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Suspension Tech / Motion Ratio / Unsprung Weight

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I haven't forgotten you. In fact you got me thinking (damn you). My current sway bar is a 1" attached to the lower control arm at approximately the stock location. The installation ratio at the stock point will be pretty low because it is well inboard of the ball joint. But, if you flip the rod end over and attach it to the strut, the motion ration will be pretty close to the strut installation ratio. What this means is that I will be able to use a much thinner (lighter) sway bar and still get the same amount of roll resistance. That is one of the things that I am still working on. I'll post the results.

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I ran an autocross yesterday with my new set-up (sort of). I had all of the new springs and struts in place, but I haven't had the opportunity to re-corner balance the car or get it aligned. Additionally, my front sway bar is much too large for the springs that I have chosen (I was pushing a bit). Nevertheless, the car did pretty well. I took first in E-mod against 4 other cars in my class.

 

I will say that the new set-up will take some getting used to. The car reacts much quicker with a 2.5 Hz suspension frequency than with a 1.8 Hz frequency. I think that I will like it as I get accustomed.

 

As I was inspecting the car today, however, a strange and troubling thought occurred to me: These cars are not symmetric left to right. The left side is heavier than the right side. Yet, the spring that I put in the left front is the same rate as the spring that I put in the right front. The left front sprung weight is 586.6 lbs and the right front sprung weight is 543.6 lbs. The resulting frequencies for the left front and right front are 2.28 and 2.37 respectively. The resulting frequencies for the left rear and right rear are 2.20 and 2.28 respectively.

 

So, what does all this mean? It means that in order to have the suspension frequencies match left to right, the car needs four different rate springs. For mine, I would use the existing 450 lb/in spring on the left front, and use a 410 lb/in right front spring. On the rear, I would use the 425 lb/in spring on the left and need a 390 lb/in spring on the right rear.

 

By doing all of this, the car should sit level when corner balanced and transfer weight forward and backward equally between the left and right tires during acceleration/braking.

 

Please someone tell me that I am full of crap. Otherwise, I will be ordering two more springs.

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Dan and I traded emails about the front sway bar rate and how that would affect his front spring choice. My experiment showed that my one inch sway bar had a rate of about 105-120 in/lbs per inch of bar movement. So Dan, your experience seems to contradict my sway bar theory I guess. Did you ever measure your sway bar rate, or did you just go with what you had already decided on? I still haven't ordered springs...

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Please someone tell me that I am full of crap. Otherwise, I will ordering two more springs.

 

You're not full of crap, but make sure all these measurements are made with you in the driver's seat.

 

And some perspective: If any of the autocross Gods drove your car the way it is now vs. you driving it the way you'll have it setup with the four different spring rates... you'll be slower. If making these changes reduces the amount of seat time in your car, you'll be slower (compared to them) longer.

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I already had my 1" sway bar in place and haven't had time to measure it's rate or install the sway bar that my calculations say should work (stock 0.71" sway bay modified for rod ends and 7.5" lever arms).

 

I ran the car with the 450 lb/in rear and 425 lb/in front with the 1" sway bar. The weight transfer worksheet gave me a magic number of 9.4% which predicts understeer (which it did). With the new sway bar and swapping the springs front to rear, the weight transfer worksheet gives me a magic number of 3.2% which is much closer to neutral.

 

My calculations for the sway bar rate agree pretty closely with what the weight transfer worksheet predicts.

 

John, I plan not to miss any more seat time regardless of the springs that I have installed. My next event is one month from now. By then, I will have the new sway bar set-up in place and hopefully the new springs. I'll wait till I get the new springs in place before I get it balanced.

 

Oh, my weights are with me in the car and a full load of fuel.

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I already had my 1" sway bar in place and haven't had time to measure it's rate or install the sway bar that my calculations say should work (stock 0.71" sway bay modified for rod ends and 7.5" lever arms).

What did the calculations say the rate of your 1" bar was? Did you use the 300 something in/lb number that I was telling you I thought was wrong? It sounds like you did. What I'm getting at is: the weight transfer worksheet seems to work with the incorrect spring rate that it calculates for the swaybar. If that is the case I should be using it's value for the swaybar rate even though I know it is incorrect.

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I dug out my statics text and went through the torsion calculations and if I assume infinitely stiff lever arms, I get pretty close to what the WTW calculates for a 1" sway bar. The WTW comes up with 659 lb/ in (That's one inch on each side), and I came up with 592 lb/in (Again one inch on each side).

