Sway bar ratios - did some math

[zlexiss]

Ok, my end goal was to try to calculate the handling balance of the car with different sway bars in the front and back. That is, for a particular sway bar set, what's the weight on the front and back wheels through a corner? We need more than just how stiffer the front and rear bars are to figure this out. Excel helps too [img]smile.gif[/img]

Here's what I did:
1. Calculate the stiffness of each sway bar. From Fred Puhn's "How to Make Your Car Handle" (read this book!!) we have:

K (lbs/in) = 500,000 D^4/((0.4244xA^2xB) + (0.2264xC^3))

D = Dia bar
B = Length of center section
A = Length of end perpendicular to B (torque arm) C = Length of each end

This formula assumes solid bars, but hollow bars are within 10%. I have new bars in my living room, so I measured those.

2. Our front and rear spring rates figure into this as well. Numbers pulled from the tech database.

3. But at the front, the springs and sway don't act at the wheel, they're further up the pivot point. This lever action scales down the force. Measuring off some nice pics (fbodyextreme wilwood brake install), the springs act about 50% of the rate and the front sway is closer to 70%.

4. The solid rear axle means pretty much all the sway and spring rates are felt.

5. Now we add up the scaled front forces for spring and sway, and compare them to the rear spring and sway. Numbers expressed are the percent of total spring force on the front = front/(front+rear)

With stock late V6 springs (257/114 front/rear) we get:
With the 400/150 springs Sam Strano suggested for me (autocrossing), we have:
Of course, there's a lot of assumptions going on which affect the results:
1. Torsional body flex will tend to move the balance closer to 50/50, lowering these numbers
2. These numbers represent the front/rear division of the weight transferred to the outside tires in a corner. They don't count the static front/rear weight distribution, which at around 57/43, will raise these numbers a bit
3. I mentioned the difference in solid/hollow sway stiffness difference already.
4. Bushings and endlinks make a big difference in sway bar performance. Puhn's book mentions a .8" solid bushing bar acting the same as a 1" rubber bushing bar.
5. My measurements on the front scaling factors are estimates from an image file. If someone went under their car and took real measurements on this, they'd be more accurate.

So, what can we see from this?
1. On any spring, changing out the front sway without touching the rear puts a lot of extra weight on the front tires. While the increased camber control will increase front traction, you're still going to push pretty bad when you hit the limit.
2. The 32/19 combo looks like it'll act pretty much the same as the stock 28/15.
3. It's going to come to personal preference. Some people love to power out of the corners, and thus should stick to a higher front%. Moving the car more towards neutral means you can't floor it out of a corner, more touch is needed. But, moving the weight towards neutral means you'll be able to take the corner at a higher speed, making up that difference and possibly coming out ahead.

Now, let's see some discussion - I know everyone has opinions on what they like. How can I make the numbers better and more realistic? What am I missing? I'd like to refine this to the point where it's a standard thread in the Technical Archive.

-Jeff

[ November 20, 2003: Message edited by: zlexiss ]</p>

[V6Bob]

There's some great thinking here, but a few things I disagree with, mostly in the conclusions.

"1. On any spring, changing out the front sway without touching the rear puts a lot of extra weight on the front tires. While the increased camber control will increase front traction, you're still going to push pretty bad when you hit the limit."

Based on people's real experiences, I think you're underestimating the camber effect a whole lot. For one example. Sam Strano (and other people) frequently runs 35/19s on V8 springs. I don't think he thinks that setup "pushes pretty bad". You could ask him.

"2. The 32/19 combo looks like it'll act pretty much the same as the stock 28/15."

I don't see how this could possibly be true. For one thing, you've increased the front bar stiffness by 70% and the rear by 160%. Since your overall front percentage stayed about the same, that leads me to believe there might be something wrong in your calculations somewhere. The bars don't seem to be making enough of a difference.

For another, camber control, as discussed above. The change in the front bar has surprisingly little effect on the balance, the change in the rear bar is all about balance.

