Suspension Tech / Motion Ratio / Unsprung Weight

[ktm]

As you can see, the wheel/tire and the brake rotors are the heavy hitters.

 

Exactly. This clearly shows where one should concentrate their efforts of reducing unsprung weight.

[74_5.0L_Z]

Where am I going with all of this?

 

I'm working through chapter 16 of Race Car Vehicle dynamics because I'm an engineering geek, and because I want to have a better understanding of how my existing suspension works before I change it.

 

Chapter 16 deals with ride and roll rates and requires that you have knowledge of the following before you can do any meaningful calculations:

 

Corner weights (been there done that)

http://forums.hybridz.org/showthread.php?t=92703&highlight=corner+weights

Unsprung weight (check)

Motion ratios (check) http://forums.hybridz.org/showthread.php?t=129623&highlight=motion+ratios

Front and rear Roll center heights (That's next)

Center of gravity height (I would like to do this but I may have to estimate)

Tire Spring rate (This would be nice, but I'm not holding my breathe). Does anyone have a good ballpark figure?

 

In parallel I plan to work through some of the Chapter 6 stability analysis.

 

As I said, "I'm a geek".

[JMortensen]

Again, thanks for posting your findings, this is really valuable info. I'll merge this thread with the motion ratio thread. If you could then keep going on that one thread that would be great. The B/W/S/C forum is getting plugged up with too many stickies, and all of this info is certainly sticky worthy!

[tholt]

Wow! You've been as busy as I have!

 

I went through a similar unsprung weight excercise, but took a different approach based on laziness.

 

In the front, since I had the upright removed and left the rest of the control arm intact, I weighed the control arm on the car, resting the end of the arm on the scale. Since I have a heimed front end, friction was minimal so I figured it would be close. so my numbers were:

 

Control arm with brake caliper - 16 lbs

Wheel+ Hoosier slick - 36 lbs

Upright + rotor - 30

Shock + spring - 8 /2 = 4lbs

So - 86 lbs on each front corner

 

In the rear I used a similar approach but there was a lot more friction in the control arm so there is probably a larger margin of error. I tried to bias the friction each way and took the average. So:

 

Control arm w/upright/half shaft and caliper - 40lbs

Wheel/slick - 36lbs

Rotor - 10lbs

spring/shock 8/2=4lbs

90 lbs per rear corner

 

We were pretty close in the front and I suspect the differnce in the rear is attributable to the halfshafts. Not sure where the CG of your CV joints are but my car using stock halfshafts the bulk of the mass is towards the diff so less outboard weight...

 

Getting back to motion ratios... Thanks for measuring that! I was planning to do the same excercise this weekend. I probably still will, but for the time being I had been using the inverse of the motion ratio as calculated by the Mitchell suspension software. That being .942 in the front and .876 in the rear. I am impressed with the presumed accuracy in the rear... our differences easily within the margin of error of my measurments or our probable camber differences. Not sure whats up in the front...

 

Tom

[74_5.0L_Z]

Another busy weekend:

 

I did the following:

1. Determined my roll centers.

2. Re-measured the motion ratios

3. Played around with Smithee's Weight Transfer Worksheet using the data that I know about my car.

 

First, I'll detail the procedure that I used to determine my roll centers. The process required measuring the following:

- Front and rear track (center to center)

-lengths of front and rear control arms (center to center)

---14.5" rear and 11.25" front.

-spacing between the left and right LCA pivot points

-height of front and rear LCA pivot points from ground.

-spacing between left and right pivots for the tops of the struts (center of spherical bearing).

-heights of front and rear strut top pivot points above ground.

 

I performed the whole process twice on the front suspension (once with no bump steer spacer and once with a 1" spacer). My results were that my rear roll center is 3" above ground and my front roll center is 2 " below ground (with no spacer). The front roll center rises to ground level (0.014") when I installed the 1" spacer. Here are screen shots showing the excel graph of the front and rear data:

 

 

 

I reperformed the motion ratio measurement (just to be sure). This time I did the front at the hub center like last time and I also redid it at the tire centerline. The hub centerline and tire centerline data agreed with each other, but both were slightly different than last time (I think I was a little more careful this time). Additionally, I decided to install the bump steer spacer and see if there was any change in the motion ratio. The results from all of this is as follows:

 

Front:

--Hub center and tire patch center (no spacer) Installation ratio = 0.915

--Hub center with 1" bump steer spacer installed Installation ratio = 0.8911.

 

Rear:

--Hub center installation ratio = 0.901

 

What can probably be discerned from the variation in my results is that the error in my measurements doesn't justify my reporting more than two significant figures. So we'll just say that the rear motion ratio is 0.90 and the front motion ratio is 0.91.

 

So, where does this information get me? Hopefully, it gets me closer to picking some new spring rates. Toward that end I plugged all of my data into Smithee's Weight Transfer Worksheet and found some possible spring combinations. I'll write up the details of that later, but I believe that I am going to end up with 350 lb/in rear springs and 375 lb/in front.

[JMortensen]

Just a reminder about the bar ratios; they would be relatively important when choosing spring rates too...

[74_5.0L_Z]

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.

[74_5.0L_Z]

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.

[JMortensen]

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...

[johnc]

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.

[74_5.0L_Z]

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.

[JMortensen]

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.

[74_5.0L_Z]

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.

[JMortensen]

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.

[74_5.0L_Z]

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?

[JMortensen]

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.

[tube80z]

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?

[74_5.0L_Z]

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.

[RTz]

The deeper you look, the deeper it gets.

 

Hence Tube80z's sig... "A little knowledge is a dangerous thing

So is a lot"

[74_5.0L_Z]

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.