 

I do plan to measure the rate, but I am pretty darn sure that it will measure greater than 120 lb/in. Is it possible that you annealed your bar by welding on it? I have seen suggestions that sway bars that have been welded need to be heat treated.

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I did not heat treat the bar, but I also didn't heat the center part much at all. I think if anything had lost it's temper it would be maybe the last 3" on each side. My rate was measured by only moving one side of the bar 1", so the rate for moving both sides one inch would be doubled, but that still isn't anywhere near what the calculations say.

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I will try to measure the bar. A simple experiment is worth a thousand calculations as long as all the variable are covered. How long are your lever arms on your sway bar? Were your bearings located near the stock location near the bend in the bar? How flexible is the workbench that it was bolted to? Were you measuring the deflection at a point equal to the end of the lever arm, or were you measuring the deflection at the end of a longer lever?

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I will try to measure the bar. A simple experiment is worth a thousand calculations as long as all the variable are covered. How long are your lever arms on your sway bar? Were your bearings located near the stock location near the bend in the bar? How flexible is the workbench that it was bolted to? Were you measuring the deflection at a point equal to the end of the lever arm, or were you measuring the deflection at the end of a longer lever?

The bar is an MSA 1" bar, nothing unusual there. The arms are ~11" long but there is another bend between the arm and the center of the bar. Add them both together and you get ~13.5" from the outer hole in the adjustable end to the center, I just went out and eyeballed it against a ruler. The workbench has a 3/4" plastic cutting board top. It's actually a food preparation table that I bought from a restaurant that was closing down. I was aware that this top might be a problem so I set the bar across the stainless welded frame of the table, and set the scale in one corner. I don't think table flex is the problem. I measured deflection at each of the three end link holes, or as close as I could get. I didn't measure at the end of a longer lever. My end links are mounted on the car directly in the center of the stock sway bar mount holes, so there will be no difference there.

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I will say that the new set-up will take some getting used to. The car reacts much quicker with a 2.5 Hz suspension frequency than with a 1.8 Hz frequency. I think that I will like it as I get accustomed.

 

It took me about three events before I started to really like the stiffer setup. After about a year you'll jump in someone elses car and be shocked at how slow to respond it is.

 

As I was inspecting the car today, however, a strange and troubling thought occurred to me: These cars are not symmetric left to right. The left side is heavier than the right side. Yet, the spring that I put in the left front is the same rate as the spring that I put in the right front.

 

Are you sure? Why I ask is if you didn't actually measure you're springs you'll find that they are often off when you measure rate and free length. You may be able to swap around what you have to get things closer. I'm not sure unless you have a lot of development on the car and a really top caliber driver that this will make much of a difference. It gets even more complicated when you start thinking about tire rates too, which vary with speed, temperature, and pressure.

 

Glad to hear you had good results with this. Another convert to the dark side?

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I switched to Hypercoil springs because I have heard that they have less variation in spring rate than some of the others. But yes, if I ever get truly serious, I would need to measure the rate and free length of every spring (and recheck periodically). In the meantime, I'll get as close as I can using off the shelf spring rates and movement of weight.

 

The deeper you look, the deeper it gets.

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I experimented with my front sway bar today. The purpose of the experiment was to quantify effective spring rate of the sway bar at the outside wheel.

 

Here are the specifics of my front sway bar:

 

Modified suspension techniques 25 mm front sway bar:

The lever arms have been shortened and fitted with rod ends.

The measured dimension of the bar are as follows:

A = 7" ---------Length of lever arm measured perpendicular to B

B = 30.5 " --------Length of bar in torsion

C = 7.75" -------Length of lever arm (along arm)

D = 1.005"-------Diameter of sway bar

 

Sway bar installation ratio 0.58

 

Fred Puhn gives the following formula for the stiffness of a sway bar on page 150 of his book, "How to make your car handle."

 

K = (500,000 x D^4) / (0.4244 x A^2 x B + 0.2264 x C ^3)

 

For the dimensions of my bar, the theoretical stiffness given by Puhn's formula would be as follows:

 

K = (500,000 x 1.005" ^4) / (0.4244 x 7" ^2 x 30.5" + 0.2264 x 7.75" ^3) = 689.6 lbf / in

 

This measurement gives the stiffness of the sway bar for one inch of deflection at one sway bar end. To find the stiffness for one inch of deflection at the wheel, you multiply the stiffness by the square of the sway bar installation ratio.

