 isn't a matched set for this chassis. That's a ride frequency of 2.2Hz front/1.9Hz rear. That should drive like a bucking bronco, conventional wisdom says that your ride frequency should be about 10% higher in the rear than the font. It would take a 1000# spring to get that done with 400# front.

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    I think most people use their car as a daily driver and don't push it to the max, so a setup that mimics what the manufacturer put on the car is in their comfort zone (more understeer than oversteer)

    You are right on the ratio F/R. The inner spring of the rear trailing arms requires a higher spring rate due to the ratio.
    I have a Z3 that is stock, but also have a track prepared E30, that shares the same rear suspension as the Z3 chassis.
    I tried many spring rates, sway bars etc, and now, I have 550/1000 for spring rates, and the car reacts like I want it to react. My spring rates are a bit on the high side, but I run slicks and stiffer shocks, but you get the idea.
    So, if you drive competitively, go with a stiffer rear spring and steer with the throttle pedal.
    ______________2000 Z3__ __1988 325ix turbo______________

  5. #5
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    My m coupe is on something like 400/700, stiffest z3 ive ever been in and I know Im a few hundred pounds short of the spring recommended by OP. I would lower spring rate and remove rear sway before ever tracking it. It pretty much just skitters about right now as it is and doesnt get any grip, its way too stiff.

    Maybe weight is a factor, just in my head, a 1000# spring in the rear of a 3000# car seems wrong.

  6. #6
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    My roadster has 500/700# and it feels fantastic to me. My coupe has 440/600# and the rear-end feels "squishy".
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  7. #7
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    Quote Originally Posted by BimmerBreaker View Post
    My m coupe is on something like 400/700, stiffest z3 ive ever been in and I know Im a few hundred pounds short of the spring recommended by OP. I would lower spring rate and remove rear sway before ever tracking it. It pretty much just skitters about right now as it is and doesnt get any grip, its way too stiff.
    Sounds more like too much shock to me rather than too much spring. Also, what tire pressures are you running?

    Quote Originally Posted by BimmerBreaker View Post
    Maybe weight is a factor, just in my head, a 1000# spring in the rear of a 3000# car seems wrong.
    Picture where the spring attaches to the rear trailing arm. the wheel attaches way farther outboard from there. This essentially means that forces in the suspension have extra leverage over the spring's resistance. So that 1000# spring acts a lot more like a 500# spring in that situation because of its leverage disadvantage.

    - - - Updated - - -

    Quote Originally Posted by Tim95M3 View Post
    My roadster has 500/700# and it feels fantastic to me. My coupe has 440/600# and the rear-end feels "squishy".
    Seems to make sense. Stock roll bars? I wonder how the balance would change if you decreased the front springs. What's the softest anyone runs in the front, I wonder?

  8. #8
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    I'm wondering if there's something else I'm missing that causes people to choose higher front rates than the math is predicting. Other thoughts:

    Track width - if the front is too narrow relative to the rear, the car will understeer. Increase front ride rate and roll resistance can compensate for this.
    Roll center height ratio front to rear - if the rear is too high relative to the front, the tendency will be to oversteer. Increasing front spring can bring the balance back towards understeer.
    Just plain old need more spring in the front - Other wise have sloppy and inconsistent response, or the car is slow to take a set

  9. #9
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    I have little to add at this point. 10 years ago I was asking the same questions, and got no helpful responses. I am no longer persuing an autocross setup. Now I'm more interested in a responsive yet safe ish street setup.

    One thing I have determined is these cars are sensitive to rear roll center moment. I feel people over-lower the rear of the car, causing sluggish response and a general tendency too understeer. The sweet spot seems to be close to stock height. This is why the E30 raise the rear subframe, were limited in this by the gas tank.

