Great GRM Math Gods, I Throw Myself Upon Your Tender Mercies

DaewooOfDeath wrote: Center of Mass axis ... I'm not familiar with this concept.

OK. Imagine the car all wadded up in a ball at the center of mass, what you probably think of a c/g. In effect, you have assumed that one can treat this physics problem as if the entire car itself is that ball. See? doesn't work. So, the helpful way to think of this is that you want to balance the car on gymals, but the c/g height and f/r weight distribution only stick one skewer through your car from one side to the other, at 38% of the wheelbase behind the front axle, and 22" up. You stick the skewer in, and when you pick up your car by both ends, the car will rotate around this axis freely. But I want to see where the car wants to roll over, so I want a skewer that runs front to back, along the distribution of mass. Then when I pick it up by this axis, it will show me where it wants to rotate. Then I can do some measurements. Now, this isn't all that hard to fudge, so don't sweat it, I just wanted to make sure you see the car this way. In effect, when we start to calculate how the front suspension affects the rear, and how the rear affects the front, we will find out that it's not always "even". And that's dependent upon the front and rear torques from the roll centers to the axis of mass. You know. When I lock the pivot in the middle of the John Deere tractor.

ransom wrote:

DaewooOfDeath wrote: So, if he wants to reduce the amount of roll the torque vector is causing him, he will increase the stiffness of his outside leg and soften the inside leg. This is exactly what a swaybar does when it transfers spring rate from the inside spring to the outside spring. If you act it out, you will see that the process of transferring spring from the inside to the outside increases the load on the outside while reducing the load on the inside. The swaybar, in other words, resists roll by causing weight transfer.

Yes, but compressing the outside spring and extending the inside spring has exactly the same effect (more force on spring = more compression and more force on that tire). And both torque via the swaybar and spring compression/extension are caused by body roll which in turn is caused by the roll torque (neither springs nor bar are proactive, both require displacement of the wheels to provide any change in force resisting roll; i.e. you have to have some roll in order to develop any roll-resisting force). The sway bar doesn't cause weight transfer any more than the springs do, just by a different mechanism. For a given cornering force (a given roll torque) the body will roll further until that force reaches equilibrium with the roll resistance of the springing mediums (both springs and sway bars combined). Any given amount of force to counter roll can be achieved with only springs, with springs and sway bar, or even with a monoshock and sway bar in which the springs contribute nothing to roll resistance. In the simplifications we've made, we are ignoring that the CG moves outward during roll. Fine, it's a small thing and we can ignore that to get the big picture. In steady state cornering, if we are not going to look at the full car and front vs rear rolls stiffness but instead look simply at weight transfer, and as long as we are going to continue to ignore the movement of the CG due to roll, the simplest diagram showing weight transfer looks just about like this: This is from here, and they're talking about braking, but the vector math applies. Bf and Br in the image are front and rear braking force. For our purposes, view the diagram as Bf + Br = cornering force. If we consider the "weight of vehicle" vector to be a 1G unit, and draw the "cornering" (Bf + Bg in this gif) to the same scale, when the cornering force increases to the point that the "Weight Transfer Vector" is pointed from the CG directly to the outside tire's contact patch, at that point the outside tire will carry 100% of the load, and the inside will have 0. I apologize if what this thread didn't need was another voice, but it seemed possible to me that we were still hoping to dislodge just the right piece of perspective to make things fall into place, and you never know what will do that...

I really do understand how the conventional wisdom of suspension tuning works. I accept the way you characterized the vector forces as well.

The only thing I think you're missing, the key piece, is how a swaybar effectively transfers spring rate from the inside suspension to the outside suspension. This is different than how springs resist body roll because springs are always the same rate (excepting weird variable rate springs, of course).

pstrbrc wrote:

DaewooOfDeath wrote: Center of Mass axis ... I'm not familiar with this concept.