 

So for my car, the theoretical sway bar stiffness for one wheel rising 1 inch with the other wheel locked in place should be

 

698.6 lbf/in x 0.58^2 *1 inch= 231 lbf

 

Formulas are great, but their results need to be verified, so here is what I did:

 

Removed both front springs.

Replaced the drivers side spring by a 7" x 2.5" x 0.125 wall aluminum tube.

Reconnected both struts (one with no spring and one with the aluminum tube to lock that side at ride height).

Disconnected the sway bar.

Placed a bathroom scale (analog type) under the passenger side front hub with a scissor jack, and raised the hub (with out spring or sway bar) to ride height.

Record weight of hub, and scissor jack. (67 lbs)

Connected sway bar.

Raise hub using scissor jack until hub rises 1 " above starting position.

Record weight of hub + scissor jack + force of sway bar. (275 lbs)

Subtract initial measurement (hub + jack) from final measurement (hub + jack + force of sway bar) to get the force at the hub caused by 1 " of wheel motion.

 

Here are the results:

 

275 lbs (hub + jack + force of sway bar)

67 lbs (hub + jack )

______

208 lbs (measured sway bar force at hub for a single wheel deflection of 1 ")

 

This is slightly less than the force predicted by Puhn's formula. The error is (231 - 208)/231 = 10.3 %. In all fairness to Mr. Puhn, much of that error can be accounted for by the inaccuracies of my own measurements.

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Tried to redo my experiment and it went like a Buster Keaton movie. I tried a different workbench with a stiffer surface and as soon as I put leverage on the bar it started cracking like the lip of the bench was going to snap off. So I looked around for something more sturdy... my extra cherry picker should do. So I welded onto the back of the cherry picker and as soon as I put pressure on the bar the thing tipped. Better move to the front legs. That was better, but when I put enough pressure on the bar to move it 1", the rear was lifting up. Added some weights from an old barbell set, still lifted. So I'm going to wait until my wife gets home and have her stand on the thing and only move the bar 1/2" instead of the full inch. Preliminary results look like my previous experiment was wrong (must have been due to the bench flexing), and the rate looks to be pretty similar to what Dan had found in his experiment. I'll report back with a final number.

 

This will probably make a really big difference in my spring rate choice, so thanks for checking my work Dan.

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Jon,

 

Go to the following link:

http://www.fromsteve.net/carstuff/suspension/SuspensionCalc.htm

 

After the page opens, select the Sway Bar Rate Calculator tab at the bottom of the page. On that page is a figure of a sway bar with dimensions A, B, C, and D. Would you measure those dimensions for me on your sway bar and post them here?

 

Ignore the extra bend in the sway bar. The extra bend in the Z sway bar provides clearance for the L6 oil pump and really only has a small affect on the stiffness.

 

Dan

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A: 8.25, 9.25, 10.25

B: 30

C: 9 3/8, 10 5/16, 11 1/4

D: 25.4

 

A and C are given for all available adjustments.

 

EDIT--Based on that guy's spreadsheet the rates should be:

474.7761 in/lbs

373.7793 in/lbs

301.2005 in/lbs respectively.

 

I'm still a bit confused about the weight transfer worksheet though. You say it shows 2" of wheel movement, isn't that right? So then that makes the required front spring quite a bit smaller than what it would be for 1" of movement. Just trying to get all my ducks in a row before I order springs...

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Jon,

 

I would really be interested in your installed vs bench stiffness to understand how your mounts (which in my opinion will stiffen the bar since they are limiting the twist in the bar) affect the bar's spring rate if at all.

 

Cameron

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The bench stiffness was tested with the same mounts. I still disagree with you on that one though and don't think the rate would be much different if at all and in actuality might be lower due to the lack of stiction. What we will be able to do is check the measured rate vs the calculated rate, compare to Dan's result and see if there is a significant difference. In the interest of getting as much info as possible I'll try to get the biggest measurement that I can in terms of deflection. I might be able to get 1" out of it the way I have it rigged...