"3. It's going to come to personal preference. Some people love to power out of the corners, and thus should stick to a higher front%. Moving the car more towards neutral means you can't floor it out of a corner, more touch is needed. But, moving the weight towards neutral means you'll be able to take the corner at a higher speed, making up that difference and possibly coming out ahead."

I don't think this is a matter of personal preference, it's right and wrong. Acceleration out of the corner is crucial to fast lap times. It's demonstrably more important than pure corner speed. Cornering lines are altered from the theoretically ideal constant radius ("late apex") to favor exit speed.

Carroll Smith ("Drive to Win", you'd probably really like his "Tune to Win", also) says several things about this. One is: "We don't race around corners, we dragrace between them." You'll find similar statements elsewhere.

You also need to consider emergency maneuvers on the street. You're much safer there with a bit of push.

"The solid rear axle means pretty much all the sway and spring rates are felt."

Since the springs are inboard of the wheels, when the car rolls (or, hits a one wheel bump) the wheel motion will be greater than the spring motion, so there is a lever effect in roll. The part of the bar that goes front to front (and doesn't twist) and connects to the part that goes side to side (and twists) also has a lever effect at the rear.

This is some of the best thinking I've seen here on bars, but it needs some additional research/work.

[ November 20, 2003: Message edited by: V6Bob ]</p>

[zlexiss]

Good points, I knew you'd make it into here ;)

First off, corrected an error in the rear sway Excel formula, those values went up by about 30%. Fronts were good.

Here's a few things I looked back and found:

Rear sway impact, here's my base numbers:
The front bar dominates its springs in roll, being 2-3x stiffer and further outboard. The stock rear bar is much smaller compared to its springs, moderating it's increase in stiffness. Both ends of the car end up about 40% stiffer in roll. I was surprised by this myself - I didn't see the springs having that much influence on the rear contribution.

I'll have to read back through Puhn to figure the correct spot for scaling both front and rear - the instantaneous center is needed. His sway formula measures both torsional stress on the center section and bending stress on the end pieces, so it's very complete.

Good point on the effect of camber control - I know from autocross that I spend time in corners(with street tires) on the outside bump stops, and my tire wear shows the large positive camber I'm getting stock. My bars are going on Saturday, btw (race on Sunday).

Here's total roll stiffness:
That 35 front bar really dominates it.

The balance and under/oversteer gets trickier depending what driving you're doing. I agree oversteer by default is bad, bad, bad. Being able to call in some oversteer can help in slaloms if it's controlled. Oval and dirt track racers live on oversteer. Understeer is "safer" though, especially wet or with unsubtle pedal work.

I think we need to swap books [img]smile.gif[/img] Puhn's opinion is "Oversteer is usually preferred for racing, because a skilled driver can control the car more easily and come out of the corners faster" and the car "must not exibit a strong tendency" to either characteristic. For general RWD handling he favors neutral to light understeer that can go oversteer with the throttle.

When I get time, I'll go over the scaling more and redo the numbers again. I think we're up for a lively debate on how the handling balance of a car affects the corner exit speed - I think that leaving the late apex at a higher speed is as great an advantage as being able to hit it a little harder for that first little bit of acceleration. Add in just a bit of later braking into the turn, and the "drag races between the turns" gets pretty interesting.

[Silver 99 Firebird]

Could you post the formulas and values you are using? I'm not doubting your results, but I'd like to see what is going on behind the scenes.

David

[zlexiss]

Sure thing.

The sway bar formula is in the first post. It's from Fred Puhn's "How to Make Your Car Handle", one of the bibles of suspension setup. The stiffness that comes out measures lbs/in for bending one end of the bar, so it looks like a spring (that only acts in roll).

The spring rates are from the tech database. Also expressed in lbs/in.