OK. Imagine the car all wadded up in a ball at the center of mass, what you probably think of a c/g. In effect, you have assumed that one can treat this physics problem as if the entire car itself is that ball. See? doesn't work. So, the helpful way to think of this is that you want to balance the car on gymals, but the c/g height and f/r weight distribution only stick one skewer through your car from one side to the other, at 38% of the wheelbase behind the front axle, and 22" up. You stick the skewer in, and when you pick up your car by both ends, the car will rotate around this axis freely. But I want to see where the car wants to roll over, so I want a skewer that runs front to back, along the distribution of mass. Then when I pick it up by this axis, it will show me where it wants to rotate. Then I can do some measurements. Now, this isn't all that hard to fudge, so don't sweat it, I just wanted to make sure you see the car this way. In effect, when we start to calculate how the front suspension affects the rear, and how the rear affects the front, we will find out that it's not always "even". And that's dependent upon the front and rear torques from the roll centers to the axis of mass. You know. When I lock the pivot in the middle of the John Deere tractor.

Ah, center of mass is the ball, cg height is the crosswise axis and center of mass is the lengthwise axis. I don't know where this is on my car. I would imagine near the middle since the engine offsets to the right and I sit on the left.

I thought it might have something to do with center of suspension, which in my car would be dead center in the middle of the floor pan.

Curmudgeon wrote: The sway bar will generate understeer by increasing the load on the outside front tire. Once the tire hits its circle of friction limit, it slides. Bingo: understeer. At rest, with both sides of the suspension at equal compression, the sway bar does nothing. It's just along for the ride. The same holds true if a bump affects both wheels equally. Once the car begins to turn, the weight begins to shift to the outside due to the body's weight rolling to the outside. Once this happens, the sway bar is deflected upward at the control arm end on the outside. The distance it deflects under a given load is entirely dependent on the bar's physical properties and the length of the 'arm' from the chassis mount point to the link to the control arm. The force required to cause that deflection is the amount of additional weight (or force, if you prefer) transferred to the outside tire by the bar. More force required to deflect = stiffer, less force = softer. Example: Let's say the bar takes 250 pounds of force to deflect 2 inches at the control arm end. Once the outside suspension deflects the bar 2" upward the bar is transferring that 250 pounds to the outside tire. But the bar does NOT change the total weight on both front tires, only when and how much weight is transferred to the outside tire by the bar. Does this help? It's possible to get real close to swaybar actions by going stupid stiff with the springs. Basically, the stupid stiff springs take over the job of transferring weight (or force, or body roll) to the outside tire that the sway bar was doing. But as Hoeschler points out, that's also very dependent on roll centers and suspension geometry. Rough (very rough) oversimplification of his ideas: go stupid stiff on the springs and drop the roll center to minimize body roll, then the control arm angle at rest needs to be such that as the car does roll the limited amount it's allowed it can't jack itself up. That would generally mean the outer ball joint would be higher than the inner pivot. Something else... by resisting the roll of the body, the sway bar also minimizes the movement of the roll center. But that's another whole discussion.

I understand how a swaybar works. All my previous projects used big swaybars to control body roll along with springs that were on the soft side. The Daewoo is the first car I've tried the spring only setup on, and I've been impressed. My intent is not so much to ask what the traditional way a car setup works is (because I did it that way too) as it is to challenge the traditional way and see if it holds up mathematically. My problem is that I'm a journalism major and have nowhere near the math skills necessary to explore the problem.

As for your explanations of Hoelscher's idea, aren't low roll centers good for promoting body roll, not controlling it? Here's the operative part of his ideas that I'm trying to mathematically explain or disprove.

But we have a problem here. Swaybars are not the dynamic equivalent of springs. A swaybar transfers load from the inside tire to the outside tire and thus reduce mechanical grip as they add spring rate. And the effect is not linear. The stiffer the bar in comparison to the springs, the greater the effect (loss of mechanical grip). To give an example of the effect, if we set our proposed STS2 car up using the target data we have assumed above using the target spring rates without any swaybar, the car should have good balance. However, if we achieved that same target spring rate using a front swaybar, the car would tend to understeer more than if we used only springs and no swaybar. And the greater percentage of the total front spring rate the bar accounted for, the more the car would understeer. I noted as much early in the thread.