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I did the test again and I'm still not satisfied with the results. I could see the cherry picker lifting ever so slightly as I put weight on the bar. What I measured for 1/2" of movement at the end of the bar was 110, 135, and 152 lbs respectively for the different adjustment holes on one side of the bar, with the side on the scale in the last or softest setting. When I tried to go for a full inch of deflection I was lifting the wheels of the cherry picker off the ground even with my wife standing on it.

 

I think I may just back off and rely on the spreadsheet at this point.

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In going through all of this process, I have installed 425 lb/in rear springs, 450 lb/in front springs, replaced my front 1" sway bar with a modified stock (18 mm) sway bar, and lowered the heck out of my car. The car is about 1.5 " lower than when I started this process and about 3.5" lower than stock with 245/45/16 tires.

 

The car is much better in transitions than it was, but I have been having trouble putting down the power since going to the higher spring rates. I have not aligned of or corner balanced the car since starting this process. Just looking at the car though, it was obvious that the rear tires had acquired a bunch of negative camber. At the old ride height with the 250 lb/in rear springs, I ran -2.0 degrees of rear camber. At the new ride height, I found that I had -3.7 degrees of rear camber.:shock: Perhaps this accounts for some of my lost rear forward traction.

 

So, I decided to try and set my rear camber to a more reasonable number. That begs the question: What is a good rear camber setting for my new suspension setup that will optimize forward traction without letting the camber go positive with body roll? To answer that question, I needed to know two things: First, how much will my suspension compress in roll? Second, how much camber gain will my rear suspension give me per inch of wheel travel?

 

To answer the first question, I did the suspension analysis as outlined in RCVD and as implemented in the weight transfer worksheet. The weight transfer worksheet predicts 1.6 degrees of roll per G of lateral acceleration.

 

To answer the second question, I spent today measuring camber curves for various positions of my rear camber plates. What I ended up with was setting the plates as far towards positive camber as the slots would allow. This yielded -1.3 degrees of camber at static ride height. The camber gain at this position is -0.74 degree/ inch in the range centered around my static ride height (The camber curve is not really linear, but can be approximated as linear over small ranges).

 

 

If we assume that the suspension rolls about the center (big assumption), that amount of roll corresponds to approximately 0.8" of bump on the outside wheels and 0.8" of rebound on the inside wheels. If we also assume that we want the tire vertical at 1 G lateral acceleration, then we choose a static camber that will yield -1.6 degrees at 0.8" of bump. For my case, the most positive that I was able to set my camber was -1.3 degrees at static ride height. At 0.8" of bump (1.6 degrees of roll), the camber should be -1.3 deg - (0.74 deg/in x 0.8 in) = -1.89 degrees. This value is more than the 1.6 degrees of body roll, so I should have a little camber more than the minimum required to keep the outside tire from going positive.

 

I'm sure that I have oversimplified some of this, but I am quite sure that the car will be a bit happier than it was with -3.7 degrees of static rear camber.

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great information! This brings up an issue that I've observed in myself as well as others, and that's the assumption what when camber plates are installed, and the car lowered, that the middle setting of the plates will equate to zero camber. I've found that for zero camber on a lowered car (depending on how low you go), usually you end up on the outer limit of the slot range.

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If we assume that the suspension rolls about the center (big assumption), that amount of roll corresponds to approximately 0.8" of bump on the outside wheels and 0.8" of rebound on the inside wheels. If we also assume that we want the tire vertical at 1 G lateral acceleration, then we choose a static camber that will yield -1.6 degrees at 0.8" of bump. For my case, the most positive that I was able to set my camber was -1.3 degrees at static ride height. At 0.8" of bump (1.6 degrees of roll), the camber should be -1.3 deg - (0.74 deg/in x 0.8 in) = -1.89 degrees. This value is more than the 1.6 degrees of body roll, so I should have a little camber more than the minimum required to keep the outside tire from going positive.

 

I'm sure that I have oversimplified some of this, but I am quite sure that the car will be a bit happier than it was with -3.7 degrees of static rear camber.

 

I really like the analysis you did and I think that will really help to get you into the ballpark. The next step, which maybe should be a new thread, is now how do you tune this at the track. There are a couple of things to keep in mind. Your car should be generating 1.3 to 1.5 gs of lateral acceleration and the tire will deform a good amount (see photo below).

 

IMG_4107.JPG

 

What I've found is that you actually need more camber than just upright for max grip. Each tire will be a little different and you'll need to experiment to find that window.

 

Cary

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