  10. #10
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    been tacking my M coupe for about 4 years now. I was running 750F / 350 R with a true rear coilover and a 32mm SB F / 22mm SB R. The car was pretty well balanced and had had plenty of grip. I talked to TC Kline (known to like a soft set up) and he suggested 400 F & R. I've since dropped the front down to 600 and kept the rear the same at 350. I went softer in the front because the car seemed to skate a bit at turn in and felt like it was getting enough weight transfer from R to F to set really set the car onto the front. I think most are running 500 to 600 F with slightly higher in the rear.
    I would tend to agree with rf900rkw in that the Z cars already sit pretty low. To keep any kind of spoiler from dragging in the front and adding some rake to the car front to rear is required so excessive lowering doesn't buy a whole lot. I think mine is only down by about 1.5" in the front.

    Also keep in mind that unless you run on silky smooth tracks a softer spring will provide more grip and in general softer springs will provide more mechanical grip. A good explanation of why in this video;
    https://www.youtube.com/watch?v=hGZRairqHNI

  11. #11
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    Quote Originally Posted by Fumanchu282 View Post
    Seems to make sense. Stock roll bars? I wonder how the balance would change if you decreased the front springs. What's the softest anyone runs in the front, I wonder?
    The 500/700# setup has a GC "large" front bar and an H&R rear bar on the soft setting. I tried removing the rear bar and didn't like the feel. I like the car to rotate a bit. On the 440/600# setup its stock front and rear bars, with the front converted to the "M" style going up to the strut body.
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  12. #12
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    Quote Originally Posted by Tim95M3 View Post
    The 500/700# setup has a GC "large" front bar
    This? https://groundcontrolstore.com/colle...nt=35652054787
    What's the diameter on that one? How is it compared to H&R front bar?

  13. #13
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    Quote Originally Posted by deni2s View Post
    This? https://groundcontrolstore.com/colle...nt=35652054787
    What's the diameter on that one? How is it compared to H&R front bar?
    That's the one. Not sure on diameter, probably in the 30-ish mm range. But it's a hollow bar, so that's a bit different.
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  14. #14
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    Fairly simple. It would be the strength of a solid bar of the major diameter minus the strength of a solid bar the minor diameter. But, as with everything performance related from suspension leverages to throttle air flow, it's an exponential function. In this case, the strength of the bar goes up to the fourth power of the bar diameter.

  15. #15
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    Quote Originally Posted by BimmerBreaker View Post
    Maybe weight is a factor, just in my head, a 1000# spring in the rear of a 3000# car seems wrong.
    Honest question here:

    My understanding is that it's better to look at the effective spring rate out at the wheel, as opposed to the manufacturers rating for the spring itself, is that incorrect?

    I have no idea if these numbers are correct or not, but back when I was reevaluating my spring setup, I used this table in this post to help make a decision:

    https://www.bimmerforums.com/forum/s...5#post27622055

    Unless I'm misunderstanding that information, which is 100% possible, a 400lb front and 700lb rear is not actually a 400lb front and 700lb rear. It's actually a 352lb front and 315lb rear.

    The thing that that chart completely changed in my mind is that increasing spring rates does not increase them in absolute values, it increases them in multiples. For example, going from a 400 lb spring to an 800 lb spring is not 400lbs stiffer, it's twice as stiff. In other words, where the rubber meets the road (hardy har har), in reality, it's 180 lb stiffer, Because the rate at the wheel goes from 180 lb to 360 lb.

    By extension, a 1000lb spring in the rear is actually a 450lb spring.

    Was I thinking about that all incorrectly?
    Last edited by kornfeld; 02-14-2018 at 08:29 PM.
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  16. #16
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    Correct on all accounts. While we commonly talk I terms of spring rate, what matters is wheel rate, the forces applied at the tire.
    Last edited by rf900rkw; 02-14-2018 at 09:56 PM.

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    Quote Originally Posted by rf900rkw View Post
    Fairly simple. It would be the strength of a solid bar of the major diameter minus the strength of a solid bar the minor diameter. But, as with everything performance related from suspension leverages to throttle air flow, it's an exponential function. In this case, the strength of the bar goes up to the fourth power of the bar diameter.
    Definitely not so simple and not just for performance related everything Reminds me of building bridge models from spaghetti and measuring/calculating their strength in university.