Scaling: Particularly on the front suspension, the sway and springs don't act at the wheel. If the spring is halfway between the wheel spindle and the control arm pivot, it only moves 1/2 inch for each inch of wheel movement, cutting the spring rate at the wheel in half. I estimated the spring at .5 and sway bar at .7, so the roll stiffness at the wheel = .5(spring rate) + .7(sway rate)

I'll take full measurements this weekend for both front and back and update.

Weight transfer: As the body rolls in a corner, weight is shifted from the inside to the outside tires. It is not shifted evenly however - the ratio of roll stiffness between the front and rear determines this. If the front is twice as stiff as the back, 66% of the weight shifted from the inside tires ends up on the outside front, and 33% on the back.

That's where the percentages come from, using the front and rear roll stiffnesses at each bar and spring combo.

An important thing to note is that the percent isn't the total front/rear weight ratio, only the ratio of transferred weight. The car starts out 57/43 moving straight. In the case of the stock setup, during cornering 73% of the weight from the inside tires ends up on the outside front, shifting the balance forward.

You can get the balance at a certain g-force of cornering by calculating the static weight at front/rear(57%/43% weight of car), and adding in the transferred weight (see Puhn's book for this).

I'll have to upload the Excel sheet somewhere so people can play with it, but I'm going to hold until we (I'll need help from guys like V6Bob) get the numbers more up to snuff.

-Jeff

[V6Bob]

Jeff - Let me know what you need. Email is probably best.

I'm working on a more detailed response on the oversteer issue. You don't want oversteer on a paved oval either. Dirt is a different (and even more complicated) story.

"If the spring is halfway between the wheel spindle and the control arm pivot, it only moves 1/2 inch for each inch of wheel movement, cutting the spring rate at the wheel in half."

The rate goes down by a factor of 4 (Puhn, p. 138, Tune to Win, p. 65).

[ November 21, 2003: Message edited by: V6Bob ]</p>

[Ike]

<blockquote>quote:</font><hr>Originally posted by zlexiss:

Here's total roll stiffness:
That 35 front bar really dominates it.
<hr></blockquote>

For some reason I can't get the combination of 32/17 on stock late model springs out of my head. I'm really curious as to what those numbers would work out to be. Purely based on the conversations--mainly "which is the best" posts--I've observed in this section, I've heard/concluded a few things. (All of this for the 98+ springs.)

1. The 32 alone give too much to the front. Makes the car twitchy.

2. The 32/21 combo is be too much bar for the rear. &lt;NOTE: Personally, I of the mind with V6Bob with this one. Although I can see cases where the driver may want to swing the rear around, I don't see this as the fastest way around the track. If my rear tires are slipping, the I'm not putting power to the ground--this is just something I cannot rationalize away in my mind, unless someone shows something I've never seen before.&gt; &lt;2nd NOTE: I'm not sure, but your numbers don't seem to support this. And from what I hear, track experience does.&gt;

3. The 32/19 may be too much bar in the rear. (Again, note above, but less drastic.)

4. The 35 combos--just too much bar for our cars--except maybe for racing and stiffer springs. &lt;NOTE: Here this is just for a mainly street car with better handling. I've felt that this would just be overkill, unless you were REALLY into this sort of thing. Otherwise, I think a smaller bar would suit the most people up front.&gt;

Again, this is just what I've remembered from the various "what's best" posts, and the "I use this and I like it, but..." posts. Also realize since I'm not terribly interested in running a 35 on my car, that I'm probably forgetting a lot when it comes to those combos.

So in short: Can you plug 'n chug the 32/17 combo for me?/Let's toss that around a bit.

Thanks

[zlexiss]

Nice catch, I suck at math for being a rocket scientist [img]graemlins/dunce.gif[/img] I'm sure this affects the sways too. I'll post this fairly big revision after I get the true front and rear leverage measurements this weekend.

I'm wondering if we want to put the balance debate in another thread - I think we're in agreement on its effects on stability, but differ in how close to neutral we're willing to shift for the driving we and others will be doing. OR put another way, if and how easily the car can shift into oversteer.