We now must choose how much bar we want to use for our final setup. As the reader may know, I don’t use swaybars on my DP car. Nor did I use swaybars on my previous racecar, a DSP X1/9. For me it is far easier to manage the setup of the car without swaybars. I also prefer the feel of the car without swaybars. It has long been my thought that; because a swaybar reduces mechanical grip, why would you want to put anything on the car that reduces mechanical grip? With this simple method, it is easy to compare the effect of the front bar by comparing the same total spring rate using just springs and no front bar to the same total spring rate incorporating a front bar. I have done extensive testing and have proven to my own satisfaction that the theory is in fact accurate. The same total front spring rate achieved using a front swaybar will produce more understeer than the same total front spring rate achieved using springs only. In addition, the effect of the front bar changes based on the level of grip the surface offers. As a result, the car does not have consistent balance from surface to surface or even from run to run as the tires heat up from and the surface cleans and heat up throughout the day. I have found that my no-swaybar setup is very consistent on different surfaces and conditions seldom if ever requiring any changes to setup. At most, a pound or two of air pressure is all that is needed to tune the balance even in the most extreme of conditions. In fact, I don’t even change the setup for rain. All I have to do is bolt on the rain tires and the car is fine. If one chooses to use a front swaybar, the effect resulting from the loss of mechanical grip will have to be accounted for by softening the front springs enough to bring the balance back to neutral. Choosing the amount of swaybar to use is now easy and dependant on driver taste. If the driver prefers a smoother/softer ride, use a very stiff front swaybar and subtract the front bar rate from the total spring rate to determine the required front spring rate. Testing can then determine how much less spring rate is necessary to bring the handling balance back to neutral. One could also compromise and use a very soft front bar, thus minimizing the loss of mechanical grip.

-Steve

pstrbrc wrote: OK, I've just wadded up my 20somethingth page off the legal pad. This opens up a whole can of worms. HOWEVER...

Dude, does your neck hurt from carrying around all the brains?

I'm gonna just start off with the first question: Does a sway bar actually add more weight to the outside tire, when only considering a single axle? Answer: No, if you could isolate an axle. The springs and sway bar merely attach the chassis to the axle, and the distance between the chassis and the axle are irrelevant to the force at the tire's contact patch. However, this is only relevant to a car that has a pivot at the center of mass. Yeah. A John Deere 4wd tractor. Otherwise, if one end of the chassis wants to use more suspension travel to come to stasis than the other end, there will be a torque around an axis that runs through the roll centers, loading one outside wheel with the other end's weight. And the more I work on the math, the more I think that this is the real value of roll centers: The moment-arms of the torque that each end exerts on the other really make the difference. A high rear roll center combined with a low front roll center, and a high front Center of mass combined with a low rear center of mass, make a fwd compact sedan w/struts a pig to really make handle. (If, however, one could lower the inner suspension pickups in the rear, just bringing them down 2" lowers the roll center from 7" to 2.75", which is lower than the front. Escorts are the FWD compact sedan I'm familiar with, and you should see how easy it's gonna be to test this!) (whew) And I'm still working on the calculations! However, I can tell you that I'm beginning to see the justification for Hoelscher's argument that springs-only are more consistent than springs+bars. The calculation of this torque battle of the roll centers at 1g come out much different than at .5g, when using springs+bars. When using springs-only, it looks remarkably close. Now, for the complicated part. The car: 2000#, 60/40 58" track 100" wheelbase Center of Mass is at 40" behind and 22" above the front tire contact axis. Spring rate: front-180#/in, rear-120#/in Roll Center Height, front-3.5", rear-7" (just in case anybody's wondering, DaeWoo Of Death's questions got me crawling around a couple of cars in my garage. These #'s are a combination of what he gave above and specs of a chump-ready '95 Escort Wagon. ) Now, I do wonder where the Axis of Mass passes over the front and rear tire axis. I have the math to do this, now I need chassis scales. (shrug) But let's work with what I have. I'm gonna have to clean up the math and the graphics, but I have real work to do. So, in my absence, discuss.

So, just to make sure I'm understanding you correctly, you are saying that I am wrong about the weight transfer across a single axle BUT that when you take into account both axles the swaybars cause large differences in the amount of weight transfer between the inside rear and outside front?

Very interesting. How does this work? I'm guessing it has something to do with the forces at the bushing vs forces at the spring, but I'm having trouble conceptualizing how.

If this helps anybody, I will explain what I've personally noticed in my no-bars build and compare it to a relatively conventional 1990 Eagle Talon TSI AWD build I did before.