  18. #18
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    Given what some people have posted here and some of the linked threads, it seems like 700# rear is a good starting place. The ride frequency will be about 2.1Hz, which is lower than it could be but I think makes sense without R Comps and extra chassis rigidity. Also like that I can use the TCKR barrel springs at 700# (rather than a Hyperco or Swift 60mm straight spring) so I don't have to worry about coil bind. Depending on testing, I may go higher in the rear eventually but then it starts to be the territory of re-valving dampers, reinforcing trailing arms. 700# seems like a good guess at where the mechanical grip starts to fall off a cliff at these speeds too.

    As far as front springs, I'm going to trust the math. Randy said it in another thread, if anyone has done this they aren't talking...but unless there's still something I'm missing, a RWD chassis with a 50/50 weight distribution should have a 10-15% higher rate in the rear than the front. If I go with Swift 60mm 5kgf/mm springs up front (280#), then my front ride frequency will be 1.9Hz. Not quite stiff enough to be a full on race car, but half of what I have up front right now.

    Seems really soft in the front, but I've gotta try it for myself. If it rolls too much, I'll use sway bars. If it reacts too slowly, I'll dial up the dampers.

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    While we tend to talk in terms of steady state grip, in reality we are in a constant state of transition. You'd be amazed what can be done with roll center moment manipulation and a set of single adjustable Konis.

  20. #20
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    Next task is to set ride height. Ultimately, the questions will be where do I want to be (how low is too low) given camber and toe curves. And maybe also where do I want to be given roll center height changes.

    Let's start with this though: how do I measure where I am, and where that puts me on the known curves? If I wanted to zero everything out, what can I measure? The trailing arm itself is a tapered piece of metal, so what do I index against?

    There's an imaginary line between the center of the wheel bearing/axle and the center of the trailing arm mount. Is that what the curves ultimately refer to? Isn't the rear axle carrier angled too, and doesn't that affect things?
    Last edited by Fumanchu282; 02-16-2018 at 11:40 AM.

  21. #21
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    OP, if you don't already have a "larger" front sway bar....get one. It's going to be the biggest performance gain for the lowest cost. Does not matter how good you spring and shock setup is, if it's a BMW it will like the larger front bar. As for ride height, that will be driven a lot by how large a front rim/tire combo you want to fit. and then set the rear from their.

  22. #22
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    Quote Originally Posted by SunzOut View Post
    OP, if you don't already have a "larger" front sway bar....get one. It's going to be the biggest performance gain for the lowest cost. Does not matter how good you spring and shock setup is, if it's a BMW it will like the larger front bar. As for ride height, that will be driven a lot by how large a front rim/tire combo you want to fit. and then set the rear from their.

    Usually this is true for BMWs with stock suspension to keep the struts from bottoming and create understeer.
    If the OP goes with stiffer springs, big chances are the suspension won't bottom out.
    A suspension should be tuned with springs, then, sway bars used only for fine tuning.
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  23. #23
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    as suggested by sunzout if you're looking for a larger bar I have a perfectly good 32mm bar which is I think the largest you can get. I upgraded to a GC slide style adjustable and have this one in my collection. If you're interested PM me with your email address and I can send some pictures.

  24. #24
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    The more I have been reading about this, the more I think I'm going to switch from 400f/700r to 300f/700r. I only drive my car on the street, and for that purpose, I really really did not like The TC Kline recommended setup of 400 front and rear. The front felt fine, but the rear felt like it was set up in a completely different way, completely out of whack with the front, and way too squishy.

    According to the table linked above, I think this would give a 264F/315R wheel rate.
    Last edited by kornfeld; 02-23-2018 at 09:59 AM.
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  25. #25
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    I'll just say -- have fun with this.

    I've been "racing" (autocross, road racing, hill climbs) cars since the '80s. Being a techie myself, I started this way, studying the math.

    Here's what the math leaves out of the equation -- "easy to drive fast." You can make a car that's theoretically, as in, by the book faster, but it's only faster if the driver is capable of driving it at the limit, consistently.

    Softer cars are easier to drive fast. They might not be as 100% capable as a stiffer, by-the-book car, but 99.99% of the time, they will get a faster lap time because the driver is more confident.

    Throw out the book. Do what the fast people do. It's better.
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