My original goal was to come up with some tables to really quantify the effects of the different setups, and let that serve as fodder for the debates that will always live in the forum. Of course, I gave enough of a push to start them right away..

Ike: once I get the _right_ numbers, I'll post more complete tables, and with enough motivation, organize and make the Excel sheet available to the board so people can have fun plugging in their own spring rates and whatnot. Maybe add a section where you can plug in a cornering g-force and end up with body roll and actual weight on each tire.


<blockquote>quote:</font><hr>Originally posted by V6Bob:
"If the spring is halfway between the wheel spindle and the control arm pivot, it only moves 1/2 inch for each inch of wheel movement, cutting the spring rate at the wheel in half."

The rate goes down by a factor of 4 (Puhn, p. 138, Tune to Win, p. 65).
<hr></blockquote>

[ November 21, 2003: Message edited by: zlexiss ]</p>

[Ike]

[img]graemlins/thumbsup.gif[/img]

[ November 21, 2003: Message edited by: Ike ]</p>

[Silver 99 Firebird]

For what it's worth... The sway bars K value should be multipled by 0.49 as opposed to 0.7. Both the spring and sway bar's effective K at the wheel will be the square of the percentage of the distane they are mounted from where the A arm bolts up. ;) AKA

Springs
0.5^2 = 0.25

Sways
0.7^2 = 0.49

David

[zlexiss]

V6Bob: here's a thought that might help explain the balance thing a bit:

Increasing the roll stiffness benefits the front end a lot through the camber control. The live axle in the rear is always zero camber, so roll makes very small difference here.

So, when adding bigger sways, the rear grip stays constant, while the front gains a lot. So while the 32/19 combo has a very similar balance to the stock setup, we've effectively moved towards neutral since the front grip has increased without the rear grip following suit.

What do you think?

-Jeff

[V6Bob]

"So while the 32/19 combo has a very similar balance to the stock setup, we've effectively moved towards neutral since the front grip has increased without the rear grip following suit."

Sure. Except that the wording is confusing. I use balance to describe the handling characteristics of the car, not suspension parameters. I believe that's the common useage.

I'd say "while the 32/19 combo has a very similar front roll percentage (I've seen the term front roll couple) to the stock setup, the balance has moved in the direction of less understeer (and maybe to oversteer, see below)."

The tough question is that stated by Ike. Is the 32/19 too much rear bar for a 98-up V6 with stock springs? For a 93-97?

Too tough a question for me. Most people I've seen post think a 21 is too big for stock V8 springs, and that the stock 19 rear bar is correct, even with a large front bar, I suspect a 19 rear is too big for stock V6 springs, even with a large front bar. But I'm just guessing.

Sway bars are very tough to figure out.

[ November 22, 2003: Message edited by: V6Bob ]</p>

[zlexiss]

Your wording was better than mine, but good that you got the point. I was running in and out of the house today and dashed it out.

Well, after putting on the 32/19 combo today, I'll be autocrossing on it tomorrow. Installed with the 1LE endlinks front/rear, prothane bushings in front (testing my secret anti-squeak mod), and stiffer GM OEM rubber bushing in the rear.

I also took all the measurements I needed while under the car, to redo the math with.

Expect to see the reworked numbers Monday or Tuesday. I'll probably start a new topic for it.

[Lord_Verminaard]

<blockquote>quote:</font><hr>Originally posted by V6Bob:


Sway bars are very tough to figure out.

[ November 22, 2003: Message edited by: V6Bob ]<hr></blockquote>

I'll say. Especially on these cars. I had no idea! Since this is my first RWD car, I have had to put a lot of thought into suspension mods. I've had the rear-end step out on me more than a few times by accident with just the stock setup. Hell, with my 91 Beretta GT, I just found the biggest rear bar I could find, (which happened to be the Z51 stock option bar) kept the front stock with heavy duty endlinks, all other suspension stock, and the car was *close* to being neutral. It was like driving on rails. Apparantly, F-bodies require a little more thought.

Brendan
2000 Camaro L36 M49