The Eagle (front strut, multilink rear) had 350/550 springs and 22mm/26mm swaybars on adjustable KYB shocks. It was lowered about 1 inch. It had poly throughout and the previous owner had deleted the funky passive rear steer thing. It weighed about 3,000lbs and ran 245/50/16 Kumho Ecstas. It had 2 degrees negative camber in the front with zero toe and 1 degree in the back with slight toe in.

The Daewoo (strut/strut) has 500/500 springs with no bars. It rides on non adjustable Bilstein cores and custom coilovers. It is lowered .75 inches in the front and .5 inches in the rear (although it's going lower in the back soon). It is also on poly all throughout. It weighs about 2,400 lbs and runs on 205/50/15 Hankook Ventus V12s. The Daewoo is running mild toe in front and zero toe in the rear. It has not proven sensitive to alignment changes, actually. It has .5 degrees negative in the front and zero camber in the rear.

As far as grip, my Daewoo would absolutely eat the Eagle alive. Before the Hankooks, back when I had no name mystery all seasons (195/55/15), it would still grip better than the Eagle, though not by much.

For responsiveness, I would give the slight edge to the Eagle, although turn-in grip is significantly better in the Daewoo.

For balance and adjustability, neither was as adjustable as I'd like, but the Daewoo is better.

The biggest difference, however, has been tire wear. On my really nose heavy Daewoo with minimal camber, it would seem obvious that it really beats up on the outside shoulders on the track. However, compared to the Eagle (or even the 1700lb, ultra gutted Corolla I used to autocross, actually) the Daewoo is very gentle on tires. I saw more carnage in a single autocross with the Eagle than I saw from two, 30 minute sessions with the Daewoo.

As for consistency between surfaces, I had not noticed much inconsistency with either car, although I've never tracked either in the rain.

And no, the stock Nubira is not some overlooked diamond in the rough as far as handling. Ask ndrwater. It was more like Buick understeer with nice, unpredictable oversteer thrown in at random moments combined with middling grip and no feel.

BTW, your car must ride like a limo. I'm at 500#/500# front and rear on my daily driven, ~2400lb car.

pstrbrc wrote: Give me a little more time, and I should have worked this out. Life has been hectic!

Take all the time you need. You are giving me more information than I could have possibly hoped for. Thank you very much.

Hooke! I should have known to ask him about springs...

I've just spent a bunch of time playing with examples, but I'm going to give it a bit more time to percolate before posting it to avoid muddying the waters further and/or looking a bigger idiot than usual.

I will note this much that I'm fairly confident of: With a bar, one wheel's effective rate is that wheel's spring's rate plus the equivalent rate of the series system of the bar and opposite wheel.

OK! Now we're getting somewhere! I knew I had a book around somewhere that had the basic algebra on this. Competition Car Suspension, by Allan Staniforth

There's a whole chapter of algebra in this book! The perfect crossroads of math geek and gearhead. So, I've plodded through his math (someone should teach him standard physics notation!!) and found some really ghastly errors, but in the end I fixed what the publishers did to the math, and I've put it into a spreadsheet. It's pretty much a "plug numbers into the yellow boxes, and watch what pops out" setup. However, there's some numbers that you really need to know the concept to really wrap your head around well. I've put some explanatory notes in the spreadsheet, but if you need more help, just ask. I've got the numbers for my '95 Escort wagon in the spreadsheet, so make sure you change all the yellow boxes to your numbers! I have to admit less than complete confidence in the formulas imbedded in the spreadsheet. No, I didn't get them wrong from the book, they don't seem to agree with the realworld numbers of my car. I mean, what I remember of my car when it ran! I have it (actually, them... I'm taking two inoperable cars apart to make one.) completely apart in a garage in the next town over, and It's just now getting the wiring put back in before I start putting the hard stuff back together. But, with the stock springs and swaybars, this car should only have a roll angle of 2.2* at 1g. I really don't think Ford put that good of a suspension under these cars! There are a lot of formula blocks. I haven't protected them. If anyone wants to go through the math and see where either I or Staniforth erred, for Pete's sake have at it! Call this Open Source. Weight Transfer Calculator

When you get down to cell D42, understand that the math that follows is based on the rule that the front and rear sprung weight transfer is directly proportional to the front and rear roll resistance. The extreme is the farm tractor that has the front axle pivoting on a pin. In this example it should be obvious that, until the tractor rolls over, the rear tire is carrying all the weight transfer, no matter where the center of mass is. Now, I crawl back into my cave to begin the work of finding a differential equation that will make this boring algebra come to life. btw- If this calculator really has any validity in the real world, The DaeWoo might really come to life with some 200# front springs!

I just requested access to the document you linked. Google wouldn't let me go there directly.

But wow, 200 lb springs on the front of the Daewoo. My car would corner like this!

I wonder if those formulas are assuming a really close roll center/COG couple?

DaewooOfDeath wrote: I wonder if those formulas are assuming a really close roll center/COG couple?

No! Those formulas take all those factors into consideration. I couldn't believe it either, and since it's just theoretical calculation I'd want to prove it to myself empirically. Just pushing some of my 'Scort's numbers through lead me to question the common wisdom that's out there in the Escort community about making these things handle. Looking at the #s I used for your chassis I realize that the low front RC and the high rear RC might have a lot to do with the numbers I got for your car. I wonder if your access to the googledoc has to do with where you are globally. Shoot me an e-mail and I'll attach it for you. That'll give me a chance to write up a bunch of explanatory notes and include them in a pdf. OK?

Oops! pstrbrc1(at)yahoo(dot)com

DaewooOfDeath wrote: Yep, this is all from the Daewoo. Track width is 68 inches front and 66.5 rear. Weight distribution is, depending on fuel load/what I have in the trunk etc, approximately 62/38. In race situations it might actually be a little more nose heavy because I prefer to run with low fuel load and I gutted the trunk. Center of Mass axis ... I'm not familiar with this concept. As for the roll center location at body roll, I have no idea. I got that figure by taking a picture of the car at max cornering g, steady throttle, high mu surface and then blowing that picture up and using a compass.

OK, real quick, Are you sure you have those track #s right? My 'Scort has 57.5 front and rear, and the internet sez the Nubira was pretty close to that.

pstrbrc wrote:

DaewooOfDeath wrote: Yep, this is all from the Daewoo. Track width is 68 inches front and 66.5 rear. Weight distribution is, depending on fuel load/what I have in the trunk etc, approximately 62/38. In race situations it might actually be a little more nose heavy because I prefer to run with low fuel load and I gutted the trunk. Center of Mass axis ... I'm not familiar with this concept. As for the roll center location at body roll, I have no idea. I got that figure by taking a picture of the car at max cornering g, steady throttle, high mu surface and then blowing that picture up and using a compass.

OK, real quick, Are you sure you have those track #s right? My 'Scort has 57.5 front and rear, and the internet sez the Nubira was pretty close to that.

I just checked and it looks like I measured the track width incorrectly. Went from the outer edge of the tire to the outer edge of the other side.

The correct numbers are 60 inches front and 58.5 rear. I'm running a different offset and fatter tires, which would explain the differences from factory.

Email sent.

Did you get my email?

DaewooOfDeath wrote: Did you get my email?

LOL. Yes. And I still wasn't happy with the math, because one number kept coming out with an unrealistic value. The problem with physics is that, even if the math is done right, and looks really impressive, it still has to translate into the real world. The problem with the real world is that you never really figure out all the variables, so you just hope you've picked the most important ones, and then see if the math makes sense. So... Just as I dozed off last night (that would have been this morning for you!) I saw the problem. So I'm reasonably confident in the spreadsheet I'm sending you, except for the final calculation, which is roll angle. However, I won't know how exact the other numbers generated are until I get an Escort back together so I can use it for a testbed. I'm really sure that TOWMBO would object if I used her Fusion!!!!

Haha! My experience with the women in my life has been that the "don't worry, it's science" explanation works precisely one time before I am forever more banished from touching her stuff.

I REALLY wish the GRM board had a "subscribe to this thread" feature, because with all the tech info and theory being thrown about, it's pretty much a goldmine for someone trying to make their car handle better (or engineer a car to handle good from the getgo, for that matter)

Go all the way to the bottom of the page, directly below the reply box and click on the heart.